Classifications

• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B5/00—Measuring for diagnostic purposes; Identification of persons
  • A61B5/0059—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence
  • A61B5/0062—Arrangements for scanning
  • A61B5/0066—Optical coherence imaging
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/30—Polarising elements
  • G02B5/3083—Birefringent or phase retarding elements
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
  • G02B27/28—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising
  • G02B27/283—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising used for beam splitting or combining
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B2562/00—Details of sensors; Constructional details of sensor housings or probes; Accessories for sensors
  • A61B2562/04—Arrangements of multiple sensors of the same type
  • A61B2562/046—Arrangements of multiple sensors of the same type in a matrix array
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/24—Coupling light guides
  • G02B6/26—Optical coupling means
  • G02B6/27—Optical coupling means with polarisation selective and adjusting means
  • G02B6/2706—Optical coupling means with polarisation selective and adjusting means as bulk elements, i.e. free space arrangements external to a light guide, e.g. polarising beam splitters

Definitions

• the present disclosure relates to an optical coherent imager having a shared input- output path and a method for sensing coherent light. More particularly, the present disclosure relates to a photonic integrated circuit having shared input-output path based on polarization diversity and a method for sensing coherent light.
• An optical coherent imager is an active imaging system that comprises an array of optical detectors (herein referred to as a “sensor”) and a light source (usually a coherent light source such as a laser).
• the light source serves the purposes of target illumination as well as providing a local oscillator (LO) for optical coherent detection (also called optical heterodyne detection).
• LO local oscillator
• optical coherent detection also called optical heterodyne detection
• Such an optical coherent imager may be used in applications including 3D frequency-modulated continuous -wave (FMCW) LIDAR and optical coherence tomography (OCT).
• FMCW frequency-modulated continuous -wave
• OCT optical coherence tomography
• the optical coherent imager operates by coherently combining the LO with the target signal in free-space using bulk optics before performing detection by the sensor of the imager.
• an optical coherent imager with a detection sensor based on the photonic integrated circuit (PIC) technology permits the mixing of the LO and the target signal on a photonic chip (also called a PIC chip in this disclosure).
• the PIC-based sensor comprises an array of coherent sensing units that plays the role of the active detection pixels of a conventional detection array such as a CCD or CMOS image sensor.
• the coherent sensing units of the PIC-based sensor couple the target signals from free space through free-space-to-waveguide couplers into a plurality of waveguides on the PIC chip.
• the target signals manifested as waveguide modes in the waveguides may then be manipulated and processed using the various photonic components that are implemented on the PIC chip, including the coherent mixing with the LO using 2x2 optical couplers and the detection by photodetectors.
• the LO may manifest as a waveguide mode by introducing the LO light into the PIC chip through couplers.
• the target scene is flooded with the illuminating light, so that the entire instantaneous field- of- view (FOV) of the sensor receives optical signals reflected or scattered from the scene.
• Advantages of the full-field approach include high frame rate and simplified output format for data post-processing, as it enables the sensor to acquire an image like an ordinary camera.
• a significant disadvantage of the full-field approach is that the illuminating laser power is spread over a large area, resulting in fewer photons reflected or scattered back to each sensing unit of the imager sensor. Consequently, the full- field approach demands the imager sensor to have higher sensitivity, which usually requires the use of exotic and expensive materials for the fabrication of the sensors.
• the full-field approach may also limit the active imager to operate in distances constrained by a maximal illuminating laser power due to practical factors such as eye safety.
• the target scene is scanned by an illuminating laser beam by steering the laser beam using some scanning mechanism.
• a finite FOV of the imager sensor receives target signals.
• This finite FOV depends on the spot size of the illuminating laser beam and the imaging optics of the imager. Due to a smaller FOV used in the finite-field illumination approach, the laser power is concentrated in a smaller region, resulting in more photons received by the imager sensor at the corresponding FOV. Consequently, the finite-field illumination approach usually allows the active imager to operate in longer distances than the full-field illumination approach given the same illuminating laser power.
• the beam scanning mechanism may be implemented on the same PIC chip of the sensor to lower the manufacturing cost of the imager.
• Common beam scanning mechanisms implementable on a PIC chip include an optical phased array (OPA).
• OPA optical phased array
• the photonic components for the beam scanning mechanism (herein referred to as a “transmitter”) nevertheless are usually implemented in a region of the PIC chip that is separate from the detection region comprising the free -space -to -wave guide couplers (herein referred to as a “receiver”) of the PIC-based sensor. Due to such separation, separate optical systems may be needed for the transmitter and receiver, in order to respectively direct the illuminating light beam to the target and to maximize the coupling of the target signal to the receiver.
• an optical coherent imager utilizing finite -field illumination
• the transmitter and receiver share the same optical system for, respectively, illuminating the target and receiving target signals.
• the optical paths of the outgoing probe beam and the incoming target signals are the same.
• Advantages of such an input-output-patlrsharing imager include a simplified optical system and simplified calibrations between the transmitter and receiver. The simplified optical system may lead to a more efficient use of laser power by enabling the imager to supply the LO light more specifically only to those coherent sensing units that receive signals from the target during the beam scanning process.
• the present disclosure provides an optical coherent imager implemented on a photonic integrated circuit (PIC) that enables shared path for transmitting and receiving optical signals by exploiting polarization diversity.
• PIC photonic integrated circuit
• the present disclosure also provides an optical coherent imager including an array of the optical coherent sensing units to simplify the design and calibrations of the imager, and a method for coherent sensing by the optical coherent imager.
• the present disclosure provides an optical coherent sensor comprising a plurality of coherent sensing units and a polarization transformer disposed on the coherent sensing units.
• Each of the coherent sensing units comprises ⁇ a polarization diversified optical coupler capable of directing optical signals having a first polarization state to and from free space and a first waveguide and capable of directing optical signals having a second polarization state to and from free space and a second waveguide! one or more 2x2 optical couplers optically coupled to the polarization diversified optical coupler through at least one of the first and second waveguides! and one or more photodetectors optically coupled to the 2x2 optical couplers.
• the polarization diversified optical coupler comprises a first sutr coupler and a second sub -coupler.
• one of the first and second sub -couplers is polarization dependent which optimally couples with optical signals of a predefined polarization state, and wherein the other one of the first and second sub -couplers is polarization independent which optimally couples with optical signals of any polarization states.
• the second sub-coupler is disposed on and vertically separated from the first sub -coupler.
• the first and second sub-couplers are disposed on a photonic substrate and laterally separated from each other.
• the polarization transformer directs an outgoing optical signal from one of the first and second sub-couplers to an optical path in free space, and separates an incoming optical signal from the optical path into a first optical signal having the first polarization state and a second optical signal having the second polarization state, either one or both of the first and second optical signals being spatially displaced by the polarization transformer such that the first and second optical signals are incident respectively on the first and second sub -couplers.
• the polarization transformer comprises at least one polarization-dependent beam-separator.
• the polarization transformer comprises one or more polarization convertors that rotate a linearly polarized optical signal by a predefined angle.
• At least one of the polarization convertors is a Faraday rotator.
• the polarization transformer comprises one or more quarter-wave plates.
• the polarization diversified optical coupler further comprises a third sub-coupler.
• the first, second, and third sub-couplers are disposed on a photonic substrate and laterally separated from each other.
• the polarization transformer directs an outgoing optical signal from one of the first, second, and third sub-couplers to an optical path in free space, and separates an incoming optical signal from the optical path into a first optical signal having the first polarization state and a second optical signal having the second polarization state, either one or both of the first and second optical signals being spatially displaced by the polarization transformer such that the first and second optical signals are incident respectively on two of the first, second, and third sub-couplers.
• the polarization diversified optical coupler further comprises a fourth sub -coupler.
• the polarization transformer directs an outgoing optical signal from two of the first, second, third, and fourth sub-couplers to an optical path in free space, and separates an incoming optical signal from the optical path into a first optical signal having the first polarization state and a second optical signal having the second polarization state, either one or both of the first and second optical signals being spatially displaced by the polarization transformer such that the first and second optical signals are incident respectively on two of the first, second, third, and fourth sub-couplers.
• the present disclosure provides an optical coherent imager comprising an optical coherent sensor described above and an imaging optics system including a plurality of lenses, wherein the imaging optics system is disposed such that the optical coherent sensor is located proximate an image plane of the imaging optics system.
• the present disclosure provides a method for optical coherent imaging, comprising: emitting, from an optical coherent imager, one or more outgoing optical signals to one or more targets respectively along one or more optical paths corresponding respectively to one or more field-of-view positions of the optical coherent imager! receiving, by the optical coherent imager along the optical paths, one or more incoming optical signals reflected from the targets illuminated by the outgoing optical signals! converting, by a polarization transformer of the optical coherent imager, each of the incoming optical signals into a first optical component having a first polarization state and a second optical component having a second polarization state, wherein the first polarization state is orthogonal to the second polarization state!
• the first and second optical components of the incoming optical signals to one or more photodetectors of the optical coherent sensor so as to perform heterodyne detection with local oscillator light at each of the field-of-view positions of the optical coherent imager, thereby determining information of the targets at the field-of-view positions.
• emitting the outgoing optical signals comprises: generating one or more source optical signals from a light source! converting the source optical signals into the outgoing optical signals, wherein each outgoing optical signal has a first emission polarization state, by the polarization diversified optical couplers! and emitting the outgoing optical signals from the polarization diversified optical couplers.
• the method further comprises transforming each of the outgoing optical signals from the first emission polarization state to a second emission polarization state by the polarization transformer of the optical coherent imager.
• converting the incoming optical signals comprises rotating the first polarization state of each of the incoming optical signals by a first predefined polarization angle and the second polarization state of each of the incoming optical signals by a second predefined polarization angle.
• converting the incoming optical signals comprises spatially displacing at least one of the first and second components of each of the incoming optical signals in accordance with the first and second polarization states such that the first and second components are incident respectively on first and second sub -couplers of each of the polarization diversified optical couplers.
• FIG. 1A shows a plan view of a coherent sensing unit for transmitting and receiving optical signals based on polarization diversity, in accordance with an embodiment of the present disclosure.
• FIG. IB shows a perspective view of a polarization-diversified free-space-to- waveguide coupler, in accordance with an embodiment of the present disclosure.
• FIG. 2 shows a perspective view of a polarization-diversified free-space-to-waveguide coupler, in accordance with another embodiment of the present disclosure.
• FIG. 3 shows a perspective view of a polarization-diversified free-space-to-waveguide coupler, in accordance with a further embodiment of the present disclosure.
• FIG. 4A shows a side view of a polarization-separation configuration for in-coupling optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 4B shows a side view of the polarization-separation configuration in FIG. 4A for out-coupling optical signals.
• FIG. 4C shows a side view of the polarization-separation configuration in FIG. 4A for in-coupling and out-coupling optical signals.
• FIG. 5A shows a perspective view of a polarization transformation configuration realized by the Faraday effect, in accordance with an embodiment of the present disclosure.
• FIG. 5B shows a top view of the polarization states of optical signals in FIG. 5A.
• FIG. 5C shows a side view of a polarization transformation-separation configuration incorporating the polarization transformation configuration in FIG. 5A and the polarization- separation configuration in FIG. 4C, in accordance with an embodiment of the present disclosure.
• FIG. 6A shows a perspective view of a polarization transformation configuration realized by a quarter-wave plate, in accordance with another embodiment of the present disclosure.
• FIG. 6B shows a top view of the polarization states of optical signals in FIG. 6A.
• FIG. 6C shows a side view of a polarization transformation-separation configuration incorporating the polarization transformation configuration in FIG. 6A and the polarization- separation configuration in FIG. 4C, in accordance with another embodiment of the present disclosure.
• FIG. 7A shows a plan view of a coherent sensing unit for transmitting and receiving optical signals based on polarization diversity, in accordance with another embodiment of the present disclosure.
• FIG. 7B shows a plan view of a coherent sensing unit for transmitting and receiving optical signals based on polarization diversity, in accordance with yet another embodiment of the present disclosure.
• FIG. 8 shows a plan view of a coherent sensing unit for transmitting and receiving optical signals based on polarization diversity, in accordance with a further embodiment of the present disclosure.
• FIG. 9 shows a plan view of a coherent sensing unit for transmitting and receiving optical signals based on polarization diversity, in accordance with a yet further embodiment of the present disclosure.
• FIG. 10A shows a top view of a three-waveguide polarization-diversified free-space- to-waveguide coupler, in accordance with an embodiment of the present disclosure.
• FIG. 10B shows a perspective view of the coupler illustrated in FIG. 10A.
• FIG. IOC shows a side view of a polarization transformation-separation configuration for use with a three-waveguide polarization-diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 10D shows a side view of the configuration illustrated in FIG. IOC used for in- coupling optical signals.
• FIG. 10E shows a top view of the polarization states of the optical signals in FIG. IOC.
• FIG. 10F shows a top view of the polarization states of the optical signals in FIG. 10D.
• FIG. 11A shows a perspective view of a three-waveguide polarization-diversified free- sp ace -to -wave guide coupler, in accordance with another embodiment of the present disclosure.
• FIG. 11B show a side view of a polarization transformation-separation configuration for use with a three-waveguide polarization-diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with another embodiment of the present disclosure.
• FIG. llC show a side view of the configuration illustrated in FIG. 11B used for in- coupling optical signals.
• FIG. 1 ID shows a top view of the polarization states of the optical signals in FIG. 1 IB.
• FIG. 1 IE shows a top view of the polarization states of the optical signals in FIG. 11C.
• FIG. 12A show a side view of a polarization transformation-separation configuration for use with a three-waveguide polarization-diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with a further embodiment of the present disclosure.
• FIG. 12B show a side view of the configuration illustrated in FIG. 12A used for in- coupling optical signals.
• FIG. 12C shows a top view of the polarization states of the optical signals in FIG. 12A.
• FIG. 12D shows a top view of the polarization states of the optical signals in FIG. 12B.
• FIG. 13A shows a top view of a three-waveguide polarization-diversified free-space- to-waveguide coupler, in accordance with a further embodiment of the present disclosure.
• FIG. 13B shows a perspective view of the coupler illustrated in FIG. 13A.
• FIG. 13C shows a side view of a polarization transformation -separation configuration for use with a three-waveguide polarization-diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with a yet further embodiment of the present disclosure.
• FIG. 13D shows another side view of the configuration illustrated in FIG. 13C.
• FIG. 13E shows a side view of the configuration as illustrated in FIG. 13C used for in- coupling optical signals.
• FIG. 13F shows another side view of the configuration illustrated in FIG. 13E.
• FIG. 13G shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 13C and 13D.
• FIG. 13H shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 13E and 13F.
• FIG. 14 shows a plan view of a coherent sensing unit for transmitting and receiving optical signals based on polarization diversity, wherein the polarization of the transmitted optical signal is adjustable, in accordance with an embodiment of the present disclosure.
• FIG. 15A shows a top view of a four-waveguide polarization-diversified free-space-to- waveguide coupler, in accordance with an embodiment of the present disclosure.
• FIG. 15B shows a perspective view of the coupler illustrated in FIG. 15A.
• FIG. 15C shows a side view of a polarization transformation-separation configuration for use with a four-waveguide polarization- diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 15D shows another side view of the configuration illustrated in FIG. 15C.
• FIG. 15E shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 15C and 15D.
• FIG. 15F shows a side view of the configuration as illustrated in FIG. 15C used for in- coupling optical signals.
• FIG. 15G shows another side view of the configuration illustrated in FIG. 15F.
• FIG. 15H shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 15F and 15G.
• FIG. 16A shows a top view of a four-waveguide polarization-diversified free-space-to- waveguide coupler, in accordance with another embodiment of the present disclosure.
• FIG. 16C shows a side view of a polarization transformation -separation configuration for use with a four-waveguide polarization- diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with another embodiment of the present disclosure.
• FIG. 16D shows a side view of the configuration illustrated in FIG. 16C used for in- coupling optical signals.
• FIG. 16E shows a top view of the polarization states of the optical signals in FIG. 16C.
• FIG. 17A shows a perspective view of a four -wave guide polarization- diversified free- space-to-waveguide coupler, in accordance with a further embodiment of the present disclosure.
• FIG. 17B show a side view of a polarization transformation-separation configuration for use with a four-waveguide polarization- diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with a further embodiment of the present disclosure.
• FIG. 17C show a side view of the configuration illustrated in FIG. 17B used for in- coupling optical signals.
• FIG. 17D shows a top view of the polarization states of the optical signals in FIG. 17B.
• FIG. 17E shows a top view of the polarization states of the optical signals in FIG. 17C.
• FIG. 18A shows a plan view of a coherent optical sensor, in accordance with an embodiment of the present disclosure.
• FIG. 18B shows a row of coherent sensing units of a coherent sensing array, in accordance with an embodiment of the present disclosure.
• FIG. 19A shows a plan view of a coherent optical sensor, in accordance with another embodiment of the present disclosure.
• FIG. 19B shows a plan view of a coherent sensing unit group, in accordance with an embodiment of the present disclosure.
• FIG. 20A shows a plan view of a coherent optical sensor, in accordance with a further embodiment of the present disclosure.
• FIG. 20B shows a plan view of a coherent sensing unit group, in accordance with another embodiment of the present disclosure.
• FIG. 20C shows a plan view of a Mach-Zehnder interferometer-based optical switch in accordance with an embodiment of the present disclosure.
• FIG. 21A shows a side view of an optical coherent imager, in accordance with an embodiment of the present disclosure.
• FIG. 21B shows a closeup view of the imager in FIG. 21A near the final image plane.
• FIG. 21C shows a polarization map of example ordinary rays and extraordinary rays on the final image plane over the field of view of the optical coherent imager in FIG. 2 IB.
• FIG. 22A shows a side view of an optical coherent imager, in accordance with another embodiment of the present disclosure.
• FIG. 22B shows side views of light rays propagating through a polarization-dependent be am -separator that effects angular displacement and light rays propagating through a polarization-dependent beam-separator that effects lateral displacement, in accordance with embodiments of the present disclosure.
• FIG. 23 illustrates a flowchart of a method of optical coherent imaging using polarization diversification to enable shared path for transmitting and receiving optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 1A shows a plan view of a coherent sensing unit 100 for transmitting and receiving optical signals based on polarization diversity, in accordance with an embodiment of the present disclosure.
• a plurality of coherent sensing units 100 may be used to form a coherent sensor array of an optical coherent imager.
• FIG. IB shows a perspective view of a polarization-diversified free-space-to-waveguide coupler 101 of coherent sensing unit 100, in accordance with an embodiment of the present disclosure.
• Coherent sensing unit 100 may be implemented using photonic integrated circuit (PIC) technology on a photonic substrate.
• the surface of the photonic substrate may be represented by a plane spanned by the x and y axes of the coordinate system illustrated in FIGs. 1A and IB.
• Photonic components of coherent sensing unit 100 implemented on the photonic substrate may or may not be covered by a cladding. Such components also may or may not be embedded in a cladding.
• the photonic substrate and the cladding are not shown in FIGs. 1A and IB, as well as in other figures of the present disclosure.
• a target that is to be detected by the optical coherent imager is taken to be located at a position along the positive z-direction away from the substrate surface and, if applicable, any optical components above the substrate surface. The target is not explicitly shown in the drawings for simplicity.
• the waveguides of coherent sensing unit 100 of the present disclosure may be fabricated with the dimension along the z direction smaller than the dimensions on the x-y plane and are made to support various waveguide modes, including but not limited to transverse electric (TE) modes, transverse magnetic (TM) modes, and TE and TM modes, according to the coordinate system in the embodiments illustrated in FIGs. 1A and IB.
