WO2017021888A1 - Optical device for demultiplexing and multiplexing a plurality of channels with different wavelength and different orbital angular momentum and optical communication system thereof - Google Patents

Optical device for demultiplexing and multiplexing a plurality of channels with different wavelength and different orbital angular momentum and optical communication system thereof Download PDF

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Publication number
WO2017021888A1
WO2017021888A1 PCT/IB2016/054650 IB2016054650W WO2017021888A1 WO 2017021888 A1 WO2017021888 A1 WO 2017021888A1 IB 2016054650 W IB2016054650 W IB 2016054650W WO 2017021888 A1 WO2017021888 A1 WO 2017021888A1
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WIPO (PCT)
Prior art keywords
optical
wavelength
different
optical element
free space
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PCT/IB2016/054650
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French (fr)
Inventor
Filippo Romanato
Gianluca Ruffato
Original Assignee
Strand S.R.L.
Universita' Degli Studi Di Padova
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Application filed by Strand S.R.L., Universita' Degli Studi Di Padova filed Critical Strand S.R.L.
Priority to EP16766619.7A priority Critical patent/EP3332497A1/en
Publication of WO2017021888A1 publication Critical patent/WO2017021888A1/en

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Classifications

    • 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
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/2804—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals forming multipart couplers without wavelength selective elements, e.g. "T" couplers, star couplers
    • G02B6/2848—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals forming multipart couplers without wavelength selective elements, e.g. "T" couplers, star couplers having refractive means, e.g. imaging elements between light guides as splitting, branching and/or combining devices, e.g. lenses, holograms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J14/00—Optical multiplex systems
    • H04J14/02—Wavelength-division multiplex systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J14/00—Optical multiplex systems
    • H04J14/04—Mode multiplex systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J14/00—Optical multiplex systems
    • H04J14/07—Orbital angular momentum [OAM] multiplex systems
    • 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
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29304—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by diffraction, e.g. grating
    • G02B6/29305—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by diffraction, e.g. grating as bulk element, i.e. free space arrangement external to a light guide
    • G02B6/29311—Diffractive element operating in transmission

Definitions

  • the present invention generally relates to the field of optical communications.
  • the present invention concerns an optical device for demultiplexing and multiplexing a plurality of channels with different wavelength and different orbital angular momentum.
  • WDM Wavelength Division Multiplexing
  • PDM Polarization Division Multiplexing
  • MDM Mode Division Multiplexing
  • OAM orbital angular momentum
  • MDM-OAM (abbreviated as MDM-OAM).
  • OAM orbital angular momentum
  • SAM spin angular momentum
  • spin The spin angular momentum (commonly referred simply as "spin") indicates the state of polarization of a photons beam.
  • OAM modes can propagate both in the free space and over an optical fiber: in the latter case, in the following the term "guided OAM modes" will be used to indicate propagation over the optical fiber, in order to distinguish them from the OAM modes propagating in the free space.
  • Guided OAM modes are a linear combination of even and odd type HE vectorial modes which propagate over a multimode optical fiber or are a linear combination of even and odd type EH vectorial modes.
  • guided OAM modes are characterised in that they have a transverse spatial component of the electric field Et (and magnetic field Ht) with uniform polarization state of a circular type (right or left) and in that the surface of the wavefront of the transverse spatial component of the electric field Et (and magnetic field Ht) has a helical trend, dextrorotatory (i.e. the direction of the screw is clockwise) or laevorotatory (i.e. the direction of the screw is anticlockwise): for this reason the guided OAM modes are commonly denoted also as “circular optical vortices" or "helical modes".
  • the pitch of the screw (of the surface of the wavefront of the transverse spatial component of the electric field Et and magnetic field Ht) is the minimum distance between two distinct points of the screw having the same coordinates in the plane (x, y) perpendicular to the propagation direction z (i.e. the pitch of the screw is equal to the wavelength ⁇ ).
  • the luminous intensity of the guided OAM modes (i.e. of the circular optical vortices) on a plane perpendicular to the propagation direction (commonly known as a "luminous spot") has a substantially circular shape and is distributed into p concentric rings (wherein p is the radial index), for / greater than or equal to 1 .
  • the luminous intensity is null on the propagation axis of the considered OAM mode, at a locus of singular points wherein the phase is not defined.
  • Guided OAM modes are a plurality of spatial modes that are orthogonal each another, i.e. they are carried independently in case wherein they are propagated over an optical fiber which maintains the circular symmetry and which is not subject to external perturbations: in this hypothesis the exchange of energy between different modes carried over the multimode optical fiber is theoretically null; in a case of propagation in vacuum, the condition of orthogonality of the OAM modes is always satisfied.
  • Wavelength Division Multiplexing (WDM) systems are subdivided into DWDM (Dense WDM) and CWDM (Coarse WDM), according to the separation (i.e. distance) between the carrier wavelengths of the channels.
  • WDM Wavelength Division Multiplexing
  • the conventional DWDM systems provide up to 40 channels in the third transmission window (band C) of the silicon fibers, centred on the value of the wavelength equal to 1550 nm, with a separation between the channels equal to 100 GHz (i.e. 0.7 nm in wavelength).
  • CWDM CWDM systems the separation between the used carrier wavelengths is greater than those used in the conventional DWDM systems, so as to be able to use less sophisticated and theus less expensive optical components.
  • a conventional CWDM system provides 8 channels separated by at least 20 nm starting from the upper limit of 1610 nm.
  • a CWDM system that provides up to 16 channels on an optical fiber entirely using the frequency band comprised between the second and the third transmission window (1310/1550 nm respectively) wherein, apart from the two windows (the minimum dispersion window and the minimum attenuation window) the critical area is also comprised wherein it can occur the attenuation of the signal owing to absorbance due to the presence of impurities constituted by hydroxyl ions OH " .
  • the two systems DWDM/CWDM can be integrated, with the possibility of expanding the total band with the addition of a plurality of DWDM channels densely distributed on the carriers of the CWDM system.
  • Patent US 7546037 discloses a system for creating a light beam with multiplexing of OAM modes for use in optical communication of data.
  • US 7546037 further discloses that the system can be used in combination with the Wavelength Division Multiplexing method, but it does not describe in detail which optical devices to use for performing a multiplexing of wavelength and also of OAM modes.
  • Patent EP 1617235 describes the use of a Fresnel lens 30 (indicated by “Fresnel zone plate”) which focuses the incident light into a focus situated at a distance ZL (with respect to the Fresnel lens) which depends on the wavelength of the incident light.
  • the article further discloses the use of a multilevel diffractive optical element (DOE) for performing mode division multiplexing (see Fig.2) and discloses the use of a diffractive optical element of binary type for performing the mode division demultiplexing (see paragraph 2 "Methods" describing two OAM modes with angular index 1 and -2 and corresponding Fig.1 ).
  • DOE multilevel diffractive optical element
  • Fig.2 discloses the use of a diffractive optical element of binary type for performing the mode division demultiplexing
  • WO 2015/024595-A1 discloses an optical switch 10, 30 which uses multiplexing and demultiplexing for carrying out the switching function.
  • Methods which allow to perform only a multiplexing/demultiplexing of a plurality of channels with different wavelength and all having a null orbital angular momentum; alternatively, the known methods allow to perform only a multiplexing/demultiplexing of a plurality of channels with a different orbital angular momentum (i.e. a multiplexing/demultiplexing of various OAM modes) and all having the same wavelength.
  • the Applicant has observed that the known methods do not allow to perform a multiplexing/demultiplexing of a plurality of channels with different wavelength and at the same time a multiplexing/demultiplexing of a plurality of channels with different orbital angular momentum (and, preferably, also a polarization division multiplexing) using optical elements that can be integrated into photonic devices with a large scale reproducibility and with sufficient reliability.
  • the present invention relates to a demultiplexing optical device and a multiplexing optical device of a plurality of channels with different wavelength and different orbital angular momentum value as defined in the enclosed claims 1 and 9 respectively and by their preferred embodiments described in the dependent claims from 2 to 8 and from 10 to 12 respectively.
  • the demultiplexing optical device and the multiplexing optical device according to the present invention allow to maintain the capability to perform the multiplexing/demultiplexing of a plurality of channels with different wavelength and allow at the same time to further perform the multiplexing/demultiplexing of a plurality of channels with different orbital angular momentum: in this way the quantity of data that can be carried in air or over an optical fiber is significantly increased.
  • optical communication system as defined in the enclosed claim 13 and by its preferred embodiment described in the dependent claim 14.
  • Figure 1 A schematically shows a perspective view of the optical device for demultiplexing a plurality of channels with different wavelength and different orbital angular momentum according to an embodiment of the invention
  • Figure 1 B is a more detailed view of the demultiplexing optical device of Figure 1 A;
  • Figure 2 schematically shows a perspective view of an optical communication system according to a first embodiment of the invention
  • Figure 3 shows more in detail a top and cross-section view of a first diffractive optical element used into the demultiplexing optical device
  • Figure 4 shows more in detail a top view of a second diffractive optical element used into the demultiplexing optical device
  • FIGS. 5A-5C schematically show a perspective, top and cross-section view f of an optical device for multiplexing a plurality of channels with different wavelength and different orbital angular momentum according to an embodiment of the invention
  • Figure 6 shows a block diagram of an optical communication system according to a second embodiment of the invention.
  • Figure 7 shows a block diagram of an optical communication system according to a third embodiment of the invention.
  • FIG. 1 shows a perspective view of the demultiplexing optical device 1 according to an embodiment of the invention.
  • the demultiplexing optical device 1 comprises optical elements which can be miniaturised by means of micro and nano-manufacturing methods.
  • the demultiplexing optical device 1 is an optical receiver having the function of receiving a multiplexed incident optical beam F_i_mux carrying a plurality of channels having different values ⁇ Ai, A ⁇ . . . AN ⁇ of the wavelength A and different values ⁇ U, ... IM ⁇ of the angular index / and of performing the demultiplexing of the plurality of channels as a function of the values of the wavelength A and of the values of the angular index /, generating a plurality of demultiplexed output optical beams F_o_dmx having values ( ⁇ , h), ⁇ A2, )... ⁇ AN, I1); ( ⁇ , h), ⁇ 2 , h)... ⁇ AN, h); ... ( ⁇ , IM), ⁇ A 2 , IM)... ⁇ AN, IM) of the wavelength A and of the angular index /.
  • the multiplexed incident optical beam F_i_mux at the input of the demultiplexing optical device 1 can be an optical beam propagating in the free space; in this case the channels are free space circular optical vortices having different wavelengths A and different orbital angular momentum.
  • the multiplexed incident optical beam F_i_mux can be an optical beam propagating over a multimode optical fiber; in this case the channels are circular optical vortices guided over the optical fiber and having different wavelengths ⁇ and different orbital angular momentum.
  • channel CH1 .1 is a circular optical vortex (guided or in free space) having a wavelength / and an angular index h;
  • channel CH1 .2 is a circular optical vortex (guided or in free space) having a wavelength / and an angular index ;
  • channel CH1 .3 is a circular optical vortex (guided or in free space) having a wavelength / and an angular index ;
  • channel CH2.1 is a circular optical vortex (guided or in free space) having a wavelength ,1 ⁇ 2and an angular index h;
  • channel CH2.2 is a circular optical vortex (guided or in free space) having a wavelength ,1 ⁇ 2and an angular index ;
  • channel CH2.3 is a circular optical vortex (guided or in free space) having a wavelength ,1 ⁇ 2and an angular index ;
  • channel CH3.1 is a circular optical vortex (guided or in free space) having a wavelength A? and an angular index h
  • channel CH3.2 is a circular optical vortex (guided or in free space) having a wavelength A? and an angular index ;
  • channel CH3.3 is a circular optical vortex (guided or in free space) having a wavelength A? and an angular index .
  • the demultiplexing optical device 1 comprises:
  • a first diffractive optical element 1 -1 a first diffractive optical element 1 -1 ;
  • the lens 1 -3 is considered to be separated from the second diffractive optical element 1 -2, but it is also possible to integrate the lens 1 -3 within the second diffractive optical element 1 -2. In other words, it is possible to design a single diffractive optical element (denoted schematically by 1 -4 in figure 1 A) performing the functionality of the second diffractive optical element 1 -2 and the functionality of the lens 1 -3.
  • the demultiplexing optical device 1 is positioned in a space defined by a cartesian reference system (x, y, z), wherein the axis z corresponds to the propagation direction of the optical beams and thus it represents the axis of the demultiplexing optical device 1 , while the plane (x, y) is perpendicular to the axis z (and thus it is perpendicular to the axis of the demultiplexing optical device 1 ).
  • the first diffractive optical element 1 -1 is a passive optical element having the function of carrying out the demultiplexing of the wavelength ⁇ , ⁇ , ⁇ , while at the same time maintaining the circular symmetry of the multiplexed incident optical beam F_i_mux at the input of the first diffractive optical element 1 -1 , so as to maintain the content of the angular indices h, , o the OAM modes carried over the multiplexed incident optical beam F_i_mux.
  • the second diffractive optical element 1 -2 is also a passive optical element.
  • the lens 1 -3 is of the converging type and it has a focal length .
  • the set of the second diffractive optical element 1 -2 and of the lens 1 -3 have the function of performing the demultiplexing of the OAM modes having an angular index h, , , i.e. of spatially separating the free space optical beam incident on the second diffractive optical element 1 -2 into a plurality of collimated luminous spots associated to the plurality of different OAM modes.
  • the converging lens 1 -3 has the function of transforming the optical beam of the near-field type at the output of the second diffractive optical element 1 -2 into a collimated optical beam of the far-field type, so as to generate at the output a plurality of collimated luminous spots which can be detected on a photodetector 5.
  • the first diffractive optical element 1 -1 is such to receive the multiplexed incident optical beam F_i_mux carrying the channels CH1 .1 , CH1 .2, CH1 .3, CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 and it has the function of performing the chromatic dispersion of the multiplexed incident optical beam F_i_mux.
  • the first diffractive optical element 1 -1 is configured to impart to the input channels CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 different radii of curvature of the wavefront (i.e. wavefronts having a different divergence), wherein the values of the radii of curvature (i.e. of the divergence) associated to the different channels at the output of the diffractive optical element 1 -1 depend on the value of the wavelength A associated to the considered channel.
  • the channels CH1 .1 , CH1 .2, CH1 .3 having the first wavelength ⁇ cross the first diffractive optical element 1 -1 and are transmitted therefrom at the output with a wavefront having a first radius of curvature Ri .
  • the channels CH2.1 , CH2.2, CH2.3 having the second wavelength A ⁇ cross the first diffractive optical element 1 -1 and are transmitted therefrom at the output with a wavefront having a second radius of curvature R2, (different to the first radius of curvature Ri).
  • channels CH3.1 , CH3.2, CH3.3 having the third wavelength A 3 cross the first diffractive optical element 1 -1 and are transmitted therefrom at the output with a wavefront having a third radius of curvature R3, (different from the first radius of curvature Ri and from the second radius of curvature R2).
  • the multiplexed incident optical beam F_i_mux is incident on the first diffractive optical element 1 -1 , which generates the following free space optical beams:
  • first free space optical beam FO1_SL (indicated in Figure 1 B with a broken- and-dotted line) converging into the first focus f1 positioned at the first focal length d_f1 , wherein the first free space beam FO1_SL is composed of an overlapping of three free space circular optical vortices having a wavelength ⁇ and angular indices h, , and wherein the three free space circular optical vortices are associated to the channels CH1 .1 , CH1 .2, CH1 .3;
  • a second free space optical beam FO2_SL (indicated in Figure 1 B with a broken line) converging into the second focus f2 positioned at the second focal length d_f2, wherein the second free space optical beam FO2_SL is composed of an overlapping of three free space circular optical vortices having a wavelength A ⁇ and angular indices h, , and wherein the three free space circular optical vortices are associated to the channels CH2.1 , CH2.2, CH2.3; - a third free space optical beam FO3_SL (indicated in Figure 1 B with a continuous line) converging into the third focus f3 positioned at the focal length d_f3, wherein the third free space optical beam FO3_SL is composed of an overlapping of three free space circular optical vortices having a wavelength 3 and angular indices h, , and wherein the three free space circular optical vortices are associated to the channels CH3.1 , CH3.2, CH3.3;
  • the wavefront of the first free space optical beam FO1_SL diverges and is incident on a first zone Ai of the second diffractive optical element 1 -2, as will be explained in greater detail in the following; therefore channels CH1 .1 , CH1 .2, CH1 .3 having the first wavelength Ai are incident on the first zone Ai of the second diffractive optical element 1 -2.
  • the wavefront of the second free space optical beam FO2_SL diverges and is incident on a second zone A2 of the second diffractive optical element 1 -2; therefore channels CH2.1 , CH2.2, CH2.3 having the second wavelength K2 are incident on the second zone A2 of the second diffractive optical element 1 -2.
  • the wavefront of the third free space optical beam FO3_SL diverges and is incident on a third zone A3 of the second diffractive optical element 1 -2; therefore channels CH3.1 , CH3.2, CH3.3 having the third wavelength K3 are incident on the third zone A3 of the second diffractive optical element 1 -2.
  • the first diffractive optical element 1 -1 acts only on the value of the radius of curvature of the wavefront of the multiplexed incident optical beam F_i_mux, i.e. the first diffractive optical element 1 -1 does not modify the content of the angular indices h, h, ho the OAM modes carried over the multiplexed incident optical beam F_i_mux.
  • the first diffractive optical element 1 -1 is implemented with a Fresnel lens, which is an optical element that exploits diffraction to focus an incident optical beam in foci having different positions which depend on the value of the wavelength ⁇ of the incident optical beam.
  • the focal length d_f of the Fresnel lens 1 -1 depends on the wavelength ⁇ of the incident collimated optical beam according to the following formula:
  • d_fo is the focal length at wavelength ⁇ for which the Fresnel lens 1 -1 has been dimensioned.
  • the Fresnel lens is an optical element having circular symmetry implemented with a plurality of concentric annuli which are transparent with respect to the incident optical beam.
  • annulus is intended to mean the set of two concentric rings, which identify an area delimited by the two rings.
  • a Fresnel lens is the diffractive equivalent of a refractive lens.
  • the transmission function TFL of the Fresnel lens 1 -1 is the following:
  • the radial thickness of the plurality of circular annuli is different between two adjacent annuli.
  • each annulus is given by the following equation: wherein n is the sequential number of the n-th annulus.
  • Figure 3 shows a top view of the first diffractive optical element 1 -1 implemented with a Fresnel lens.
  • Figure 3 further shows a section view of the Fresnel lens 1 -1 , wherein it is possible to observe the trend of the thickness of the material composing the Fresnel lens 1 -1 .
  • the thickness of the material of each annulus is multi-level, i.e. it has a plurality of discrete values comprised between a substantially null value and a maximum value.
  • the thickness of the most internal annulus has a maximum value at the centre and then it decreases towards a substantially null value with a quadratically decreasing trend;
  • the thickness of the external annuli with respect to the central annulus is maximum in the radial position closest to the most internal annulus and then it decreases towards a substantially null value with quadratically decreasing trend.
