CN113805347A - Method for mapping space phase to space-time light field time-space domain phase - Google Patents
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Abstract
The invention provides a method for mapping a space phase to a space-time light field space-time phase, which comprises the following steps: s1: the collimated space-time light field wave packet is transmitted to a modulator; s2: adjusting the distance among the first light splitting element, the first optical collimating element and the phase regulating element to be the focal length of the first optical collimating element; s3: if the phase control element is a reflective device, the space-time light field wave packet returns to the first light splitting element according to the original path after phase control; if the phase regulating element is a transmission-type device, the space-time light field wave packet is reconstructed into a collimated emergent space-time light field through a second optical collimating element and a second light splitting element after phase regulation; s4: after the space-time light field exits the modulator, the phase of the space-time light field in the space-time domain is the mapping of the space phase applied by the phase adjusting element in the modulator. The method for mapping the space phase to the time-space domain phase of the space-time light field solves the problem that the traditional method cannot directly regulate and control the phase of the time-space domain phase of the light field.
Description
Technical Field
The invention relates to the technical field of optics, in particular to a method for mapping a space phase to a space-time light field space-time phase.
Background
Optical field refers to an electromagnetic field of optical frequency having a specific distribution in the time domain and in the spatial domain. In general, the study of the light field can be divided into the study of the light field distributed in the transverse x-y plane, i.e. the study of the light beam; the optical field distributed in the time domain, i.e. the study of the optical pulses, and the three-dimensional wave packet having a specific distribution in the x-y plane and in the time domain, respectively. For three-dimensional wave packets that are not coupled in the spatio-temporal domain, the light field can be expressed in the form of E (x, y, t) ═ E (x, y) · E (t).
In recent years, scientists find that a three-dimensional wave packet coupled in a space-time domain can have unique space-time propagation characteristics and physical characteristics, and is of great significance to research on novel light quantum devices, novel light quantum communication and basic physics, and a space-time light field becomes a new research hotspot. For example, a spatiotemporal light field with a specific distribution may achieve a significant anomalous spatiotemporal refraction phenomenon. The light field can ' break ' the old Snell's law in the process of propagation, and propagate with controllable group velocity after passing through the interface. The space-time light field can provide new possibility for the technical application of novel remote sensing, underground imaging, optical synchronization, phased array radar and the like.
Generating a novel space-time light field requires a new light field regulation and control technology, and the traditional light field regulation and control technology relies on utilizing a phase regulation and control element to regulate and control the phase of the light field in a transverse x-y plane and utilizing a pulse shaping technology based on one-dimensional Fourier transform to regulate and control the phase of the light field in a time domain. For new space-time light fields, especially complex space-time light fields coupled in the space-time domain, these techniques lack the ability to regulate and control the phase of the light field in the space-time domain.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for mapping a space phase to a space-time light field time-space phase, the generated space-time light field can carry complex space-time phases in the space-time domain, and the problem that the traditional method cannot directly regulate and control the phases of the space-time domain of the light field is solved.
In order to achieve the above object, the present invention provides a method for mapping a spatial phase to a spatio-temporal optical field spatio-temporal phase, comprising the steps of:
s1: the method comprises the steps that collimated space-time light field wave packets are incident to a modulator, wherein the modulator comprises a first light splitting element, a first optical collimating element and a phase regulating element which are sequentially arranged;
s2: adjusting the distance among the first light splitting element, the first optical collimating element and the phase regulating element to be the focal length of the first optical collimating element, wherein the space frequency domain light field of the incident space-time light field wave packet is projected to the plane of the phase regulating element;
s3: if the phase control element is a reflective device, after phase control, the space-time light field wave packet returns to the first light splitting element according to the original path and is reconstructed into a collimated emergent space-time light field;
if the phase control element is a transmission-type device, the space-time light field wave packet passes through a group of second optical collimation element and second light splitting element which are in mirror symmetry with the first light splitting element and the first optical collimation element after being subjected to phase control, and is reconstructed into a collimated emergent space-time light field;
s4: and the phase of the emergent space-time light field after the modulator in the space-time domain is a mapping of the space phase applied by the phase control element in the modulator.