• TE transverse electric
• TM transverse magnetic
• a TE mode may refer to a waveguide mode that has a dominant electric field component transverse to the propagation direction of the mode and the surface of the photonic substrate on which the waveguide resides
• a TM mode may refer to a waveguide mode that has a dominant magnetic field component transverse to the propagation direction of the mode and the surface of the photonic substrate on which the waveguide resides.
• optical source signal Es may be supplied to coherent sensing unit 100 through waveguide 121, while a local oscillator (LO) ELO maybe supplied to coherent sensing unit 100 through waveguide 123.
• Optical source signal Es and LO ELO may or may not come from the same light source, where the light source may or may not be implemented on the same PIC chip comprising coherent sensing unit 100.
• optical source signal Es may be made to manifest as the fundamental TE mode in waveguide
• the LO ELO may be made to manifest as the fundamental TE mode in waveguide 123, by proper designs of system and method to couple the light source (or light sources) that gives rise to Es and ELO in the waveguides of the PIC chip comprising coherent sensing unit 100. Such designs are well-known to those skilled in the art.
• the optical source signal Es may intentionally be made to manifest as a TM mode or a TE mode other than the fundamental TE mode in waveguide 121.
• the LO ELO may intentionally be made to manifest as a TM mode or a TE mode other than the fundamental TE mode in waveguide 123.
• polarization-diversified free-space-to-waveguide coupler 101 may function as both a transmitter and a receiver. It is a two-waveguide coupler that is connected to waveguides 121 and 122, wherein a primary role of waveguide 121 is to direct signal light to coupler 101 and a primary role of waveguide
• waveguide 121 may be regarded as an out-coupling waveguide and waveguide 122 may be regarded as an in-coupling waveguide.
• a distinguishing feature of polarization-diversified free-space-to-waveguide coupler 101 is that, when the polarization state of an incoming optical signal (Em in FIG. 1A) arriving at coupler 101 is orthogonal to the polarization state of the outgoing optical signal (E out in FIG.
• the incoming optical signal may be in-coupled and directed to an in-coupling waveguide (waveguide 122 in FIG. 1A) that is distinct from the out-coupling waveguide (waveguide 121 in FIG. 1A).
• free space may refer to vacuum, air, a region above the surface of the coupler, or any homogenous medium with boundaries that have length-scales much larger (e.g., at least 10 times) than the wavelength of the optical signals propagating in it.
• coupler 101 may couple optical source signal Es from waveguide 121 into free space as an outgoing optical signal E 0ut , which may be used for target illumination by the optical coherent imager.
• the outgoing optical signal E out output by coupler 101 propagates in a direction that is out of the x-y plane (i.e., the propagation direction of E out has a nonzero z component) and is polarized with a polarization determined by the design of coupler 101.
• the polarization may be one of a pair of orthogonal linear polarizations according to a coordinate system defined by the design of coupler 101, wherein the coordinate system may or may not be the same as the coordinate system defined by the x, y, and z axes shown in FIGs. 1A and IB.
• the polarization may be one of a pair of orthogonal polarizations other than a pair of linear polarizations, such as but not limited to, the right and left circular polarizations, and two orthogonal elliptical polarizations.
• coupler 101 may couple an incoming optical signal Ein into coherent sensing unit 100.
• Incoming optical signal Ein is essentially an optical signal from a target (or a target signal) described previously.
• the incoming optical signal Ei n coupled by coupler 101 may be directed to either or both waveguides 121 and 122, depending on the polarization state of the incoming optical signal Ein.
• the polarization components of the incoming optical signal Ei n that are coupled to waveguides 121 and 122 depend on the design of coupler 101.
• a first polarization component of the incoming optical signal Ein that is orthogonal to the polarization of the outgoing optical signal E out may be directed to waveguide 122 as an in-coupled optical signal Em( wg)i
• a second polarization component of the incoming optical signal Ein that is orthogonal to the first polarization of the incoming optical signal Ein may be directed to waveguide 121 as an in-coupled optical signal Em( wg) 2. More details about the two polarization components in-coupled to coupler 101 will be described below with reference to FIG. IB.
• the in-coupled optical signal Em( wg)i may be processed by the rest of the circuits of coherent sensing unit 100. In FIG.
• in-coupled optical signal Em( wg)2 propagates in a direction opposite to the propagation direction of optical source signal Es.
• in-coupled optical signal Em( wg)2 may be left unattended without affecting the other parts of the PIC chip comprising the sensing unit
• the in-coupled optical signal Em( wg)2 may be processed by some other parts of the PIC chip comprising the sensing unit 700.
• coupler 101 may comprise a single photonic component or multiple photonic components.
• coupler 101 may be realized by a polarization-splitting free -space -to -wave guide coupler.
• Examples of a polarization-splitting free-space-to-waveguide coupler include, but not limited to, a polarization-splitting grating coupler as described in “POLARIZATION SPLITTING GRATING COUPLERS,” U.S. Patent No.
• Coupler 101 may also comprise any of TE-TM mode converters, splitters, and combiners.
• coupler 101 may comprise a single layer of photonic material.
• coupler 101 may comprise multiple layers of photonic materials, wherein the photonic materials of the different layers may be the same or different.
• the optical source signal Es that propagates towards coupler 101 may manifest as a transverse electric (TE) mode in waveguide 121.
• TE transverse electric
• optical source signal Es in FIG. IB propagates towards the negative y direction with a dominant electric field component along the x direction.
• Coupler 101 may then couple optical source signal Es into free space to give rise to an outgoing optical signal E out that is polarized according to a polarization determined by the design of coupler
• outgoing optical signal E out can be linearly polarized along the x direction in FIG. IB.
• outgoing optical signal E out may propagate in a direction perpendicular to the substrate surface.
• E out as shown in FIG. IB propagates in the z direction.
• outgoing optical signal E out may propagate in a direction not perpendicular to the substrate surface, that is, E out may propagate in a direction at a slanted angle with respect to the substrate surface.
• an incoming optical signal Ein may comprise either one or both of two orthogonal polarization components: a first polarization component Eini and a second polarization component Ein2. It is appreciated that when incoming optical signal Ein comprises only first polarization component Eini, the amplitude of second polarization component Ein2 is zero, and vice versa.
• Coupler 101 may be designed in such a way that the first polarization component Eini maybe in-coupled and directed to waveguide 122 as in-coupled optical signal Ein(w g )i, wherein the first polarization component Eini is orthogonal to the polarization of outgoing optical signal E ou t.
• coupler 101 may be designed in such a way that the second polarization component Ei n 2 may be in-coupled and directed to waveguide 121 as in- coupled optical signal Em(w g )2, which propagates in a direction opposite to the propagation direction of optical source signal Es.
• the first polarization component Emi that is in-coupled and directed to waveguide 122 is orthogonal to the polarization of outgoing optical signal E ou t
• the second polarization component Ei n 2 that is in-coupled and directed to waveguide 121 is orthogonal to the first polarization Eini.
• the second polarization Ein2 may or may not be the same as (up to a proportionality factor) the polarization of the outgoing optical signal Eout, as outgoing optical signal E ou t and incoming optical signal Ein may propagate along the same or different directions.
• the specific polarization components of incoming optical signal Ei n that are coupled to waveguides 121 and 122 depend on the design of coupler 101.
• coupler 101 may be designed to optimally in-couple optical signals according to a preferred polarization basis, which is referred to as the coupling polarization basis.
• the coupling polarization basis may be the same as the polarization of outgoing optical signal E ou t output by coupler 101. As shown in FIG.
• the coupling polarization basis may be a linear polarization basis (e.g., x and y polarizations), and coupler 101 may in-couple a first linear polarization component Eini (e.g., polarized along the y direction) of the incoming optical signal Ei n and direct it to waveguide 122, wherein the first linear polarization component Eini is orthogonal to the polarization of the linearly-polarized outgoing optical signal E 0ut (e.g., x direction) and lies on a plane (e.g., yz plane) parallel to a first component of the coupling polarization basis (i.e., y direction).
• a first linear polarization component Eini e.g., polarized along the y direction
• the first linear polarization component Eini is orthogonal to the polarization of the linearly-polarized outgoing optical signal E 0ut (e.g., x direction) and lies on a plane (e.g.
• coupler 101 may in-couple a second linear polarization component E m 2 (e.g., along a direction on the x-z plane in FIG. IB) of the incoming optical signal Ei n and direct it to waveguide 121, wherein the second linear polarization component Ei n 2 lies on a plane (i.e., x-z plane) parallel to the polarization of the linearly-polarized outgoing optical signal E out (i.e., x direction) and a second component of the coupling polarization basis (i.e., x direction), and the second polarization Ein2 is orthogonal to the first polarization Eini.
• a second linear polarization component E m 2 e.g., along a direction on the x-z plane in FIG. IB
• the second linear polarization component Ei n 2 lies on a plane (i.e., x-z plane) parallel to the polarization of the linearly-polarized outgoing optical signal E out (i.e.
• Coupler 101 may couple the incoming optical signal component Eini from free space to give rise to the in-coupled optical signal Em( wg)i in waveguide 122.
• in-coupled optical signal Em( wg)i may manifest as a TE mode in waveguide 122.
• in-coupled optical signal Em( wg)i propagates towards the positive x direction in FIG. IB with a dominant electric field component along the y direction.
• coupler 101 may couple incoming optical signal component Ei n 2 from free space to give rise to in- coupled optical signal Em( wg)2 in waveguide 121.
• the in- coupled optical signal Em( wg)2 may manifest as a TE mode in waveguide 121.
• in-coupled optical signal Em( wg)2 propagates towards the positive y direction in FIG. IB with a dominant electric field component along the x direction.
• in-coupled optical signal Em( wg)i in waveguide 122 may manifest as a single waveguide mode.
• the single waveguide mode may be the fundamental TE mode.
• the single waveguide mode may be the fundamental TM mode.
• the single waveguide mode may be a mode other than the fundamental TE mode or the fundamental TM mode.
• the in-coupled optical signal Em( wg)i in waveguide 122 may manifest as a combination of multiple waveguide modes.
• in-coupled optical signal Ei n(wg)2 in waveguide 121 may manifest as a single waveguide mode.
• the single waveguide mode may be the fundamental TE mode.
• the single waveguide mode may be the fundamental TM mode.
• the single waveguide mode may be a mode other than the fundamental TE mode or the fundamental TM mode.
• in-coupled optical signal Em( wg)2 in waveguide 121 may manifest as a combination of multiple waveguide modes.
• coupler 101 is intended to separate orthogonal polarization components of optical signals into two separate waveguides 121 and 122, it is not uncommon that cross- couplings may occur in some embodiments of coupler 101.
• the incoming optical signal Ein may be linearly polarized along a direction that is orthogonal to the polarization of E out and lies on a plane parallel to the first component of the linear polarization basis (e.g., the incoming optical signal is Eini)
• a nonzero fraction of Ei n may be directed to waveguide 121 in addition to the fraction of Ei n directed to waveguide 122.
• incoming optical signal Ein may be linearly polarized along a direction that lies on a plane parallel to the polarization of E out and the second component of the linear polarization basis (e.g., the incoming optical signal is E ⁇ )
• a nonzero fraction of Ei n may be directed to waveguide 122 in addition to the fraction of Ei n directed to waveguide 121.
• a nonzero fraction of Es in waveguide 121 may propagate to waveguide 122 directly through coupler 101 in addition to the fraction of Es coupled to free space as the outgoing optical signal E out by coupler 101.
• Such cross-couplings may be regarded as imperfections of the design of coupler 101.
• coupler 101 may be designed to maximize the couplings of the respective polarization components with their intended waveguides while the cross -couplings may be minimized.
• incoming optical signal Ein may be coupled to coupler 101 at a spatial location on the surface of coupler 101 that is the same as the spatial location of outgoing optical signal E ou t emitted from coupler 101, even though E ou t and Ein are drawn at different spatial locations on the surface of coupler 101 in FIG. IB.
• incoming optical signal Ei n may be coupled to coupler 101 at a spatial location on the surface of coupler 101 different from the spatial location of outgoing optical signal E ou t emitted from coupler 101.
• coupler 101 may emit outgoing optical signal E ou t into free space and couple incoming optical signal Ein into sensing unit 100 at the same time. In other aspects, coupler 101 may emit outgoing optical signal E ou t into free space and couple incoming optical signal Ein into sensing unit 100 at different times. In general, optical signals Ein and E ou t may propagate along the same or different directions, though optical signals Ein and E ou t are drawn to propagate along different directions in FIG. IB.
• component 102 is a 2x2 optical coupler that mixes in- coupled optical signal Em(w g )i from waveguide 122 and the LO ELO from waveguide 123, and splits and directs the mixed signal to waveguides 124 and 125.
• Embodiments of 2x2 optical coupler 102 include, but not limited to, a directional coupler and a multi-mode interferometer (MMI).
• MMI multi-mode interferometer
• the mixing and splitting ratios of 2x2 optical coupler 102 depend on the design of coupler 102. In some aspects, 2x2 optical coupler 102 may have a splitting ratio of 50/50. In other aspects, 2x2 optical coupler 102 may have a splitting ratio other than 50/50.
• in-coupled optical signal Em( wg)i propagating in waveguide 122 and the LO ELO propagating in waveguide 123 may manifest as the same waveguide mode. In other aspects, in-coupled optical signal Em( wg)i propagating in waveguide 122 and LO ELO propagating in waveguide 123 may manifest as different waveguide modes.
• 2x2 optical coupler 102 may additionally include one or more mode converters at one or both of its input ports (i.e., waveguides 122 and 123), so as to convert one or both of in-coupled optical signal Em( wg)i propagating in waveguide 122 and LO ELO propagating in waveguide 123 to manifest as the same waveguide mode.
• 2x2 optical coupler 102 may not include such mode converters and may still mix, split and direct in-coupled optical signal Em( wg)i propagating in waveguide 122 and LO ELO propagating in waveguide 123 that manifest as different waveguide modes.
• component 103 is a square -law photodetector (responding to the power of an optical signal proportional to the square of its electric field) that receives and detects the optical signal from waveguide 124.
• component 104 is a square-law photodetector that receives and detects the optical signal from waveguide 125.
• 2x2 optical coupler 102 may be a 50/50 2x2 optical coupler, and coupler 102 together with photodetectors 103 and 104 may form a balanced optical heterodyne detection setup.
• one of photodetectors 103 and 104 may be omitted from coherent sensing unit 100 wherein the other remaining photodetector together with coupler 102, which may or may not be a 50/50 coupler, may form a single- detector optical heterodyne detection setup.
• photodetectors 103 and 104 may manifest as a single combined photodetector with two optical inputs connecting to waveguides 124 and 125.
• the combined photodetector with two optical inputs may measure any one or more of the intensities, the sum of the intensities, and the difference of the intensities of the optical signals from the two inputs.
• photodetectors 103 and 104 may be connected to an output electronic circuit comprising electronic components such as, but not limited to, any one or more of transimpedance amplifiers (TIA), transistors, diodes, resistors, capacitors, and electrical switches, that are used to process the electrical outputs of photodetectors 103 and 104.
• TIA transimpedance amplifiers
• transistors transistors
• diodes resistors
• capacitors capacitors
• electrical switches that are used to process the electrical outputs of photodetectors 103 and 104.
• This output electronic circuit is not shown in FIG. 1A.
• coherent sensing unit 100 may comprise components not explicitly shown, including but not limited to any one or more of electro-optical components and thermo-optical components, for any one or more of phase, amplitude, frequency, wavelength, and temporal controls.
• FIG. 2 shows a perspective view of a polarization-diversified free-space-to-waveguide coupler 200, in accordance with another embodiment of the present disclosure.
• Coupler 200 comprises two sub-couplers 201 and 202 implemented on different layers of the PIC chip.
• one of the two sub-couplers 201 or 202 may be designed to optimally couple optical signals with a specific polarization state and the other sub-coupler may be designed to optimally couple optical signals with a corresponding orthogonal polarization state.
• sub-coupler 201 may be designed to optimally couple incoming or outgoing optical signal Ei that is linearly polarized along a certain direction (e.g., along the x direction), whereas sub -coupler 202 may be designed to optimally couple incoming or outgoing optical signal E2 that is linearly polarized along a direction orthogonal to the polarization of Ei (e.g., along the y direction).
• Sub-couplers 201 and 202 may or may not be aligned to the same x-y positions.
• sub-coupler 201 may be a free-space-to-waveguide coupler, such as but not limited to a grating coupler, that may optimally couple with optical signal Ei polarized according to a polarization (e.g., linear polarization along the x direction) and minimally couple with optical signal E2 polarized according to a polarization (e.g., linear polarization along the y direction) orthogonal to the polarization of Ei.
• a polarization e.g., linear polarization along the x direction
• a polarization e.g., linear polarization along the y direction
• sub-coupler 202 may be a free-space-to-waveguide coupler, such as but not limited to a grating coupler, that may optimally couple with optical signal E2 polarized according to a polarization (e.g., linear polarization along the y direction) and minimally couple with optical signal Ei polarized according to a polarization (e.g., linear polarization along the x direction) orthogonal to the polarization of E2.
• Sub -couplers 201 and 202 may or may not be of the same design.
• the pair of orthogonally polarized optical signals Ei and E2 that are optimally coupled with one and minimally coupled with the other of sub -couplers 201 and 202 may be any of a pair of orthogonal linear polarizations, right and left circular polarizations, and a pair of orthogonal elliptical polarizations.
• orthogonal optical signals Ei and E2 are drawn at different spatial locations on the surface of sub-couplers 201 and 202 for illustrative purpose.
• sub -coupler 201 may optimally couple with optical signal Ei and minimally couple with E2 at the same spatial location or at different spatial locations on the surface of sub-coupler 201.
• sub -coupler 202 may optimally couple with optical signal E2 and minimally couple with Ei at the same spatial location or at different spatial locations on the surface of sub ⁇ coupler 202.
• optical signals Ei and E2 are drawn to propagate along a direction perpendicular to the plane of the substrate surface, i.e., along the z direction.
• optical signals Ei and E2 may propagate along directions that may or may not be perpendicular to the plane of the substrate surface.
• optical signals Ei and E2 may propagate along different directions, though optical signals Ei and E2 are drawn to propagate along the same direction in FIG. 2.
• the cross coupling between sub-couplers 201 and 202 may be minimized by choosing an appropriate vertical separation 299 between them.
• Vertical separation 299 may be formed by disposing a photonic material layer (or an air gap) between sub-couplers 201 and 202 having a thickness from 50 nanometers to 5 millimeters.
• the choice of separation 299 may depend on a combination of factors, including but not limited to the PIC technology, fabrication process, photonic materials used between sub -couplers 201 and 202, the wavelength of signal Ei, the wavelength of signal E2, the design of sub-coupler 201, and the design of sub-coupler 202.
• sub-coupler 201 may comprise a single layer of photonic material. According to other embodiments, sub -coupler 201 may comprise multiple layers of photonic materials, wherein the photonic materials of the different layers may be the same or different. Similarly, according to some embodiments, sub -coupler 202 may comprise a single layer of photonic material. According to other embodiments, sub-coupler
• 202 may comprise multiple layers of photonic materials, wherein the photonic materials of the different layers may be the same or different.
• sutr coupler 201 in FIG. 2 may be used as a transmitter whereas sub-coupler 202 in FIG. 2 may be used as a receiver, wherein sub -coupler 201 as a transmitter is farther away from the target and sub-coupler 202 as a receiver is closer to the target.