  • the first diffractive optical element 1 -1 operates as an "axicon", which is a lens composed of a flat surface and a conical surface, the latter facing towards the second diffractive optical element 1 -2.
  • the axicon 1 -1 operates as a prism having a circular symmetry performing the dispersion of the different wavelengths ⁇ , ⁇ , A? and maintaining at the same time the circular symmetry of the distribution of the luminous intensity of the multiplexed incident optical beam F_i_mux: in this way it is maintained its content of the angular indices h, , of the OAM modes carried over the multiplexed incident optical beam F_i_mux.
  • a further lens (not shown in the figures) is interposed between the axicon 1 -1 and the second diffractive optical element 1 -2, with the purpose of correcting the phase of the free space optical beams FO1_SL, FO2_SL, FO3_SL incident on the second diffractive optical element 1 -2.
  • the first diffractive optical element 1 -1 is implemented with a holographic mask having the structure of a surface composed of a plurality of discrete locations indicated with pixels (i.e. a pixel matrix), each pixel having continuous values of phase and amplitude.
  • the first diffractive optical element 1 -1 is implemented with a holographic mask having a multilevel surface structure, i.e. it is composed of a plurality of pixels (i.e. a pixel matrix), each pixel having discrete values of phase and amplitude.
  • the continuous or multilevel surface can be implementedusing the photolithography method or the lithography method with electron beam on polymeric materials, such as for example PMMA (poly-methyl-metacrylate).
  • polymeric materials such as for example PMMA (poly-methyl-metacrylate).
  • the pattern of the multilevel holographic mask of the first diffractive optical element 1 -1 is calculated by means of algorithms of numerical calculation executed on a computer.
  • the Applicant has observed that the OAM modes have the special characteristic of having a central singularity which is shown as a dark region around which the luminous intensity is distributed in the form of concentric rings. Therefore the useful signal of an OAM mode with a determined value of the angular index / and of the radial index p is bounded into the region of the space wherein the luminous intensity is not zero.
  • the second diffractive optical element 1 -2 It is possible to exploit this trend of the luminous intensity of an OAM mode to design the second diffractive optical element 1 -2. Only the zones of the second diffractive optical element 1 -2 which are illuminated by a specific considered OAM mode are considered, leaving the remaining zones available for manipulating other OAM modes. In fact the zones of the second diffractive optical element 1 -2 on which the considered OAM mode with null luminous intensity is incident (i.e. the central zone and the most external zone) are irrelevant for the considered OAM mode and thus they can be used for manipulating other incident OAM modes different from the considered one, without influencing the considered OAM mode.
  • the second diffractive optical element 1 -2 comprises a plurality of zones ⁇ , A2, ... AN, each constituting a diffractive optical element suitably designed for a specific wavelength ⁇ and operating as an OAM modes demultiplexer for said specific wavelength.
  • the orders of diffraction are not pure. A portion of the initial energy of the single OAM mode is not concentrated in a single diffraction order, but it is distributed on other orders. In the case of many OAM modes having different incident wavelength on the same region of the second diffractive optical element 1 -2, the luminous intensity of each one is distributed on different diffraction orders , mixing the signals transmitted over the different OAM modes and reducing the ratio between the signal transmitted by the single OAM mode and the noise generated by the other OAM modes.
  • the second diffractive optical element 1 -2 in such a way that it also operates in a broad interval of wavelengths A i, ⁇ ... AN, implementing the second diffractive optical element 1 -2 with a set of single diffractive optical elements, each one operating in respective optimal ranges of different carrier wavelengths.
  • the plurality of zones ⁇ , A2, . . . AN can be of the transmitting type or of the reflecting type.
  • Figure 4 shows a first transmitting zone Ai denoted with sloped lines, a second transmitting zone A2 denoted with a dotted pattern and a third transmitting zone A3 denoted with squares.
  • Each transmitting zone Ai , A2, A3 is configured to receive an incident free space optical beam having a different wavelength ⁇ and a plurality of angular indices h, , -
  • each transmitting zone Ai , A2, A3 (in combination with the lens 1 - 3) is configured to deviate the incident optical beam into different directions in the space, as a function of the different values of the angular indices h, , of the optical beam incident on the second diffractive optical element 1 -2.
  • direction in the space is understood to mean the direction identified by a point of reference on the second diffractive optical element 1 -2 and a point having three coordinates in the case wherein it is considered that the demultiplexing optical device 1 is positioned in the cartesian reference system (x, y, z).
  • the direction is identified by the reference point and a point having two coordinates in the case wherein it is considered that the demultiplexing optical device 1 is positioned in a reference system having cylindrical coordinates (p, ⁇ ).
  • the separation between the different wavelengths ⁇ , ⁇ 2, ⁇ 3 is obtained by means of the first diffractive optical element 1 -1 which performs a chromatic dispersion of the multiplexed incident optical beam F_i_mux and thus the first diffractive optical element 1 -1 is such to transmit free space optical beams FO1_SL, FO2_SL, FO3_SL having respective different wavelengths ⁇ - ⁇ , ⁇ 2, ⁇ 3 towards different transmitting sections Ai , A2, A3 respectively of the second diffractive optical element 1 -2.
  • the set of the first transmitting zone Ai and of the lens 1 -3 is configured to:
  • the free space optical beam FO1 .1_SL carries the channel CH1 .1 having a wavelength ⁇ and angular index h;
  • the free space optical beam FO1 .2_SL carries the channel CH1 .2 having a wavelength ⁇ and angular index ;
  • the free space optical beam FO1 .3_SL carries the channel CH1 .3 having a wavelength ⁇ and angular index I3.
  • the set of the second transmitting zone A2 and the lens 1 -3 is configured to:
  • the free space optical beam FO2.1_SL carries the channel CH2.1 having a wavelength ⁇ and angular index h;
  • the free space optical beam FO2.2_SL carries the channel CH2.2 having a wavelength ⁇ and angular index ;
  • the free space optical beam FO2.3_SL carries the channel CH2.3 having a wavelength ⁇ and angular index I3.
  • the set of the third transmitting zone A3 and ofthe lens 1 -3 is configured to: receive the third free space optical beam FO3_SL having a wavelength A3 and having a wavefront with a third radius of curvature R3;
  • the free space optical beam FO3.1 _SL carries the channel CH3.1 having a wavelength A? and angular index h;
  • the free space optical beam FO3.2_SL carries the channel CH3.2 having a wavelength A? and angular index ;
  • the free space optical beam FO3.3_SL carries the channel CH3.3 having a wavelength A? and angular index I3.
  • the second diffractive optical element 1 -2 is implemented with an optical element having a circular radial symmetry: in this case the plurality of transmitting zones ⁇ , A2,... AN is implemented with a corresponding plurality of concentric annuli defined by respective radii n , r2, . . . ⁇ .
  • annulus is again intended to mean the set of two concentric rings, which identify an area bounded by the two rings.
  • Figure 4 shows the second diffractive optical element 1 -2 composed of three concentric annuli ⁇ , A2, A3 of a transmitting type defined by three respective radii n , X2, xz, wherein the first annulus Ai is the most internal one, the third annulus A3 is the most external one and the second annulus A2 is interposed between the internal annulus Ai and the external annulus A3.
  • the three concentric circular annuli Ai , A2, A3 are associated to the wavelengths ⁇ , K ⁇ , respectively ⁇ 3, i.e:
  • the internal annulus Ai is associated to the wavelength ⁇ - ⁇ ;
  • the intermediate annulus A2 is associated to the wavelength ⁇ 2;
  • the external annulus A3 is associated to the wavelength ⁇ 3.
  • the second diffractive optical element 1 -2 is implemented with a holographic mask having the structure of a surface composed of a plurality of pixel (i.e. a pixel matrix), each pixel having continuous values of the phase and amplitude.
  • the second diffractive optical element 1 -2 is implemented with a holographic mask having the structure of a multilevel surface, i.e. composed of a plurality of pixel (i.e. a pixel matrix), each pixel having discrete values of the phase and amplitude.
  • the continuous or multilevel surface can implemented using the photolithography method or the lithography method with electron beam on polymeric materials, such as for example PMMA (poly-methyl-metacrylate).
  • polymeric materials such as for example PMMA (poly-methyl-metacrylate).
  • the pattern of the multilevel holographic mask of the second diffractive optical element 1 -2 is calculated by means of an algorithm of numerical calculation executed on a computer, which will be described in detail in the following.
  • the second diffractive optical element 1 -2 is an optical element operating only in phase, i.e. it is such to modify only the phase of the incident free space optical beam: in this way the diffraction efficiency of the second diffractive optical element 1 -2 is greater than the one with only the amplitude modulation, because the absorbance of the material composing the second diffractive optical element 1 -2 is negligible.
  • the transmission function ⁇ of the second diffractive optical element 1 -2 composed of N concentric annuli is represented in cylindrical coordinates (r, ⁇ ) by the following formula:
  • ⁇ is the transmission function of the i-th annulus designed to receive optical beams with i-th wavelength K;
  • n is the radius of the i-th annulus having a transmission function ( Figure 4 shows, for the sake of simplicity, three radii n , r2, r3 associated to the circular annuli A1 , A2, A3 respectively);
  • ⁇ is the Heaviside function thus defined
  • the product of the two Heaviside functions ® ⁇ ⁇ - ⁇ _ ⁇ ) ® ⁇ - ⁇ ) has the value 1 in the range r i _ ⁇ r ⁇ r i , while it has the value 0 for r values outside such interval.
  • the calculation of the phase values of the transmission function ⁇ of the i- th annulus is performedwith an iterative numerical algorithm executed assuming at the input the i-th wavelength . .
  • [ ⁇ ⁇ 1 ] which are in particular the Laguerre-Gauss modes identified by a pair of indices (p, I), wherein p is the radial index and / is the angular index.
  • the transmission function r in cylindrical coordinates (r, ⁇ ) of the diffractive optical element is the followin :
  • (p pl , & pl ) are the vectors of the parameters in polar coordinates; - ⁇ E pl ) are complex coefficients having module values correlated to the response of the diffractive optical element with respect to the channel corresponding to the OAM mode having radial index p and angular index /; the values of the phases of are free parameters which can be used as degrees of freedom in the process of optimisation of the pattern of the transmission function rof the diffractive optical element.
  • the minimisation algorithm for the calculation of the pattern of the transmission function r of the diffractive optical element is based on the following recursive procedure which employs the preceding equations (1 ) and (2) according to the following steps:
  • phase ⁇ is discretised into a finite number of levels M;
  • T pl 1
  • - 0 ⁇ ⁇ 2 is an adaptive or relaxation parameter which controls the convergence of the algorithm.
  • steps a)-d) are repeated assuming the output ⁇ Ejf' ⁇ of step d) as input coefficients to be used into step a) in the decomposition of the transmission function ⁇ of the diffractive optical element expressed as indicated in the equation
  • Steps a)-e) are repeated till the convergence of the algorithm, which can be controlled with different parameters, in particular by means of the following coefficient of error ⁇ :
  • the step of the minimisation algorithm wherein the discretization of the phase into M levels is carried out depends on the precision of the manufacturing process of the diffractive optical element.
  • phase ⁇ is discretised into a finite number of levels M>2.
  • a diffractive optical element in air constituted by a material with a refractive index ⁇ ( ⁇ ) which depends on the wavelength ⁇ .
  • the thickness dk of the k-th level of the diffractive optical element will be the following:
  • the optical beam Q at the output of the considered annulus of the second diffractive optical element 1 -2 is calculated by means of the Fourier transform of the product of the incident optical beam F(x,y) and of the transmission function rof the diffractive optical element defined by the equation (1 ).
  • the output optical beam Q is the following: g oc J dx dyF(x, y)r(x, y) exp -i (ux + vy)
  • ⁇ u, v) are the cartesian coordinates on the CCD screen 5;
  • the position on the CCD screen 5 of the different luminous spots associated to the different OAM modes can be controlled in advance by defining for each OAM mode having radial index p and angular index / the parameters
  • the lens 1 -3 (used for creating the luminous spots on the CCD screen 5) has a focal length / and it is positioned at a distance equal to the focal length both from the second diffractive optical element 1 -2 and from the CCD screen 5 (these positions are also denoted by "configuration f-f).
  • the radiation incident on the considered annulus of the second diffractive optical element 1 -2 is an OAM mode having a wavelength ⁇ and having a radial index p and an angular index /, thuse having parameters (ppi ⁇ pi ) (see equation(l ) ).
  • the luminous spot of said OAM mode will appear on the CCD screen 5 in the following position expressed ⁇ r ⁇ , q> pl ) in polar coordinates:
  • the position (u p i, v p i) of said OAM mode can be equivalent ⁇ expressed in Cartesian coordinates ( ⁇ 1 , ⁇ ⁇ 1 ) :
  • ⁇ ⁇ 1 , ⁇ ⁇ 1 are the parameters ( ⁇ ⁇ 1 , ⁇ ⁇ 1 ) expressed in cartesian coordinates.
  • the diameter of the luminous spots of the OAM modes is in the order of 50 ⁇ (micro metres).
  • the maximum value of the angular divergence OMAX which can be obtained for a determined OAM mode depends on the minimum dimension of the pixels which form the structure of the second diffractive optical element 1 -2.
  • the dimension L of the side of the pixels of the multi-level matrix of the second diffractive optical element 1 -2 is greater than at least about five times the wavelength, i.e. L > 5 ⁇ .
  • the value of the dimension L of the side of the pixels of the multilevel matrix of the second diffractive optical element 1 -2 is comprised between five times and ten times the value of the considered wavelength ⁇ , i.e. 5 ⁇ ⁇ _ ⁇ 10 ⁇ .
  • each annulus of the second diffractive optical element 1 -2 design the pattern of each annulus of the second diffractive optical element 1 -2 according to a predefined arrangement of the luminous spots corresponding to the different OAM modes with angular indices h, , or other degrees of freedom (for example the radial index
  • CWDM coarse wavelength division multiplexing systems
  • the dimension of the luminous spot on the CCD screen 5 is controlled by the dimension D of the incident optical beam F and the focal length / of the lens 1 - 3.
  • the value of the diameter d of the luminous spots can be further reduced by increasing the value of the dimension D of the incident optical beam and/or by reducing the value of the focal length f of the lens 1 -3 used for generating the image on the CCD screen 5.
  • the second diffractive optical element 1 -2 can be implemented with a matrix structure.
  • the axis of the Fresnel lens i.e. the axis which passes along the centre of the concentric annuli
  • the axis of the Fresnel lens is aligned to the axis of the plurality of concentric annuli of the second diffractive optical element 1 -2 along the axis of propagation z, i.e.
  • the centre of the Fresnel lens is positioned on the axis z and also the centre of the plurality of concentric annuli is positioned on the axis z; moreover, the concentric annuli of the Fresnel lens 1 -1 and the concentric annuli of the second diffractive optical element 1 -2 are orientated like the cartesian plane
  • the first diffractive optical element 1 -1 is implemented with an axicon, i.e. the axicon has an axis aligned to the axis of the second diffractive optical element 1 -2 along the propagation axis z; moreover, the flat surface of the axicon is orientated like the concentric annuli of the second diffractive optical element 1 -2, in the cartesian plane (x, y).
  • the second diffractive optical element 1 -2 can be implemented with an electronically controlled liquid crystal pixel matrix.
  • phase or amplitude variation imparted on the incident optical beam on the single pixel is proportional to the potential difference to which the layer of liquid crystals is subjected: this can be obtained with the spatial light modulators, which can be of the transmitting type or the reflecting type. It will be now described how to dimension the reciprocal distance between the first diffractive optical element 1 -1 and the second diffractive optical element 1 - 2, supposing the the first diffractive optical element 1 -1 is implemented with a Fresnel lens.
  • RA defines the radius (on said perpendicular plane) wherein there is the maximum value of luminous intensity with annular trend of the circular optical vortex (at the output of Fresnel lens 1 -1 and incident on 1 -2) as a function of the wavelength ⁇ .
  • Width Ar A also defines the difference between the values of the radii (on said perpendicular plane) RA,I e RA,2 wherein the luminous intensity of said circular optical vortex (at the output of the Fresnel lens 1 -1 and incident on 1 -2) is equal to a fraction of the maximum value of the luminous intensity (for example, half the maximum value of the luminous intensity).
  • the criterion for dimensioning the reciprocal distance d_z between the Fresnel lens 1 -1 and the second diffractive optical element 1 -2 is that the variation of the increase in the value of said radius RA is greater than said width Ar A , so as to avoid any overlapping between the OAM modes with different wavelength on the second diffractive optical element 1 -2.
  • said dimensioning criterion can be expressed by the following formula:
  • the second diffractive optical element 1 -2 can be alternatively an optical element operating only in amplitude, i.e. it is such to modify only the amplitude of the transverse component of the electric field Et (and magnetic Ht) of the incident free space optical beam, without modifying the phase term.
  • the demultiplexing optical device 1 is configured to further perform the polarization demultiplexing.
  • the multiplexed incident optical beam F_i_mux carries a plurality of channels having different values f , ... IM ⁇ of the angular index /, having different values ⁇ , A2 ... AN ⁇ of the wavelength A and having orthogonal polarization states.
  • reception of circular optical vortices for example in output from an optical fiber
  • they have dextrorotatory or laevorotatory circular polarization.
  • the demultiplexing optical device 1 further comprises a quarter-wave plate
  • the quarter-wave plate can be positioned both before the first diffractive optical element 1 -1 and after the second diffractive optical element 1 -2.
  • said quarter-wave plate is configured to receive at the input the plurality of demultiplexed output optical beams F_o_dmx, i.e. the free space optical beams FO1 .1 _SL, FO1 .2_SL, FO1 .3_SL, FO2.1_SL, FO2.2_SL, FO2.3_SL, FO3.1 _SL, FO3.2_SL, FO3.3_SL transmitted by the lens 1 -3; for each one of them, the quarter-wave plate is configured to generate an output optical beam which carries two channels having orthogonal linear polarizations.
  • the quarter-wave plate is configured to generate an output optical beam which carries two channels having orthogonal linear polarizations.
  • the quarter-wave plate receives the free space optical beam
  • FO1 .1 _SL which is the overlap of two beams having laevorotatory or dextrorotatory circular polarization and generates therefrom the free space optical beam FO1 .1 _o_SL having horizontal polarization and the free space optical beam FO1 .1 _v_SL having vertical polarization; therefore the free space optical beam FO1 .1 _o_SL has an angular index h, wavelength A i and horizontal polarization, while the free space optical beam FO1 .1 _v_SL has an angular index h, wavelength Ai and vertical polarization.
  • FIG. 2 shows a perspective view of an optical communication system 50 according to a first embodiment of the invention.
  • the optical communication system 50 comprises:
  • a multimode optical fiber 4 having an output facet coupled to the input of the demultiplexing optical device 1 ;
  • an photo-detector 5 which performs an optical-electrical conversion and which is coupled with the output of the demultiplexing optical device 1 .
  • the photo-detector 5 is for example a CCD screen.
  • the multiplexed optical beam F_i_mux incident on the demultiplexing optical device 1 (and thus incident on the first diffractive optical element 1 -1 ) is a guided multiplexed optical beam propagating over the optical fiber 4.