Preferably, the first light splitting element and the second light splitting element comprise a reflective grating, a transmissive grating or a triangular prism; the first and second optical collimating elements comprise cylindrical lenses or cylindrical mirrors; the phase modulating element includes a spatial light modulator, a phase panel, or a deformable mirror.
Preferably, in the step S4, the mapping relationship between the spatial phase and the spatio-temporal-spatial-field phase may be obtained by equations (1) to (4):
φ(x′，y′)＝φ(x，a·Ω) (1)；
E(x，Ω)＝E0(x，Ω)·ei·φ(x′，y′)＝E0(x，Ω)·ei·φ(x，a·Ω) (2)；
Ω(t)＝kGDD·t (3)；
φ(x，t)＝φ(x，Ω/kGDD)＝φ(x′，y′/a/kGDD) (4)；
wherein φ (x ', y') represents the application of the phase modulating element in the modulatorX represents the spatial domain coordinates of the incident light field, Ω represents the optical frequency domain coordinates of the light field, a represents the splitting coefficient of the modulator for the incident light field, determined by the first splitting element and the first optical collimating element or the second splitting element and the second optical collimating element; e0(x, omega) represents a spatial frequency domain light field of an incident space-time light field on a phase control element plane, and E (x, omega) represents the spatial frequency domain light field after phase control; omega (t) is a function of the temporal variation of the transient frequency of the emergent spatio-temporal light field in the time domain, kGDDIs the chirp coefficient; t represents time; φ (x, t) represents the null vortex phase.
Preferably, when the space-time light field is in different chirp states, the space phase phi (x ', y') loaded by the modulator is mapped to the space-time phase of the space-time light field in different forms; in the formula (4), kGDDDetermining the chirp state of the optical field;
when k isGDDIf the phase is more than 0, the optical field is in a positive chirp state, and the space phase phi (x ', y') is mapped to the time-space domain phase of the space-time optical field in a positive mapping mode;
when k isGDD< 0, the light field is in a negative chirp state, the spatial phase phi (x ', y') will be mapped to the time-space domain phase of the space-time light field in a reverse mapping mode;
when k isGDD0, the light field is in a zero chirp state, the spatial phase phi (x ', y') will map the mapping mode in one-dimensional fourier transform to the time-space domain phase of the space-time light field, which can be written as:
wherein E (x, t; 0) represents the exit spatio-temporal light field.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
(1) the traditional light field regulation and control are limited to the regulation and control of the light field space phase and the pulse shaping based on one-dimensional Fourier transform, and the complex space-time light field coupled in a space-time domain cannot be generated. The invention realizes the phase regulation and control in the time-space domain of the time-space light field, and can be used for generating complex time-space light fields;
(2) the traditional regulation and control method of the pulse time domain phase is based on one-dimensional Fourier transform, and the time domain phase of the pulse cannot be directly mapped and regulated. The invention realizes the function of mapping any space phase to the time-space domain phase of the space-time light field in different modes by regulating and controlling the chirp state of the space-time light field, wherein the function comprises the step of directly mapping the space phase to the time-space domain phase of the space-time light field.
Drawings
Fig. 1 is a schematic structural diagram of a modulator according to an embodiment of the present invention.
Detailed Description
The following description of the preferred embodiment of the present invention, with reference to the accompanying drawings and fig. 1, will provide a better understanding of the function and features of the invention.