• waveguide 221 in FIG. 2 maybe the same as (or equivalently connected to) waveguide 121 in FIG. 1A as an out-coupling waveguide
• waveguide 222 in FIG. 2 maybe the same as (or equivalently connected to) waveguide 122 in FIG. 1A as an in-coupling waveguide.
• sub-coupler 201 in FIG. 2 may be used as a receiver whereas sub -coupler 202 in FIG. 2 may be used as a transmitter, wherein sub -coupler 201 as a receiver is farther away from the target and sutr coupler 202 as a transmitter is closer to the target.
• waveguide 221 in FIG. 2 may be the same as (or equivalently connected to) waveguide 122 in FIG. 1A as an in-coupling waveguide
• waveguide 222 in FIG. 2 maybe the same as (or equivalently connected to) waveguide 121 in FIG. 1A as an out-coupling waveguide.
• FIG. 3 shows a perspective view of a polarization-diversified free-space-to-waveguide coupler 300, in accordance with a further embodiment of the present disclosure.
• Coupler 300 comprises two sub-couplers 301 and 302 implemented as two separate couplers on the same layer of the PIC chip.
• one of the two sub -couplers may be designed to optimally couple with optical signals with a polarization state and the other sutr coupler may be designed to optimally couple with optical signals with another polarization state.
• the two polarization states may be orthogonal to each other.
• the two polarization states may not be orthogonal to each other.
• sub-coupler 301 may be designed to optimally couple with optical signal Ei that is linearly polarized along the x direction
• sub -coupler 302 may be designed to optimally couple with optical signal E2 that is linearly polarized along the y direction.
• sub-coupler 301 may be a free-space-to-waveguide coupler, such as but not limited to a grating coupler, that may optimally couple with optical signal Ei polarized according to a certain polarization (e.g., linear polarization along the x direction) and minimally couple with optical signal with a polarization (e.g., linear polarization along y direction) orthogonal to that of Ei.
• a polarization e.g., linear polarization along the x direction
• a polarization e.g., linear polarization along y direction
• one of sub -couplers 301 and 302 may be designed to optimally couple with optical signals with a polarization state and the other sub -coupler may be a polarization-independent free-space-to-waveguide coupler that is designed to optimally couple with optical signals with any polarization state.
• a polarization- independent free-space-to-waveguide coupler is described in “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Optics Letters Vol. 36, No. 6, p. 796 (2011).
• the cross coupling between sub-couplers 301 and 302 may be minimized by choosing an appropriate lateral separation 399 between the sub-couplers.
• Lateral separation 399 may be formed by disposing sub-couplers 301 and 302 on the same substrate surface but separated by a distance from 50 nanometers to 5 millimeters.
• the choice of lateral separation 399 may depend on a combination of factors, including but not limited to the PIC technology, fabrication process, photonic materials used for the medium between sub- couplers 301 and 302, the wavelength of the signal Ei, the wavelength of the signal E2, the design of coupler 301, and the design of coupler 302.
• sub-coupler 301 may comprise a single layer of photonic material. According to other embodiments, sub-coupler 301 may comprise multiple layers of photonic materials, wherein the photonic materials of the different layers may be the same or different. Similarly, according to some embodiments, sub -coupler 302 may comprise a single layer of photonic material. According to other embodiments, sub-coupler 302 may comprise multiple layers of photonic materials, wherein the photonic materials of the different layers may be the same or different.
• optical signals Ei and E2 are drawn to propagate along a direction perpendicular to the plane of the substrate surface, i.e., along the z direction.
• optical signals Ei and E2 may propagate along directions that may or may not be perpendicular to the plane of the substrate surface.
• optical signals Ei and E2 may propagate along different directions, though optical signals Ei and E2 are drawn to propagate along the same direction in FIG. 3.
• sub ⁇ coupler 301 in FIG. 3 may be used as a transmitter whereas sub-coupler 302 in FIG. 3 may be used as a receiver.
• waveguide 3 may be the same as (or equivalently connected to) waveguide 121 in FIG. 1A as an out-coupling waveguide whereas waveguide 322 in FIG. 3 may be the same as (or equivalently connected to) waveguide 122 in FIG. 1A as an in-coupling waveguide.
• FIG. 4A shows a side view of a polarization-separation configuration for in-coupling optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 4B shows a side view of the polarization-separation configuration in FIG. 4A for out-coupling optical signals.
• FIG. 4C shows a side view of the polarization-separation configuration in FIG. 4A for in-coupling and out-coupling optical signals.
• the polarization-separation configuration as shown in FIGs. 4A, 4B and 4C, may be used with polarization-diversified free-space-to- waveguide coupler 300 in FIG. 3 to direct optical signal Ei (coupled with sub-coupler 301) and optical signal E2 (coupled with sub-coupler 302) to propagate along a common optical path in free space, wherein the common optical path lies between an optical component 401 and the target.
• the polarization-separation configuration comprises a polarization- dependent be am -separator 401.
• polarization- dependent beam-separator 401 may be a birefringent beam displacer.
• a birefringent beam displacer may be made of one or more materials such as, but not limited to, calcite crystal, alpha barium borate crystal, yttrium vanadate crystal, or rutile crystal.
• a birefringent beam displacer is well-known in the art.
• polarization-dependent beam-separator 401 may be a polarization- dependent be am -separator other than a birefringent beam displacer, such as but not limited to a birefringent wedge, a polarization beam splitter, a polarization- dependent grating, or a polarization- dependent metalens.
• polarization- dependent beam-separator 401 may be a component that is separate from the PIC chip comprising polarization- diversified free- sp ace -to -wave guide coupler 300 as illustrated in FIG. 4A. According to other embodiments, polarization- dependent beam-separator 401 may be attached to the surface of the PIC chip comprising coupler 300. According to further embodiments, polarization- dependent beam- separator 401 may be within or be part of the PIC chip comprising coupler 300. For optical signal reception, according to the embodiment in FIG. 4A, an incoming optical signal Fi n may arrive at the polarization- dependent be am -separator 401 from a target.
• Polarization- dependent beam-separator 401 may split the incoming optical signal Fi n into two optical signals Ei and E2, wherein the polarizations of optical signals Ei and E2 are orthogonal to each other.
• the splitting of the optical signal may depend on the polarization of the incoming optical signal.
• One of optical signals Ei and E2 is the ordinary ray (o-ray) and the other is the extraordinary ray (e-ray).
• optical signal Ei may be the o-ray whereas optical signal E2 maybe the e-ray.
• o-ray and e-ray used herein may generally be referred to two orthogonally polarized light rays that are split by polarization- dependent beam-separator 401, wherein the splitting is defined by the characteristics of the polarization- dependent be am -separator.
• the polarizations of optical signals Ei and E2 depend on the permittivities of the materials of polarization-dependent beam-separator 401, the orientation of optic axis 498 and the incident angle of incoming optical signal Ein.
• the incident angle of incoming optical signal Ei n is close to the normal of the surface of polarization- dependent be am -separator 401.
• polarization- dependent be am -separator 401 maybe fabricated and optic axis 498 may be oriented in such a way that the o-ray (Ei) is polarized along the x direction and the ' -ray (E2) is polarized along the y direction upon emerging from and exiting polarization- dependent beam-separator 401.
• the o-ray and e-ray may be laterally displaced upon emergence from polarization- dependent beam- separator 401.
• the lateral displacements may depend on any one or more of the factors including but not limited to the geometries (e.g., shape and thickness), permittivities of the materials, and orientation of optic axis 498 of polarization- dependent beam-separator 401, and the wavelength and incident angle of incoming optical signal Ein.
• o-ray Ei may propagate along a first optical path with a first lateral displacement (e.g., Ei continues the path of the incoming optical signal Ein with null lateral displacement as illustrated in FIG. 4A), whereas the e-ray E2 may propagate along a second optical path with a second lateral displacement 499 with respect to the path of incoming optical signal Ei n as illustrated in FIG. 4A, wherein the second optical path of e- ray E2 is distinct from the first optical path of o-ray Ei, and the second lateral displacement of e-ray E2 is different from the first lateral displacement of o-ray Ei.
• a first lateral displacement e.g., Ei continues the path of the incoming optical signal Ein with null lateral displacement as illustrated in FIG. 4A
• the e-ray E2 may propagate along a second optical path with a second lateral displacement 499 with respect to the path of incoming optical signal Ei n as illustrated in FIG. 4A, wherein the second optical path of e- ray
• optical signals Ei and E2 may be incident on sutr couplers 301 and 302 at angles close to normal incidence, as shown in FIG. 4A. According to other embodiments, optical signals Ei and E2 may be incident on sub-couplers 301 and 302 at angles other than normal incidence. With any incident angle of incoming optical signal E m and the properties of polarization- dependent be am -separator 401 (such as its geometries, permittivities, and orientation of the optic axis), the polarizations and propagation directions of o-ray Ei and ' -ray E2 may be determined through the Maxwell’s equations.
• sub-coupler 301 may be configured to optimally couple with o-ray Ei based on its polarization and propagation direction, wherein the polarization and propagation direction of o-ray Ei may be pre-determined.
• sub -coupler 302 may be configured to optimally couple with e-ray E2 based on its polarization and propagation direction, wherein the polarization and propagation direction of e-ray E2 may be pre-determined. For example, as shown in FIG.
• the incident angle of incoming optical signal Fi n may be close to the normal of the surface of polarization- dependent be am -separator 401 and optic axis 498 may be oriented at an angle on the y-z plane.
• sub-coupler 301 may be configured to optimally couple with o-ray Ei propagating along the z direction and polarized along the x direction
• sub-coupler 302 may be configured to optimally couple with e-ray E2 propagating along the z direction and polarized along the y direction.
• Lateral separation 399 between sub-couplers 301 and 302 may be determined by incorporating the information of lateral separation 499 between o-ray Ei and e-ray E2.
• sub-coupler 301 may not be configured to optimally couple with o-ray Ei based on its polarization. That is, the optimal polarization for coupling with sub-coupler 301 may not be the same as the polarization of o-ray Ei.
• sub-coupler 302 may not be configured to optimally couple with ' -ray E2 based on its polarization. That is, the optimal polarization for coupling with sub-coupler 302 may not be the same as the polarization of e-ray E2.
• sub-coupler 301 may not be configured to optimally couple with o-ray Ei based on the propagation direction of o-ray Ei.
• sub-coupler 302 may not be configured to optimally couple with e-ray E2 based on the propagation direction of e-ray E2.
• sub-coupler 301 may be a polarization-independent coupler and may be configured to optimally couple with o-ray Ei based only on the propagation direction of o-ray Ei.
• sub-coupler 302 may be a polarization-independent coupler and may be configured to optimally couple with e-ray E2 based only on the propagation direction of e-ray E2.
• optical signal Ei outgoing from sub -coupler 301 may be polarized according to the polarization of the o-ray defined by polarization-dependent beam-separator 401 (e.g., linear polarization along the x direction as shown in FIG. 4B) and optical signal E2 outgoing from sub -coupler 302 may be polarized according to the polarization of the e-ray defined by polarization- dependent beam-separator 401 (e.g., linear polarization along the y direction as shown in FIG. 4B). Propagation of optical signals through polarization- dependent beam-separator 401 is reversible.
• optical signals Ei and E2 may be combined to give rise to an outgoing optical signal E out that propagates along an optical path away from an upper surface of polarization- dependent be am -separator 401 (e.g., a path that continues the path of optical signal Ei with null lateral displacement as illustrated in FIG. 4B), wherein optical signals Ei and E2 are coherent with respect to each other and the outgoing optical signal E out is polarized according to the polarizations, amplitudes, and relative phase of optical signals Ei and E2.
• optical signals Ei and E2 emerging from and exiting polarization- dependent be am -separator 401 may not perfectly overlap spatially. This may give rise to spatially varying polarization of outgoing optical signal E 0ut .
• polarization- dependent beam-separator 401 and sub-couplers 301 and 302 may be configured in such a way that the spatial overlap between optical signals Ei and E2 may give rise to an outgoing optical signal E out that has a dominant (i.e., greater than 50%) polarization state.
• Polarization-dependent beam-separator 401 maybe used with coupler 300 to transmit and receive optical signals, wherein one of sub-couplers 301 and 302 may be used for transmitting an outgoing optical signal E 0ut , while the other one of sub -couplers 301 and 302 may be used for receiving an incoming optical signal Em.
• Optical signals E out and Ein may propagate along a common optical path that lies between optical component 401 and the target. As shown in FIG. 4C, on one hand, optical signal Ei outgoing from sub-coupler 301 may be polarized according to the polarization of the o-ray defined by polarization- dependent be am -separator 401.
• optical signal Ei After passing through polarization- dependent beam-separator 401, optical signal Ei may give rise to outgoing optical signal E 0ut , wherein the polarizations of optical signals Ei and E out are the same.
• outgoing optical signal E out may emerge from and exit polarization- dependent beam-separator 401 with a polarization that is the same as the polarization of optical signal Ei (i.e., along the x direction) and propagate along an optical path away from polarization- dependent be am -separator 401 (e.g., a path that continues the path of optical signal Ei without lateral displacement as illustrated in FIG. 4C).
• an incoming optical signal Fi n may be polarized according to the polarization of the e-ray defined by polarization- dependent be am -separator 401 and propagate along the same optical path as the outgoing optical signal Eo ut , but in a reversed direction.
• incoming optical signal Em may give rise to optical signal E2 that may be coupled with sub-coupler 302, wherein the polarizations of optical signals Fin and E2 are the same. For example, as shown in FIG.
• an incoming optical signal Fin linearly polarized along the y direction incident at a direction normal to an upper surface of polarization- dependent be am -separator 401 may give rise to optical signal E2 that is linearly polarized along the y direction and couples with sub -coupler 302, wherein optical signal E2 is laterally displaced by polarization- dependent beam-separator 401.
• the polarizations of outgoing optical signal E out and incoming optical signal Ein are orthogonal to each other, and the polarizations of optical signals Ei and E2 are orthogonal to each other.
• incoming optical signal Fin may be split into an 0- ray and an ' -ray, wherein the o-ray may couple with sub-coupler 301 and the ' -ray may couple with sub-coupler 302, as illustrated in the embodiment in FIG. 4A.
• sub-couplers 301 and 302 may be interchanged, so that the outgoing optical signal may be e-ray E2, instead of o-ray Ei as illustrated in FIG. 4C.
• a coupling polarization basis may be formed by a pair of polarizations of optical signals which couple with sub -couplers 301 and 302 optimally.
• the coupling polarization basis may be the same as the polarizations of the o-ray and e-ray corresponding to polarization- dependent beam-separator 401.
• the coupling polarization basis may be different from the polarizations of the o-ray and e-ray corresponding to polarization- dependent beam- separator 401.
• the difference between the coupling polarization basis and the polarizations of the o-ray and e-ray corresponding to polarization-dependent be am -separator 401 maybe minimized by proper designs of the optical coherent imager.
• Such proper designs may comprise an optical component (such as one or more lenses) to ensure incoming optical signals and outgoing optical signals to propagate along directions that maintain near normal incidence upon the surfaces of polarization-dependent beam-separator 401.
• Such proper designs may also comprise an optical component (such as one or more lenses) to ensure incoming optical signals and outgoing optical signals to couple with sub -couplers 301 and 302 at incident angles close to the optimal coupling directions of sub -couplers 301 and 302.
• the optical signal out-coupled by coupler 300 may give rise to two outgoing optical signals emerging from polarization-dependent beam-separator 401, wherein the two outgoing optical signals are optical signals corresponding to the o-ray and the e-ray.
• optical signal Ei emitted by sub-coupler 301 may give rise to an outgoing o-ray that is the same as the outgoing optical signal E out and an outgoing e-ray that propagates along an optical path different from that of outgoing optical signal E out (not shown).
• the outgoing e-ray in this circumstance maybe disregarded, as an incoming optical signal that shares the same optical path as the outgoing e-ray may not be able to be coupled with in-coupling sub -coupler 302 as exemplified in FIG. 4C.
• either one or both of sub -couplers 301 and 302 in FIG. 4C may be a polarization-independent free-space-to-waveguide coupler.
• a polarization-independent free-space-to-waveguide coupler maybe able to optimally couple an incoming optical signal Ein irrespective of the polarizations of the o-ray and the e-ray corresponding to polarization- dependent beam-separator 401.
• the optical signal reflected by the target has a dominant polarization component that is the same as the optical signal that illuminates the target.
• Such circumstances include but not limited to specular reflection and light reflection off a shiny target surface.
• a polarization transformation mechanism may thus be desirable to be used with a coherent sensing unit that utilizes polarization diversity for out-coupling and in-coupling optical signals.
• FIG. 5A shows a perspective view of a polarization transformation configuration 510 realized by the Faraday effect, in accordance with an embodiment of the present disclosure.
• Polarization transformation configuration 510 is arranged for in-coupling and out-coupling optical signals with coupler 101 and comprises Faraday rotator 501 and an optional polarization rotator 502.
• FIG. 5B shows a top view of the polarization states of optical signals in FIG. 5A.
• Faraday rotator 501 is an optical component disposed between the target and polarization-diversified free-space-to-waveguide coupler 101.
• Faraday rotator 501 may be configured to rotate a linearly polarized optical signal by an angle (e.g., 45 degrees).
• an angle e.g. 45 degrees
• coupler 101 may emit optical signal Ei that is linearly polarized along the x direction.
• Faraday rotator 501 may then rotate the polarization of optical signal Ei by 45 degrees to give rise to optical signal E2 that is linearly polarized along a direction that makes an angle of 45 degrees with respect to the x direction.
• optional polarization rotator 502 (herein referred to as polarization rotator for simplicity) is disposed between the target and Faraday rotator 501.
• polarization rotator 502 may include but not limited to a quartz rotator.
• polarization rotator 502 may be configured in such a way that further rotates the polarization of optical signal E2 by an angle. As shown in FIG. 5A, for example, polarization rotator 502 rotates the polarization of optical signal E2, that is linearly polarized along a direction that makes an angle of 45 degrees with respect to the x direction, by 45 degrees to give rise to optical signal E3 that is linearly polarized along the y direction.
• Polarization rotator 502 is a reciprocal optical component, that is, the polarization rotation by polarization rotator 502 does not depend on the propagation direction of the optical signal. According to FIG. 5A, polarization rotator 502 may rotate the polarization of an incoming optical signal E4, that has the same linear polarization as E3, by an angle (e.g., 45 degrees) to give rise to optical signal E5 that has the same polarization as E2. In contrast, Faraday rotator 501 is a nonreciprocal optical component.
• Faraday rotator 501 may rotate the polarization of optical signal E5 by an angle (e.g., 45 degrees) to give rise to an optical signal Eb that is linearly polarized along a direction (i.e., y direction according to FIG. 5A) orthogonal to the polarization of the optical signal Ei.
• the angular rotation effected by F ar aday rotator 501 may not be sensitive to the incident angle of the optical signal onto Faraday rotator 501, as the effects of the length of the propagation path of the optical signal inside Faraday rotator 501 and the magnetic field strength along the propagation path on polarization rotation may compensate each other.
• the operation principle of a Faraday rotator is well-known to those skilled in the art.
• optional polarization rotator 502 may be used to transform the polarization of E3 to one of the polarization basis components defined by coupler 101.
• the polarization basis defined by coupler 101 in FIG. 5A are the linear polarizations along the x and y directions.