  • the guided multiplexed optical beam F_i_mux carries nine channels CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 having different wavelength ⁇ and different orbital angular momentum, then the nine channels CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 are demultiplexed by means of the demultiplexing optical device 1 as above explained, finally the nine demultiplexed channels are detected by means of the photo- detector 5.
  • the free space optical beam FO1 .1_SL (carrying the channel CH1 .1 having a wavelength ⁇ and angular index h) is incident to a point P1 .1 on the detecting surface of the optical-electrical sensor 5 generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S1 .1 is generated that is proportional to the intensity of the incident free space optical beam F01 .1_SL;
  • the free space optical beam FO1 .2_SL (carrying the channel CH1 .2 having a wavelength ⁇ and angular index ) is incident to a point P1 .2 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S1 .2 is generated that is proportional to the intensity of the incident free space optical beam FO1 .2_SL;
  • the free space optical beam FO1 .3_SL (carrying the channel CH1 .3 having a wavelength ⁇ and angular index ) is incident to a point P1 .3 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S1 .3 is generated that is proportional to the intensity of the incident free space optical beam FO1 .3_SL;
  • the free space optical beam FO2.1_SL (carrying the channel CH2.1 having a wavelength A ⁇ and angular index h) is incident to a point P2.1 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S2.1 is generated that is proportional to the intensity of the incident free space optical beam FO2.1_SL;
  • the free space optical beam FO2.2_SL (carrying the channel CH2.2 having a wavelength A ⁇ and angular index ) is incident to a point P2.2 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S2.2 is generated that is proportional to the intensity of the incident free space optical beam FO2.2_SL;
  • the free space optical beam FO2.3_SL (carrying the channel CH2.3 having a wavelength A2 and angular index ) is incident to a point P2.3 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S2.3 is generated that is proportional to the intensity of the incident free space optical beam FO2.3_SL;
  • the free space optical beam FO3.1_SL (carrying the channel CH3.1 having a wavelength A3 and angular index h) is incident to a point P3.1 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S3.1 is generated that is proportional to the intensity of the incident free space optical beam FO3.1_SL;
  • the free space optical beam FO3.2_SL (carrying the channel CH3.2 having a wavelength A3 and angular index ) is incident to a point P3.2 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S3.2 is generated that is proportional to the intensity of the incident free space optical beam FO3.2_SL;
  • the free space optical beam FO3.3_SL (carrying the channel CH3.3 having a wavelength A3 and angular index ) is incident to a point P3.3 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S3.3 is generated that is proportional to the intensity of the incident free space optical beam FO3.3_SL.
  • FIG. 5A shows a perspective view of an optical device 1 0 for multiplexing a plurality of channels with different wavelength and different orbital angular momentum.
  • the multiplexing optical device 1 0 comprises optical elements which can be miniaturised by means of micro and nano-manufacturing methods.
  • the multiplexing optical device 1 0 is an optical transmitter having the function of receiving a plurality of incident optical beams, each associated to a channel and having a wavelength A value; said plurality of incident optical beams is generated for example by a respective plurality of laser sources 1 5-1 , 1 5-2, as will be explained in greater detail in the following in the description of Figure 5B.
  • the demultiplexing optical device 1 0 has also the function of performing the multiplexing of the plurality of incident optical beams over a multiplexed output optical beam F_o_mux which carries a plurality of multiplexed channels having different values ⁇ , ⁇ ... AN ⁇ of the wavelength A and different values f , ... IM ⁇ of the angular index /, wherein the number of the plurality of incident optical beams on the multiplexing optical device 1 0 is equal to the number of the plurality of multiplexed channels.
  • the multiplexed output optical beam F_o_mux can be an optical beam which propagates in the free space; in this case the multiplexed channels are free space circular optical vortices having different wavelengths A and different orbital angular momentum values.
  • the multiplexed output optical beam F_o_mux can be coupled to the input facet of a multimode optical fiber and excites a plurality of guided OAM modes which propagate on the optical fiber, as will be explained in greater detail in the following in the description relating to Figure 6.
  • the first channel CH1_1 having a wavelength Ai and an angular index h;
  • the second channel CH1_2 having a wavelength Ai and an angular index
  • the third channel CH2_1 having a wavelength A2 and an angular index h
  • the fourth channel CH2_2 having a wavelength A2 and an angular index
  • the fifth channel CH3_1 having a wavelength A3 and an angular index h
  • the sixth channel CH3_2 having a wavelength A3 and angular index ;
  • the multiplexing optical device 10 comprises:
  • the six axicon 12-1, 12-2, 12-3, 12-4, 12-5, 12-6 have the function of transforming the six incident optical beams F1.1_i, F1.2_i, F2.1_i, F2.2_i, F3.1_i, F3.2_i of Gaussian type into six respective free space transmitted optical beams
  • F1.1_SL, F1.2_SL, F2.1_SL, F2.2_SL, F3.1_SL, F3.2_SL having wavefronts with annular trend of the luminous intensity on the plane perpendicular to the propagation direction.
  • the six convergent lenses 12-7, 12-8, 12-9, 12-10, 12-11, 12-12 have the function of collimating the six free space incident optical beams F1.1_SL, F1.2_SL, F2.1_SL, F2.2_SL, F3.1_SL, F3.2_SL into respective six free space collimated optical beams F1.1_CL, F1.2_CL, F2.1_CL, F2.2_CL, F3.1_CL, F3.2_CL, which have different propagation direction in the space which depends on the different values ⁇ Ai, A2, A3 ⁇ of the wavelength ⁇ and on the different values f , h ⁇ of the angular index.
  • the third diffractive optical element 11-1 has the function of transforming the six free space collimated optical beams F1.1_CL, F1.2_CL, F2.1_CL, F2.2_CL, F3.1_CL, F3.2_CL incident on it with a different spatial direction into respective six free space circular optical vortices (i.e. into six OAM modes) having angular indices fh, h ⁇ and wavelength fh, ⁇ , ⁇ , as a function of the different direction of incidence on the third diffractive optical element 1 1 -1 : in this way it is performed the multiplexing of the plurality of OAM modes having different angular indices fh, h ⁇ .
  • the third diffractive optical element 1 1 -1 has the function of imparting a determined value of the angular index / to the incident optical beams on it as a function of the direction of incidence in the space, thus generating the appropriate OAM modes.
  • the operation and implementation of the third diffractive optical element 1 1 - 1 are similar to those of the second diffractive optical element 1 -2 of the demultiplexing optical device 1 previously illustrated, with the difference that the third diffractive optical element 1 1 -1 is used in dual mode with respect to the second diffractive optical element 1 -2.
  • the third diffractive optical element 1 1 -1 comprises three zones An , A12, A13, each constituting a diffractive optical element suitably designed for a respective specific wavelength ⁇ , K ⁇ , and operating as an OAM mode multiplexer for said specific wavelength.
  • the three zones An , A12, A13 can be of the transmitting type or of the reflecting type.
  • Each zone An , A12, A13 is configured to receive two free space optical beams with a circular wavefront having the same wavelength ⁇ and having different directions in space and is configured to generate two free space circular optical vortices respectively having angular indices h and , as will be more fully explained in the following.
  • the three zones An , A12, A13 of the third diffractive optical element 1 1 -1 are three concentric annuli An , A12, A13 of the transmitting type or of the reflecting type.
  • Figure 5A shows six axicon, but more in general it is possible to use a plurality N x M of axicon that is greater than or equal to four, wherein N is the number of wavelengths and M is the number of OAM modes identified by M respective values of the angular indices h, h, ... IM.
  • N is the number of wavelengths
  • M is the number of OAM modes identified by M respective values of the angular indices h, h, ... IM.
  • three values ⁇ Ai, ⁇ , ⁇ have been considered of the carrier wavelength, but more in general it is possible to use a number N of carrier wavelengths greater than or equal to two.
  • the six axicon 12-1 , 12-2, 12-3, 12-4, 12-5, 12-6 are arranged into three groups associated to the three values ⁇ , ⁇ , ⁇ respectively of the wavelength A, i.e:
  • a first group of axicon is composed of the axicon 12-1 , 12-2 associated to the wavelength ⁇ ;
  • a second group of axicon is composed of the axicon 12-3, 12-4 associated to the wavelength ⁇ .
  • a third group of axicon is composed of the axicon 12-5, 12-6 associated to the wavelength A?.
  • each group comprises a number of axicon that is equal to the number of the different orbital angular momentum values (and thus of the angular index I) of the OAM modes to be generated.
  • each group comprises two axicon because the multiplexing optical device 10 is such to generate two OAM modes with two different values of the orbital angular momentum (and thus two different values h, k of the angular index I).
  • the set of the first axicon 12-1 and of the first lens 12-7 is configured to receive the incident optical beam F1 .1 i having wavelength ⁇ and to generate the free space collimated optical beam F1 .1_CL (indicated in Figure 5A with a broken- and-dotted line) having an annular trend of the luminous intensity and having a first propagation direction in the space which depends on the value of the wavelength ⁇ and on the value of the angular index h, so that the free space collimated optical beam F1 .1_CL is incident on a first annulus An of the third diffractive optical element 1 1 -1 .
  • the set of the second axicon 12-2 and of the second lens 12-8 is configured to receive the incident optical beam F1 .2_i having wavelength ⁇ and to generate the free space collimated optical beam F1 .2_CL (indicated in Figure 5A again with a broken-and-dotted line) having an annular trend of the luminous intensity and having a second propagation direction in space which depends on the value of the wavelength ⁇ and on the value of the angular index , so that the free space collimated optical beam F1 .2_SL is incident on the first annulus An of the third diffractive optical element 1 1 -1 ;
  • the set of the third axicon 12-3 and of the third lens 12-9 is configured to receive the incident optical beam F2.1_i having wavelength A2 and to generate the free space collimated optical beam F2.1_CL (indicated in Figure 5A with a broken line) having an annular trend of the luminous intensity and having a third propagation direction in space which depends on the value of the wavelength A2 and on the value of the angular index h, so that the free space collimated optical beam F2.1_CL is incident on a second annulus A12 of the third diffractive optical element 1 1 -1 ;
  • the set of the fourth axicon 12-4 and of the fourth lens 12-10 is configured to receive the incident optical beam F2.2_i having wavelength A2 and to generate the free space collimated optical beam F2.2_CL (indicated in Figure 5A again with a broken line) having an annular trend of the luminous intensity and having a fourth propagation direction in space which depends on the value of the wavelength A2 and on the value of the angular index , so that the free space collimated optical beam F2.2_CL is incident on a second annulus A12 of the third diffractive optical element 1 1 -1 ;
  • the set of the fifth axicon 12-5 and of the fifth lens 12-1 1 is configured to receive the incident optical beam F3.1_i having wavelength A3 and to generate the free space collimated optical beam F3.1_CL (indicated in Figure 5A with a continuous line) having an annular trend of the luminous intensity and having a fifth propagation direction in space which depends on the value of the wavelength A3 and on the value of the angular index h, so that the free space collimated optical beam F3.1_CL is incident on a third annulus A13 of the third diffractive optical element 1 1 -1 ;
  • the set of the sixth axicon 12-6 and of the sixth lens 12-12 is configured to receive the incident optical beam F3.2_i having wavelength A3 and to generate the free space collimated optical beam F3.2_CL (indicated in Figure 5A again with a continuous line) having an annular trend of the luminous intensity and having a sixth propagation direction in space which depends on the value of the wavelength A3 and on the value of the angular index , so that the free space collimated optical beam F3.1_CL is incident on a third annulus A13 of the third diffractive optical element 1 1 -1 .
  • the third diffractive optical element 1 1 -1 comprises;
  • the first most internal annulus An that is such to receive the free space collimated optical beams F1 .1_CL, F1 .2_CL having the same first wavelength ⁇ and two different incident propagation directions;
  • the second intermediate annulus A12 comprised between the first internal annulus An and the third external annulus A13, wherein the second annulus A12 is configured to receive the free space collimated optical beams F2.1_CL, F2.2_CL having the same second wavelength K2 and having two different incidence propagation directions.
  • Each of the three annuli An , A12, A13 of the third diffractive optical element 1 1 -1 is a transmitting diffractive optical element suitably designed for a respective specific wavelength ⁇ - ⁇ , ⁇ 2, ⁇ 3 and operating as an OAM mode multiplexer for said specific wavelength.
  • the first annulus An is configured to receive the two free space collimated optical beams F1 .1_CL, F1 .2_CL having the same first wavelength ⁇ and having two different directions of incidence in the space, and is configured to generate:
  • the second annulus A12 is configured to receive the two free space collimated optical beams F2.1_CL, F2.2_CL having the same second wavelength ⁇ 2 and having two different directions of incidence in the space, and is configured to generate: • a multiplexed free space circular optical vortex F2.1 _MUX_SL (denoted in Figure 5A with a broken line) having a wavelength K2 and an angular index h associated to the first of the two directions of incidence;
  • the third annulus A13 is configured toreceive the two free space collimated optical beams F3.1 _CL, F3.2_CL having the same third wavelength A3 and having two different directions of incidence in the space, and is configured to generate:
  • FIG. 5B shows a top view of a multiplexing optical device 1 0.
  • the six axicon 1 2-1 , 1 2-2, 1 2-3, 1 2-4, 1 2-5, 1 2-6 and the respective six lenses 1 2-7, 1 2-8, 1 2-9, 1 2-1 0, 1 2-1 1 , 1 2-1 2 are arranged radially around the third diffractive optical element 1 1 -1 along a circumference C concentric thereto (indicated by a broken line).
  • Figure 5B further shows six laser sources 1 5-1 , 1 5-2, 1 5-3, 1 5-4, 1 5-5, 15- 6, wherein:
  • the first laser source 1 5-1 is such to generate the Gaussian optical beam F1 .1 _i (Ai ) incident on the first axicon 1 2-1 and having a wavelength Ai ;
  • the second laser source 1 5-2 is such to generate the Gaussian optical beam F1 .2_i (Ai ) incident on the second axicon 1 2-2 and having a wavelength Ai ;
  • the third laser source 1 5-3 is such to generate the Gaussian optical beam F2.1 _i (A2) incident on the third axicon 1 2-3 and having a wavelength A2;
  • the fourth laser source 15-4 is such to generate the Gaussian optical beam F2.2_i (A2) incident on the fourth axicon 12-4 and having a wavelength A2;
  • the fifth laser source 15-5 is such to generate the Gaussian optical beam F3.1_i ( ⁇ ) incident on the fifth axicon 12-5 and having a wavelength ⁇ 3;
  • the sixth laser source 15-6 is such to generate the Gaussian optical beam F3.2_i ( ⁇ ) incident on the sixth axicon 12-6 and having a wavelength ⁇ 3.
  • the laser sources 15-1, 15-2, 15-3, 15-4, 15-5, 15-6 are coupled respectively with the axicon 12-1, 12-2, 12-3, 12-4, 12-5, 12-6 by means of respective segments of optical fiber or portions of photonic guide 17-1, 17-2, 17-3, 17-4, 17-5, 17-6.
  • the multiplexing optical device 10 comprises a plurality M x N of axicon (and respective lenses) arranged radially around the third diffractive optical element 11- 1 along the circumference C concentric thereto.
  • Figure 5C shows a section view of a multiplexing optical device 10 along the line A-A of Figure 5B.
  • the laser source 15-4 coupled to the axicon 12-4 by means of a segment of optical fiber 17-4 and a converging lens 16-4;
  • the laser source 15-1 coupled to the axicon 12-1 by means of a segment of optical fiber 17-1 and a converging lens 16-1 ;
  • the multiplexing optical device 10 further comprises a polariser, in case wherein the light sources generate non-polarized light.
  • the multiplexing optical device 10 further comprises a quarter-wave plate 18 having the function of circularly polarizing the incident optical beam.
  • the quarter-wave plate 18 is interposed between the laser sources 15-1,
  • the quarter-wave plate 18 is configured to receive at the input two optical beams having orthogonal linear polarizations and to generate therefrom an optical beam having a right or left circular polarization: in this way the coupling with the optical fiber 4 is optimised, as the guided OAM modes have a circular polarization.
  • the quarter-wave plate 18 is configured to receive the Gaussian optical beam F1.1_i ( ⁇ - ⁇ ) having linear polarization and is configured to generate a Gaussian optical beam F1 .1 _c(Ai) having circular polarization, which is incident on the first axicon 12-1 .
  • the preceding considerations relating to the Gaussian optical beam F1 .1 _i(Ai) are applicable in a similar way to the other Gaussian optical beams F1 .2_i (Ai), F2.1 _i (A 2 ), F2.2_i (A 2 ), F3.1 _i (A 3 ), F3.2_i (A 3 ), and thus the Gaussian optical beams F1 .2_c (Ai), F2.1 _c (A2), F2.2_c (A2), F3.1 _c (A3), F3.2_c (A3) are generated having circular polarization, which are incident on the axicon 1 2-2, 1 2-3, 12-4, 1 2-5, 1 2-6 respectively.
  • FIG. 6 shows an optical communication system 60 according to a second embodiment of the invention.
  • the optical communication system 60 comprises:
  • a multimode optical fiber 4 having an input facet
  • a converging lens 61 for regulating the dimension of the incident optical beam on the input facet of the optical fiber 4.
  • the optical beam F_o_mux at the output of the multiplexing optical device 1 0 is coupled to the optical fiber 4 by means of the converging lens 61 which generates a collimated output optical beam F_o_cm, then three guided modes having three wavelengths Ai , A2, A3, are excited in the optical fiber 4, wherein each guided mode carries two guided circular optical vortices (i.e. two guided OAM modes) having two different values h, of the angular index /; therefore a guided multiplexed optical beam Fg is propagated over the optical fiber 4 which in total carries six channels CH1 _1
  • FIG. 7 shows an optical communication system 70 according to a third embodiment of the invention.
  • the optical communication system 70 comprises:
  • a multimode optical fiber 4 having an input facet coupled to the output of the multiplexing optical device 20 and having an output facet coupled with the input of the demultiplexing optical device 1 ; the photo-detector 5 which performs an optical-electrical conversion and which is coupled with the output of the demultiplexing optical device 1 .
  • the laser sources 15-1 , 15-2, 15-3 are such to generate a Gaussian optical beam having wavelength ⁇ - ⁇ .
  • the laser sources 15-4, 15-5, 15-6 are such to generate a Gaussian optical beam having wavelength ⁇ 2.
  • the laser sources 15-7, 15-8, 15-9 are such to generate a Gaussian optical beam having wavelength ⁇ 3.
  • the multiplexing optical device 20 is implemented in a way similar to the multiplexing optical device 10 previously described, with the difference that the multiplexing optical device 20 is such to generate three OAM modes having three different values h, , of the angular index /; therefore the multiplexed output optical beam F_o_mux carries nine channels having three different values ⁇ , A ⁇ , A3 of the wavelength A and three different values h, , h of the angular index /.
  • optical communication system 70 It will be described hereinafter the operation of the optical communication system 70, making also reference to Figures 1 A, 1 B, 5A and 7.