Referring to fig. 1, a method for mapping a space phase to a space-time light field space-time domain phase according to an embodiment of the present invention includes the steps of:
s1: the method comprises the following steps that collimated space-time light field wave packets are incident to a modulator, wherein the modulator comprises a first light splitting element 1, a first optical collimating element 2 and a phase regulating element 3 which are sequentially arranged;
the first light splitting element 1 comprises a reflection grating, a transmission grating or a prism; the first optical collimating element 2 comprises a cylindrical lens or a cylindrical mirror; the phase control element 3 comprises a spatial light modulator, a phase panel or a deformable mirror;
s2: adjusting the distance among the first light splitting element 1, the first optical collimating element 2 and the phase regulating element 3 to be the focal length of the first optical collimating element 2, and projecting the space frequency domain light field of the incident space-time light field wave packet to the plane where the phase regulating element 3 is located;
s3: if the phase control element 3 is a reflective device, after phase control, the wave packet of the space-time light field returns to the first light splitting element 1 according to the original path and is reconstructed into a collimated emergent space-time light field;
if the phase control element 3 is a transmission-type device, the space-time light field wave packet passes through a group of second optical collimating elements 4 and 5 which are in mirror symmetry with the first optical collimating element 1 and the first optical collimating element 2 after phase control, and is reconstructed into a collimated emergent space-time light field;
space-frequency domain light field E of incident light field0(x, Ω) is projected onto the plane of the phase modulating element 3. The phase modulating element 3 will impose a phase of phi (x ', y') on the incident space-frequency domain. According to the first light splitting element 1 and the first optical collimating element 2 in the modulator, the following coordinate mapping relationship exists:
φ(x′，y′)＝φ(x，a·Ω) (1)
where a is the spectral coefficient of the modulator to the incident light field, and is determined by the first spectroscopic element 1 and the first optical collimating element 2, and has the unit of [ m · s ]. Taking fig. 1 as an example, when the first light splitting element 1 is a reflective grating (grating period is Λ), the first optical collimating element 2 is a cylindrical lens (cylindrical lens focal length is f), and assuming that the diffraction order of the split light is m ═ 1, the splitting coefficient a can be determined by the following formula:
via the phase modulation element 3, the light field becomes:
E(x，Ω)＝E0(x，Ω)·ei·φ(x′，y′)＝E0(x，Ω).ei·φ(x，a·Ω) (2)；
s4: the emergent space-time light field passes through a second optical collimating element 4 and a second light splitting element 5 and is reconstructed into a collimated emergent space-time light field after the modulator. The phase of the spatio-temporal light field in the spatio-temporal domain is a mapping of the spatial phase imposed by the phase modulating element 3 in the modulator.
S41: the spatial phase phi (x ', y') can be mapped to the spatial-temporal phase phi (x, t) of the optical field in different modes depending on the chirp state that the spatial-temporal optical field has. The spatio-temporal light field is assumed to have a chirp as follows:
Ω(t)＝kGDD·t (3)；
wherein Ω (t) is the temporal change in the transient frequency of the optical fieldFunction of kGDDIs the chirp coefficient, and has the unit of [ s-2 ]]. For positively chirped spatio-temporal optical fields, kGDDIs greater than 0. At this time, the transient frequency of the spatio-temporal light field corresponds to the time domain one to one, and the spatial phase phi (x ', y') is forward-mapped to the spatio-temporal phase of the spatio-temporal light field. The forward direction here means that there is no inversion of the direction of the phase in the mapping relation. At this time, the time-space domain phase of the time-space optical field can be written as:
φ(x，t)＝φ(x，Ω/kGDD)＝φ(x′，y′/a/kGDD) (4)；
taking a space-time vortex optical volume (STOV) as an example, when the modulator applies a spatial vortex phase phi (x ', y') -l · theta to the positively chirped optical fieldx′-y′，θx′-y′Is the azimuth in the (x ', y') plane, and l is the topological charge number. The spatial vortex phase is forward mapped to the phase of the spatio-temporal light field in the spatio-temporal domain, resulting in the STOV light field. The spatio-temporal vortex phase direction of the light field coincides with the vortex direction of phi (x ', y').