• optional polarization rotator 502, which may be a quartz rotator may be used to enable a broadband polarization rotation when using together with Faraday rotator 501.
• Conventional polarization rotators such as quartz rotators are sensitive to the incident angle of the incident optical signal.
• polarization rotator 502 may be a polarization rotator that may accept incident optical signal with a large angular range while the intended phase shift may be maintained.
• Examples of such a wide-angle polarization rotator include but not limited to artificial photonic structures designed with the field transformation approach as described in “A Wide-angle Multi-Octave Broadband Waveplate Based on Field Transformation Approach,” Scientific Reports, 5, 17532 (2015).
• the components of polarization transformation configuration 510 may exhibit as separate components as illustrated in FIG. 5A. According to other embodiments, some or all components of polarization transformation configuration 510 may exhibit as a single combined component. Additionally, according to some embodiments, polarization transformation configuration 510 maybe an optical assembly that is separate from the PIC chip comprising polarization-diversified free-space-to-waveguide coupler 101 as illustrated in FIG. 5A. According to other embodiments, some or all components of polarization transformation configuration 510 may be attached to the surface of the PIC chip comprising coupler 101. According to further embodiments, some or all components of polarization transformation configuration 510 may be within or be part of the PIC chip comprising coupler 101.
• the propagation path of in-coupling optical signals Ei, E2, and E3 and the propagation path of out-coupling optical signals E4, Es, and Eb are distinctly drawn.
• the propagation paths of the in-coupling and out-coupling signals may or may not be spatially distinct.
• optical signals Ei, E2, E3, E4, E5 and F ⁇ ; are depicted to propagate along the z direction and are at normal incident on coupler 101, Faraday rotator 501 and polarization rotator 502.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 5C shows a side view of a polarization transformation-separation configuration for use with coupler 300, in accordance with an embodiment of the present disclosure, wherein the polarization transformation configuration 510 in FIG. 5A is incorporated with the polarization-separation configuration in FIG. 4C.
• polarization- dependent beam-separator 401 is disposed between coupler 300 (comprising sub-couplers 301 and 302) and polarization transformation configuration 510 (comprising Faraday rotator 501 and polarization rotator 502).
• 5C may be used to enable optical signals that are coupled with sub-couplers 301 and 302 to propagate along a common optical path, wherein the common optical path lies between polarization- dependent beam-separator 401 and the target.
• sub-coupler 301 may output optical signal Ei into free space, wherein Ei is linearly polarized along a direction defined by sub-coupler 301 (e.g., the x direction in FIG. 5C).
• optical signal Ei may give rise to optical signal E3 that is linearly polarized along a direction orthogonal to that of Ei (e.g., the y direction).
• incoming optical signal E4 that has the same polarization as E3 and propagates along a common optical path as the outgoing optical signal E3, but in a reversed direction, through polarization rotator 502, Faraday rotator 501 and polarization- dependent be am -separator 401, may give rise to optical signal Eb that is linearly polarized along a direction orthogonal to the polarization of Ei (i.e., the y direction) and is spatially separated from the path of Ei so that optical signal F ⁇ ; may couple with sub-coupler 302.
• the components of polarization transformation configuration 510 and polarization- dependent beam-separator 401 may exhibit as separate components as illustrated in FIG. 5C. According to other embodiments, some or all components of polarization transformation configuration 510 and polarization-dependent be am -separator 401 may exhibit as a single combined component. Additionally, according to some embodiments, polarization transformation configuration 510 and polarization- dependent beam-separator 401 may be an optical assembly that is separate from the PIC chip comprising polarization- diversified free-space-to-waveguide coupler 300 as illustrated in FIG. 5C.
• some or all components of polarization transformation configuration 510 and polarization- dependent beam-separator 401 may be attached to the surface of the PIC chip comprising coupler 300. According to further embodiments, some or all components of polarization transformation configuration 510 and polarization- dependent beam-separator 401 may be within or be part of the PIC chip comprising coupler 300.
• optical signals Ei, E3, E4, and Eb are depicted to propagate along the z direction and are at normal incident on coupler 300, polarization- dependent beam-separator 401, Faraday rotator 501, and polarization rotator 502.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 6A shows a perspective view of a polarization transformation configuration realized by a quarter-wave plate 601, in accordance with another embodiment of the present disclosure.
• the polarization transformation is realized by means of phase retardation through quarter-wave plate.
• quarter-wave plate 601 is an optical component disposed between the target and polarization- diversified free-space-to-waveguide coupler 101.
• Quarter-wave plate 601 maybe configured, through an appropriate orientation of its optic axis, to transform a linearly polarized optical signal into a circularly polarized optical signal. For example, as shown in FIG.
• quarter- wave plate 601 may transform optical signal Ei, that is linearly polarized along the x direction, into optical signal E2 that is right-circularly polarized with respect to the propagation direction of E2 (the positive z direction).
• FIG. 6B shows a top view of the polarization states of optical signals in FIG. 6A.
• optical signal E3 has a polarization with the same circular rotation direction as the polarization rotation direction of E2, but propagates in a direction opposite to the propagation direction of E2 (i.e., E2 and E3 effectively have opposite handedness).
• Quarter-wave plate 601 may be used to transform optical signal E3 to give rise to optical signal E4 that is linearly polarized along a direction orthogonal to the polarization of Ei.
• quarter-wave plate 601 transforms optical signal E3, that is left -circularly polarized with respect to its propagation direction (negative z direction), into optical signal E4 that is linearly polarized along the y direction.
• quarter- wave plate 601 may be a component that is separate from the PIC chip comprising polarization-diversified free-space-to-waveguide coupler 101 as illustrated in FIG. 6A. According to other embodiments, quarter-wave plate 601 may be attached to the surface of the PIC chip comprising coupler 101. According to further embodiments, quarter-wave plate 601 may be within or be part of the PIC chip comprising coupler 101.
• the propagation path of in-coupling optical signals Ei and E2 and the propagation path of out-coupling optical signals E3 and E4 are distinctly drawn.
• the propagation paths of the in-coupling and out-coupling signals may or may not be spatially distinct.
• optical signals Ei, E2, E3, and E4 are depicted to propagate along the z direction and are at normal incident on coupler 101 and quarter-wave plate 601.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 6C shows a side view of a polarization transformation-separation configuration for use with coupler 300, in accordance with another embodiment of the present disclosure, wherein the polarization transformation configuration in FIG. 6A is incorporated with the polarization-separation configuration in FIG. 4C.
• polarization- dependent beam-separator 401 is disposed between coupler 300 (comprising sub-couplers 301 and 302) and quarter-wave plate 601. Polarization- dependent beam-separator 401 in FIG.
• 6C may be used to enable optical signals that are coupled with sub -couplers 301 and 302 to propagate along a common optical path, wherein the common optical path lies between polarization- dependent beam-separator 401 and the target.
• sub-coupler 301 may output optical signal Ei into free space, wherein Ei is linearly polarized along a direction defined by the design of sub-coupler 301 (e.g., the x direction in FIG. 6C). According to FIG. 6C and with reference to FIGs.
• optical signal Ei may give rise to optical signal E2 that is right -circularly polarized with respect to the propagation direction of E2 (e.g., along the positive z direction).
• incoming optical signal E3 has a polarization with the same circular rotation direction as the polarization rotation direction of E2 and propagates along a common optical path as the outgoing optical signal E2, but in a reversed direction (i.e., E3 is left-circularly polarized with respect to its propagation direction).
• Incoming optical signal E3, through quarter-wave plate 601 and polarization- dependent beam-separator 401, may give rise to optical signal E4 that is linearly polarized along a direction orthogonal to the polarization of Ei (e.g., the y direction in FIG. 6C) and is spatially separated from the path of Ei, so that optical signal E4 may couple with sub -coupler 302.
• quarter-wave plate 601 and polarization-dependent be am -separator 401 may exhibit as separate components as illustrated in FIG. 6C.
• quarter-wave plate 601 and polarization- dependent beam-separator 401 may exhibit as a single combined component.
• quarter-wave plate 601 and polarization-dependent beam-separator 401 may be an optical assembly that is separate from the PIC chip comprising polarization-diversified free-space-to-waveguide coupler 300 as illustrated in FIG. 6C. According to other embodiments, either one or both of quarter-wave plate 601 and polarization- dependent beam- separator 401 may be attached to the surface of the PIC chip comprising coupler 300. According to further embodiments, either one or both of quarter- wave plate 601 and polarization- dependent beam-separator 401 may be within or be part of the PIC chip comprising coupler 300.
• optical signals Ei, E2, E3, and E4 are depicted to propagate along the z direction and are at normal incident on coupler 300, polarization- dependent beam-separator 401 and quarter-wave plate 601.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• the target may reflect or scatter the optical signal that illuminates the target, in such a way that the returning optical signal is polarized with a polarization substantially different from the polarization of the illuminating optical signal.
• a coherent sensing unit may be desirable for a coherent sensing unit to be able to detect incoming optical signals with any polarization states.
• FIG. 7A shows a plan view of a coherent sensing unit 700 for transmitting and receiving optical signals based on polarization diversity, in accordance with another embodiment of the present disclosure.
• Coherent sensing unit 700 in FIG. 7A is similar to coherent sensing unit 100 in FIG. 1A.
• the primary difference between coherent sensing unit 700 and coherent sensing unit 100 is that coherent sensing unit 700 may also process the component of the incoming optical signal Ei n that is coupled by coupler 101 and directed to waveguide 121 according to the embodiment of coherent sensing unit 100 in FIG. 1A.
• optical source signal Es is supplied to coherent sensing unit 700 through waveguide 731 and local oscillator (LO) ELO is supplied to coherent sensing unit 700 through waveguide 734.
• component 705 is a 2x2 optical coupler. Since there is no signal input from waveguide 733, 2x2 optical coupler 705 may function as a splitting coupler that splits the optical source signal Es from waveguide 731 and directs a fraction of Es as an optical signal Ei through waveguide 721 into polarization-diversified free- sp ace -to -wave guide coupler 701. A fraction of Es may also pass to waveguide 732.
• the fraction of Es passed into waveguide 732 may be used for other purposes (for example, as in coherent sensing unit 710 in FIG. 7B) or may simply be regarded as a loss. For the latter situation, the fraction of Es passed to waveguide 732 may need to be attenuated properly to avoid any back reflection.
• the fractions of Es that are passed to waveguides 721 and 732 respectively depend on the splitting ratio and loss of 2x2 optical coupler 705.
• 2x2 optical coupler 705 maybe a 50/502x2 optical coupler.
• 2x2 optical coupler 705 may have a splitting ratio other than 50/50.
• polarization- diversified free-space-to-waveguide coupler 701 (herein referred to as coupler 701 for simplicity) is similar to coupler 101 of coherent sensing unit 100 in FIG. 1A that functions as both a transmitter and a receiver. It is a two-waveguide coupler that is connected to waveguides 721 and 722.
• coupler 701 may couple optical signal Ei from waveguide 721 into free space as an outgoing optical signal E out , which may be used for target illumination by the optical coherent imager.
• the outgoing optical signal E out output by coupler 701 propagates in a direction that is out of the x-y plane (i.e., the propagation direction of E out has a nonzero z component) and is polarized with a polarization defined by the design of coupler 701.
• coupler 701 may couple an incoming optical signal Fin into coherent sensing unit 700.
• the incoming optical signal Ein coupled by coupler 701 may be directed to either or both waveguides 721 and 722, depending on the polarization state of the incoming optical signal Ein.
• the polarization components of the incoming optical signal Fi n that are coupled to waveguides 721 and 722 depend on the design of coupler 701.
• the polarization component of incoming optical signal Fin that is orthogonal to the polarization of outgoing optical signal E ou t may be directed to waveguide 722 as an in-coupled optical signal E2, and the polarization component of the incoming optical signal Ein that is orthogonal to the polarization component of the incoming optical signal Ei n directed to waveguide 722 may be directed to waveguide 721 as an in- coupled optical signal E3.
• the in-coupled optical signal E3 propagates in a direction opposite to the propagation direction of optical signal Ei.
• 2x2 optical coupler 705 may function as a splitting coupler that splits the in-coupled optical signal E3 from waveguide 721 and directs a fraction of E3 as an optical signal E4 through waveguide 733 into 2x2 optical coupler 712.
• a fraction of E3 may also pass to waveguide 731 and propagate in a direction opposite to the propagation direction of optical source signal Es.
• the component of E3 in waveguide 731 may be left unattended without affecting the other parts of the PIC chip comprising the sensing unit 700.
• the fractions of E3 that are passed respectively to waveguides 731 and 733 depend on the splitting ratio and loss of 2x2 optical coupler 705.
• coupler 701 in general may comprise a single photonic component or multiple photonic components.
• coupler 701 may be realized by a polarization-splitting free-space-to-waveguide coupler.
• coupler 701 maybe realized by coupler 200 in FIG. 2, wherein waveguides 221 and 222 may be the same as waveguides 721 and 722 (i.e., waveguide 721 being waveguide 221 and waveguide 722 being waveguide 222, or waveguide 721 being waveguide 222 and waveguide 722 being waveguide 221).
• coupler 701 maybe realized by coupler 300 in FIG. 3, wherein waveguides 321 and 322 may be the same as waveguides 721 and 722 (i.e., waveguide 721 being waveguide 321 and waveguide 722 being waveguide 322, or waveguide 721 being waveguide 322 and waveguide 722 being waveguide 321).
• polarization- dependent beam-separator 401 in FIG. 4C may be used with coherent sensing unit 700 to enable outgoing optical signal E out and incoming optical signal Ei n to propagate along a common optical path, wherein the common optical path lies between polarization- dependent be am -separator 401 and the target.
• coupler 701 may also comprise any of TE-TM mode converters, splitters, and combiners.
• Faraday rotator 501 and optional polarization rotator 502 illustrated in FIGs. 5A and 5C may be used with coupler 701, to rotate the polarizations of the outgoing and incoming optical signals.
• quarter-wave plate 601 illustrated in FIGs. 6A and 6C may be used with coupler 701 to transform the outgoing optical signal into a linearly-polarized, circularly- polarized or ellipticallypolarized optical signal, depending on the polarization of the outgoing optical signal.
• component 706 is a splitting coupler that splits the LO from waveguide 734 and directs a fraction of the LO to waveguide 723 as the LO ELO,I and a fraction of the LO to waveguide 735 as the LO ELO,2.
• the fractions of the LO that are passed respectively to waveguides 723 and 735 depend on the splitting ratio and loss of splitting coupler 706.
• splitting coupler 706 may be a 50/50 splitting coupler.
• splitting coupler 706 may have a splitting ratio other than 50/50.
• component 702 is a 2x2 optical coupler that mixes the in-coupled optical signal E2 from waveguide 722 and the LO ELO,I from waveguide 723, and splits and directs the mixed signal to waveguides 724 and 725.
• 2x2 optical coupler 702 may be similar to 2x2 optical coupler 102 of coherent sensing unit 100 in FIG. 1.
• component 703 is a square-law photodetector that receives and detects the optical signal from waveguide 724.
• component 704 is a square -law photodetector that receives and detects the optical signal from waveguide 725.
• photodetectors 703 and 704 may be similar to photodetectors 103 and 104 of coherent sensing unit 100 in FIG. 1.
• photodetectors 703 and 704 may be connected to an output electronic circuit comprising electronic components, such as, but not limited to, any one or more of transimpedance amplifiers (TIA), transistors, diodes, resistors, capacitors, and electrical switches, that are used to process the electrical outputs of photodetectors 703 and 704.
• TAA transimpedance amplifiers
• transistors transistors, diodes, resistors, capacitors, and electrical switches
• component 712 is a 2x2 optical coupler that mixes the in-coupled signal E4 from waveguide 733 and the LO ELO,2 from waveguide 735, and splits and directs the mixed signal to waveguides 736 and 737.
• component 713 is a square-law photodetector that receives and detects the optical signal from waveguide 736.
• component 714 is a square -law photodetector that receives and detects the optical signal from waveguide 737.
• photodetectors 713 and 714 may be similar to photodetectors 703 and 704.
• photodetectors 713 and 714 may be connected to an output electronic circuit comprising electronic components, such as, but not limited to, any one or more of transimpedance amplifiers (T ⁇ A), transistors, diodes, resistors, capacitors, and electrical switches, that are used to process the electrical outputs of photodetectors 713 and 714.
• T ⁇ A transimpedance amplifiers
• the output electronic circuit connected to photodetectors 713 and 714 may form a single electronic circuit with the output electronic circuit connected to photodetectors 703 and 704. According to other embodiments, the output electronic circuit connected to photodetectors 713 and 714 may be separate from the output electronic circuit connected to photodetectors 703 and 704.
• coherent sensing unit 700 may comprise components not explicitly shown, including but not limited to any one or more of electro-optical components and thermo-optical components, for any one or more of phase, amplitude, frequency, wavelength, and temporal controls.
• FIG. 7B shows a plan view of a coherent sensing unit 710 for transmitting and receiving optical signals based on polarization diversity, in accordance with yet another embodiment of the present disclosure.
• Coherent sensing unit 710 in FIG. 7B is similar to coherent sensing unit 700 in FIG. 7A.
• the primary difference between coherent sensing unit 700 and coherent sensing unit 710 is that, in coherent sensing unit 710, waveguide 734 is connected to waveguide 732 so that the LO FLO comes from a fraction of optical source signal Es that is passed into waveguide 732.
• FIG. 8 shows a plan view of a coherent sensing unit 800 for transmitting and receiving optical signals based on polarization diversity, in accordance with a further embodiment of the present disclosure.
• Coherent sensing unit 800 in FIG. 8 is similar to coherent sensing unit 700 in FIG. 7A.
• the primary difference between coherent sensing unit 800 and coherent sensing unit 700 is that an optical circulator 805 is used in coherent sensing unit 800 to replace 2x2 optical coupler 705 in coherent sensing unit 700 to direct the flow of optical signals.
• optical circulator 805 may include but not limited to an optical circulator based on heterogeneous CeYIC/sdicon waveguides in a Mach-Zehnder interferometer (MZI) configuration as described in “Broadband TE Optical Isolators and Circulators in Silicon Photonics Through Ce ⁇ YIG Bonding,” Journal of Lightwave Technology, Vol. 37, No. 5, p. 1463 (2019).
• MZI Mach-Zehnder interferometer
• optical circulator 805 is a three-port optical circulator that routes optical signals in a circular direction.
• optical circulator 805 may route optical signals in a clockwise direction: optical signal inputting from waveguide 731 is directed to waveguide 721, optical signal inputting from waveguide 721 is directed to waveguide 733, and optical signal inputting from waveguide 733 is directed to waveguide 731.
• optical circulator 805 couples with waveguides 721, 731, and 733. Waveguide 732 of coherent sensing unit 700 in FIG. 7 may then be omitted from coherent sensing unit 800 in FIG. 8. Optical circulator 805 may route the optical source signal Es in waveguide 731 to give rise to optical signal Ei in waveguide 721. In-coupled optical signal E3 received by coupler 701 may be directed through waveguide 721 to optical circulator 805, where optical circulator 805 may route the in-coupled optical signal E3 to waveguide 733 to give rise to the optical signal Eu
• a four-port optical circulator such as one realized by a four-port MZFbased optical circulator, may be used instead of a three-port optical circulator for optical circulator 805, and waveguide 732 of coherent sensing unit 700 in FIG. 7 may be retained in coherent sensing unit 800 in FIG. 8.