  • the laser source 15-1 At the initial instant to the laser source 15-1 generates a first Gaussian optical beam F1 .1 i ( ⁇ - ⁇ ) having a wavelength ⁇ - ⁇ , the laser source 15-2 generates a second Gaussian optical beam F1 .2_i ( ⁇ - ⁇ ) having a wavelength ⁇ , the laser source 15-3 generates a third Gaussian optical beam F1 .3_i ( ⁇ - ⁇ ) having a wavelength ⁇ , the laser source 15-4 generates a fourth Gaussian optical beam F2.1_i ( ⁇ 2) having a wavelength ⁇ 2, the laser source 15-5 generates a fifth Gaussian optical beam F2.2_i (ta) having a wavelength ⁇ 2, the laser source 15-6 generates a sixth Gaussian optical beam F2.3_i (ta) having a wavelength K ⁇ , the laser source 15-7 generates a seventh Gaussian optical beam F3.1_i ( ⁇ ) having a wavelength ⁇ 3, the laser source 15-8 generates an eighth Gaussian optical beam F3.2_i ( ⁇ 3) having
  • the multiplexing optical device 20 receives the first Gaussian optical beam F 1 .1 i ( ⁇ ), the second Gaussian optical beam F1 .2_i ( ⁇ ), the third Gaussian optical beam F1 .3_i ( ⁇ ), the fourth Gaussian optical beam F2.1_i (ta), the fifth Gaussian optical beam F2.2_i (ta), the sixth Gaussian optical beam F2.3_i (ta), the seventh Gaussian optical beam F3.1_i ( ⁇ ), the eighth Gaussian optical beam F3.2_i ( ⁇ 3), the ninth Gaussian optical beam F3.3_i ( ⁇ ), then the multiplexing optical device 20 generates therefrom the multiplexed optical beam F_o_mux carrying nine channels CH1_1 , CH1_2, CH1_3, CH2_1 , CH2_2, CH2_3, CH3_1 , CH3_2, CH3_3 in way similar to what was described previously relatively to the description of the multiplexing optical device 10 of Figure 5A, wherein:
  • the first channel CH1_1 has a wavelength A i and an angular index h;
  • the second channel CH1_2 has a wavelength Ai and an angular index ;
  • the third channel CH1_3 has a wavelength A i and an angular index ;
  • the fourth channel CH2_1 has a wavelength ⁇ and an angular index h;
  • the fifth channel CH2_2 has a wavelength ⁇ and an angular index ;
  • the sixth channel CH2_3 has a wavelength A2 and an angular index ;
  • the seventh channel CH3_1 has a wavelength A3 and an angular index h;
  • the eighth channel CH3_2 has a wavelength A3 and angular index ;
  • the ninth channel CH3_3 has a wavelength A3 and an angular index .
  • the multiplexed optical beam F_o_mux enters the multimode optical fiber 4 and excites a guided multiplexed optical beam Fg carrying three channels having three different values ⁇ , ⁇ , A3 of the wavelength A, wherein each channel carries three guided OAM modes having three values h, , h of the angular index /, thus obtaining the following nine channels carried over the optical fiber 4:
  • the first channel CH1_1_g has a wavelength Ai and an angular index h;
  • the second channel CH1_2_g has a wavelength A i and an angular index
  • the third channel CH1_3_g has a wavelength Ai and an angular index
  • the fourth channel CH2_1_g has a wavelength A2 and an angular index h;
  • the fifth channel CH2_2_g has a wavelength A2 and an angular index ;
  • the sixth channel CH2_3_g has a wavelength A2 and an angular index ;
  • the seventh channel CH3_1_g has a wavelength A3 and an angular index h; the eighth channel CH3_2_g has a wavelength A3 and an angular index ; the ninth channel CH3_3_g has a wavelength A3 and an angular index .
  • the guided multiplexed optical beam Fg propagates from the input facet to the output facet of the optical fiber 4, wherein the multiplexed incident optical beam is indicated with F_i_mux.
  • the demultiplexing optical device 1 receives the multiplexed incident optical beam F_i_mux carrying the nine channels CH1 .1 , CH1 .2, CH1 .3, CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3, which correspond to the nine channels CH1_1_g, CH1_2_g, CH1_3_g, CH2_1_g, CH2_2_g, CH2_3_g, CH3_1_g, CH3_2_g, CH3_3_g respectively.
  • the demultiplexing optical device 1 performs the demultiplexing of the nine channels CH1 .1 , CH1 .2, CH1 .3, CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 in the way as explained previously relatively to the description of the demultiplexing optical device 1 of Figure 1 B.
  • the demultiplexing optical device 1 the demultiplexing optical device 1 :
  • the photo-detector 5 receives the nine free space circular optical vortices F01 .1_SL, FO2.1_SL, FO3.1_SL, FO1 .2_SL, FO2.2_SL, FO3.2_SL, FO1 .3_SL, FO2.3_SL, FO3.3_SL in nine different points P1 .1 , P2.1 , P3.1 , P1 .2, P2.2, P3.2, P1 .3, P2.3, P3.3 respectively which are far- field spots, as explained previously relatively to the description of Figure 2.
  • the photo-detector 5 performs the optical-electrical conversion and generates nine electrical signals S1 .1 , S1 .2, S1 .3, S2.1 , S2.2, S2.3, S3.1 , S3.2, S3.3, wherein: the first electrical signal S1 .1 carries channel CH1 .1 ;
  • the second electrical signal S1 .2 carries channel CH1 .2;
  • the third electrical signal S1 .3 carries channel CH1 .3;
  • the fourth electrical signal S2.1 carries channel CH2.1 ;
  • the sixth electrical signal S2.3 carries channel CH2.3;
  • the seventh electrical signal S3.1 carries channel CH3.1 ;
  • the eighth electrical signal S3.2 carries channel CH3.2;
  • the ninth electrical signal S3.3 carries channel CH3.3.
  • the communication system 70 has performed the multiplexing of nine channels having three different values of the wavelength A and three different values of the angular index /, performed the carry of nine channels over the multimode optical fiber 4, performed the demultiplexing of the nine channels having three different values of the wavelength A and three different values of the angular index / and lastly performed the reception of the optical signals and its conversion into electronic signals.
  • the second diffractive optical element 1 -2 and the third diffractive optical element 1 1 -1 constitute an independent invention.
  • the second diffractive optical element 1 -2 solves the technical problem of generating a relation between:
  • the second diffractive optical element 1 -2 comprising a plurality of zones ⁇ , A2, A3 equal to a plurality of different values ⁇ , ⁇ , ⁇ of the wavelength A, wherein each zone of the second diffractive optical element 1 -2 is configured to:
  • ⁇ generate at the output, as a function of the first free space circular optical vortex, a plurality of second free space circular optical vortices over different output directions in the space which depend on the plurality of different values of the orbital angular momentum, wherein each of the second free space circular vortices carries a same value of the wavelength and a different value of the orbital angular momentum.
  • the third diffractive optical element 1 1 -1 solves the technical problem of generating a relation between:
  • the third diffractive optical element 1 1 - 1 comprising a plurality of zones An , A12, A13 equal to the plurality of different values ⁇ , ⁇ 2, A? of the wavelength A, wherein each zone of the third diffractive optical element 1 1 -1 is configured to:

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Abstract

It is disclosed an optical device (1) for demultiplexing a plurality of channels with different wavelength (λ1, λ2, λ3) and different orbital angular momentum (I1, I2, I3). The device comprises a first diffractive optical element (1 -1 ) for performing a wavelength division demultiplexing and a second diffractive optical element (1 -2) for performing a mode demultiplexing. The first diffractive optical element (1 -1) is configured to receive a multiplexed incident optical beam (F_i_mux) carrying the plurality of channels having a plurality of different values of the wavelength (λ1, λ2, λ3) and a plurality of different values of the orbital angular momentum (I1, I2, I3), and is configured to generate at the output, as a function of the multiplexed incident optical beam (F_i_mux), a plurality of first free space circular optical vortices (FO1_SL, FO2_SL, FO3_SL) having respective wavefronts with different radii of curvature which depend on the plurality of different values of the wavelength, wherein each of the first free space circular optical vortices carries said plurality of different values of the orbital angular momentum. The second diffractive optical element (1 -2) comprises a plurality of zones (Α1, A2, A3) equal to the plurality of different values (λ1, λ2, λ3) of the wavelength. Each zone is configured to receive at the input a respective first free space circular optical vortex (FO1_SL) carrying said plurality of different values of the orbital angular momentum, and is configured to generate at the output, as a function of the respective first free space circular optical vortex (FO1_SL), a plurality of second free space circular optical vortices (FO1.1_SL, FO1.2_SL, FO1.3_SL) oriented in different directions in the space which depend on the plurality of different values of the orbital angular momentum, wherein the plurality of the second free space circular optical vortices generated by the respective zone carries a same value of the wavelength and a different value of the orbital angular momentum.

Description

Optical device for demultiplexing and multiplexing a plurality of channels with different wavelength and different orbital angular momentum and optical communication system thereof
DESCRIPTION TECHNICAL FIELD OF THE INVENTION
The present invention generally relates to the field of optical communications.
More in particular, the present invention concerns an optical device for demultiplexing and multiplexing a plurality of channels with different wavelength and different orbital angular momentum.
PRIOR ART
The capability of carrying data in optical fibers has increased over recent decades by means of the use of Wavelength Division Multiplexing (WDM) and
Polarization Division Multiplexing (PDM) methods; this however is not sufficient to satisfy the significant increase in quantity of data requested.
Therefore Efforts have been made to further increase the capability of carrying data by means of the use of Mode Division Multiplexing (MDM) method, according to which it is possible to carry over the optical fiber a plurality of spatial modes which are orthogonal each another.
Among the spatial modes which can be carried over a multimode optical fiber, modes have been considered with orbital angular momentum, known also as OAM modes (OAM): in this case it is referred as OAM type mode multiplexing
(abbreviated as MDM-OAM).
The total angular momentum of a photon can be considered as the sum of an orbital angular momentum (OAM) and a spin angular momentum (SAM), wherein the latter assumes only two values s= ±1 .
The spin angular momentum (commonly referred simply as "spin") indicates the state of polarization of a photons beam.
OAM modes can propagate both in the free space and over an optical fiber: in the latter case, in the following the term "guided OAM modes" will be used to indicate propagation over the optical fiber, in order to distinguish them from the OAM modes propagating in the free space. Guided OAM modes are a linear combination of even and odd type HE vectorial modes which propagate over a multimode optical fiber or are a linear combination of even and odd type EH vectorial modes.
More in particular, guided OAM modes are characterised in that they have a transverse spatial component of the electric field Et (and magnetic field Ht) with uniform polarization state of a circular type (right or left) and in that the surface of the wavefront of the transverse spatial component of the electric field Et (and magnetic field Ht) has a helical trend, dextrorotatory (i.e. the direction of the screw is clockwise) or laevorotatory (i.e. the direction of the screw is anticlockwise): for this reason the guided OAM modes are commonly denoted also as "circular optical vortices" or "helical modes".
The pitch of the screw (of the surface of the wavefront of the transverse spatial component of the electric field Et and magnetic field Ht) is the minimum distance between two distinct points of the screw having the same coordinates in the plane (x, y) perpendicular to the propagation direction z (i.e. the pitch of the screw is equal to the wavelength λ).
Guided OAM modes are identified by the following parameters:
a radial index "p" having integer values greater than zero (p= 1 , 2, 3, . . .), which defines the trend of the amplitude of the transverse spatial component of the electric field Et (and magnetic field Ht) as the radial distance changes from the propagation axis z of the guided OAM modes, which coincides with the axis of the optical fiber (therefore the amplitude of the electric field Et has (p-1 ) radial nodes);
an angular index "f (commonly also indicated with "topological charge") having integer values (/= 0, ±1 , ±2, ±3, . . .), wherein for />1 the wavefront is constituted by / interlaced screws;
the direction of the screw, which can be dextrorotatory or laevorotatory, according to the positive or negative value of the angular index /;
the type of circular polarization, i.e. right (dextrorotatory) or left (laevorotatory). The luminous intensity of the guided OAM modes (i.e. of the circular optical vortices) on a plane perpendicular to the propagation direction (commonly known as a "luminous spot") has a substantially circular shape and is distributed into p concentric rings (wherein p is the radial index), for / greater than or equal to 1 . In particular, the luminous intensity is null on the propagation axis of the considered OAM mode, at a locus of singular points wherein the phase is not defined.
Guided OAM modes are a plurality of spatial modes that are orthogonal each another, i.e. they are carried independently in case wherein they are propagated over an optical fiber which maintains the circular symmetry and which is not subject to external perturbations: in this hypothesis the exchange of energy between different modes carried over the multimode optical fiber is theoretically null; in a case of propagation in vacuum, the condition of orthogonality of the OAM modes is always satisfied.
In real conditions, if the circular symmetry of the optical fiber is not maintained due to deformations, lack of homogeneity in the material of the optical fiber and/or external perturbations, a non negligible exchange of energy can occur between the different guided OAM modes propagating over the optical fiber, with the consequence that the quality of the received information is deteriorated.
In the field of telecommunications, Wavelength Division Multiplexing (WDM) systems are subdivided into DWDM (Dense WDM) and CWDM (Coarse WDM), according to the separation (i.e. distance) between the carrier wavelengths of the channels.
The conventional DWDM systems provide up to 40 channels in the third transmission window (band C) of the silicon fibers, centred on the value of the wavelength equal to 1550 nm, with a separation between the channels equal to 100 GHz (i.e. 0.7 nm in wavelength).
Today it is possible to reduce the separation between the carrier wavelengths and use the same transmission window in band C, reaching to 80/96 channels separated by intervals of 50 GHz.
Lastly it is possible to further reduce the separation between the carrier wavelengths and use the same transmission window in band C, reaching to 160 channels separated by intervals of 25 GHz: these system are known as "ultra- dense" WDM.
In CWDM systems the separation between the used carrier wavelengths is greater than those used in the conventional DWDM systems, so as to be able to use less sophisticated and theus less expensive optical components. In particular, a conventional CWDM system provides 8 channels separated by at least 20 nm starting from the upper limit of 1610 nm. It is also possible to have a CWDM system that provides up to 16 channels on an optical fiber entirely using the frequency band comprised between the second and the third transmission window (1310/1550 nm respectively) wherein, apart from the two windows (the minimum dispersion window and the minimum attenuation window) the critical area is also comprised wherein it can occur the attenuation of the signal owing to absorbance due to the presence of impurities constituted by hydroxyl ions OH".
The two systems DWDM/CWDM can be integrated, with the possibility of expanding the total band with the addition of a plurality of DWDM channels densely distributed on the carriers of the CWDM system.
Patent US 7546037 discloses a system for creating a light beam with multiplexing of OAM modes for use in optical communication of data.
US 7546037 further discloses that the system can be used in combination with the Wavelength Division Multiplexing method, but it does not describe in detail which optical devices to use for performing a multiplexing of wavelength and also of OAM modes.
Patent EP 1617235 describes the use of a Fresnel lens 30 (indicated by "Fresnel zone plate") which focuses the incident light into a focus situated at a distance ZL (with respect to the Fresnel lens) which depends on the wavelength of the incident light.
Article "Manipulation of orbital angular momentum beams based on space diffraction compensation", authors Hailong Zhou et al., Vol. 22, num.15, Optics Express 17756-17761 , published on July 14th 2014, discloses a device for manipulating three OAM modes (with an angular index /= 1 , 4, 8) which uses a phase mask (see Fig.4a), which comprises three circular annuli, each one designed for processing a respective OAM mode. In particular, the most internal annulus processes the OAM mode having angular index /=1 , the intermediate annulus processes the OAM mode having angular index /= 4 and the most external annulus processes the OAM mode having angular index /= 8.
Article "Experimental excitation and detection of angular harmonics in a step-index optical fiber", authors S.V.Karpeev and S.N.Khonina, Optical memory and neural networks (information optics), vol.16, no.4, 2007, discloses an experiment of excitation of angular harmonics and their overlap over an optical fiber of the few-mode step-index type in order to perform a MDM mode division multiplexing. The article further discloses the use of a multilevel diffractive optical element (DOE) for performing mode division multiplexing (see Fig.2) and discloses the use of a diffractive optical element of binary type for performing the mode division demultiplexing (see paragraph 2 "Methods" describing two OAM modes with angular index 1 and -2 and corresponding Fig.1 ).
WO 2015/024595-A1 discloses an optical switch 10, 30 which uses multiplexing and demultiplexing for carrying out the switching function.
Document Mihailescu M. et al., "Diffraction patterns from holographic masks generated using combined axicon and helical phase distributions", Proceedings of SPIE, SPIE - International Society for optical Engineering, US, vol. 9258, February 20th 2015, from page 92580T-1 to page 92580T-7, discloses diffraction diagrams from holographic masks generated using a combination of axicon and helical phase distributions.
Methods are known which allow to perform only a multiplexing/demultiplexing of a plurality of channels with different wavelength and all having a null orbital angular momentum; alternatively, the known methods allow to perform only a multiplexing/demultiplexing of a plurality of channels with a different orbital angular momentum (i.e. a multiplexing/demultiplexing of various OAM modes) and all having the same wavelength.
Complex laboratory optical configurations are known which are constituted by groups of optical elements assembled on a table which allows to perform at the same time a multiplexing/demultiplexing of a plurality of channels with different wavelength and different orbital angular momentum, using optical elements which can't be integrated.
The Applicant has observed that the known methods do not allow to perform a multiplexing/demultiplexing of a plurality of channels with different wavelength and at the same time a multiplexing/demultiplexing of a plurality of channels with different orbital angular momentum (and, preferably, also a polarization division multiplexing) using optical elements that can be integrated into photonic devices with a large scale reproducibility and with sufficient reliability.
SUMMARY OF THE INVENTION
The present invention relates to a demultiplexing optical device and a multiplexing optical device of a plurality of channels with different wavelength and different orbital angular momentum value as defined in the enclosed claims 1 and 9 respectively and by their preferred embodiments described in the dependent claims from 2 to 8 and from 10 to 12 respectively.
The Applicant has perceived that the demultiplexing optical device and the multiplexing optical device according to the present invention allow to maintain the capability to perform the multiplexing/demultiplexing of a plurality of channels with different wavelength and allow at the same time to further perform the multiplexing/demultiplexing of a plurality of channels with different orbital angular momentum: in this way the quantity of data that can be carried in air or over an optical fiber is significantly increased.
Moreover, the demultiplexing optical device and the multiplexing optical device according to the present invention have the following further advantages: they can be integrated into a photonic device (PIC = photonic integrated component);
they can be reproduced on a large scale with sufficient reliability;
- they have a high degree of optical efficiency, i.e. the dispersion of the luminous intensity between the optical beam entering and exiting from the demultiplexing/multiplexing optical device is reduced;
they can be effectively used for reception of the signal carried over an optical fiber and for injecting a signal into the optical fiber and carrying it thereon.
It is also an object of the present invention an optical communication system as defined in the enclosed claim 13 and by its preferred embodiment described in the dependent claim 14.