Further, if the input optical field is zero chirp or negative chirp, the second-order phase phi (omega) in the omega-direction can be applied to GDD · omega by the modulator2(GDD > 0), the optical field is converted into a positive chirp state, and the function of forward mapping of the spatial phase phi (x ', y') is realized.
S42: when the spatio-temporal light field is negatively chirped, the spatial phase phi (x ', y') will be back-projected to the spatio-temporal light field. For negatively chirped spatio-temporal optical fields, the transient frequency of the field decreases linearly with time, i.e. kGDDIs less than 0. At this time, the transient frequency of the space-time light field and the time domain are still in one-to-one correspondence. The spatial phase phi (x ', y') is inverse mapped to the spatio-temporal phase of the spatio-temporal light field. The reverse direction means that the direction of the phase is reversed in the mapping relationship,
y′＝kGDD·a·t (6)；
for negative chirp space-time light field, kGDDIs less than 0. Taking an STOV wave packet as an example, when the modulator applies a spatial vortex phase phi (x ', y') -l · theta to a negatively chirped optical fieldx′-y′The generated space-time light field carries the space-time vortex phase phi (x, t) ═ l · thetax-tSpace-time vortex phase direction andthe vortex direction of phi (x ', y') is opposite.
Further, if the input optical field is zero-chirped or positive-chirped, the modulator may apply a second-order phase phi (omega) in the omega-direction, GDD-omega2(GDD is less than 0), the optical field is converted into a negative chirp state, and the function of reverse mapping of the spatial phase phi (x ', y') is realized.
S43: when the space-time light field is in a zero chirp state, the emergent space-time light field E (x, t) is one-dimensional Fourier transform of E (x, omega) with respect to frequency-time. The spatio-temporal light field E (x, t) can be written as:
at this time, the spatial phase φ (x ', y'), i.e., φ (x, a · Ω), applied by the modulator is mapped to the spatial-temporal phase of the optical field in the form of a one-dimensional Fourier transform.
For example: the method for mapping the space phase to the space-time light field space-time phase in the embodiment of the invention comprises the following steps:
the method comprises the following steps: after the collimated gaussian-gaussian spatiotemporal light field wave packet is input to the modulator shown in fig. 1, after the wave packet passes through the reflective grating (i.e. at point a0 in fig. 1), different optical frequency components of the incident wave packet will pass through the cylindrical lens at different angles and be collimated to the plane where the Spatial Light Modulator (SLM) is located. When the distance between the reflective grating, the cylindrical lens and the SLM is the focal length f of the cylindrical lens, the space-frequency domain light field of the incident space-time light field wave packet is projected to the SLM plane;
step two: the modulated light field passes through the second group of cylindrical lenses and the reflective grating and is reconstructed into a collimated emergent wave packet at the grating (point A1);
step three: when the SLM is loaded with spatial phase (e.g., spatial vortex phase), the outgoing spatio-temporal light field at the departure point a1 (defined here as z ═ 0) its spatio-temporal phase will be some mapping of the spatial phase loaded by the modulator. The specific mapping mode depends on the chirp state of the light field;
step four: when the spatio-temporal light field is positively chirped, its spatio-temporal phase will be a direct mapping of the spatial phase applied by the modulator. For example, when the spatial phase is a vortex phase, the spatio-temporal optical field will carry spatio-temporal vortex phases with the same vortex direction; when the spatio-temporal light field is negatively chirped, its spatio-temporal phase will be an inverse mapping of the spatial phase applied by the modulator. For example, when the spatial phase is a vortex phase, the spatio-temporal optical field will carry spatio-temporal vortex phases with opposite vortex directions; when the space-time light field is zero chirp, the space-time domain phase of the space-time light field will be one-dimensional Fourier transform of the added space phase.
While the present invention has been described in detail and with reference to the embodiments thereof as illustrated in the accompanying drawings, it will be apparent to one skilled in the art that various changes and modifications can be made therein. Therefore, certain details of the embodiments are not to be interpreted as limiting, and the scope of the invention is to be determined by the appended claims.