• the four-port optical circulator may be coupled to waveguides 721, 731, 732, and 733, wherein the four-port optical circulator routes optical signals from waveguide 731 to waveguide 721, from waveguide 721 to waveguide 733, from waveguide 733 to waveguide 732, and from waveguide 732 to waveguide 731.
• optical circulator 805 in coherent sensing unit 800 to replace 2x2 optical coupler 705 in coherent sensing unit 700 may have the advantage of avoiding the loss of a fraction of optical source signal Es that is passed into waveguide 732. Nevertheless, current state-of-the-art on-chip optical circulator has an insertion loss (> 10 dB) that may still be too high to impose an advantage over the use of 2x2 optical coupler 705 in the configuration of coherent sensing unit 700.
• FIG. 9 shows a plan view of a coherent sensing unit 900 for transmitting and receiving optical signals based on polarization diversity, in accordance with a yet further embodiment of the present disclosure.
• Coherent sensing unit 900 is similar to coherent sensing units 700, 710, and 800 that detect an incoming optical signal with any polarization state.
• the primary difference between coherent sensing unit 900 and coherent sensing units 100, 700, 710, and 800 is that coherent sensing unit 900 comprises a polarization-diversified free-space-to- waveguide coupler that directs in-coupled optical signals with any polarization states to waveguides that are distinct from the waveguide carrying an outgoing optical signal.
• optical source signal Es is supplied to coherent sensing unit 900 through waveguide 921 and local oscillator (LO) ELO is supplied to coherent sensing unit 900 through waveguide 934.
• LO local oscillator
• polarization- diversified free -space -to -wave guide coupler 901 (herein referred to as coupler 901 for simplicity) is a three-waveguide coupler that is connected to waveguides 921, 922, and 933. Coupler 901 may function as both a transmitter and areceiver.
• coupler 901 may couple outgoing optical signal Ei (which is essentially the same as the optical source signal Es) from waveguide 921 into free space as an outgoing optical signal E 0 ut, which may be used for target illumination by the optical coherent imager.
• Outgoing optical signal E out output by coupler 901 propagates in a direction that is out of the x-y plane (i.e., the propagation direction of E out has a nonzero z component) and is polarized with a polarization state defined by the design of coupler 901.
• coupler 901 may couple an incoming optical signal Ein into coherent sensing unit 900.
• Incoming optical signal Ei n coupled by coupler 901 may be directed to either or both waveguides 922 and 933, depending on the polarization state of incoming optical signal Ein.
• the polarization components of the incoming optical signal Ein that are coupled to waveguides 922 and 933 depend on the design of coupler 901.
• the polarization component of incoming optical signal Ein that is orthogonal to the polarization of the outgoing optical signal E ou t may be directed to waveguide 922 as an in- coupled optical signal E 2
• the polarization component of incoming optical signal Ein that is orthogonal to the polarization component of incoming optical signal Ein directed to waveguide 922 may be directed to waveguide 933 as an in-coupled optical signal E 3 .
• coupler 901 is drawn as a single entity, coupler 901 in general may comprise a single photonic component or multiple photonic components. Embodiments of coupler 901 are illustrated in FIGs. 10A, 11 A, and 13A to be described in further detail below. According to some embodiments, similar to coupler 101 in FIGs. 1A and IB, coupler 901 may also comprise any of TE-TM mode converters, splitters, and combiners.
• splitting coupler 906 splits the LO ELO from waveguide 934 and directs a fraction of the LO to waveguide 923 as the LO ELO,I and a fraction of the LO to waveguide 935 as the LO ELO,2.
• the fractions of the LO that are passed respectively to waveguides 923 and 935 depend on the splitting ratio and loss of splitting coupler 906.
• splitting coupler 906 may be a 50/50 splitting coupler.
• splitting coupler 906 may have a splitting ratio other than 50/50.
• component 902 is a 2x2 optical coupler that mixes the in-coupled optical signal E2 from waveguide 922 and the LO ELO,I from waveguide 923, and splits and directs the mixed signal to waveguides 924 and 925.
• 2x2 optical coupler 902 may be similar to 2x2 optical coupler 702 of coherent sensing unit 700 in FIG. 7A.
• component 903 is a square-law photodetector that receives and detects the optical signal from waveguide 924.
• component 904 is a square-law photodetector that receives and detects the optical signal from waveguide 925.
• photodetectors 903 and 904 may be similar to photodetectors 703 and 704 of coherent sensing unit 700 in FIG. 7A.
• component 912 is a 2x2 optical coupler that mixes the in-coupled optical signal E3 from waveguide 933 and the LO ELO,2 from waveguide 935, and splits and directs the mixed signal to waveguides 936 and 937.
• component 913 is a square-law photodetector that receives and detects the optical signal from waveguide 936.
• component 914 is a square-law photodetector that receives and detects the optical signal from waveguide 937.
• photodetectors 913 and 914 may be similar to photodetectors 713 and 714 of coherent sensing unit 700 in FIG. 7A.
• FIG. 10A shows a top view of a three-waveguide polarization-diversified free-space- to-waveguide coupler 1000, in accordance with an embodiment of the present disclosure.
• FIG. 10B shows a perspective view of coupler 1000 illustrated in FIG. 10A.
• FIG. 10B additionally shows polarized outgoing and incoming optical signals E10, E23, and E33 coupling with sub ⁇ couplers 1001 and 1002.
• Coupler 1000 as indicated by the dash line in FIG. 10A, comprises two sub -couplers 1001 and 1002.
• sub -coupler 1001 may be realized by either polarization-diversified free-space-to-waveguide coupler 101 as illustrated in FIG.
• sub-coupler 1002 may be realized by a free-space-to-waveguide coupler, including but not limited to a grating coupler, that is coupled to a single waveguide. According to other embodiments, sub-coupler 1002 may be realized by a polarization-independent free- sp ace -to -wave guide coupler.
• waveguide 921 is connected to sub-coupler
• waveguide 922 is connected to sub-coupler 1001 as a first in-coupling waveguide.
• waveguide 933 is connected to sub-coupler
• waveguides 921, 922, and 933 are the same waveguides 921, 922, and 933 of coherent sensing unit 900 as illustrated in FIG. 9.
• sub-coupler 1001 one primary function of sub-coupler 1001 is to act as a transmitter to out-couple an optical signal for target illumination.
• Optical signal Ei in waveguide 921 maybe out-coupled by sub-coupler 1001 into free space as an outgoing optical signal Eio.
• outgoing optical signal Eio is polarized according to the design of sub-coupler 1001. For example, as shown in FIG. 10B, optical signal Eio is linearly polarized along the x direction.
• sub-coupler 1001 another primary function of sub-coupler 1001 is to act as a receiver to in-couple an incoming optical signal into coherent sensing unit 900, wherein the polarization state of the incoming optical signal is orthogonal to the polarization of the outgoing optical signal.
• An incoming optical signal E23 that has a polarization orthogonal to outgoing optical signal Eio is in-coupled by sub-coupler 1001 to give rise to in- coupled optical signal E2 in waveguide 922. Similar to coupler 101 in FIG. 1, the polarization of incoming optical signal E23 that is optimally in-coupled by sub-coupler 1001 is determined according to the design of sub-coupler 1001. For example, as shown in FIG. 10B, optical signal E23 that is optimally in-coupled is linearly polarized along the y direction.
• a primary function of sub-coupler 1002 is to act as a receiver to in-couple an incoming optical signal into coherent sensing unit 900, wherein the polarization state of the incoming optical signal is orthogonal to the polarization of the incoming optical signal coupled by sub-coupler 1001 into waveguide 922.
• An incoming optical signal E33 that has a polarization orthogonal to that of optical signal E23 is in-coupled by sutr coupler 1002 to give rise to the in-coupled optical signal E3 in waveguide 933.
• FIG. 10B shows a side view of a polarization transformation-separation configuration 1010 for use with a three-waveguide polarization-diversified free-space-to-waveguide coupler for out-coupling optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 10D shows a side view of configuration 1010 illustrated in FIG.
• Polarization transformation-separation configuration 1010 enables incoming optical signals E23 and E33 arriving at coupler 1000 and outgoing optical signal E10 emitted by coupler 1000 to propagate along a common optical path, wherein the common optical path lies between configuration 1010 and the target.
• the polarization transformation -separation configuration 1010 comprises Faraday rotator 1051, an optional polarization rotator 1052, and polarization- dependent beam-separator 1041 as illustrated in FIGs. IOC and 10D.
• FIG. 10E shows a top view of the polarization states of the optical signals in FIG. IOC.
• FIG. 10F shows a top view of the polarization states of the optical signals in FIG. 10D.
• sub-coupler 1001 of coupler 1000 may out-couple optical signal Ei from waveguide 921 to give rise to optical signal E10, which is linearly polarized according to the design of sub-coupler 1001 (e.g., linearly polarized along the x direction) and propagates out of sub-coupler 1001 (e.g., towards the positive z direction) into free space.
• optical signal E10 which is linearly polarized according to the design of sub-coupler 1001 (e.g., linearly polarized along the x direction) and propagates out of sub-coupler 1001 (e.g., towards the positive z direction) into free space.
• Faraday rotator 1051 may rotate the polarization of optical signal E10 by an angle (e.g., 45 degrees) to give rise to optical signal En (e.g., En is linearly polarized along a direction at an angle of 45 degrees with respect to the x direction).
• Optional polarization rotator 1052 which is similar to polarization rotator 502 in FIG. 5C, may further rotate the polarization of En by an angle (e.g., 45 degrees) to give rise to optical signal E12 (e.g., E12 is linearly polarized along the y direction).
• Polarization- dependent beam-separator 1041 which is similar to polarization- dependent be am -separator 401 in FIG.
• optical signal E12 may manifest as the o-ray according to the configuration of polarization- dependent beam-separator 1041
• optical signal E13 may be polarized with the same polarization as E12 (i.e., linearly polarized along the y direction).
• Optical signal E13 may then be used for target illumination. Similar to polarization rotator 502 in FIGs.
• a function of the optional polarization rotator 1052 may be to enable the optical signal emerging from polarization- dependent beam-separator 1041 for target illumination to be polarized along a direction the same as one of the polarization basis components defined by coupler 1000 (e.g., orthogonal to the polarization of optical signal Eio according to the embodiment in FIG. IOC).
• optional polarization rotator 1052 in polarization transformation-separation configuration 1010 may be omitted, so that an outgoing optical signal with a polarization state that is the same as optical signal En may be used for target illumination.
• polarization- dependent beam-separator 1041 may need to be configured, such as by orientating the optic axis of polarization- dependent beam- separator 1041 in accordance with the polarization direction of optical signal En, in such a way that optical signal En may emerge from polarization- dependent be am -separator 1041 as a single optical signal that propagates along an intended optical path (e.g., continues with the path of En without lateral displacement).
• polarization- dependent beam-separator 1041 may be configured with respect to sub -coupler 1001 such that optical signal En may manifest as an o-ray according to the configuration of polarization- dependent beam-separator 1041.
• an incoming optical signal from a target that propagates along an optical path that is the same as, but in an opposite direction to, optical signal E 13 in FIG. IOC may comprise either one or both of two incoming optical signal components with polarizations the same as that of incoming optical signals E 20 and E30 illustrated in FIG. 10D, wherein optical signal E 20 is linearly polarized along the same direction as the polarization of optical signal E 13 and optical signal E30 is linearly polarized along a direction orthogonal to the polarization of optical signal E 20 .
• E 20 is linearly polarized along the y direction
• E30 is linearly polarized along the x direction.
• incoming optical signal E20 may pass through polarization-dependent beam-separator 1041 to give rise to optical signal E21 with the same polarization as E12 in FIG. IOC (i.e., linearly polarized along the y direction), wherein optical signal E21 may manifest as an o-ray with respect to polarization- dependent beam-separator 1041.
• polarization rotator 1052 may then rotate the polarization of E21 by an angle (e.g., 45 degrees) to give rise to optical signal E22 which is linearly polarized along a direction the same as the polarization of optical signal En in FIG. IOC.
• Faraday rotator 1051 which breaks optical propagation reciprocity, may rotate the polarization of optical signal E22 by an angle (e.g., 45 degrees) to give rise to optical signal E23 with a linear polarization (i.e., along the y direction) that is orthogonal to the polarization of optical signal E10.
• Optical signal E23 may then be in-coupled by sub-coupler 1001 to give rise to in-coupled optical signal E2 that is directed to waveguide 922 as illustrated in FIG. 10B.
• optical signal E30 since optical signal E30 is linearly polarized along a direction orthogonal to the polarization of E20, through polarization- dependent beam- separator 1041, optical signal E30 may give rise to optical signal E31 that propagates along an optical path spatially distinct from the optical path of optical signal E21 and is polarized with a polarization orthogonal to that of E21.
• incoming optical signal E31 is linearly polarized along the x direction and propagates along an optical path in the same direction as optical signal E21 but laterally displaced towards the negative x direction. As illustrated in FIG.
• optical signal E31 may manifest as an e-ray with respect to polarization- dependent be am -separator 1041.
• Polarization rotator 1052 may then rotate the polarization of E31 by an angle (e.g., 45 degrees) to give rise to optical signal E32 which is linearly polarized along a direction orthogonal to the polarization of optical signal E22.
• Faraday rotator 1051 may rotate the polarization of optical signal E32 by an angle (e.g., 45 degrees) to give rise to optical signal E33 with a linear polarization (i.e., along the x direction) that is orthogonal to the polarization of optical signal E23.
• Optical signal E33 may then be in-coupled by sub-coupler 1002 to give rise to the in-coupled optical signal E3 that is directed to waveguide 933 as illustrated in FIG. 10B.
• an incoming optical signal from a target that propagates along an optical path the same as, but in an opposite direction to, optical signal En in FIG. IOC may comprise either one or both of two incoming optical signal components with polarizations the same as that of optical signals E22 and E32 illustrated in FIG. 10D, wherein optical signal E22 is linearly polarized along the same direction as the polarization of optical signal En and optical signal E32 is linearly polarized along a direction orthogonal to the polarization of optical signal E22.
• polarization- dependent beam-separator 1041 that is configured in accordance with the polarization direction of optical signal En may give rise to an optical path for optical signal E22 that is the same as, but in opposite direction to, the optical path of En, whereas optical signal E32 may propagate along another spatially distinct optical path that is displaced differently from the situation with the polarization rotator 1052.
• incoming optical signal E32 may now propagate along an optical path in the same direction as optical signal E22 but laterally displaced towards a direction on the x-y plane that is no longer the negative x direction as in FIG. 10D.
• the position of sub -coupler 1002 may need to be adjusted on the substrate surface accordingly.
• the components of polarization transformation- separation configuration 1010 may exhibit as separate components as illustrated in FIG. IOC. According to other embodiments, some or all components of polarization transformation- separation configuration 1010 may exhibit as a single combined component. Additionally, according to some embodiments, polarization transformation-separation configuration 1010 may be an optical assembly that is separate from the PIC chip comprising polarization- diversified free-space-to-waveguide coupler 1000 as illustrated in FIG. IOC. According to other embodiments, some or all components of polarization transformation-separation configuration 1010 may be attached to the surface of the PIC chip comprising coupler 1000. According to further embodiments, some or all components of polarization transformation- separation configuration 1010 may be within or be part of the PIC chip comprising coupler 1000.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1000, polarization- dependent beam-separator 1041, Faraday rotator 1051, and polarization rotator 1052.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 11A shows a perspective view of a three-waveguide polarization-diversified free- space-to-waveguide coupler 1100, in accordance with another embodiment of the present disclosure.
• Three-waveguide polarization-diversified free-space-to-waveguide coupler 1100 (herein referred to as coupler 1100 for simplicity), as indicated by the dash line in FIG. 11A, comprises three sub-couplers 1101, 1102, and 1103.
• each of sub-couplers 1101, 1102, and 1103 may be realized by a free-space-to-waveguide coupler, including but not limited to a grating coupler, that is coupled to a single waveguide.
• each of sub -couplers 1102 and 1103 maybe realized by a polarization- independent free-space-to-waveguide coupler.
• waveguide 921 is connected to sub-coupler 1101 as an out- coupling waveguide
• waveguide 922 is connected to sub-coupler 1102 as a first in-coupling waveguide
• waveguide 933 is connected to sub -coupler 1103 as a second in-coupling waveguide.
• waveguides 921, 922, and 933 in FIG. 11A are the same waveguides 921, 922, and 933 of coherent sensing unit 900 in FIG. 9.
• a primary function of sub -coupler 1101 is to act as a transmitter to out-couple an optical signal for target illumination.
• Optical signal Ei in waveguide 921 is out-coupled by sub-coupler 1101 into free space as an outgoing optical signal Eoi.
• Outgoing optical signal Eoi is polarized according to the design of sub-coupler 1101. For example, optical signal Eoi is linearly polarized along the x direction as illustrated in FIG. 11A.
• a primary function of sub -coupler 1102 is to act as a receiver to in-couple an incoming optical signal into coherent sensing unit 900 in FIG. 9, wherein the polarization state of the incoming optical signal is orthogonal to the polarization of the outgoing optical signal.
• an incoming optical signal E24 that has a polarization orthogonal to outgoing optical signal Eoi may be in-coupled by sub-coupler 1102 to give rise to in-coupled optical signal E2 in waveguide 922.
• the polarization of incoming optical signal E24 that is optimally in-coupled by sub-coupler 1102 is determined according to the design of sub-coupler 1102. As an example, optical signal E24 that is optimally in-coupled is linearly polarized along the y direction as illustrated in FIG. 11A.
• a primary function of sub -coupler 1103 is to act as a receiver to in-couple an incoming optical signal into coherent sensing unit 900 in FIG. 9, wherein the polarization state of the incoming optical signal is orthogonal to the polarization of the incoming optical signal coupled by sub-coupler 1102 into waveguide 922.
• an incoming optical signal E34 that has a polarization orthogonal to optical signal E24 is in-coupled by sub -coupler 1103 to give rise to the in-coupled optical signal E3 in waveguide 933.
• the polarization of incoming optical signal E34 that is optimally in-coupled by sub-coupler 1103 is determined according to the design of sub-coupler 1103. For example, optical signal E34 that is optimally in-coupled is linearly polarized along the x direction as illustrated in FIG. 11A.
• FIG. 11B show a side view of a polarization transformation-separation configuration 1110 for use with three -wave guide polarization-diversified free-space-to-waveguide coupler 1100 for out-coupling optical signals, in accordance with another embodiment of the present disclosure.
• FIG. 11C show a side view of the configuration 1110 illustrated in FIG. 11B used for in-coupling optical signals.
• configuration 1110 enables the incoming optical signals E24 and E34 arriving at coupler 1100 and outgoing optical signal E01 emitted by coupler 1100 to propagate along a common optical path, wherein the common optical path lies between configuration 1110 and the target.
• the polarization transformation- separation configuration 1110 comprises Faraday rotator 1151, an optional polarization rotator 1152, and polarization-dependent beam-separators 1141 and 1142 as illustrated in FIGs. 11B and 11C.
• FIG. 11D shows a top view of the polarization states of the optical signals in FIG. 11B.
• FIG. HE shows a top view of the polarization states of the optical signals in FIG. 11C.
• Polarization transformation-separation configuration 1110 in FIGs. 11B and 11C is similar to polarization transformation-separation configuration 1010 in FIGs. IOC and 10D.
• the primary difference between configuration 1110 and configuration 1010 is that configuration 1110 as illustrated in FIGs. 11B and 11C has an additional polarization- dependent be am -separator 1142 that is disposed between Faraday rotator 1151 and polarization-diversified free -space -to -wave guide coupler 1100.