BRIEF DESCRIPTION OF THE DRAWINGS
Further features and advantages of the invention will become more apparent from the following description of a preferred embodiment and the variants thereof, provided by way of example with reference to the enclosed drawings, wherein:
Figure 1 A schematically shows a perspective view of the optical device for demultiplexing a plurality of channels with different wavelength and different orbital angular momentum according to an embodiment of the invention;
Figure 1 B is a more detailed view of the demultiplexing optical device of Figure 1 A;
Figure 2 schematically shows a perspective view of an optical communication system according to a first embodiment of the invention; Figure 3 shows more in detail a top and cross-section view of a first diffractive optical element used into the demultiplexing optical device;
Figure 4 shows more in detail a top view of a second diffractive optical element used into the demultiplexing optical device;
- Figures 5A-5C schematically show a perspective, top and cross-section view f of an optical device for multiplexing a plurality of channels with different wavelength and different orbital angular momentum according to an embodiment of the invention;
Figure 6 shows a block diagram of an optical communication system according to a second embodiment of the invention;
Figure 7 shows a block diagram of an optical communication system according to a third embodiment of the invention;
DETAILED DESCRIPTION OF THE INVENTION
It should be observed that in the following description, identical or analogous blocks, components or modules are indicated in the figures with the same numerical references even if they are shown in different embodiments of the invention.
With reference to Figure 1 , it shows a perspective view of the demultiplexing optical device 1 according to an embodiment of the invention.
The demultiplexing optical device 1 comprises optical elements which can be miniaturised by means of micro and nano-manufacturing methods.
The demultiplexing optical device 1 is an optical receiver having the function of receiving a multiplexed incident optical beam F_i_mux carrying a plurality of channels having different values {Ai, A∑ . . . AN} of the wavelength A and different values {U, ... IM} of the angular index / and of performing the demultiplexing of the plurality of channels as a function of the values of the wavelength A and of the values of the angular index /, generating a plurality of demultiplexed output optical beams F_o_dmx having values (λι, h), {A2, )... {AN, I1); (λι, h), {λ2, h)... {AN, h); ... (λι, IM), {A2, IM)... {AN, IM) of the wavelength A and of the angular index /.
The multiplexed incident optical beam F_i_mux at the input of the demultiplexing optical device 1 can be an optical beam propagating in the free space; in this case the channels are free space circular optical vortices having different wavelengths A and different orbital angular momentum. Alternatively, the multiplexed incident optical beam F_i_mux can be an optical beam propagating over a multimode optical fiber; in this case the channels are circular optical vortices guided over the optical fiber and having different wavelengths λ and different orbital angular momentum.
The plurality of channels having different wavelength λ and different orbital angular momentum will be indicated in the following with CHi.l, wherein:
i= 1 , 2,... N is a positive integer number representing the index identifying the value of the wavelength λ of the considered channel, i.e. i=1 identifies the wavelength λι, i=2 identifies the wavelength λ2, etc.;
I= 0, 1 , 2, ... K is a positive integer number representing the value of the angular index / identifying the orbital angular momentum of the considered channel, i.e. 1=1 identifies the OAM mode with angular index Ιι=λ , l=2 identifies the OAM mode with angular index 12= 2, etc.
With reference to Figure 1 B, for the purposes of the explanation of the invention, for the sake of simplicity nine channels are considered having three different values λι, λ∑, A? of the wavelength and having three different values , , of the angular index, thus the nine channels will be indicated in the following by CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3.
In particular:
channel CH1 .1 is a circular optical vortex (guided or in free space) having a wavelength / and an angular index h;
channel CH1 .2 is a circular optical vortex (guided or in free space) having a wavelength / and an angular index ;
channel CH1 .3 is a circular optical vortex (guided or in free space) having a wavelength / and an angular index ;
channel CH2.1 is a circular optical vortex (guided or in free space) having a wavelength ,½and an angular index h;
channel CH2.2 is a circular optical vortex (guided or in free space) having a wavelength ,½and an angular index ;
channel CH2.3 is a circular optical vortex (guided or in free space) having a wavelength ,½and an angular index ;
channel CH3.1 is a circular optical vortex (guided or in free space) having a wavelength A? and an angular index h; channel CH3.2 is a circular optical vortex (guided or in free space) having a wavelength A? and an angular index ;
channel CH3.3 is a circular optical vortex (guided or in free space) having a wavelength A? and an angular index .
The demultiplexing optical device 1 comprises:
a first diffractive optical element 1 -1 ;
a second diffractive optical element 1 -2;
a lens 1 -3;
Note that for the purposes of the explanation of the invention, in the following the lens 1 -3 is considered to be separated from the second diffractive optical element 1 -2, but it is also possible to integrate the lens 1 -3 within the second diffractive optical element 1 -2. In other words, it is possible to design a single diffractive optical element (denoted schematically by 1 -4 in figure 1 A) performing the functionality of the second diffractive optical element 1 -2 and the functionality of the lens 1 -3.
Let's consider that the demultiplexing optical device 1 is positioned in a space defined by a cartesian reference system (x, y, z), wherein the axis z corresponds to the propagation direction of the optical beams and thus it represents the axis of the demultiplexing optical device 1 , while the plane (x, y) is perpendicular to the axis z (and thus it is perpendicular to the axis of the demultiplexing optical device 1 ).
The first diffractive optical element 1 -1 is a passive optical element having the function of carrying out the demultiplexing of the wavelength λι, λ∑, λβ, while at the same time maintaining the circular symmetry of the multiplexed incident optical beam F_i_mux at the input of the first diffractive optical element 1 -1 , so as to maintain the content of the angular indices h, , o the OAM modes carried over the multiplexed incident optical beam F_i_mux.
The second diffractive optical element 1 -2 is also a passive optical element.
The lens 1 -3 is of the converging type and it has a focal length .
The set of the second diffractive optical element 1 -2 and of the lens 1 -3 have the function of performing the demultiplexing of the OAM modes having an angular index h, , , i.e. of spatially separating the free space optical beam incident on the second diffractive optical element 1 -2 into a plurality of collimated luminous spots associated to the plurality of different OAM modes. More in particular, the converging lens 1 -3 has the function of transforming the optical beam of the near-field type at the output of the second diffractive optical element 1 -2 into a collimated optical beam of the far-field type, so as to generate at the output a plurality of collimated luminous spots which can be detected on a photodetector 5.
In particular, the first diffractive optical element 1 -1 is such to receive the multiplexed incident optical beam F_i_mux carrying the channels CH1 .1 , CH1 .2, CH1 .3, CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 and it has the function of performing the chromatic dispersion of the multiplexed incident optical beam F_i_mux.
Moreover, the first diffractive optical element 1 -1 is configured to impart to the input channels CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 different radii of curvature of the wavefront (i.e. wavefronts having a different divergence), wherein the values of the radii of curvature (i.e. of the divergence) associated to the different channels at the output of the diffractive optical element 1 -1 depend on the value of the wavelength A associated to the considered channel.
In other words, the channels CH1 .1 , CH1 .2, CH1 .3 having the first wavelength λι cross the first diffractive optical element 1 -1 and are transmitted therefrom at the output with a wavefront having a first radius of curvature Ri .
Likewise, the channels CH2.1 , CH2.2, CH2.3 having the second wavelength A∑ cross the first diffractive optical element 1 -1 and are transmitted therefrom at the output with a wavefront having a second radius of curvature R2, (different to the first radius of curvature Ri).
Lastly, the channels CH3.1 , CH3.2, CH3.3 having the third wavelength A3 cross the first diffractive optical element 1 -1 and are transmitted therefrom at the output with a wavefront having a third radius of curvature R3, (different from the first radius of curvature Ri and from the second radius of curvature R2).
Therefore the multiplexed incident optical beam F_i_mux is incident on the first diffractive optical element 1 -1 , which generates the following free space optical beams:
a first free space optical beam FO1_SL (indicated in Figure 1 B with a broken- and-dotted line) converging into the first focus f1 positioned at the first focal length d_f1 , wherein the first free space beam FO1_SL is composed of an overlapping of three free space circular optical vortices having a wavelength λι and angular indices h, , and wherein the three free space circular optical vortices are associated to the channels CH1 .1 , CH1 .2, CH1 .3;
a second free space optical beam FO2_SL (indicated in Figure 1 B with a broken line) converging into the second focus f2 positioned at the second focal length d_f2, wherein the second free space optical beam FO2_SL is composed of an overlapping of three free space circular optical vortices having a wavelength A∑ and angular indices h, , and wherein the three free space circular optical vortices are associated to the channels CH2.1 , CH2.2, CH2.3; - a third free space optical beam FO3_SL (indicated in Figure 1 B with a continuous line) converging into the third focus f3 positioned at the focal length d_f3, wherein the third free space optical beam FO3_SL is composed of an overlapping of three free space circular optical vortices having a wavelength 3 and angular indices h, , and wherein the three free space circular optical vortices are associated to the channels CH3.1 , CH3.2, CH3.3;
Starting from the position of the first focus f1 , the wavefront of the first free space optical beam FO1_SL diverges and is incident on a first zone Ai of the second diffractive optical element 1 -2, as will be explained in greater detail in the following; therefore channels CH1 .1 , CH1 .2, CH1 .3 having the first wavelength Ai are incident on the first zone Ai of the second diffractive optical element 1 -2.
Likewise, starting from the position of the second focus f2, the wavefront of the second free space optical beam FO2_SL diverges and is incident on a second zone A2 of the second diffractive optical element 1 -2; therefore channels CH2.1 , CH2.2, CH2.3 having the second wavelength K2 are incident on the second zone A2 of the second diffractive optical element 1 -2.
Lastly, starting from the position of the third focus f3, the wavefront of the third free space optical beam FO3_SL diverges and is incident on a third zone A3 of the second diffractive optical element 1 -2; therefore channels CH3.1 , CH3.2, CH3.3 having the third wavelength K3 are incident on the third zone A3 of the second diffractive optical element 1 -2.
Note that the first diffractive optical element 1 -1 acts only on the value of the radius of curvature of the wavefront of the multiplexed incident optical beam F_i_mux, i.e. the first diffractive optical element 1 -1 does not modify the content of the angular indices h, h, ho the OAM modes carried over the multiplexed incident optical beam F_i_mux.
Advantageously, the first diffractive optical element 1 -1 is implemented with a Fresnel lens, which is an optical element that exploits diffraction to focus an incident optical beam in foci having different positions which depend on the value of the wavelength λ of the incident optical beam.
In particular, the focal length d_f of the Fresnel lens 1 -1 depends on the wavelength λ of the incident collimated optical beam according to the following formula:
d_f= (λο * d_fo)/ λ
wherein d_fo is the focal length at wavelength λο for which the Fresnel lens 1 -1 has been dimensioned.
The Fresnel lens is an optical element having circular symmetry implemented with a plurality of concentric annuli which are transparent with respect to the incident optical beam.
The term "annulus" is intended to mean the set of two concentric rings, which identify an area delimited by the two rings.
A Fresnel lens is the diffractive equivalent of a refractive lens.
Supposing to disregard the absorbance of the material, the transmission function TFL of the Fresnel lens 1 -1 , as a function of the radius r from the centre of the Fresnel lens 1 -1 , is the following:
TFL (r) = exp (iSlFL (r))
wherein:
Figure imgf000013_0001
wherein "mod" is the module function which provides the rest of the division of the phase [(k*r2)/(2f)] by the value 2*ττ.
The result is the split of the lens into a series of transparent concentric circular sections (known as "Fresnel rings") having a limited thickness, with a reduction of dimensions.
The radial thickness of the plurality of circular annuli is different between two adjacent annuli.
The radius rn of each annulus is given by the following equation:
Figure imgf000014_0001
wherein n is the sequential number of the n-th annulus.
Therefore the following is obtained:
For high values of n, the difference between contiguous zones following:
Figure imgf000014_0002
which decreases with inverse proportionality with respect to the radius.
Figure 3 shows a top view of the first diffractive optical element 1 -1 implemented with a Fresnel lens.
It can be observed the presence of seven concentric annuli, which have different radial thicknesses which decrease as a function of the increasing value of the radius: this allows to perform the chromatic dispersion in a range of values of the wavelength λ wherein the material (composing the first diffractive optical element 1 -1 is transparent with respect to the incident optical beams.
Figure 3 further shows a section view of the Fresnel lens 1 -1 , wherein it is possible to observe the trend of the thickness of the material composing the Fresnel lens 1 -1 .
In particular, the thickness of the material of each annulus is multi-level, i.e. it has a plurality of discrete values comprised between a substantially null value and a maximum value.
Even more in particular:
the thickness of the most internal annulus has a maximum value at the centre and then it decreases towards a substantially null value with a quadratically decreasing trend;
the thickness of the external annuli with respect to the central annulus is maximum in the radial position closest to the most internal annulus and then it decreases towards a substantially null value with quadratically decreasing trend.
Alternatively, the first diffractive optical element 1 -1 operates as an "axicon", which is a lens composed of a flat surface and a conical surface, the latter facing towards the second diffractive optical element 1 -2. In this case the axicon 1 -1 operates as a prism having a circular symmetry performing the dispersion of the different wavelengths λι, λ∑, A? and maintaining at the same time the circular symmetry of the distribution of the luminous intensity of the multiplexed incident optical beam F_i_mux: in this way it is maintained its content of the angular indices h, , of the OAM modes carried over the multiplexed incident optical beam F_i_mux.
Preferably, a further lens (not shown in the figures) is interposed between the axicon 1 -1 and the second diffractive optical element 1 -2, with the purpose of correcting the phase of the free space optical beams FO1_SL, FO2_SL, FO3_SL incident on the second diffractive optical element 1 -2.
Advantageously, the first diffractive optical element 1 -1 is implemented with a holographic mask having the structure of a surface composed of a plurality of discrete locations indicated with pixels (i.e. a pixel matrix), each pixel having continuous values of phase and amplitude.
Alternatively, the first diffractive optical element 1 -1 is implemented with a holographic mask having a multilevel surface structure, i.e. it is composed of a plurality of pixels (i.e. a pixel matrix), each pixel having discrete values of phase and amplitude.
The continuous or multilevel surface can be implementedusing the photolithography method or the lithography method with electron beam on polymeric materials, such as for example PMMA (poly-methyl-metacrylate).
Preferably, the pattern of the multilevel holographic mask of the first diffractive optical element 1 -1 is calculated by means of algorithms of numerical calculation executed on a computer.
In the following it will be described more in detail the second diffractive optical element 1 -2.
The Applicant has observed that the OAM modes have the special characteristic of having a central singularity which is shown as a dark region around which the luminous intensity is distributed in the form of concentric rings. Therefore the useful signal of an OAM mode with a determined value of the angular index / and of the radial index p is bounded into the region of the space wherein the luminous intensity is not zero.
It is possible to exploit this trend of the luminous intensity of an OAM mode to design the second diffractive optical element 1 -2. Only the zones of the second diffractive optical element 1 -2 which are illuminated by a specific considered OAM mode are considered, leaving the remaining zones available for manipulating other OAM modes. In fact the zones of the second diffractive optical element 1 -2 on which the considered OAM mode with null luminous intensity is incident (i.e. the central zone and the most external zone) are irrelevant for the considered OAM mode and thus they can be used for manipulating other incident OAM modes different from the considered one, without influencing the considered OAM mode.
Therefore on the other zones of the second diffractive optical element 1 -2 it is possible to implementfurther diffractive optical elements, each one such to manipulate different OAM modes.
In particular, the second diffractive optical element 1 -2 comprises a plurality of zones Αι, A2, ... AN, each constituting a diffractive optical element suitably designed for a specific wavelength λ and operating as an OAM modes demultiplexer for said specific wavelength.
In this way it is possible to overcome the functional limit of a diffractive optical element, being that it is monochromatic, i.e. it guarantees an optimal diffraction efficiency in a reduced wavelength range centred on a particular value of the wavelength λ.
In fact it is known that outside the optimal wavelength range, the orders of diffraction are not pure. A portion of the initial energy of the single OAM mode is not concentrated in a single diffraction order, but it is distributed on other orders. In the case of many OAM modes having different incident wavelength on the same region of the second diffractive optical element 1 -2, the luminous intensity of each one is distributed on different diffraction orders , mixing the signals transmitted over the different OAM modes and reducing the ratio between the signal transmitted by the single OAM mode and the noise generated by the other OAM modes.
In the specific case of OAM modes with angular index / different from zero (for example, /= ±1 , /= ±2) and with a not optimal wavelength λ incident on the second diffractive optical element 1 -2, said OAM modes generate a spurious intensity expecially in the diffraction order corresponding to the OAM mode having angular index /= 0.
Consequently, the amplitude of the signal of the diffraction diagram decreases till the point wherein it is no longer possible to distinguish the OAM modes each other, thus preventing to perform the demultiplexing of the OAM modes.
According to the invention, it is possible to overcome this drawback by designing the second diffractive optical element 1 -2 in such a way that it also operates in a broad interval of wavelengths A i, λ∑ ... AN, implementing the second diffractive optical element 1 -2 with a set of single diffractive optical elements, each one operating in respective optimal ranges of different carrier wavelengths.
Note that the plurality of zones Αι , A2, . . . AN can be of the transmitting type or of the reflecting type.
For the sake of simplicity, for the purpose of the explanation of the invention three transmitting zones Αι , A2, A3 are considered associated to the wavelengths λι , λ2, λ3 respectively.
In particular, Figure 4 shows a first transmitting zone Ai denoted with sloped lines, a second transmitting zone A2 denoted with a dotted pattern and a third transmitting zone A3 denoted with squares.
Each transmitting zone Ai , A2, A3 is configured to receive an incident free space optical beam having a different wavelength λ and a plurality of angular indices h, , -
Moreover, each transmitting zone Ai , A2, A3 (in combination with the lens 1 - 3) is configured to deviate the incident optical beam into different directions in the space, as a function of the different values of the angular indices h, , of the optical beam incident on the second diffractive optical element 1 -2.
The term "direction in the space" is understood to mean the direction identified by a point of reference on the second diffractive optical element 1 -2 and a point having three coordinates in the case wherein it is considered that the demultiplexing optical device 1 is positioned in the cartesian reference system (x, y, z). Alternatively, the direction is identified by the reference point and a point having two coordinates in the case wherein it is considered that the demultiplexing optical device 1 is positioned in a reference system having cylindrical coordinates (p, φ).
As previous explained, the separation between the different wavelengths λι , λ2, λ3 is obtained by means of the first diffractive optical element 1 -1 which performs a chromatic dispersion of the multiplexed incident optical beam F_i_mux and thus the first diffractive optical element 1 -1 is such to transmit free space optical beams FO1_SL, FO2_SL, FO3_SL having respective different wavelengths λ-ι , λ2, λ3 towards different transmitting sections Ai , A2, A3 respectively of the second diffractive optical element 1 -2.
In particular, the set of the first transmitting zone Ai and of the lens 1 -3 is configured to:
receive the first free space optical beam FO1_SL having a wavelength λι and having a wavefront with a first radius of curvature Ri ,
transmit three free space optical beams FO1 .1_SL, FO1 .2_SL, FO1 .3_SL orientated into three different directions in the space in the reference system
(x. y. z),
wherein:
• the free space optical beam FO1 .1_SL carries the channel CH1 .1 having a wavelength λι and angular index h;
• the free space optical beam FO1 .2_SL carries the channel CH1 .2 having a wavelength λι and angular index ;
• the free space optical beam FO1 .3_SL carries the channel CH1 .3 having a wavelength λι and angular index I3.