Claims (4)
1. A method for mapping a spatial phase to a spatio-temporal light field spatio-temporal phase, comprising the steps of:
s1: the method comprises the steps that collimated space-time light field wave packets are incident to a modulator, wherein the modulator comprises a first light splitting element, a first optical collimating element and a phase regulating element which are sequentially arranged;
s2: adjusting the distance among the first light splitting element, the first optical collimating element and the phase regulating element to be the focal length of the first optical collimating element, wherein the space frequency domain light field of the incident space-time light field wave packet is projected to the plane of the phase regulating element;
s3: if the phase control element is a reflective device, after phase control, the space-time light field wave packet returns to the first light splitting element according to the original path and is reconstructed into a collimated emergent space-time light field;
if the phase control element is a transmission-type device, the space-time light field wave packet passes through a group of second optical collimation element and second light splitting element which are in mirror symmetry with the first light splitting element and the first optical collimation element after being subjected to phase control, and is reconstructed into a collimated emergent space-time light field;
s4: and the phase of the emergent space-time light field after the modulator in the space-time domain is a mapping of the space phase applied by the phase control element in the modulator.
2. The method of mapping spatial phase to spatio-temporal light field spatio-temporal phase according to claim 1 wherein the first and second light splitting elements comprise reflective gratings, transmissive gratings or prisms; the first and second optical collimating elements comprise cylindrical lenses or cylindrical mirrors; the phase modulating element includes a spatial light modulator, a phase panel, or a deformable mirror.
3. The method for mapping spatial phases to spatio-temporal light field spatio-temporal phases according to claim 1, wherein in the step S4, the mapping relationship between the spatial phases to spatio-temporal light field spatio-temporal phases can be obtained by the following equations (1) to (4):
φ(x′，y′)＝φ(x，a·Ω) (1)；
E(x，Ω)＝E0(x，Ω)·ei·φ(x′，y′)＝E0(x，Ω)·ei·φ(x，a·Ω) (2)；
Ω(t)＝kGDD·t (3)；
φ(x，t)＝φ(x，Ω/kGDD)＝φ(x′，y′/a/kGDD) (4)；
wherein φ (x ', y') represents the phase applied by the phase modulating element in the modulator, x represents the spatial domain coordinate of the incident light field, Ω represents the optical frequency domain coordinate of the light field, and a represents the splitting coefficient of the modulator for the incident light field, determined by the first splitting element and the first optical collimating element or the second splitting element and the second optical collimating element; e0(x, omega) represents a spatial frequency domain light field of an incident space-time light field on a phase control element plane, and E (x, omega) represents the spatial frequency domain light field after phase control; omega (t) is the transient frequency variation of the emergent space-time light field in the time domain along with the timeFunction of kGDDIs the chirp coefficient; t represents time; phi (x, t) represents the spatio-temporal vortex phase.
4. The method of mapping spatial phases to spatio-temporal optical fields spatio-temporal phases according to claim 3, wherein when the spatio-temporal optical fields are in different chirp states, the spatial phases loaded by the modulator φ (x ', y') will map to the spatio-temporal phases of the spatio-temporal optical fields in different forms; in the formula (4), kGDDDetermining the chirp state of the optical field;
when k isGDDIf the phase is more than 0, the optical field is in a positive chirp state, and the space phase phi (x ', y') is mapped to the time-space domain phase of the space-time optical field in a positive mapping mode;
when k isGDD< 0, the light field is in a negative chirp state, the spatial phase phi (x ', y') will be mapped to the time-space domain phase of the space-time light field in a reverse mapping mode;
when k isGDD0, the light field is in a zero chirp state, the spatial phase phi (x ', y') will map the mapping mode in one-dimensional fourier transform to the time-space domain phase of the space-time light field, which can be written as:
wherein E (x, t; 0) represents the exit spatio-temporal light field.
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