• component 1141 in FIGs. 11B and 11C is a polarization-dependent beam-separator that is similar to polarization-dependent beam-separator 1041 in FIGs. IOC and 10D.
• 11B and 11C is an optional polarization rotator that is similar to polarization rotator 1052 in FIGs. IOC and 10D.
• Component 1151 in FIGs. 11B and 11C is a Faraday rotator that is similar to Faraday rotator 1051 in FIGs. IOC and 10D.
• sub-coupler 1101 of coupler 1100 may output an outgoing optical signal E01 into free space.
• the additional polarization- dependent beam-separator 1142 in configuration 1110 may be configured in such a way that optical signal E01 may be laterally displaced on the x-y plane to give rise to optical signal E10 that has the same polarization as optical signal E01, wherein optical signal E01 may manifest as an e-ray with respect to polarization- dependent be am -separator 1142.
• optical signal E01 is linearly polarized along the x direction and the outgoing optical signal is displaced towards the positive x direction.
• Faraday rotator 1151, polarization rotator 1152, and polarization-dependent beam-separator 1141 of polarization transformation-separation configuration 1110 may transform optical signal E10 in FIG. 11B to give rise to optical signal E13.
• optical signal E13 is linearly polarized along a direction orthogonal to that of optical signal E01 (i.e., along the y direction).
• an incoming optical signal from a target that propagates along an optical path that is the same as, but in an opposite direction to, optical signal E13 in FIG.
• 11B may comprise either one or both of two incoming optical signal components with polarizations that are the same as that of incoming optical signals E20 and E30, as illustrated in FIG. llC, wherein optical signal E20 is linearly polarized along the same direction as the polarization of optical signal E13 and optical signal E30 is linearly polarized along a direction orthogonal to the polarization of optical signal E20.
• E20 is linearly polarized along the y direction
• E30 is linearly polarized along the x direction.
• polarization- dependent be am -separator 1141, polarization rotator 1152, and Faraday rotator 1151 of polarization transformation-separation configuration 1110 may transform optical signal E20 in FIG. llC to give rise to optical signal E23 that has a polarization orthogonal to that of optical signal E10 in FIG. 11B.
• the additional polarization- dependent beam-separator 1142 in configuration 1110 is configured in such a way that optical signal E23 may give rise to an optical signal E24 that has a polarization orthogonal to that of optical signal E01 in FIG.
• optical signal E24 may manifest as an o-ray with respect to polarization-dependent be am -separator 1142. Optical signal E24 may then be in-coupled by sub -coupler 1102 to give rise to in-coupled optical signal E2 that is directed to waveguide 922 as illustrated in FIG. 11 A.
• polarization-dependent beam-separator 1141, polarization rotator 1152, and Faraday rotator 1151 of polarization transformation-separation configuration 1110 may transform optical signal E30 in FIG. 11C to give rise to optical signal E33 that has a polarization orthogonal to that of optical signal E23 in FIG. 11C.
• optical signal E33 may be laterally displaced on the x-y plane to give rise to optical signal E34, that has a polarization orthogonal to that of optical signal E24, in a way the same as optical signal E01 giving rise to optical signal E10 but in an opposite direction. As shown in FIG.
• optical signal E33 is linearly polarized along the x direction and is displaced towards the negative x direction to give rise to optical signal E34 that is also linearly polarized along the x direction. Similar to optical signal E01, optical signal E33 may manifest as an e-ray with respect to polarization- dependent beam-separator 1142. Optical signal E34 may then be in-coupled by sub-coupler 1103 to give rise to the in-coupled optical signal E3 that is directed to waveguide 933 as illustrated in FIG. 11A.
• optional polarization rotator 1152 in polarization transformation-separation configuration 1110 may be omitted, so that an outgoing optical signal with a polarization state that is the same as optical signal En may be used for target illumination. Similar to the omission of optional polarization rotator 1052 from polarization transformation-separation configuration 1010, omission of polarization rotator 1152 in polarization-separation configuration 1110 may require polarization- dependent beam- separator 1141 to be reconfigured, such as by orientating the optic axis of polarization- dependent beam-separator 1141, in accordance with the polarization direction of optical signal En. Either or both of the positions of sub-couplers 1102 and 1103 may also need to be adjusted on the substrate surface accordingly in order to compensate for the different orientation of the optic axis of polarization- dependent beam-separator 1141.
• polarization transformation-separation configuration 1110 may exhibit as separate components as illustrated in FIG. 11B. According to other embodiments, some or all components of polarization transformation-separation configuration 1110 may exhibit as a single combined component. Additionally, according to some embodiments, polarization transformation-separation configuration 1110 may be an optical assembly that is separate from the PIC chip comprising polarization-diversified free- sp ace -to -wave guide coupler 1100 as illustrated in FIG. 11B. According to other embodiments, some or all components of polarization transformation-separation configuration 1110 may be attached to the surface of the PIC chip comprising coupler 1100. According to further embodiments, some or all components of polarization transformation-separation configuration 1110 may be within or be part of the PIC chip comprising coupler 1100.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1100, polarization- dependent beam-separators 1141 and 1142, Faraday rotator 1151, and polarization rotator 1152.
• the propagation directions of the optical signals maybe at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 12A show a side view of a polarization transformation-separation configuration 1210 for use with three -wave guide polarization-diversified free-space-to-waveguide coupler 1100 for out-coupling optical signals, in accordance with a further embodiment of the present disclosure.
• FIG. 12B show a side view of configuration 1210 illustrated in FIG. 12A used for in-coupling optical signals.
• Configuration 1210 enables incoming optical signals E24 and E34 arriving at coupler 1100 and outgoing optical signal E01 emitted by coupler 1100 to propagate along a common optical path, wherein the common optical path lies between configuration 1210 and the target. As shown in FIGs.
• polarization transformation-separation configuration 1210 comprises Faraday rotator 1251, an optional polarization rotator 1252, polarization-dependent beam-separators 1241 and 1242, and an optional quarter-wave plate 1261.
• FIG. 12C shows a top view of the polarization states of the optical signals in FIG. 12A.
• FIG. 12D shows a top view of the polarization states of the optical signals in FIG. 12B.
• Polarization transformation -separation configuration 1210 in FIGs. 12A and 12B is a modified embodiment of polarization transformation-separation configuration 1110 in FIGs. 11B and 11C.
• Primary modifications of configuration 1210 from configuration 1110 comprise the followings ⁇ (l) polarization rotator 1252 of configuration 1210, if present, is configured in such a way that effects a polarization rotation in a direction opposite to the rotation direction effected by polarization rotator 1152 of configuration 1110;
• polarization- dependent beam- separator 1241 of configuration 1210 is configured by, for example, orienting the optic axis of 1241 in such a way that effects a lateral displacement, if any, in a direction opposite to the lateral displacement effected by polarization- dependent beam-separator 1242 for the case when optional polarization rotator 1252 is present!
• configuration 1210 comprises an additional quarter-wave plate 1261 that is disposed between polarization- dependent beam- separator 1241 and the target. Accordingly, polarization- dependent beam-separator 1242 of configuration 1210 is similar to polarization-dependent beam-separator 1142 of configuration 1110, and Faraday rotator 1251 of configuration 1210 is simil r to Faraday rotator 1151 of configuration 1110.
• modifications (l) and (2) in configuration 1210 described above may result in an optical path for optical signals E20, E21, E22, E23, and E24 with a path length that is similar to the path length of the optical path for optical signals E30, E31, E32, E33, and E34, in comparison to the corresponding optical paths in configuration 1110 as illustrated in FIG. 11C.
• Modifications (l) and (2) may thus have an advantage of minimizing the phase difference between optical signals E24 and E34 arriving respectively at sub -couplers 1102 and 1103.
• modifications (l) and (2) described above may, if optional polarization rotator 1252 is present, also enable optical signal E13 to be emitted at a location and direction on the surface of polarization- dependent beam- separator 1241 that are similar to the emitting location and direction of optical signal Eoi on the surface of sub-coupler 1101. Modifications (l) and (2) may thus have another advantage of enabling simplified optical alignment for the installation of polarization transformation- separation configuration 1210 with coupler 1100 by using the outgoing optical signal from sub-coupler 1101 of coupler 1100.
• modification (3) described above may enable the use of a circularly-polarized optical signal Eic for target illumination. More specifically, quarter-wave plate 1261 may transform a linearly polarized optical signal Ei 3 to give rise to a circularly-polarized optical signal Eic for target illumination. As shown in FIGs. 12A and 12C, optical signal E13 is linearly polarized along the x direction and optical signal Eic is right-circularly polarized with respect to its propagation direction. For optical signal reception, an incoming optical signal from a target may be decomposed according to any two orthogonal polarizations. As shown in FIGs.
• an incoming optical signal from the target which propagates towards the negative z direction, may comprise either one or both of two polarization components E2C and E3C, wherein one of them is right-circularly polarized and the other one of them is left -circularly polarized with respect to their propagation direction.
• E2C is right-circularly polarized
• E3C is left-circularly polarized with respect to the negative z direction.
• quarter-wave plate 1261 may transform optical signal E2C to give rise to a linearly polarized optical signal E20, and transform optical signal E3C to give rise to optical signal E30 that has a polarization orthogonal to E20.
• E20 is linearly polarized along the x direction
• E30 is linearly polarized along the y direction.
• using a circularly-polarized optical signal instead of a linearly-polarized optical signal for target illumination that is enabled by modification (3) may have an advantage of minimizing the odd of significant signal loss due to certain properties of the target or target surface.
• Such significant signal loss may arise in circumstances such as, but not limited to, when a target surface preferentially reflects light with a linear polarization that is by coincidence orthogonal to a linearly polarized illuminating optical signal.
• a circularly- polarized illuminating optical signal always comprises a pair of orthogonal linearly-polarized components that may avoid the vanishing of reflected optical signal under such a situation.
• optional polarization rotator 1252 in polarization transformation-separation configuration 1210 may be omitted. Similar to the omission of optional polarization rotator 1152 from polarization transformation-separation configuration 1110, the omission of polarization rotator 1252 in polarization transformation-separation configuration 1210 may require polarization- dependent beam-separator 1241 and quarter- wave plate 1261 to be reconfigured, such as by orientating the optic axes of polarization- dependent beam-separator 1241 and quarter-wave plate 1261 in accordance with the polarization direction of optical signal En.
• Either or both of the positions of sub-couplers 1102 and 1103 may also need to be adjusted on the substrate surface accordingly in order to compensate for the different orientations of the optic axes of polarization- dependent beam- separator 1241 and quarter-wave plate 1261.
• polarization transformation-separation configuration 1210 may exhibit as separate components as illustrated in FIG. 12A. According to other embodiments, some or all components of polarization transformation-separation configuration 1210 may exhibit as a single combined component. Additionally, according to some embodiments, polarization transformation-separation configuration 1210 may be an optical assembly that is separate from the PIC chip comprising polarization-diversified free- sp ace -to -wave guide coupler 1100 as illustrated in FIG. 12A. According to other embodiments, some or all components of polarization transformation-separation configuration 1210 may be attached to the surface of the PIC chip comprising coupler 1100. According to further embodiments, some or all components of polarization transformation-separation configuration 1210 may be within or be part of the PIC chip comprising coupler 1100.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1100, polarization- dependent beam-separators 1241 and 1242, Faraday rotator 1251, polarization rotator 1252, and quarter-wave plate 1261.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 13A shows a top view of a three-waveguide polarization-diversified free-space- to-waveguide coupler 1300, in accordance with a further embodiment of the present disclosure.
• FIG. 13B shows a perspective view of coupler 1300 illustrated in FIG. 13A.
• FIG. 13B shows polarized outgoing and incoming optical signals Eoi, E24, and E34 coupling respectively with sub-couplers 1301, 1302, and 1303.
• Three-waveguide polarization- diversified free-space-to-waveguide coupler 1300 (herein referred to as coupler 1300 for simplicity), as indicated by the dash line in FIGs. 13A and 13B, comprises three sub-couplers 1301, 1302, and 1303.
• each of sub-couplers 1301, 1302, and 1303 may be realized by a free -space -to -wave guide coupler, including but not limited to a grating coupler, that is coupled to a single waveguide.
• each of sub-couplers 1302 and 1303 may be realized by a polarization-independent free-space-to- waveguide coupler.
• Coupler 1300 is a modified embodiment of coupler 1100 as illustrated in FIG. 11A.
• Sub-coupler 1301 of coupler 1300 in FIGs. 13A and 13B is similar to sub-coupler 1101 of coupler 1100 in FIG. 11A.
• sub-coupler 13A and 13B is similar to sub-coupler 1102 of coupler 1100 in FIG. 11A.
• Sub-coupler 1303 of coupler 1300 in FIGs. 13A and 13B is similar to sub -coupler 1103 of coupler 1100 in FIG. 11A.
• the spatial arrangement of sub-couplers of coupler 1300 may be advantageous (for example, being more compact) to some embodiments of coherent sensing unit 900 in FIG. 9.
• FIG. 13C shows a side view of a polarization transformation -separation configuration 1310 for use with three -wave guide polarization-diversified free-space-to-waveguide coupler 1300 for out-coupling optical signals, in accordance with a yet further embodiment of the present disclosure.
• FIG. 13D shows another side view of configuration 1310 illustrated in FIG. 13C.
• FIG. 13E shows a side view of configuration 1310 as illustrated in FIG. 13C used for in-coupling optical signals.
• FIG. 13F shows another side view of configuration 1310 illustrated in FIG. 13E. As shown in FIGs.
• configuration 1310 enables incoming optical signals E24 and E34 arriving at coupler 1300 and outgoing optical signal E01 emitted by coupler 1300 to propagate along a common optical path, wherein the common optical path lies between configuration 1310 and the target.
• FIG. 13G shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 13C and 13D. Also shown in FIG. 13G is an inset showing the top view of coupler 1300 indicating the locations of sub-couplers 1301, 1302, and 1303 on the x-y plane as a reference for the path locations of the optical signals in FIG. 13G.
• FIG. 13H shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 13E and 13F. The path locations on the x-y plane in FIG. 13H may be referenced to the locations of sub-couplers 1301, 1302, and 1303 indicated in the inset of FIG. 13G.
• the polarization transformation- separation configuration 1310 comprises Faraday rotator 1351, an optional polarization rotator 1352, polarization- dependent be am -separators 1341 and 1342, and an optional quarter- wave plate 1361.
• Polarization transformation-separation configuration 1310 shown in FIGs. 13C, 13D, 13E, and 13F is a modified embodiment of polarization transformation-separation configuration 1110 in FIGs. 11B and 11C.
• Primary modifications of configuration 1310 from configuration 1110 comprise the followings ⁇ (l) polarization-dependent beam-separator 1341 of configuration 1310 is configured such as, but not limited to, by orienting the optic axis of polarization- dependent beam-separator 1341 in such a way that effects a lateral displacement, if any, in a direction on the x-y plane that is perpendicular to the lateral displacement effected by polarization- dependent be am -separator 1342 for the case when optional polarization rotator 1352 is present!
• configuration 1310 comprises an additional quarter-wave plate 1361 disposed between polarization- dependent beam- separator 1341 and the target.
• polarization- dependent beam-separator 1342 of configuration 1310 is similar to polarization-dependent beam-separator 1142 of configuration 1110
• Faraday rotator 1351 of configuration 1310 is similar to Faraday rotator 1151 of configuration 1110
• polarization rotator 1352 of configuration 1310 is similar to polarization rotator 1152 of configuration 1110.
• polarization-dependent beam-separator 1342 effects a lateral displacement, if any, along the x direction as shown in FIGs. 13C and 13E
• polarization-dependent beam-separator 1341 effects a lateral displacement, if any, along the y direction as shown in FIGs. 13D and 13F.
• polarization transformation-separation configurations 1110 and 1210 wherein the polarization- dependent beam-separators in either configuration effect lateral displacements, if any, along the x direction.
• modification (l) in configuration 1310 described above may result in an optical path for optical signals E20, E21, E22, E23, and E24 with a path length that is similar to the path length of the optical path for optical signals E30, E31, E32, E33, and E34, in comparison to the corresponding optical paths in configuration 1110 as illustrated in FIG. 11C.
• Modification (l) may thus have an advantage of minimizing the phase difference between optical signals E2C and E3C arriving respectively at sub-couplers 1302 and 1303.
• modification (2) described above may also enable the use of a circularly polarized optical signal Eic for target illumination.
• optional polarization rotator 1352 in polarization transformation-separation configuration 1310 may be omitted. Similar to the omission of optional polarization rotator 1252 from polarization transformation-separation configuration 1210, the omission of polarization rotator 1352 in polarization-separation configuration 1310 may require polarization- dependent beam-separator 1341 and quarter-wave plate 1361 to be reconfigured by, for example, orientating the optic axes of polarization-dependent beam- separator 1341 and quarter-wave plate 1361 in accordance with the polarization direction of optical signal En.
• Either or both of the positions of sub-couplers 1302 and 1303 may also need to be adjusted on the substrate surface accordingly in order to compensate for the different orientations of the optic axes of polarization- dependent beam-separator 1341 and quarter- wave plate 1361.
• polarization transformation-separation configuration 1310 may exhibit as separate components as illustrated in FIG. 13C. According to other embodiments, some or all components of polarization transformation-separation configuration 1310 may exhibit as a single combined component. Additionally, according to some embodiments, polarization transformation-separation configuration 1310 may be an optical assembly that is separate from the PIC chip comprising polarization-diversified free- sp ace -to -wave guide coupler 1300 as illustrated in FIG. 13C. According to other embodiments, some or all components of polarization transformation-separation configuration 1310 may be attached to the surface of the PIC chip comprising coupler 1300. According to further embodiments, some or all components of polarization transformation-separation configuration 1310 may be within or be part of the PIC chip comprising coupler 1300.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1300, polarization-dependent beam-separators 1341 and 1342, Faraday rotator 1351, polarization rotator 1352, and quarter-wave plate 1361.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• Coherent sensing units 100, 700, 710, 800, and 900 may give rise to outgoing optical signals with a fixed polarization for target illumination.
• FIG. 14 shows a plan view of a coherent sensing unit 1400 for transmitting and receiving optical signals based on polarization diversity, wherein the polarization of the transmitted optical signal is adjustable, in accordance with an embodiment of the present disclosure.
• Coherent sensing unit 1400 is similar to coherent sensing units 700, 710, 800, and 900 that detect an incoming optical signal with any polarization state.
• coherent sensing unit 1400 comprises a polarization-diversified free-space-to-waveguide coupler that may be used to out-couple an outgoing optical signal with any polarization state, in addition to directing in-coupled optical signals with any polarization states to waveguides that are distinct from the waveguides carrying the outgoing optical signals.
• optical source signals Esi and ES2 are supplied to coherent sensing unit 1400.
• Optical source signals Esi and Es2 are respectively guided into coherent sensing unit 1400 through waveguides 1421 and 1431.
• optical source signals Esi and Es2 may come from the same light source. In such a circumstance, the outgoing optical signals arising from Esi and Es2 may be coherently combined to form a single optical signal.
• optical source signals Esi and Es2 may come from different light sources.
• Either one or both of waveguides 1421 and 1431 may be connected to an optional phase shifter, which is used to adjust the relative phase between the optical signals in waveguides 1421 and 1431. As an example, in FIG.
• waveguide 1431 may be connected to phase shifter 1451, which directs phase-shifted optical source signal Es2 as optical signal E4 to waveguide 1432.