Likewise, the set of the second transmitting zone A2 and the lens 1 -3 is configured to:
receive the second free space optical beam FO2_SL having a wavelength λ∑ and having a wavefront with a second radius of curvature R2;
- transmit three free space optical beams FO2.1_SL, FO2.2_SL, FO2.3_SL orientated into three different directions in the space in the reference system
(x. y. z),
wherein:
• the free space optical beam FO2.1_SL carries the channel CH2.1 having a wavelength λ∑ and angular index h;
• the free space optical beam FO2.2_SL carries the channel CH2.2 having a wavelength λ∑ and angular index ;
• the free space optical beam FO2.3_SL carries the channel CH2.3 having a wavelength λ∑ and angular index I3.
Lastly, the set of the third transmitting zone A3 and ofthe lens 1 -3 is configured to: receive the third free space optical beam FO3_SL having a wavelength A3 and having a wavefront with a third radius of curvature R3;
- transmit three free space optical beams FO3.1 _SL, FO3.2_SL, FO3.3_SL orientated into three different directions in the space in the reference system (x, y, z),
wherein:
• the free space optical beam FO3.1 _SL carries the channel CH3.1 having a wavelength A? and angular index h;
• the free space optical beam FO3.2_SL carries the channel CH3.2 having a wavelength A? and angular index ;
• the free space optical beam FO3.3_SL carries the channel CH3.3 having a wavelength A? and angular index I3.
Preferably, the second diffractive optical element 1 -2 is implemented with an optical element having a circular radial symmetry: in this case the plurality of transmitting zones Αι , A2,... AN is implemented with a corresponding plurality of concentric annuli defined by respective radii n , r2, . . . ΓΝ.
The term "annulus" is again intended to mean the set of two concentric rings, which identify an area bounded by the two rings.
In particular, Figure 4 shows the second diffractive optical element 1 -2 composed of three concentric annuli Αι , A2, A3 of a transmitting type defined by three respective radii n , X2, xz, wherein the first annulus Ai is the most internal one, the third annulus A3 is the most external one and the second annulus A2 is interposed between the internal annulus Ai and the external annulus A3.
Moreover, the three concentric circular annuli Ai , A2, A3 are associated to the wavelengths λι , K≥, respectively λ3, i.e:
the internal annulus Ai is associated to the wavelength λ-ι ;
the intermediate annulus A2 is associated to the wavelength λ2;
the external annulus A3 is associated to the wavelength λ3.
Advantageously, the second diffractive optical element 1 -2 is implemented with a holographic mask having the structure of a surface composed of a plurality of pixel (i.e. a pixel matrix), each pixel having continuous values of the phase and amplitude.
Alternatively, the second diffractive optical element 1 -2 is implemented with a holographic mask having the structure of a multilevel surface, i.e. composed of a plurality of pixel (i.e. a pixel matrix), each pixel having discrete values of the phase and amplitude.
The continuous or multilevel surface can implemented using the photolithography method or the lithography method with electron beam on polymeric materials, such as for example PMMA (poly-methyl-metacrylate).
Preferably, the pattern of the multilevel holographic mask of the second diffractive optical element 1 -2 is calculated by means of an algorithm of numerical calculation executed on a computer, which will be described in detail in the following.
Advantageously, the second diffractive optical element 1 -2 is an optical element operating only in phase, i.e. it is such to modify only the phase of the incident free space optical beam: in this way the diffraction efficiency of the second diffractive optical element 1 -2 is greater than the one with only the amplitude modulation, because the absorbance of the material composing the second diffractive optical element 1 -2 is negligible.
Preferably, the transmission function τ of the second diffractive optical element 1 -2 composed of N concentric annuli is represented in cylindrical coordinates (r, φ) by the following formula:
n
k=l
wherein:
τ is the transmission function of the i-th annulus designed to receive optical beams with i-th wavelength K;
n is the radius of the i-th annulus having a transmission function (Figure 4 shows, for the sake of simplicity, three radii n , r2, r3 associated to the circular annuli A1 , A2, A3 respectively);
Θ is the Heaviside function thus defined;
Figure imgf000020_0001
Therefore the product of the two Heaviside functions ® { Γ - η_λ ) ® {η - Γ) has the value 1 in the range ri_ < r < ri , while it has the value 0 for r values outside such interval. The calculation of the phase values of the transmission function τ of the i- th annulus is performedwith an iterative numerical algorithm executed assuming at the input the i-th wavelength . .
It will be described in the following said iterative numerical algorithm (indicated with "minimisation algorithm"), which is based on the Fourier transform and can be attributed to an additive-adaptive version of the Gerchberg-Saxton algorithm.
For the purposes of explanation of the minimisation algorithm, let's consider the calculation of the transmission function r of a generic diffractive optical element, but the following considerations are applicable to the calculation of the transmission function of the i-th annulus which composes the second diffractive optical element 1 -2.
Moreover, for the purposes of explaining said algorithm, let's consider the demultiplexing of the Laguerre-Gauss modes, but more in general the following considerations are applicable to any set of orthogonal optical modes.
Therefore let's consider a diffractive optical element operating in phase which performs an analysis of the OAM modes on a basis of orthonormal functions
[ψρ1] , which are in particular the Laguerre-Gauss modes identified by a pair of indices (p, I), wherein p is the radial index and / is the angular index.
The transmission function r in cylindrical coordinates (r, φ) of the diffractive optical element is the followin :
Figure imgf000021_0001
wherein:
(ppl, &pl ) are the vectors of the parameters in polar coordinates; - {Epl) are complex coefficients having module values correlated to the response of the diffractive optical element with respect to the channel corresponding to the OAM mode having radial index p and angular index /; the values of the phases of are free parameters which can be used as degrees of freedom in the process of optimisation of the pattern of the transmission function rof the diffractive optical element.
Figure imgf000022_0001
The minimisation algorithm for the calculation of the pattern of the transmission function r of the diffractive optical element is based on the following recursive procedure which employs the preceding equations (1 ) and (2) according to the following steps:
a) the transmission function T \S calculated by means of the equation (1 );
b) phase Ω is discretised into a finite number of levels M;
c) the values of the coefficients {E^} are calculated by means of the formula
(2);
d) the values of the coefficients {E^} calculated in step c) are substituted by the following:
Figure imgf000022_0002
Γ) = 0 (P, i) e w
wherein:
- k is the index of iteration;
- T≠ > 0 are predetermined numbers that characterise the response of each OAM mode (usually Tpl = 1 );
- W is the set of pairs of radial indices p and angular indices / of the considered OAM modes;
- 0 < ≤2 is an adaptive or relaxation parameter which controls the convergence of the algorithm.
e) steps a)-d) are repeated assuming the output {Ejf'} of step d) as input coefficients to be used into step a) in the decomposition of the transmission function τ of the diffractive optical element expressed as indicated in the equation
(1 )-
Steps a)-e) are repeated till the convergence of the algorithm, which can be controlled with different parameters, in particular by means of the following coefficient of error ε:
Figure imgf000023_0001
Note that the coefficient of error ε decreases with the increase of the index of iteration k.
The step of the minimisation algorithm wherein the discretization of the phase into M levels is carried out depends on the precision of the manufacturing process of the diffractive optical element.
Advantageously, phase Ω is discretised into a finite number of levels M>2. In particular, let's consider a determined wavelength λ and let's consider a diffractive optical element in air constituted by a material with a refractive index η(λ) which depends on the wavelength λ.
In this hypothesis the thickness dk of the k-th level of the diffractive optical element will be the following:
Figure imgf000023_0002
It will be described in the following how to implement the pattern of each annulus Αι , A2, A3 of the second diffractive optical element 1 -2 in order to obtain on the CCD screen 5 a predefined position of the luminous spots associated to the different OAM modes having angular index I1 , 12, .
First of all, let's suppose to illuminate an annulus (associated to a particular value of the wavelength λ) of the second diffractive optical element 1 -2 with the following optical beam F composed 0 the overlapping of different OAM modes {ψΔ with contribution {Cmn} :
F {x, y) =∑cfmwmn {x, y) (4) wherein (x,y) are the cartesian coordinates.
The optical beam Q at the output of the considered annulus of the second diffractive optical element 1 -2 is calculated by means of the Fourier transform of the product of the incident optical beam F(x,y) and of the transmission function rof the diffractive optical element defined by the equation (1 ).
In cartesian coordinates (x,y) the output optical beam Q is the following: g oc J dx dyF(x, y)r(x, y) exp -i (ux + vy)
+∞ +∞
-i—(ux + vy)
f f
Figure imgf000024_0001
(5)
wherein:
{u, v) are the cartesian coordinates on the CCD screen 5;
- (x, y) are the cartesian coordinates on the second diffractive optical element 1 - 2;
(α≠,β≠) are the parameters [ρ≠, ύ≠) expressed in cartesian coordinates.
The final approximation in the equation (5) is based on the fact of disregarding the oscillating terms for p≠ n, l≠ m this becomes progressively more correct as the spatial separation between the different OAM modes increases.
The presence in the optical beam F(x, y) (incident on the considered annulus of the second diffractive optical element 1 -2) of a determined OAM mode having a radial index p and angular index / is translated on the CCD screen 5 into the f rmation of a collimated luminous spot having an intensity that is proportional to i that is thus determined by the contribution Cpl of the OAM mode itself.
The position on the CCD screen 5 of the different luminous spots associated to the different OAM modes can be controlled in advance by defining for each OAM mode having radial index p and angular index / the parameters
[Ρρΐ , &ρΐ ) previously used in the calculation of the transmission function r of the second diffractive optical element 1 -2.
Let's suppose that the lens 1 -3 (used for creating the luminous spots on the CCD screen 5) has a focal length / and it is positioned at a distance equal to the focal length both from the second diffractive optical element 1 -2 and from the CCD screen 5 (these positions are also denoted by "configuration f-f).
Let's also suppose that the radiation incident on the considered annulus of the second diffractive optical element 1 -2 is an OAM mode having a wavelength λ and having a radial index p and an angular index /, thuse having parameters (ppi ^pi ) (see equation(l ) ).
The luminous spot of said OAM mode will appear on the CCD screen 5 in the following position expressed {r≠, q>pl ) in polar coordinates:
The position (upi, vpi) of said OAM mode can be equivalent^ expressed in Cartesian coordinates ( ρ1 ,βρ1 ) :
Figure imgf000025_0001
where αρ1 ,βρ1 ) are the parameters (ρρ1 , ΰρ1 ) expressed in cartesian coordinates.
Let's consider for example =1 cm, λ=λ 530 nm, ( ρ1 ,βρ1 ) = {ηι≠α, ηρ1α) , wherein mpi, npi are integer values and a is a grating parameter on the annulus considered of the second diffractive optical element 1 -2.
Therefore the different OAM modes are distributed on the CCD screen 5 in an array having the following grating parameter:
* f
a = a
2π
For example a= 2500 cm 1 , thus it results a = 0.6 mm.
Let's consider that the diameter of the luminous spots of the OAM modes is in the order of 50 μιη (micro metres).
The maximum value of the angular divergence OMAX which can be obtained for a determined OAM mode (calculated with respect to the direction perpendicular to the plane defined by the surface of the second diffractive optical element 1 -2) depends on the minimum dimension of the pixels which form the structure of the second diffractive optical element 1 -2.
Let's consider, for the sake of simplicity, that all the pixels are a square having a side of dimension L; in this case the maximum value of the angular divergence is the one to which a periodicity corresponds on the second diffractive optical element 1 -2 equal to the dimension of two pixels, as indicated by the following formula: _ 2π _ π
° -— --
The previous considerations are based on the approximation in scalar regime of the diffraction of the electromagnetic radiation; for this approximation to be valid, the dimension L of the side of the pixels of the multi-level matrix of the second diffractive optical element 1 -2 is greater than at least about five times the wavelength, i.e. L > 5λ.
Preferably, the value of the dimension L of the side of the pixels of the multilevel matrix of the second diffractive optical element 1 -2 is comprised between five times and ten times the value of the considered wavelength λ, i.e. 5λ< Ι_ <10λ.
Considering for example L=5 μιη, that the lens 1 -3 has a focal length f= 1 cm and considering OAM modes having only one wavelength =1530 nm, it is obtained that the maximum value of the angular divergence a MAX (calculated with respect to the centre of the image formed on the CCD screen 5) is equal to the following formula: a =— = 1.53mm
2L
The previous considerations thus allow to design the pattern of each annulus of the second diffractive optical element 1 -2 according to a predefined arrangement of the luminous spots corresponding to the different OAM modes with angular indices h, , or other degrees of freedom (for example the radial index
P)-
In coarse wavelength division multiplexing systems (CWDM) the separation between the wavelengths carrying the channels is in the order of 20 nm.
The dimension of the luminous spot on the CCD screen 5 is controlled by the dimension D of the incident optical beam F and the focal length / of the lens 1 - 3.
In the first approximation the diameter d of the luminous spot depends on the focal length / of the lens 1 -3, on the wavelength λ of the incident beam F and on the dimension of the incident beam F according to the following formula: d = J- π D Considering for example that the focal length /of the lens 1 -3 is = 1 cm and that the value of the wavelength is ^ 530 nm, then the value of the diameter c/ of the luminous spots is d= 20,000/ D, with D expressed in micrometres.
Further considering a value of the dimension of the incident optical beam D= 500 μιη, then the value of the diameter of the luminous spots on the CCD screen 5 is d= 40 μιη.
The value of the diameter d of the luminous spots can be further reduced by increasing the value of the dimension D of the incident optical beam and/or by reducing the value of the focal length f of the lens 1 -3 used for generating the image on the CCD screen 5.
Alternatively, the second diffractive optical element 1 -2 can be implemented with a matrix structure.
In case wherein the first diffractive optical element 1 -1 is implemented with a Fresnel lens and the second diffractive optical element 1 -2 is implemented with a plurality of concentric annuli, the axis of the Fresnel lens (i.e. the axis which passes along the centre of the concentric annuli) is aligned to the axis of the plurality of concentric annuli of the second diffractive optical element 1 -2 along the axis of propagation z, i.e. the centre of the Fresnel lens is positioned on the axis z and also the centre of the plurality of concentric annuli is positioned on the axis z; moreover, the concentric annuli of the Fresnel lens 1 -1 and the concentric annuli of the second diffractive optical element 1 -2 are orientated like the cartesian plane
( , y).
Similar considerations can be made in case wherein the first diffractive optical element 1 -1 is implemented with an axicon, i.e. the axicon has an axis aligned to the axis of the second diffractive optical element 1 -2 along the propagation axis z; moreover, the flat surface of the axicon is orientated like the concentric annuli of the second diffractive optical element 1 -2, in the cartesian plane (x, y).
Alternatively, the second diffractive optical element 1 -2 can be implemented with an electronically controlled liquid crystal pixel matrix.
In this case the phase or amplitude variation imparted on the incident optical beam on the single pixel is proportional to the potential difference to which the layer of liquid crystals is subjected: this can be obtained with the spatial light modulators, which can be of the transmitting type or the reflecting type. It will be now described how to dimension the reciprocal distance between the first diffractive optical element 1 -1 and the second diffractive optical element 1 - 2, supposing the the first diffractive optical element 1 -1 is implemented with a Fresnel lens.
Let's consider a plane perpendicular to the propagation direction of a circular optical vortex at the output of the Fresnel lens 1 -1 and incident on the second diffractive optical element 1 -2.
RA defines the radius (on said perpendicular plane) wherein there is the maximum value of luminous intensity with annular trend of the circular optical vortex (at the output of Fresnel lens 1 -1 and incident on 1 -2) as a function of the wavelength λ.
Width ArA also defines the difference between the values of the radii (on said perpendicular plane) RA,I e RA,2 wherein the luminous intensity of said circular optical vortex (at the output of the Fresnel lens 1 -1 and incident on 1 -2) is equal to a fraction of the maximum value of the luminous intensity (for example, half the maximum value of the luminous intensity).
The criterion for dimensioning the reciprocal distance d_z between the Fresnel lens 1 -1 and the second diffractive optical element 1 -2 is that the variation of the increase in the value of said radius RA is greater than said width ArA , so as to avoid any overlapping between the OAM modes with different wavelength on the second diffractive optical element 1 -2.
dR
By indicating said variation as the product between the derivative — - and άλ the variation of the wavelength Δ2 between the contiguous wavelengths, said dimensioning criterion can be expressed by the following formula:
λ άλ
The second diffractive optical element 1 -2 can be alternatively an optical element operating only in amplitude, i.e. it is such to modify only the amplitude of the transverse component of the electric field Et (and magnetic Ht) of the incident free space optical beam, without modifying the phase term.
Preferably, the demultiplexing optical device 1 is configured to further perform the polarization demultiplexing. In this case, the multiplexed incident optical beam F_i_mux carries a plurality of channels having different values f , ... IM} of the angular index /, having different values {λι, A2 ... AN} of the wavelength A and having orthogonal polarization states. In particular, in the case of reception of circular optical vortices (for example in output from an optical fiber), they have dextrorotatory or laevorotatory circular polarization.
Therefore it is possible to associate, to a value of the angular index / and to a value of the wavelength A, two separate channels having dextrorotatory or laevorotatory polarization.
The demultiplexing optical device 1 further comprises a quarter-wave plate
(not illustrated in the figures) having the function of performing the conversion of the incident optical beam carrying two channels with circular polarization (right or left) into an output optical beam carrying two channels having orthogonal linear polarizations; subsequently, the two channels having orthogonal linear polarizations are separated by means of a polarizing beam splitter or with a beam displacer prism, positioned in cascade to the quarter-wave plate.
The quarter-wave plate can be positioned both before the first diffractive optical element 1 -1 and after the second diffractive optical element 1 -2.
In this latter case, said quarter-wave plate is configured to receive at the input the plurality of demultiplexed output optical beams F_o_dmx, i.e. the free space optical beams FO1 .1 _SL, FO1 .2_SL, FO1 .3_SL, FO2.1_SL, FO2.2_SL, FO2.3_SL, FO3.1 _SL, FO3.2_SL, FO3.3_SL transmitted by the lens 1 -3; for each one of them, the quarter-wave plate is configured to generate an output optical beam which carries two channels having orthogonal linear polarizations.
For example, the quarter-wave plate receives the free space optical beam
FO1 .1 _SL which is the overlap of two beams having laevorotatory or dextrorotatory circular polarization and generates therefrom the free space optical beam FO1 .1 _o_SL having horizontal polarization and the free space optical beam FO1 .1 _v_SL having vertical polarization; therefore the free space optical beam FO1 .1 _o_SL has an angular index h, wavelength A i and horizontal polarization, while the free space optical beam FO1 .1 _v_SL has an angular index h, wavelength Ai and vertical polarization.
The preceding considerations relative to the quarter-wave plate and the free space optical beam FO1 .1 _SL are applicable in a like way to the other free space optical beams F01 .2_SL, F01 .3_SL, FO2.1_SL, FO2.2_SL, FO2.3_SL, FO3.1_SL, FO3.2_SL, FO3.3_SL.
With reference to Figure 2, it shows a perspective view of an optical communication system 50 according to a first embodiment of the invention.