• phase shifter 1451 may be, but not limited to, an electro-optic phase shifter or a thermo-optic phase shifter.
• Local oscillator (LO) ELO is supplied to coherent sensing unit 1400 through waveguide 1434.
• polarization-diversified free-space-to-waveguide coupler 1401 (herein referred to as coupler 1401 for simplicity) is a four-waveguide coupler that is connected to waveguides 1421, 1422, 1432, and 1433. Coupler 1401 may function as both a transmitter and a receiver.
• coupler 1401 may couple optical signal Ei (which is essentially the same as optical source signal Esi) from waveguide 1421 and optical signal E4 from waveguide 1432 into free space as one or more outgoing optical signals, which may be used for target illumination by the optical coherent imager.
• the outgoing optical signals output by coupler 1401 propagate in a direction that is out of the x-y plane (i.e., the propagation direction of E out has a nonzero z component).
• the outgoing optical signals are polarized with polarization states defined by the design of coupler 1401.
• the outgoing optical signal arising from optical signal Ei may be orthogonally polarized with respect to the outgoing optical signal arising from optical signal E4.
• the outgoing optical signals may manifest as a single outgoing optical signal E out with a polarization state defined by the design of coupler 1401, and the amplitudes and the relative phase of optical signals Ei and E4.
• coupler 1401 may couple an incoming optical signal Ein into coherent sensing unit 1400.
• Incoming optical signal Ei n coupled by coupler 1401 may be directed to either or both waveguides 1422 and 1433, depending on the polarization state of incoming optical signal Ein.
• the polarization components of incoming optical signal Ein that are coupled to waveguides 1422 and 1433 depend on the design of coupler 1401.
• the polarization component of incoming optical signal Ein that is orthogonal to the polarization component of outgoing optical signal Eo ut arising from optical signal Ei may be directed to waveguide 1422 as an in-coupled optical signal E 2
• the polarization component of incoming optical signal Ein that is orthogonal to the polarization component of incoming optical signal Ei n directed to waveguide 1422 may be directed to waveguide 1433 as an in-coupled optical signal E 3 .
• coupler 1401 may comprise a single photonic component or multiple photonic components. Embodiments of coupler 1401 are illustrated in FIGs. 15A, 16A, and 17A to be described below. According to some embodiments, similar to coupler 101 in FIGs. 1A and IB, coupler 1401 may also comprise any of TE-TM mode converters, splitters, and combiners.
• splitting coupler 1406 splits the LO FLO from waveguide 1434 and directs a fraction of the LO to waveguide 1423 as the LO ELO,I and a fraction of the LO to waveguide 1435 as the LO ELO,2.
• the fractions of the LO that are passed respectively to waveguides 1423 and 1435 depend on the splitting ratio and loss of splitting coupler 1406.
• splitting coupler 1406 may be a 50/50 splitting coupler.
• splitting coupler 1406 may have a splitting ratio other than 50/50.
• component 1402 is a 2x2 optical coupler that mixes in-coupled optical signal E2 from waveguide 1422 and the LO ELO,I from waveguide 1423, and splits and directs the mixed signal to waveguides 1424 and 1425.
• 2x2 optical coupler 1402 may be similar to 2x2 optical coupler 902 of coherent sensing unit 900 in FIG. 9.
• component 1403 is a square -law photodetector that receives and detects the optical signal from waveguide 1424.
• component 1404 is a square - law photodetector that receives and detects the optical signal from waveguide 1425.
• photodetectors 1403 and 1404 may be similar to photodetectors 903 and 904 of coherent sensing unit 900 in FIG. 9.
• component 1412 is a 2x2 optical coupler that mixes in-coupled optical signal E3 from waveguide 1433 and the LO ELO,2 from waveguide 1435, and splits and directs the mixed signal to waveguides 1436 and 1437.
• component 1413 is a square-law photodetector that receives and detects the optical signal from waveguide 1436.
• component 1414 is a square- law photodetector that receives and detects the optical signal from waveguide 1437.
• photodetectors 1413 and 1414 may be similar to photodetectors 913 and 914 of coherent sensing unit 900 in FIG. 9.
• FIG. 15A shows a top view of a four-waveguide polarization-diversified free-space-to- waveguide coupler 1500 (herein referred to as coupler 1500 for simplicity), in accordance with an embodiment of the present disclosure.
• FIG. 15B shows a perspective view of coupler 1500 illustrated in FIG. 15A.
• FIG. 15B additionally shows polarized outgoing and incoming optical signals Eoi, E24, E34, and Eo 4 coupling respectively with sub-couplers 1501, 1502, 1503, and 1504.
• Coupler 1500 as indicated by the dash line in FIG. 15A, comprises four sub-couplers
• Coupler 1500 is a modified embodiment of coupler 1300 as illustrated in FIG. 13A, with an addition of sub-coupler 1504 that is connected to waveguide 1432 of coherent sensing unit 1400 in FIG. 14.
• FIG. 15C shows a side view of a polarization transformation-separation configuration 1510 for use with four-waveguide polarization-diversified free-space-to-waveguide coupler 1500 for out-coupling optical signals, in accordance with an embodiment of the present disclosure.
• FIG. 15F shows a side view of configuration 1510 as illustrated in FIG. 15C used for in-coupling optical signals.
• Configuration 1510 enables incoming optical signals E24 and E34 arriving at coupler 1500 and outgoing optical signals Eoi and Eo 4 emitted by coupler 1500 to propagate along a common optical path, wherein the common optical path lies between configuration 1510 and the target.
• FIG. 15D shows another side view of configuration 1510 illustrated in FIG. 15C.
• 15G shows another side view of configuration 1510 illustrated in FIG. 15F.
• Embodiments of the optical paths and the polarization states of the outgoing optical signals arising from optical signals Ei and E4 and the incoming optical signals that give rise to E2 and E3 are shown in FIGs. 15C, 15D, 15F, and 15G.
• waveguides 1421, 1422, 1432, and 1433 are not shown explicitly in FIGs. 15C, 15D, 15F, and 15G.
• FIG. 15E shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 15C and 15D.
• FIG. 15E additionally shows an inset for the top view of coupler 1500 indicating the locations of sub-couplers 1501, 1502, 1503, and 1504 on the x-y plane as a reference for the path locations of the optical signals in FIG. 15E.
• FIG. 15H shows a top view of the polarization states and path locations on the x-y plane of the optical signals in FIGs. 15F and 15G.
• Polarization transformation-separation configuration 1510 shown in FIGs. 15C, 15D, 15F, and 15G is essentially the same as polarization transformation-separation configuration 1310 shown in FIGs. 13C, 13D, 13E, and 13F, except for the omission of quarter-wave plate 1361 that is used to produce a circularly polarized outgoing optical signal for target illumination.
• Coherent sensing unit 1400 operating with coupler 1500 and polarization transformation-separation configuration 1510 may produce an outgoing optical signal with any polarization state, including linear polarization, circular polarization or elliptical polarization, for target illumination by adjusting the amplitudes and relative phase of optical signals Ei and E4 in waveguides 1421 and 1432.
• sub-couplers 1501, 1502, 1503, and 1504 of coupler 1500 may need to be designed and configured in such a way that maximizes the spatial overlap of outgoing optical signals E13 and E43 as illustrated in FIGs. 15C, 15D, and 15E, so as to minimize the spatial variation of the polarization of the outgoing optical signal combined from optical signals E13 and E43.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1500, polarization- dependent beam-separators 1541 and 1542, Faraday rotator 1551, and polarization rotator 1552.
• the propagation directions of the optical signals maybe at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 16A shows a top view of a four-waveguide polarization-diversified free-space-to- waveguide coupler 1600 (herein referred to as coupler 1600 for simplicity), in accordance with another embodiment of the present disclosure.
• FIG. 16B shows a perspective view of coupler 1600 illustrated in FIG. 16A.
• FIG. 16B additionally shows polarized outgoing and incoming optical signals E10, E40, E23, and E33 coupling with sub-couplers 1601 and 1602.
• Coupler 1600 as indicated by the dash line in FIG. 16A, comprises two sub-couplers 1601 and 1602. According to some embodiments, each of sub-couplers 1601 and 1602 may be realized by either polarization-diversified free-space-to-waveguide coupler 101 as illustrated in FIG.
• Coupler 1600 is a modified embodiment of coupler 1000 as illustrated in FIG. 10A, with an additional waveguide 1432 connecting to sub-coupler 1602 of coherent sensing unit 1600 in FIG. 16A for out-coupling optical signal E4.
• outgoing optical signal Eio and incoming optical signal E23 are drawn to couple with sub-coupler 1601 at different spatial locations.
• outgoing optical signal Eio and incoming optical signal E23 may couple with sub-coupler 1601 at the same spatial locations according to some embodiments, or at different spatial locations according to other embodiments.
• outgoing optical signal E40 and incoming optical signal E33 may couple with sub -coupler 1602 at the same spatial locations according to some embodiments, or at different spatial locations according to other embodiments.
• FIG. 16C shows a side view of a polarization transformation -separation configuration 1610 for use with four-waveguide polarization-diversified free -space -to -wave guide coupler 1600 for out-coupling optical signals, in accordance with another embodiment of the present disclosure.
• FIG. 16D shows a side view of configuration 1610 illustrated in FIG. 16C used for in-coupling optical signals.
• FIG. 16E shows a top view of the polarization states of the optical signals in FIG. 16C
• FIG. 16F shows a top view of the polarization states of the optical signals in FIG. 16D.
• Polarization transformation-separation configuration 1610 is essentially the same as polarization transformation-separation configuration 1010 as illustrated in FIGs.
• FIGs. 16C, 16D, 16E, and 16F Embodiments of the optical paths and the polarization states of the outgoing optical signals arising from optical signals Ei and E4 and the incoming optical signals that give rise to optical signals E2 and E3 are shown in FIGs. 16C, 16D, 16E, and 16F.
• waveguides 1421, 1422, 1432, and 1433 are not shown explicitly in FIGs. 16C and 16D.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1600, polarization- dependent beam-separator 1641, Faraday rotator 1651, and polarization rotator 1652.
• the propagation directions of the optical signals may be at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 17A shows a perspective view of a four -wave guide polarization- diversified free- sp ace -to -wave guide coupler 1700 (herein referred to as coupler 1700 for simplicity), in accordance with a further embodiment of the present disclosure.
• FIG. 17A additionally shows polarized outgoing and incoming optical signals E01, Eo 4 , E24, and E34 coupling with sutr couplers 1701, 1702, and 1703.
• Coupler 1700 as indicated by the dash line in FIG. 17A, comprises three sub-couplers 1701, 1702, and 1703.
• sub ⁇ coupler 1701 may be realized by either polarization-diversified free-space-to-waveguide coupler 101 as illustrated in FIG.
• Coupler 1700 is a modified embodiment of coupler 1100 as illustrated in FIG. 11A, with an additional waveguide 1432 connecting to sub -coupler 1701 of coherent sensing unit 1700 in FIG. 17A for out-coupling optical signal E4 in addition to the out-coupling of optical signal Ei from waveguide 1421.
• outgoing optical signal E01 and outgoing optical signal Eo 4 are drawn to couple with sub-coupler 1701 at different spatial locations.
• outgoing optical signal E01 and outgoing optical signal Eo 4 may couple with sub-coupler 1701 at the same spatial locations so as to ensure maximal spatial overlap of the two outgoing optical signals.
• outgoing optical signal E01 and outgoing optical signal Eo 4 may couple with sub-coupler 1701 at different spatial locations.
• FIG. 17B show a side view of a polarization transformation-separation configuration 1710 for use with four-waveguide polarization-diversified free-space-to-waveguide coupler 1700 for out-coupling optical signals, in accordance with a further embodiment of the present disclosure.
• FIG. 17C show a side view of configuration 1710 illustrated in FIG. 17B used for in-coupling optical signals.
• FIG. 17D shows a top view of the polarization states of the optical signals in FIG. 17B
• FIG. 17E shows a top view of the polarization states of the optical signals in FIG. 17C.
• Polarization transformation-separation configuration 1710 is essentially the same as polarization transformation-separation configuration 1110 as illustrated in FIGs.
• Embodiments of the optical paths and the polarization states of the outgoing optical signals arising from optical signals Ei and E4 and the incoming optical signals that give rise to optical signals E2 and E3 are shown in FIGs. 17B, 17C, 17D, and 17E.
• the use of polarization transformation-separation configuration 1710 with coupler 1700 may ensure that the optical path length of the signals E01, E10, E11, E12, and E13 is essentially the same as the optical path length of the signals E04, E40, E41, E42, and E43, so that the polarization of the coherently combined optical signal from optical signals E13 and E43 is essentially the same as the polarization of the coherently combined optical signal from optical signals E01 and E04.
• waveguides 1421, 1422, 1432, and 1433 are not shown explicitly in FIGs. 17B and 17C.
• the optical signals are depicted to propagate along the z direction and are at normal incident on coupler 1700, polarization- dependent beam-separators 1741 and 1742, Faraday rotator 1751, and polarization rotator 1752.
• the propagation directions of the optical signals maybe at normal incidence or at incident angles other than normal incidence with respect to these components.
• FIG. 18A shows a plan view of a coherent optical sensor 1800 in accordance with an embodiment of the present disclosure.
• Coherent optical sensor 1800 comprises a coherent sensing array 1810 and optical routing circuits 1820 and 1830 that are implemented on a PIC chip.
• optical routing circuit 1820 is used for routing the LO FLO into coherent sensing array 1810.
• optical routing circuit 1820 in FIG. 18A routes the LO FLO into the different rows of coherent sensing array 1810.
• Optical routing circuit 1820 comprises a network of optical waveguides wherein the flow of the LO FLO is controlled by a plurality of optical switches in the network.
• optical routing circuit 1820 comprises optical switches 1821, 1822, and 1823, which may be, but not limited to, Mach- Zehnder interferometer (MZI)-based optical switches, or MEMS-based optical switches.
• MZI Mach- Zehnder interferometer
• optical routing circuit 1820 in FIG. 18A may be in the form of a binary tree.
• An optical switch directs the LO FLO from an input to one or more output ports of the switch.
• optical switch 1821 in FIG. 18A may direct the LO FLO in waveguide 1824 to either one or both of waveguides 1825 and 1826.
• Optical routing circuit 1830 is used for routing optical source signal Es into coherent sensing array 1810. According to some embodiments, optical routing circuit 1830 may exhibit a structure similar to that of optical routing circuit 1820. In one embodiment, optical routing circuit 1830 may be in the form of a binary tree comprising optical switches 1831, 1832, and 1833. According to other embodiments, optical routing circuit 1830 may exhibit a structure different from that of optical routing circuit 1820.
• coherent sensing array 1810 comprises an array of coherent sensing units 1801.
• coherent sensing array 1810 comprises 24 coherent sensing units 1801 arranged in a 4x6 rectangular format (i.e., 4 rows and 6 columns).
• FIG. 18B shows a row of 6 coherent sensing units of coherent sensing array 1810, in accordance with an embodiment of the present disclosure.
• each coherent sensing unit 1801 of coherent sensing array 1810 is connected to two waveguides that function as optical input ports for the coherent sensing unit.
• coherent sensing unit 1801 may be coherent sensing unit 100 as illustrated in FIG. 1A.
• coherent sensing unit 1801 may be coherent sensing unit 700 as illustrated in FIG. 7A.
• coherent sensing unit 1801 maybe coherent sensing unit 800 as illustrated in FIG. 8.
• coherent sensing unit 1801 may be coherent sensing unit 900 as illustrated in FIG. 9.
• the two waveguides that are connected to coherent sensing unit 1801 may be used to direct optical source signal Es and the LO FLO into that sensing unit 1801.
• waveguide 1843 maybe used to direct optical source signal Es into coherent sensing unit 1801 that is connected to waveguides 1843 and 1844 in FIG. 18B
• waveguide 1844 may be used to direct the LO FLO into the same coherent sensing unit.
• Splitting couplers may be used in coherent sensing array 1810 to distribute optical source signal Es and the LO FLO into different coherent sensing units 1801. As shown in FIG.
• splitting couplers 1811, 1812, 1813, 1814, and 1815 may be used to distribute optical source signal Es into the six coherent sensing units 1801.
• Splitting couplers 1811, 1812, 1813, 1814. and 1815 may have the same or different splitting ratios.
• splitting coupler 1811 may have a splitting ratio of 5-1
• splitting coupler 1812 may have a splitting ratio of 4-l
• splitting coupler 1813 may have a splitting ratio of 3 ⁇
• splitting coupler 1814 may have a splitting ratio of 2-1
• splitting coupler 1815 may have a splitting ratio of LI.
• splitting couplers 1851, 1852, 1853, 1854, and 1855 may be used to distribute the LO FLO into the six coherent sensing units 1801, wherein splitting couplers 1851, 1852, 1853, 1854, and 1855 are similar to splitting couplers 1811, 1812, 1813, 1814, and 1815 that may or may not evenly distribute the LO FLO to the six coherent sensing units 1801.
• Coherent optical sensor 1800 in FIG. 18A may also comprise laser sources, electrical control circuits, and electrical readout circuits that are not shown explicitly in the figure.
• FIG. 19A shows a plan view of a coherent optical sensor 1900, in accordance with another embodiment of the present disclosure.
• Coherent optical sensor 1900 comprises an array of coherent sensing units 1901 that are coupled to optical source signal Es through an optical routing circuit in the topology of an LFtree.
• coherent optical sensor 1900 as shown in FIG. 19A manifests as a three-level H-tree with eight coherent sensing units 1901.
• the H-tree optical routing circuit in coherent optical sensor 1900 is constructed by a network of waveguides that are coupled with a plurality of optical switches 1902.
• Optical switches 1902 in FIG. 19A may be similar to optical switches 1821, 1822, 1823, 1831, 1832, and 1833 of coherent optical sensor 1800 in FIG. 18A.
• each of coherent sensing units 1901 may be coupled to a single waveguide that supplies optical source signal Es to the coherent sensing unit.
• the optical source signal Es may be used as both the optical source signal for target illumination and the LO for heterodyne detection in a coherent sensing unit 1901.
• each of coherent sensing units 1901 may be a coherent sensing unit 710 as illustrated in FIG. 7B.
• each of coherent sensing units 1901 may be a coherent sensing unit 100 as illustrated in FIG. 1A, a coherent sensing unit 700 as illustrated in FIG. 7A, a coherent sensing unit 800 as illustrated in FIG. 8, or a coherent sensing unit 900 as illustrated in FIG.
• each of coherent sensing units 1901 may be a coherent sensing unit group 1910 as illustrated in FIG. 19B.
• Coherent optical sensor 1900 in FIG. 19A may also comprise laser sources, electrical control circuits, and electrical readout circuits that are not shown explicitly in the figure.
• FIG. 19B shows a plan view of a coherent sensing unit group 1910, in accordance with an embodiment of the present disclosure.
• coherent sensing unit group 1910 comprises a plurality of coherent sensing units 1911 arranged in an H-tree topology.
• coherent optical sensor 1910 in FIG. 19B manifests as a two-level H-tree with four coherent sensing units 1911.
• components 1913 are splitting couplers that may be used to split optical source signal Es so as to supply a fraction of optical source signal Es to each of coherent sensing units 1911 of coherent sensing unit group 1910.
• the splitting ratios of splitting couplers 1913 may be 50/50 so as to distribute the source signal evenly to all coherent sensing units 1911 of coherent sensing unit group 1910.
• components 1912 are splitting couplers that may be used to split optical source signal Es that is supplied to each coherent sensing unit 1911 into a fraction of optical source signal Es as the optical source signal and a fraction of optical source signal Es as the LO for the coherent sensing unit.
• the splitting ratio of splitting coupler 1912 may or may not be 50/50.
• each of coherent sensing unit 1911 may be coherent sensing unit 100 as illustrated in FIG. 1A, coherent sensing unit 700 as illustrated in FIG. 7A, coherent sensing unit 800 as illustrated in FIG. 8, or coherent sensing unit 900 as illustrated in FIG. 9.
• FIG. 20A shows a plan view of a coherent optical sensor 2000, in accordance with a further embodiment of the present disclosure.
• Coherent optical sensor 2000 comprises a sensing region 2010 and optical routing circuits 2020 and 2030 that are implemented on a PIC chip.
• sensing region 2010 comprises a plurality of coherent sensing unit groups 2001.
• Each coherent sensing unit group 2001 comprises a plurality of coherent sensing units that emit outgoing optical signals for target illumination wherein the polarization of the outgoing optical signals is adjustable.
• optical routing circuit 2020 may be used for routing the local oscillator FLO to coherent sensing unit groups 2001 in sensing region 2010. According to some embodiments, optical routing circuit 2020 may be similar to optical routing circuit 1820 of coherent optical sensor 1800.
• optical routing circuit 2030 maybe used for routing source light Es to coherent sensing unit groups 2001 in sensing region 2010. According to some embodiments, optical routing circuit 2030 may be similar to optical routing circuit 1830 of coherent optical sensor 1800.
• FIG. 20B shows a plan view of a coherent sensing unit group 2001, in accordance with another embodiment of the present disclosure.
• Coherent sensing unit group 2001 comprises a plurality of coherent sensing units 2002 that emit outgoing optical signals with adjustable polarizations for target illumination.
• coherent sensing unit group 2001 is drawn to comprise four coherent sensing units 2002 in FIG. 20B.
• Each coherent sensing unit 2002 comprises one input waveguide for in-coupling the LO FLO and two input waveguides for in-coupling source light, wherein the amplitudes and the relative phase of the source light in the two waveguides determine the polarization state of the outgoing optical signal emitted from coherent sensing unit 2002.
• a coherent sensing unit 2002 may be realized by coherent sensing unit 1400 as illustrated in FIG. 14.
• each coherent sensing unit group 2001 comprises a plurality of splitting couplers 2051, 2052, and 2053 to distribute the LO FLO to each of coherent sensing units 2002 of coherent sensing unit group 2001.
• splitting couplers 2051, 2052, and 2053 may be similar to splitting couplers 1851, 1852, 1853, 1854, and 1855 that may or may not distribute the LO ELO evenly to each coherent sensing unit 2002 of coherent sensing unit group 2001.
• each coherent sensing unit group 2001 may comprise an optical switch 2021 that divides source light Es into two fractions.
• the two fractions of source light Es may then be distributed to each coherent sensing unit 2002 through splitting couplers.
• a fraction of source light Es may be distributed to coherent sensing units 2002 through splitting couplers 2011, 2012, and 2013.
• splitting couplers 2011, 2012, and 2013 may be similar to splitting couplers 1811, 1812, 1813, 1814, and 1815 that may or may not distribute source light Es evenly to each coherent sensing unit 2002 of coherent sensing unit group 2001.
• coherent sensing unit group 2001 may comprise waveguide crossings 2022 to enable optical signals to cross each other with minimal loss and cross-talk in a compact PIC layout.
• FIG. 20C shows a plan view of a Mach-Zehnder interferometer-based optical switch 2021, in accordance with an embodiment of the present disclosure.
• Optical switch 2021 which is a Mach-Zehnder interferometer, includes a phase shifter 2031 to control the output fractions of optical switch 2021.
• phase shifter 2031 may be an electro-optic phase shifter or a thermo-optic phase shifter.
• Coherent optical sensor 2000 in FIG. 20A may comprise laser sources, electrical control circuits, and electrical readout circuits that are not shown explicitly.
• coherent sensing unit group 2001 in FIG. 20B may comprise electrical control circuits and electrical readout circuits that are not shown explicitly.
• FIG. 21A shows a side view of an optical coherent imager 2100, in accordance with an embodiment of the present disclosure.
• Optical coherent imager 2100 comprises a coherent optical sensor 2101, a polarization transformation-separation assembly 2102, and an imaging optics system 2103.
• Optical coherent imager 2100 may also comprise other components including but not limited to any one or more of laser sources, electronic controllers, electronic interfaces, and digital signal processors that are not shown explicitly in FIG. 21A for simplicity.
• Coherent optical sensor 2101 in FIG. 21A is a sensor comprising a plurality of coherent sensing units of the present disclosure.
• coherent optical sensor 2101 may be one of coherent optical sensors 1800, 1900, and 2000 respectively illustrated in FIGs. 18A, 19A, and 20A.
• Outgoing optical signals are emitted from coherent optical sensor 2101 for target illumination.
• Outgoing optical signals emitted from different coherent sensing units of coherent optical sensor 2101 through imaging optics system 2103 may give rise to illuminating beams of different field-of-view positions, so that each field-of- view position corresponds to a coherent sensing unit of the coherent optical sensor.
• the details of imaging optics system 2103 in FIG. 21A are shown only for illustrative purpose.
• polarization transformation-separation assembly 2102 may be one of the configurations shown in FIGs. 4C, 5A, 5C, 6A, 6C, IOC, 11B, 12A, 13C, 15C, 16C, and 17B.
• Polarization transformation-separation assembly 2102 may be used to enable the outgoing optical signals emitted from coherent optical sensor 2101 for target illumination and the incoming optical signals (i.e., target signals) received by coherent optical sensor 2101 to propagate along common optical paths, wherein the common optical paths lie between assembly 2102 and target 2104.
• light rays 2171 illustrate example optical paths of a field-of-view position of optical coherent imager 2100
• light rays 2172 illustrate example optical paths of another field-of-view position of optical coherent imager 2100
• Imaging optics system 2103 may have at least one image plane.
• Polarization transformation-separation assembly 2102 may be disposed at a location proximate an image plane of imaging optics system 2103.
• polarization transformation-separation assembly 2102 is disposed at a location proximate coherent optical sensor 2101, which is disposed at the final image plane 2161 of imaging optics system 2103.
• FIG. 2 IB shows a closeup view of imager 2100 in FIG. 21A near the final image plane 2161.
• polarization transformation-separation assembly 2102 may be manifested as the polarization transformation-separation configuration illustrated in FIG. 6C.
• incoming optical signals from the target that share common optical paths with respect to outgoing optical signals may be spatially separated on the final image plane by polarization- dependent be am -separator 401.
• spatial separation 2198 is the spatial separation of the incoming and outgoing light rays 2171 effected by polarization- dependent beam-separator 401
• spatial separation 2199 is the spatial separation of the incoming and outgoing light rays 2172 effected by polarization- dependent be am -separator 401.
• imaging optics system 2103 may possess image space telecentricity that enables the spatial separations by polarization- dependent beam-separator 401 to be uniform across the field of view of optical coherent imager 2100. Spatial separation 2198 of light rays 2171 may thus be similar to spatial separation 2199 of light rays 2172.
• angular subtense 2188 of light rays 2171 may also be similar to angular subtense 2189 of light rays 2172.
• the polarization-diversified free-space-to-waveguide couplers of the coherent sensing units in coherent optical sensor 2101 may be designed to optimally couple with optical signals according to a common incident angle (e.g., normal incidence), a common angular subtense and, if applicable, a common separation between sub-couplers.
• each of the polarization- diversified free-space-to-waveguide couplers of the coherent sensing units in coherent optical sensor 2101 may be designed individually to optimally couple with optical signals according to the specifications of polarization transformation-separation assembly 2102 and imaging optics system 2103.
• FIG. 21C shows a polarization map of example ordinary rays (o-rays) and extraordinary rays (e-rays) with respect to polarization- dependent be am -separator 401 on coherent optical sensor 2101 over the field of view of the optical coherent imager in FIG. 2 IB.
• polarizations 2191 illustrate examples of the o-ray polarizations
• polarizations 2192 illustrate examples of the e-ray polarizations.
• optic axis 498 which lies on the x-z plane in FIG.
• the o-ray polarizations are linear polarizations that have dominant components along the y direction
• the e-ray polarizations are linear polarizations that have dominant components along the x direction.
• both the o-ray and e-ray polarizations may be unform over the field of view of the optical coherent imager.
• the polarizations of the o-rays and e-rays may depart from uniformity when imaging optics system 2103 is not exactly image-space telecentric.
• the polarization-diversified free-space-to-waveguide couplers of the coherent sensing units in coherent optical sensor 2101 may be designed wherein the non -uniformity is ignored.
• each of the polarization-diversified free-space-to-waveguide couplers of the coherent sensing units in coherent optical sensor 2101 may be designed individually to optimally couple with optical signals according to the variations of the polarizations of the o-rays and e-rays over the field of view of imaging optics system 2103.
• FIG. 22A shows a side view of an optical coherent imager 2200, in accordance with another embodiment of the present disclosure.
• Optical coherent imager 2200 comprises a coherent optical sensor 2201, an imaging optics system 2203, and a polarization transformation-separation assembly with components disposed with the optical components of imaging optics system 2203.
• the polarization transformation-separation assembly comprises polarization- dependent beam-separators 2241 and 2242, Faraday rotator 2251, polarization rotator 2252, and quarter- wave plate 2261. This polarization transformation-separation assembly is similar to polarization transformation-separation configuration 1210 in FIGs.
• polarization- dependent be am -separator 2241 may be a birefringent wedge.
• light rays 2271 illustrate example optical paths of a field-of-view position of optical coherent imager 2200
• light rays 2272 illustrate example optical paths of another field-of-view position of optical coherent imager 2200.
• FIG. 22B shows side views of light rays propagating through a polarization- dependent be am -separator 2241 that effects angular displacement and light rays propagating through a polarization-dependent be am -separator 2242 that effects lateral displacement, in accordance with embodiments of the present disclosure.
• polarization- dependent beam-separator 2242 may give rise to a lateral displacement to an incoming light ray with the lateral displacement depending on the polarization of the light ray. For example, in FIG.
• the x polarization component and the y polarization component of a light ray is laterally displaced with different displacements when the light ray passes through polarization- dependent beam-separator 2242.
• polarization- dependent be am -separator 2241 may give rise to an angular displacement to an incoming light ray with the angular displacement depending on the polarization of the light ray.
• the x polarization component and the y polarization component of a light ray is angularly displaced at different angles when the light ray passes through polarization- dependent beam-separator 2241.
• polarization- dependent be am -separator 2242 is disposed at a location proximate an image plane of imaging optics system 2203, whereas polarization- dependent be am -separator 2241 is disposed at a location proximate a focal plane of imaging optics system 2203. Angular displacements by polarization- dependent be am -separator 2241 on the focal plane may effectively give rise to lateral displacements on the image plane.
• polarization-dependent beam-separator 2241 may have an advantage of enabling a greater flexibility in various locations for disposing optical components, including but not limited to polarization-dependent beam-separators 2241 and 2242, Faraday rotator 2251, polarization rotator 2252, and quarter-wave plate 2261, in imaging optics system 2203.
• Faraday rotator 2251, polarization rotator 2252, and quarter- wave plate 2261 may be disposed at locations in imaging optics system 2203 where the incident angles of light rays are relatively small (i.e., close to normal incidence).
• some polarization- dependent components may have larger performance tolerances than others for certain applications of optical coherent imaging.
• Faraday rotator 2251 that is tolerant to the incident angles of light rays may be disposed at any location between polarization rotator 2252 and polarization-dependent be am -separators 2242.
• quarter-wave plate 2261 may be disposed at a location where there is a larger variation in the incident angles of light rays at different field-of-view positions.
• Quarter-wave plate 2261 may transform a linearly-polarized outgoing optical signal at normal incidence to a circularly-polarized optical signal, and a linearly-polarized outgoing optical signal at an incident angle other than normal incidence to an elliptically- polarized optical signal.
• the consequence of the variations in incident angle on quarter-wave plate 2261 at different field-of-view positions may thus essentially result in different elliptically-polarized light for the illumination of different positions of the target scene, which may not impose significant issue for the relevant applications of optical coherent imaging.
• coherent optical sensor 2201 such as coherent optical sensor 2000 illustrated in FIG. 20A, may enable dynamical polarization adjustment, which may mitigate the issue of the different elliptically-polarized light for the illumination of different positions of the target scene.
• the components of the polarization transformation-separation assembly are individually disposed with the optical components of imaging optics system 2203. According to some embodiments, one or more of the components of the polarization transformation-separation assembly may be disposed collectively with the optical components of imaging optics system 2203.
• FIG. 23 illustrates a flowchart of a method of optical coherent imaging using polarization diversification to enable shared path for transmitting and receiving optical signals, in accordance with an embodiment of the present disclosure.
• Step 2301 source light is generated from a light source.
• the source light is guided through a waveguide circuit to one or more polarization-diversified free-space-to-waveguide couplers in a coherent optical sensor of an optical coherent imager.
• the guiding of the source light through the waveguide circuit may be accomplished by controlling electro-optical or thermo- optical switches in the waveguide circuit using a control system.
• the choice of the polarization-diversified free-space-to-waveguide couplers to which the source light is guided may be determined by the positions of a target scene to be illuminated. More specifically, each target scene position corresponds to a field-of-view position of the optical coherent imager, which in turn corresponds to a polarization- diversified free-space-to-waveguide coupler in the coherent optical sensor of the optical coherent imager.
• Step 2305 for each of the chosen polarization- diversified free-space-to-waveguide couplers (herein referred to as the couplers for simplicity) to which the source light is guided, the source light is out-coupled into free space from the coupler to give rise to outgoing light with a first polarization.
• free space may refer to vacuum, air, a region above the surface of the coupler, or any homogenous medium with boundaries that have length-scales much larger (e.g., at least 10 times) than the wavelength of the optical signals propagating in it.
• the polarization-diversified free-space-to-waveguide coupler may be realized by coupler 101 shown and described with respect to FIG. IB, coupler 200 shown and described with respect to FIG.
• coupler 300 shown and described with respect to FIG. 3 coupler 1000 shown and described with respect to FIG. 10A, coupler 1100 shown and described with respect to FIG. 11A, coupler 1300 shown and described with respect to FIG. 13A, coupler 1500 shown and described with respect to FIG. 15A, coupler 1600 shown and described with respect to FIG. 16A, or coupler 1700 shown and described with respect to FIG. 17A.
• the first polarization of the outgoing light may be transformed to a second polarization by a polarization transformation configuration.
• the second polarization may be the same or different from the first polarization.
• the second polarization may be any of a linear polarization, a circular polarization, or an elliptical polarization.
• the polarization transformation may be realized by one or a combination of optical components including but not limited to Faraday rotator, polarization rotator, and quarter-wave plate.
• the optical path of the outgoing light may additionally be laterally or angularly displaced, or both laterally and angularly displaced.
• the displacement may be realized by at least one of optical-path- displacing components such as but not limited to polarization- dependent beam-separator.
• the operations of polarization transformation and optical path displacement may be realized by a combination of optical components including but not limited to Faraday rotator, polarization rotator, quarter-wave plate, and polarization- dependent beam- separator. According to some embodiments, such operations may be realized by at least one of, but not limited to, the configurations illustrated in FIGs.
• a polarization transformation configuration with optical path displacement comprises components 2241, 2242, 2251, 2252, and 2261 that are disposed with the optical components (lenses) of imaging optics system 2203.
• the transformed outgoing light is directed to one or more targets located at the field-of-view positions of the optical coherent imager that correspond to the chosen polarization-diversified free -space -to -wave guide couplers according to Step 2303.
• the transformed outgoing light may be directed to the targets with an additional imaging optics system disposed between the chosen couplers and the targets.
• the targets may reflect or scatter the transformed outgoing light that illuminates them.
• the reflected or scattered light from the targets may be received by the optical coherent imager at the field-of-view positions of the imager that correspond to the chosen polarization-diversified free -space -to -wave guide couplers described in Step 2309.
• the reflected or scattered light may be received with an additional imaging optics system disposed between the chosen couplers and the targets.
• the optical imaging system may be the same as the imaging optics system in Step 2309.
• the received light that is reflected or scattered from the target may be transformed by the same polarization transformation configuration as described in Step 2307.
• the received light may comprise either one or both of a component with a third polarization that is the same as the second polarization of the transformed outgoing light, and a component with a fourth polarization that is orthogonal to the third polarization component.
• the polarization transformation configuration may transform the third polarization of the received light to a fifth polarization that is orthogonal to the first polarization of the outgoing light at that position.
• the polarization transformation configuration may transform the fourth polarization of the received light to a sixth polarization that is orthogonal to the fifth polarization of the transformed received light.
• the optical path of at least one polarization component of the received light may additionally be displaced by the same optical-path- displacing components described in Step 2307.
• the polarization components of the received light that are displaced may be either one or both of the third and fourth polarizations.
• the transformed received light may be coupled from free space into in- coupling waveguides using one or more polarization- diversified free-space-to-waveguide couplers.
• these polarization-diversified free-space-to- waveguide couplers may be the same set of polarization-diversified free-space-to-waveguide couplers used to emit the outgoing polarized light in Step 2305.
• At least one of the in-coupling waveguides receiving some or all of the transformed received light through the polarization-diversified free-space-to-waveguide coupler is different from the waveguide that guides the source light to the coupler (i.e., the out-coupling waveguide) according to Step 2303.
• the polarization- diversified free-space-to-waveguide coupler may in-couple the fifth polarization of the transformed received light, which is orthogonal to the first polarization of the outgoing light emitted from the coupler, to at least one waveguide that is different from the out-coupling waveguide. This may be accomplished by the design of the polarization-diversified free-space- to-waveguide coupler that couples the fifth polarization of the transformed received light to an in-coupling waveguide that is different from the out-coupling waveguide.
• this may be accomplished by the optical path displacement of the third polarization of the received light, so that the fifth polarization of the transformed received light may arrive at the coupler at a spatial location that is different from the spatial location where the outgoing light is emitted from the coupler.
• the polarization-diversified free- sp ace -to -wave guide coupler may in-couple the sixth polarization of the transformed received light, which is orthogonal to the fifth polarization of the transformed received light, to at least one waveguide that is different from the out-coupling waveguide. This may be accomplished by the optical path displacement of the fourth polarization of the received light, so that the sixth polarization of the transformed received light may arrive at the coupler at a spatial location that is different from the spatial location where the outgoing light is emitted from the coupler.
• the optical path displacements of the third and fourth polarizations of the received light may be realized through the same optical-path- displacement components described in Step 2313.
• the in-coupled received light in the in-coupling waveguides may be detected by detectors that are disposed in proximity to the polarization-diversified free-space- to-waveguide couplers that in-couple the transformed received light.
• the detectors may be arranged as heterodyne detection setups to carry out heterodyne detection with local oscillator light that is supplied to the heterodyne detection setups.
• the detected signals may be processed to extract information about the target.
• the processing of signals may be performed by a signal processing unit that may or may not be a part of the optical coherent imager.
• the information of the target may include but not limited to the coordinates of the target and the reflectivity of the target surface.
• the information of the target may include the distance of the target from the optical coherent imager.
• the information of the target may include the velocity information of the target.
• the distance and velocity information may be obtained by modulating the source light in Step 2301 according to the approach of FMCW LIDAft and be extracted by means of Fourier transformations of the detected signals.

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