The optical communication system 50 comprises:
the demultiplexing optical device 1 previously illustrated;
a multimode optical fiber 4 having an output facet coupled to the input of the demultiplexing optical device 1 ;
an photo-detector 5 which performs an optical-electrical conversion and which is coupled with the output of the demultiplexing optical device 1 .
The photo-detector 5 is for example a CCD screen.
Therefore in this case the multiplexed optical beam F_i_mux incident on the demultiplexing optical device 1 (and thus incident on the first diffractive optical element 1 -1 ) is a guided multiplexed optical beam propagating over the optical fiber 4.
The guided multiplexed optical beam F_i_mux carries nine channels CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 having different wavelength λ and different orbital angular momentum, then the nine channels CH1 .1 , CH2.1 , CH3.1 , CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 are demultiplexed by means of the demultiplexing optical device 1 as above explained, finally the nine demultiplexed channels are detected by means of the photo- detector 5.
In particular:
the free space optical beam FO1 .1_SL (carrying the channel CH1 .1 having a wavelength λι and angular index h) is incident to a point P1 .1 on the detecting surface of the optical-electrical sensor 5 generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S1 .1 is generated that is proportional to the intensity of the incident free space optical beam F01 .1_SL;
- the free space optical beam FO1 .2_SL (carrying the channel CH1 .2 having a wavelength λι and angular index ) is incident to a point P1 .2 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S1 .2 is generated that is proportional to the intensity of the incident free space optical beam FO1 .2_SL;
the free space optical beam FO1 .3_SL (carrying the channel CH1 .3 having a wavelength λι and angular index ) is incident to a point P1 .3 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S1 .3 is generated that is proportional to the intensity of the incident free space optical beam FO1 .3_SL;
the free space optical beam FO2.1_SL (carrying the channel CH2.1 having a wavelength A∑ and angular index h) is incident to a point P2.1 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S2.1 is generated that is proportional to the intensity of the incident free space optical beam FO2.1_SL;
the free space optical beam FO2.2_SL (carrying the channel CH2.2 having a wavelength A∑ and angular index ) is incident to a point P2.2 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot, an optical- electrical conversion is performed and an electrical signal S2.2 is generated that is proportional to the intensity of the incident free space optical beam FO2.2_SL;
the free space optical beam FO2.3_SL (carrying the channel CH2.3 having a wavelength A2 and angular index ) is incident to a point P2.3 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S2.3 is generated that is proportional to the intensity of the incident free space optical beam FO2.3_SL;
the free space optical beam FO3.1_SL (carrying the channel CH3.1 having a wavelength A3 and angular index h) is incident to a point P3.1 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S3.1 is generated that is proportional to the intensity of the incident free space optical beam FO3.1_SL;
the free space optical beam FO3.2_SL (carrying the channel CH3.2 having a wavelength A3 and angular index ) is incident to a point P3.2 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S3.2 is generated that is proportional to the intensity of the incident free space optical beam FO3.2_SL;
the free space optical beam FO3.3_SL (carrying the channel CH3.3 having a wavelength A3 and angular index ) is incident to a point P3.3 on the detecting surface of the optical-electrical sensor 5, generating a far-field spot; an optical- electrical conversion is performed and an electrical signal S3.3 is generated that is proportional to the intensity of the incident free space optical beam FO3.3_SL.
With reference to Figure 5A, it shows a perspective view of an optical device 1 0 for multiplexing a plurality of channels with different wavelength and different orbital angular momentum.
The multiplexing optical device 1 0 comprises optical elements which can be miniaturised by means of micro and nano-manufacturing methods.
The multiplexing optical device 1 0 is an optical transmitter having the function of receiving a plurality of incident optical beams, each associated to a channel and having a wavelength A value; said plurality of incident optical beams is generated for example by a respective plurality of laser sources 1 5-1 , 1 5-2, as will be explained in greater detail in the following in the description of Figure 5B.
The demultiplexing optical device 1 0 has also the function of performing the multiplexing of the plurality of incident optical beams over a multiplexed output optical beam F_o_mux which carries a plurality of multiplexed channels having different values {λι, λ∑ ... AN} of the wavelength A and different values f , ... IM} of the angular index /, wherein the number of the plurality of incident optical beams on the multiplexing optical device 1 0 is equal to the number of the plurality of multiplexed channels.
The multiplexed output optical beam F_o_mux can be an optical beam which propagates in the free space; in this case the multiplexed channels are free space circular optical vortices having different wavelengths A and different orbital angular momentum values.
Alternatively, the multiplexed output optical beam F_o_mux can be coupled to the input facet of a multimode optical fiber and excites a plurality of guided OAM modes which propagate on the optical fiber, as will be explained in greater detail in the following in the description relating to Figure 6.
For the purposes of explanation of the invention, for the sake of simplicity in Figures 5A-5C six optical beams F1.1_i, F1.2_i, F2.1_i, F2.2_i, F3.1_i, F3.2_i are considered incident on the multiplexing optical device 10, which generates the following six multiplexed channels having three different wavelengths Ai, λ2, A? and two different angular indices h, :
the first channel CH1_1 having a wavelength Ai and an angular index h;
the second channel CH1_2 having a wavelength Ai and an angular index ; - the third channel CH2_1 having a wavelength A2 and an angular index h;
the fourth channel CH2_2 having a wavelength A2 and an angular index ; the fifth channel CH3_1 having a wavelength A3 and an angular index h;
the sixth channel CH3_2 having a wavelength A3 and angular index ;
In this case, the multiplexing optical device 10 comprises:
- six axicon 12-1, 12-2, 12-3, 12-4, 12-5, 12-;
- six converging lenses 12-7, 12-8, 12-9, 12-10, 12-11, 12-12;
a third diffractive optical element 11-1.
The six axicon 12-1, 12-2, 12-3, 12-4, 12-5, 12-6 have the function of transforming the six incident optical beams F1.1_i, F1.2_i, F2.1_i, F2.2_i, F3.1_i, F3.2_i of Gaussian type into six respective free space transmitted optical beams
F1.1_SL, F1.2_SL, F2.1_SL, F2.2_SL, F3.1_SL, F3.2_SL having wavefronts with annular trend of the luminous intensity on the plane perpendicular to the propagation direction.
The six convergent lenses 12-7, 12-8, 12-9, 12-10, 12-11, 12-12 have the function of collimating the six free space incident optical beams F1.1_SL, F1.2_SL, F2.1_SL, F2.2_SL, F3.1_SL, F3.2_SL into respective six free space collimated optical beams F1.1_CL, F1.2_CL, F2.1_CL, F2.2_CL, F3.1_CL, F3.2_CL, which have different propagation direction in the space which depends on the different values {Ai, A2, A3} of the wavelength λ and on the different values f , h} of the angular index.
The third diffractive optical element 11-1 has the function of transforming the six free space collimated optical beams F1.1_CL, F1.2_CL, F2.1_CL, F2.2_CL, F3.1_CL, F3.2_CL incident on it with a different spatial direction into respective six free space circular optical vortices (i.e. into six OAM modes) having angular indices fh, h} and wavelength fh, λ∑, λβ}, as a function of the different direction of incidence on the third diffractive optical element 1 1 -1 : in this way it is performed the multiplexing of the plurality of OAM modes having different angular indices fh, h }.
In other words, the third diffractive optical element 1 1 -1 has the function of imparting a determined value of the angular index / to the incident optical beams on it as a function of the direction of incidence in the space, thus generating the appropriate OAM modes.
The operation and implementation of the third diffractive optical element 1 1 - 1 are similar to those of the second diffractive optical element 1 -2 of the demultiplexing optical device 1 previously illustrated, with the difference that the third diffractive optical element 1 1 -1 is used in dual mode with respect to the second diffractive optical element 1 -2.
The third diffractive optical element 1 1 -1 comprises three zones An , A12, A13, each constituting a diffractive optical element suitably designed for a respective specific wavelength λι, K≥, and operating as an OAM mode multiplexer for said specific wavelength.
The three zones An , A12, A13 can be of the transmitting type or of the reflecting type.
Each zone An , A12, A13 is configured to receive two free space optical beams with a circular wavefront having the same wavelength λ and having different directions in space and is configured to generate two free space circular optical vortices respectively having angular indices h and , as will be more fully explained in the following.
Preferably, the three zones An , A12, A13 of the third diffractive optical element 1 1 -1 are three concentric annuli An , A12, A13 of the transmitting type or of the reflecting type.
Note that for the purposes of explanation of the invention Figure 5A shows six axicon, but more in general it is possible to use a plurality N x M of axicon that is greater than or equal to four, wherein N is the number of wavelengths and M is the number of OAM modes identified by M respective values of the angular indices h, h, ... IM. Likewise, for the purposes of explanation of the invention three values {Ai, λ∑, λβ} have been considered of the carrier wavelength, but more in general it is possible to use a number N of carrier wavelengths greater than or equal to two.
Referring more in particular to Figure 5A, the six axicon 12-1 , 12-2, 12-3, 12-4, 12-5, 12-6 are arranged into three groups associated to the three values λι, λ∑, λβ respectively of the wavelength A, i.e:
a first group of axicon is composed of the axicon 12-1 , 12-2 associated to the wavelength λι;
a second group of axicon is composed of the axicon 12-3, 12-4 associated to the wavelength λ∑.;
a third group of axicon is composed of the axicon 12-5, 12-6 associated to the wavelength A?.
Moreover, each group comprises a number of axicon that is equal to the number of the different orbital angular momentum values (and thus of the angular index I) of the OAM modes to be generated.
Therefore in the considered example of Figure 5A, each group comprises two axicon because the multiplexing optical device 10 is such to generate two OAM modes with two different values of the orbital angular momentum (and thus two different values h, k of the angular index I).
The set of the first axicon 12-1 and of the first lens 12-7 is configured to receive the incident optical beam F1 .1 i having wavelength λι and to generate the free space collimated optical beam F1 .1_CL (indicated in Figure 5A with a broken- and-dotted line) having an annular trend of the luminous intensity and having a first propagation direction in the space which depends on the value of the wavelength λι and on the value of the angular index h, so that the free space collimated optical beam F1 .1_CL is incident on a first annulus An of the third diffractive optical element 1 1 -1 .
Likewise:
the set of the second axicon 12-2 and of the second lens 12-8 is configured to receive the incident optical beam F1 .2_i having wavelength λι and to generate the free space collimated optical beam F1 .2_CL (indicated in Figure 5A again with a broken-and-dotted line) having an annular trend of the luminous intensity and having a second propagation direction in space which depends on the value of the wavelength λι and on the value of the angular index , so that the free space collimated optical beam F1 .2_SL is incident on the first annulus An of the third diffractive optical element 1 1 -1 ;
the set of the third axicon 12-3 and of the third lens 12-9 is configured to receive the incident optical beam F2.1_i having wavelength A2 and to generate the free space collimated optical beam F2.1_CL (indicated in Figure 5A with a broken line) having an annular trend of the luminous intensity and having a third propagation direction in space which depends on the value of the wavelength A2 and on the value of the angular index h, so that the free space collimated optical beam F2.1_CL is incident on a second annulus A12 of the third diffractive optical element 1 1 -1 ;
the set of the fourth axicon 12-4 and of the fourth lens 12-10 is configured to receive the incident optical beam F2.2_i having wavelength A2 and to generate the free space collimated optical beam F2.2_CL (indicated in Figure 5A again with a broken line) having an annular trend of the luminous intensity and having a fourth propagation direction in space which depends on the value of the wavelength A2 and on the value of the angular index , so that the free space collimated optical beam F2.2_CL is incident on a second annulus A12 of the third diffractive optical element 1 1 -1 ;
the set of the fifth axicon 12-5 and of the fifth lens 12-1 1 is configured to receive the incident optical beam F3.1_i having wavelength A3 and to generate the free space collimated optical beam F3.1_CL (indicated in Figure 5A with a continuous line) having an annular trend of the luminous intensity and having a fifth propagation direction in space which depends on the value of the wavelength A3 and on the value of the angular index h, so that the free space collimated optical beam F3.1_CL is incident on a third annulus A13 of the third diffractive optical element 1 1 -1 ;
the set of the sixth axicon 12-6 and of the sixth lens 12-12 is configured to receive the incident optical beam F3.2_i having wavelength A3 and to generate the free space collimated optical beam F3.2_CL (indicated in Figure 5A again with a continuous line) having an annular trend of the luminous intensity and having a sixth propagation direction in space which depends on the value of the wavelength A3 and on the value of the angular index , so that the free space collimated optical beam F3.1_CL is incident on a third annulus A13 of the third diffractive optical element 1 1 -1 . The third diffractive optical element 1 1 -1 comprises;
the first most internal annulus An that is such to receive the free space collimated optical beams F1 .1_CL, F1 .2_CL having the same first wavelength λι and two different incident propagation directions;
the third most external annulus A13 that is such to receive the free space collimated optical beams F3.1_CL, F3.2_CL having the same third wavelength λ3 and two different incidence propagation directions;
the second intermediate annulus A12 comprised between the first internal annulus An and the third external annulus A13, wherein the second annulus A12 is configured to receive the free space collimated optical beams F2.1_CL, F2.2_CL having the same second wavelength K2 and having two different incidence propagation directions.
Each of the three annuli An , A12, A13 of the third diffractive optical element 1 1 -1 is a transmitting diffractive optical element suitably designed for a respective specific wavelength λ-ι , λ2, λ3 and operating as an OAM mode multiplexer for said specific wavelength.
In particular:
the first annulus An is configured to receive the two free space collimated optical beams F1 .1_CL, F1 .2_CL having the same first wavelength λι and having two different directions of incidence in the space, and is configured to generate:
• a multiplexed free space circular optical vortex F1 .1_MUX_SL (denoted in Figure 5A with a broken-and-dotted line) having a wavelength λι and an angular index h associated to the first of the two directions of incidence;
• a further multiplexed free space circular optical vortex F1 .2_MUX_SL (denoted in Figure 5A again with a broken-and-dotted line) having a wavelength λι and an angular index h associated to the second of the two directions of incidence;
the second annulus A12 is configured to receive the two free space collimated optical beams F2.1_CL, F2.2_CL having the same second wavelength λ2 and having two different directions of incidence in the space, and is configured to generate: • a multiplexed free space circular optical vortex F2.1 _MUX_SL (denoted in Figure 5A with a broken line) having a wavelength K2 and an angular index h associated to the first of the two directions of incidence;
• a further multiplexed free space circular optical vortex F2.2_MUX_SL (denoted in Figure 5A also with a broken line) having a wavelength K2 and an angular index associated to the second of the two directions of incidence;
the third annulus A13 is configured toreceive the two free space collimated optical beams F3.1 _CL, F3.2_CL having the same third wavelength A3 and having two different directions of incidence in the space, and is configured to generate:
• a multiplexed free space circular optical vortex F3.1 _MUX_SL (denoted in Figure 5A with a continuous line) having a wavelength A3 and an angular index h associated to the first of the two directions of incidence;
• a further multiplexed free space circular optical vortex F3.2_MUX_SL (denoted in Figure 5A again with a continuous line) having a wavelength A3 and an angular index h associated to the second of the two directions of incidence.
With reference to Figure 5B, it shows a top view of a multiplexing optical device 1 0.
It can be observed that the six axicon 1 2-1 , 1 2-2, 1 2-3, 1 2-4, 1 2-5, 1 2-6 and the respective six lenses 1 2-7, 1 2-8, 1 2-9, 1 2-1 0, 1 2-1 1 , 1 2-1 2 are arranged radially around the third diffractive optical element 1 1 -1 along a circumference C concentric thereto (indicated by a broken line).
Figure 5B further shows six laser sources 1 5-1 , 1 5-2, 1 5-3, 1 5-4, 1 5-5, 15- 6, wherein:
the first laser source 1 5-1 is such to generate the Gaussian optical beam F1 .1 _i (Ai ) incident on the first axicon 1 2-1 and having a wavelength Ai ;
the second laser source 1 5-2 is such to generate the Gaussian optical beam F1 .2_i (Ai ) incident on the second axicon 1 2-2 and having a wavelength Ai ; the third laser source 1 5-3 is such to generate the Gaussian optical beam F2.1 _i (A2) incident on the third axicon 1 2-3 and having a wavelength A2;
the fourth laser source 15-4 is such to generate the Gaussian optical beam F2.2_i (A2) incident on the fourth axicon 12-4 and having a wavelength A2; the fifth laser source 15-5 is such to generate the Gaussian optical beam F3.1_i (λβ) incident on the fifth axicon 12-5 and having a wavelength λ3;
the sixth laser source 15-6 is such to generate the Gaussian optical beam F3.2_i (λβ) incident on the sixth axicon 12-6 and having a wavelength λ3.
The laser sources 15-1, 15-2, 15-3, 15-4, 15-5, 15-6 are coupled respectively with the axicon 12-1, 12-2, 12-3, 12-4, 12-5, 12-6 by means of respective segments of optical fiber or portions of photonic guide 17-1, 17-2, 17-3, 17-4, 17-5, 17-6.
More in general, in the case of a multiplexing of a plurality M of OAM modes having angular indices h, h, ... IM, each OAM mode having N wavelengths Αι, λ∑ ... AN, the multiplexing optical device 10 comprises a plurality M x N of axicon (and respective lenses) arranged radially around the third diffractive optical element 11- 1 along the circumference C concentric thereto.
With reference to Figure 5C, it shows a section view of a multiplexing optical device 10 along the line A-A of Figure 5B.
It can be observed he presence of:
the laser source 15-4 coupled to the axicon 12-4 by means of a segment of optical fiber 17-4 and a converging lens 16-4;
the laser source 15-1 coupled to the axicon 12-1 by means of a segment of optical fiber 17-1 and a converging lens 16-1 ;
Advantageously, the multiplexing optical device 10 further comprises a polariser, in case wherein the light sources generate non-polarized light.
Further, the multiplexing optical device 10 further comprises a quarter-wave plate 18 having the function of circularly polarizing the incident optical beam.
The quarter-wave plate 18 is interposed between the laser sources 15-1,
15-2, 15-3, 15-4, 15-5, 15-6 and the axicon 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, as illustrated in Figure 5C.
The quarter-wave plate 18 is configured to receive at the input two optical beams having orthogonal linear polarizations and to generate therefrom an optical beam having a right or left circular polarization: in this way the coupling with the optical fiber 4 is optimised, as the guided OAM modes have a circular polarization.
In particular, the quarter-wave plate 18 is configured to receive the Gaussian optical beam F1.1_i (λ-ι) having linear polarization and is configured to generate a Gaussian optical beam F1 .1 _c(Ai) having circular polarization, which is incident on the first axicon 12-1 .
The preceding considerations relating to the Gaussian optical beam F1 .1 _i(Ai) are applicable in a similar way to the other Gaussian optical beams F1 .2_i (Ai), F2.1 _i (A2), F2.2_i (A2), F3.1 _i (A3), F3.2_i (A3), and thus the Gaussian optical beams F1 .2_c (Ai), F2.1 _c (A2), F2.2_c (A2), F3.1 _c (A3), F3.2_c (A3) are generated having circular polarization, which are incident on the axicon 1 2-2, 1 2-3, 12-4, 1 2-5, 1 2-6 respectively.
With reference to Figure 6, it shows an optical communication system 60 according to a second embodiment of the invention.
The optical communication system 60 comprises:
the multiplexing optical device 1 0 previously illustrated;
a multimode optical fiber 4 having an input facet;
a converging lens 61 for regulating the dimension of the incident optical beam on the input facet of the optical fiber 4.
In this case the optical beam F_o_mux at the output of the multiplexing optical device 1 0 is coupled to the optical fiber 4 by means of the converging lens 61 which generates a collimated output optical beam F_o_cm, then three guided modes having three wavelengths Ai , A2, A3, are excited in the optical fiber 4, wherein each guided mode carries two guided circular optical vortices (i.e. two guided OAM modes) having two different values h, of the angular index /; therefore a guided multiplexed optical beam Fg is propagated over the optical fiber 4 which in total carries six channels CH1 _1
Figure imgf000040_0001
Figure imgf000040_0002
With reference to Figure 7, it shows an optical communication system 70 according to a third embodiment of the invention.
The optical communication system 70 comprises:
nine laser sources 1 5-1 , 1 5-2, ... 15-9;
a multiplexing optical device 20;
the demultiplexing optical device 1 previously illustrated;
a multimode optical fiber 4 having an input facet coupled to the output of the multiplexing optical device 20 and having an output facet coupled with the input of the demultiplexing optical device 1 ; the photo-detector 5 which performs an optical-electrical conversion and which is coupled with the output of the demultiplexing optical device 1 .
The laser sources 15-1 , 15-2, 15-3 are such to generate a Gaussian optical beam having wavelength λ-ι .
The laser sources 15-4, 15-5, 15-6 are such to generate a Gaussian optical beam having wavelength λ2.
The laser sources 15-7, 15-8, 15-9 are such to generate a Gaussian optical beam having wavelength λ3.
The multiplexing optical device 20 is implemented in a way similar to the multiplexing optical device 10 previously described, with the difference that the multiplexing optical device 20 is such to generate three OAM modes having three different values h, , of the angular index /; therefore the multiplexed output optical beam F_o_mux carries nine channels having three different values Αι, A∑, A3 of the wavelength A and three different values h, , h of the angular index /.
It will be described hereinafter the operation of the optical communication system 70, making also reference to Figures 1 A, 1 B, 5A and 7.
At the initial instant to the laser source 15-1 generates a first Gaussian optical beam F1 .1 i (λ-ι) having a wavelength λ-ι, the laser source 15-2 generates a second Gaussian optical beam F1 .2_i (λ-ι) having a wavelength λι, the laser source 15-3 generates a third Gaussian optical beam F1 .3_i (λ-ι) having a wavelength λι, the laser source 15-4 generates a fourth Gaussian optical beam F2.1_i (λ2) having a wavelength λ2, the laser source 15-5 generates a fifth Gaussian optical beam F2.2_i (ta) having a wavelength λ2, the laser source 15-6 generates a sixth Gaussian optical beam F2.3_i (ta) having a wavelength K≥, the laser source 15-7 generates a seventh Gaussian optical beam F3.1_i (λβ) having a wavelength λ3, the laser source 15-8 generates an eighth Gaussian optical beam F3.2_i (λ3) having a wavelength λ3, the laser source 15-9 generates a ninth Gaussian optical beam F3.3_i (λβ) having a wavelength λ3.
The multiplexing optical device 20 receives the first Gaussian optical beam F 1 .1 i (λι), the second Gaussian optical beam F1 .2_i (λι), the third Gaussian optical beam F1 .3_i (λι), the fourth Gaussian optical beam F2.1_i (ta), the fifth Gaussian optical beam F2.2_i (ta), the sixth Gaussian optical beam F2.3_i (ta), the seventh Gaussian optical beam F3.1_i (λβ), the eighth Gaussian optical beam F3.2_i (λ3), the ninth Gaussian optical beam F3.3_i (λβ), then the multiplexing optical device 20 generates therefrom the multiplexed optical beam F_o_mux carrying nine channels CH1_1 , CH1_2, CH1_3, CH2_1 , CH2_2, CH2_3, CH3_1 , CH3_2, CH3_3 in way similar to what was described previously relatively to the description of the multiplexing optical device 10 of Figure 5A, wherein:
- the first channel CH1_1 has a wavelength A i and an angular index h;
the second channel CH1_2 has a wavelength Ai and an angular index ;
the third channel CH1_3 has a wavelength A i and an angular index ;
the fourth channel CH2_1 has a wavelength λ∑ and an angular index h;
the fifth channel CH2_2 has a wavelength λ∑ and an angular index ;
- the sixth channel CH2_3 has a wavelength A2 and an angular index ;
the seventh channel CH3_1 has a wavelength A3 and an angular index h;
the eighth channel CH3_2 has a wavelength A3 and angular index ;
the ninth channel CH3_3 has a wavelength A3 and an angular index .
At instant t1 (subsequent to tO) the multiplexed optical beam F_o_mux enters the multimode optical fiber 4 and excites a guided multiplexed optical beam Fg carrying three channels having three different values Αι, λ∑, A3 of the wavelength A, wherein each channel carries three guided OAM modes having three values h, , h of the angular index /, thus obtaining the following nine channels carried over the optical fiber 4:
- the first channel CH1_1_g has a wavelength Ai and an angular index h;
the second channel CH1_2_g has a wavelength A i and an angular index ; the third channel CH1_3_g has a wavelength Ai and an angular index ;
the fourth channel CH2_1_g has a wavelength A2 and an angular index h; the fifth channel CH2_2_g has a wavelength A2 and an angular index ;
- the sixth channel CH2_3_g has a wavelength A2 and an angular index ;
the seventh channel CH3_1_g has a wavelength A3 and an angular index h; the eighth channel CH3_2_g has a wavelength A3 and an angular index ; the ninth channel CH3_3_g has a wavelength A3 and an angular index .
In the instants comprised between t1 and t2 (excluded) the guided multiplexed optical beam Fg propagates from the input facet to the output facet of the optical fiber 4, wherein the multiplexed incident optical beam is indicated with F_i_mux.
At instant t2 (subsequent to t1 ) the demultiplexing optical device 1 receives the multiplexed incident optical beam F_i_mux carrying the nine channels CH1 .1 , CH1 .2, CH1 .3, CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3, which correspond to the nine channels CH1_1_g, CH1_2_g, CH1_3_g, CH2_1_g, CH2_2_g, CH2_3_g, CH3_1_g, CH3_2_g, CH3_3_g respectively.
The demultiplexing optical device 1 performs the demultiplexing of the nine channels CH1 .1 , CH1 .2, CH1 .3, CH2.1 , CH2.2, CH2.3, CH3.1 , CH3.2, CH3.3 in the way as explained previously relatively to the description of the demultiplexing optical device 1 of Figure 1 B.
In particular, the demultiplexing optical device 1 :
transmits, in a first space direction, a first free space circular optical vortex FO1 .1_SL having a wavelength λι and an angular index h;
transmits, in a second space direction, a second free space circular optical vortex FO2.1_SL having a wavelength ,½and an angular index h;
transmits, in a third space direction, a third free space circular optical vortex FO3.1_SL having a wavelength A? and an angular index h;
- transmits, in a fourth space direction, a fourth free space circular optical vortex FO1 .2_SL having a wavelength λι and an angular index ;
transmits, in a fifth space direction, a fifth free space circular optical vortex FO2.2_SL having a wavelength ,½and an angular index ;
transmits, in a sixth space direction, a sixth free space circular optical vortex FO3.2_SL having a wavelength A? and an angular index ;
transmits, in a seventh space direction, a seventh free space circular optical vortex FO1 .3_SL having a wavelength λι and an angular index ;
transmits, in an eighth space direction, an eighth free space circular optical vortex FO2.3_SL having a wavelength ,½and an angular index ;
- transmits, in a ninth space direction, a ninth free space circular optical vortex FO3.3_SL having a wavelength A? and an angular index ;
At instant t3 (subsequent to t2) the photo-detector 5 receives the nine free space circular optical vortices F01 .1_SL, FO2.1_SL, FO3.1_SL, FO1 .2_SL, FO2.2_SL, FO3.2_SL, FO1 .3_SL, FO2.3_SL, FO3.3_SL in nine different points P1 .1 , P2.1 , P3.1 , P1 .2, P2.2, P3.2, P1 .3, P2.3, P3.3 respectively which are far- field spots, as explained previously relatively to the description of Figure 2.
Subsequently, the photo-detector 5 performs the optical-electrical conversion and generates nine electrical signals S1 .1 , S1 .2, S1 .3, S2.1 , S2.2, S2.3, S3.1 , S3.2, S3.3, wherein: the first electrical signal S1 .1 carries channel CH1 .1 ;
the second electrical signal S1 .2 carries channel CH1 .2;
the third electrical signal S1 .3 carries channel CH1 .3;
the fourth electrical signal S2.1 carries channel CH2.1 ;
- the fifth electrical signal S2.2 carries channel CH2.2;
the sixth electrical signal S2.3 carries channel CH2.3;
the seventh electrical signal S3.1 carries channel CH3.1 ;
the eighth electrical signal S3.2 carries channel CH3.2;
the ninth electrical signal S3.3 carries channel CH3.3.
Therefore the communication system 70 has performed the multiplexing of nine channels having three different values of the wavelength A and three different values of the angular index /, performed the carry of nine channels over the multimode optical fiber 4, performed the demultiplexing of the nine channels having three different values of the wavelength A and three different values of the angular index / and lastly performed the reception of the optical signals and its conversion into electronic signals.
Note that the second diffractive optical element 1 -2 and the third diffractive optical element 1 1 -1 constitute an independent invention.
In fact the second diffractive optical element 1 -2 solves the technical problem of generating a relation between:
a plurality of OAM modes with different wavelengths incident on the second diffractive optical element 1 -2; and
the different directions in space of the optical beams generated.
Said technical problem is solved with the second diffractive optical element 1 -2 comprising a plurality of zones Αι , A2, A3 equal to a plurality of different values λι, λ∑, λβ of the wavelength A, wherein each zone of the second diffractive optical element 1 -2 is configured to:
• receive at the input a first free space circular vortex carrying a plurality of different values of the orbital angular momentum;
· generate at the output, as a function of the first free space circular optical vortex, a plurality of second free space circular optical vortices over different output directions in the space which depend on the plurality of different values of the orbital angular momentum, wherein each of the second free space circular vortices carries a same value of the wavelength and a different value of the orbital angular momentum.
Viceversa, the third diffractive optical element 1 1 -1 solves the technical problem of generating a relation between:
the different directions of incidence in the space of a plurality of incident optical beams on the third diffractive optical element 1 1 -1 ; and
a plurality of OAM modes with different generated wavelengths.
Said technical problem is solved with the third diffractive optical element 1 1 - 1 comprising a plurality of zones An , A12, A13 equal to the plurality of different values λι, λ2, A? of the wavelength A, wherein each zone of the third diffractive optical element 1 1 -1 is configured to:
• receive in input a plurality of output optical beams equal to the plurality of the different orbital angular momenta and having a same wavelength value and different directions of incidence in the space associated to the plurality of the different orbital angular momenta;
• generate at the output, as a function of the plurality of the received optical beams, a corresponding plurality of multiplexed circular optical vortices having different values of the orbital angular momenta which depend on the different directions of incidence.

Claims

1 . Optical device (1 ) for demultiplexing a plurality of channels with different wavelength (λι, λ∑, λβ) and different orbital angular momentum ( , h, h), the device comprising:
a first diffractive optical element (1 -1 ) for performing a wavelength division demultiplexing, the first diffractive optical element being configured to:
• receive a multiplexed incident optical beam (F_i_mux) carrying the plurality of channels having a plurality of different values of the wavelength (λι, λ∑, λβ) and a plurality of different values of the orbital angular momentum ( , h, h)
• generate at the output, as a function of the multiplexed incident optical beam (F_i_mux), a plurality of first free space circular optical vortices (FO1_SL, FO2_SL, FO3_SL) having respective wavefronts with different radii of curvature which depend on the plurality of different values of the wavelength, wherein each of the first free space circular optical vortices carries said plurality of different values of the orbital angular momentum;
a second diffractive optical element (1 -2) for performing a mode division demultiplexing, the second diffractive optical element comprising a plurality of zones (Ai , A2, A3) equal to the plurality of different values (λι, λ∑, λβ) of the wavelength, each zone being configured to:
• receive at the input a respective first free space circular optical vortex (FO1_SL) carrying said plurality of different values of the orbital angular momentum;
• generate at the output, as a function of the respective first free space circular optical vortex (FO1_SL), a plurality of second free space circular optical vortices (F01 .1_SL, FO1 .2_SL, F01 .3_SL) oriented in different directions in the space which depend on the plurality of different values of the orbital angular momentum, wherein the plurality of the second free space circular optical vortices generated by the respective zone carries a same value of the wavelength and a different value of the orbital angular momentum.
2. Demultiplexing optical device (1 ) according to claim 1 , wherein the plurality of zones of the second diffractive optical element (1 -2) are a plurality of concentric annuli of transmitting type, each one associated to a different value of the wavelength.
3. Demultiplexing optical device (1 ) according to claim 2, wherein the second diffractive optical element (1 -2) is an holographic mask having the structure of a multi-level surface composed of a plurality of pixel having discrete values of the phase and amplitude.
4. Demultiplexing optical device (1 ) according to any of the previous claims, wherein the distance (d_z) between the first diffractive optical element (1 -1 ) and the second diffractive optical element (1 -2) is calculated according to the following formula: λ άλ
wherein:
- d is the derivative mathematical operator;
RA is the radius wherein it is maximum the value of the luminous intensity with annular trend of a first free space circular optical vortex incident on the second diffractive optical element;
Αλ is the wavelength change between contiguous wavelengths;
- ArA \s the difference between the values of the radii wherein the luminous intensity of said first free space circular optical vortex is equal to a fraction of the maximum value of the luminous intensity;
wherein the radius RA and the radii of the difference Δτλ are measured on a plane perpendicular to the propagation direction of said first free space circular optical vortex incident on the second diffractive optical element.
5. Demultiplexing optical device (1 ) according to any of the previous claims, further comprising a converging lens (1 -3) configured to transform the plurality of the second free space circular optical vortices into a respective plurality of collimated optical beams (P1 .1 , P1 .2, P1 .3, P2.1 , P2.2, P2.3, P3.1 , P3.2, P3.3).
6. Demultiplexing optical device (1 ) according to the previous claim, wherein the converging lens (1 -3) is integrated inside the second diffractive optical element.
7. Demultiplexing optical device (1 ) according to any of claims from 3 to 6, wherein the second diffractive optical element (1 -2) is configured to modify only the phase of the first free space circular optical vortices incident on it,
and wherein the pattern of each annulus of the multi-level holographic mask is calculated by means of the following iterative numerical algorithm: a) calculation of the transmission function rof the i-th annulus;
b) discretization of the phase into a finite number of levels;
c) calculation of coefficient values by means of the inverse Fourier transform; d) substitution of the calculated coefficient values with new values;
e) repeating steps a)-d) taking the result of step d) as input of step a);
f) repeating steps a)-e) till when the value of a coefficient of error is not smaller than a defined value.
8. Demultiplexing optical device (1 ) according to any of the previous claims, wherein the first diffractive optical element (1 -1 ) is selected between:
- a Fresnel lens comprising a plurality of concentric annuli of transmitting type;
an axicon having the conical surface oriented towards the second diffractive optical element.
9. Optical device (1 0) for multiplexing a plurality of channels with different wavelength (λι, λ∑, A?) and different orbital angular momentum ( , h), the device comprising:
a plurality of axicon (1 2-1 , 12-2, ... 12-6) configured to change a plurality of incident optical beams (F1 .1 _i(Ai), F1 .2_i(Ai), F2.1 _i(A2), F2.2_i(A2), F3.1 _i(A3), F3.2_i(A3) ) into a corresponding plurality of output optical beams (F1 .1 _CL(Ai), F1 .2_CL(Ai), F2.1 _CL(A2), F2.2_CL(A2), F3.1 _CL(A3),
F3.2_CL(A3)) having wavefronts with an annular trend of the luminous intensity;
a third diffractive optical element (1 1 -1 ) configured to perform a mode division multiplexing of said plurality of output optical beams, the third diffractive optical element comprising a plurality of zones (An , Αι2, A13) equal to the plurality of different values (λι, λ∑, λβ) of the wavelength,
the plurality of axicon comprising a plurality of groups of axicon (1 2-1 , 1 2-2; 1 2-3, 1 2-4; 1 2-5, 1 2-6) associated to the different values of the wavelength, wherein each group comprises a plurality of axicon (1 2-1 , 1 2-2) equal to the number of different values of the orbital angular momentum,
wherein each axicon (1 2-1 ) is configured to receive an incident optical beam
( F 1 .1 i ) having a wavelength value (λι) and generate therefrom an output optical beam (F1 .1 _SL, F1 .1_CL) having a wavefront with annular trend of the luminous intensity and propagation direction which depends on said wavelength value and on an orbital angular momentum value;
wherein each zone of the third diffractive optical element (1 1 -1 ) is configured to:
• receive at the input, from a respective group of the plurality of axicon, the output optical beams having a respective same value of the wavelength and having different incident propagation directions associated to the different values of the orbital angular momentum;
• generate at the output, as a function of the plurality of optical beams of the respective group, a corresponding plurality of multiplexed circular optical vortices (F1 .1_MUX_SL, F1 .2_MUX_SL) having the different values of the orbital angular momentum which depend on the different incident propagation directions.
10. Multiplexing optical device (10) according to the previous claim, wherein the plurality of zones of the third diffractive optical element (1 1 -1 ) are a plurality of concentric annuli (An , A12, A13), each one associated to a different value of the wavelength.
1 1 . Multiplexing optical device (10) according to the previous claim, wherein the third diffractive optical element (1 1 -1 ) is an holographic mask having the structure of a multi-level surface composed of a plurality of pixel having discrete values of the phase and amplitude.
12. Multiplexing optical device (10) according to any of the claims from 9 to 1 1 , further comprising a plurality of converging lenses (12-7, 12-8, ... 12-12) coupled to the plurality of axicon and configured to collimate said plurality of output optical beams into a corresponding plurality of collimated optical beams (F1 .1_CL(Ai), F1 .2_CL(Ai), F2.1_CL(A2), F2.2_CL(A2), F3.1_CL(A3), F3.2_CL(A3)).
13. Optical communication system (50) comprising:
- a multimode optical fiber (4) configured to transmit a plurality of channels with different wavelength (λι, λ∑, A?) and different orbital angular momentum ( , h, I3);
a demultiplexing optical device (1 ) according to any of the claims from 1 to 8; a first coupling optical device of an output facet of the optical fiber with the demultiplexing optical device.
14. Optical communication system (70) according to the previous claim, further comprising:
a multiplexing optical device (10, 20) according to any of the claims from 9 to 12; a second coupling optical device (61 ) of an input facet of the optical fiber with the multiplexing optical device.
PCT/IB2016/054650 2015-08-04 2016-08-02 Optical device for demultiplexing and multiplexing a plurality of channels with different wavelength and different orbital angular momentum and optical communication system thereof WO2017021888A1 (en)

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