CN113589560B - Method and system for generating orbital angular momentum optical comb based on angular binarization phase - Google Patents

Method and system for generating orbital angular momentum optical comb based on angular binarization phase Download PDF

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CN113589560B
CN113589560B CN202110877868.XA CN202110877868A CN113589560B CN 113589560 B CN113589560 B CN 113589560B CN 202110877868 A CN202110877868 A CN 202110877868A CN 113589560 B CN113589560 B CN 113589560B
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付时尧
尚紫君
高春清
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
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    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
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    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
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    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on liquid crystals, e.g. single liquid crystal display cells
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Abstract

The invention discloses an orbital angular momentum optical comb generation method and system based on an angular binarization phase. The invention introduces a phase turning point for the pure phase grating along the angular coordinate, and the phase jump from 0 to pi or pi to 0 occurs at the turning point, thereby generating the 0-pi angular binary phase grating. Setting proper number of phase turning points and angular position coordinates thereof, the incident fundamental mode Gaussian beam can be modulated into a structural beam containing a series of orbital angular momentum modes with equal mode intervals and equal mode intensity, namely an orbital angular momentum optical comb. The orbital angular momentum mode range and mode interval of the generated orbital angular momentum optical comb are only related to the number of angular phase turning points and angular position coordinates. The orbital angular momentum optical comb generation system based on the angular binarization phase adopts the fundamental mode Gaussian beam to directly irradiate the angular binarization phase grating, has simple structure and strong stability, and has wide application prospect in the fields of holographic information encryption, polymorphic orbital angular momentum keying communication and the like.

Description

Method and system for generating orbital angular momentum optical comb based on angular binarization phase
The technical field is as follows:
the invention relates to the technical field of photoelectricity, in particular to a method and a system for generating an orbital angular momentum optical comb based on an angular binarization phase.
Background art:
like macroscopic objects, microscopic particles such as photons also carry angular momentum. The angular momentum carried by the photons includes both Spin Angular Momentum (SAM) and Orbital Angular Momentum (OAM). Wherein the SAM corresponds to a macroscopic left-right hand circular polarization state; OAM corresponds to the spiral wavefront of the beam. Research shows that the complex amplitude contains a spiral phase factor
Figure BDA0003185215390000013
Is a vortex beam, where l is the topological charge, also known as OAMThe order of the mode is,
Figure BDA0003185215390000014
are angular coordinates. Each photon of the vortex beam carries a value of
Figure BDA0003185215390000011
OAM of (2), (b)
Figure BDA0003185215390000012
To approximate planck constant), the spiral phase makes the beam center have a phase singularity, making the cross-section light intensity distribution ring. The topological charge l is an intrinsic value of the vortex light beam, can take any integer value, and determines the amount of OAM carried by the vortex light beam, and the topological charge l at the moment corresponds to an OAM mode of the vortex light beam. Due to the introduction of OAM freedom degree, the vortex light beam has extremely high application value in a plurality of fields such as large-capacity optical communication, rotator detection, optical tweezers and gravitational wave detection.
Previous research provides various vortex beam generation schemes, mainly including two modes of laser intracavity direct generation and extracavity modulation. However, most of the above methods only focus on how to generate a single or simple multiplexed OAM pattern. In fact, generating a multimode multiplexing OAM optical beam, i.e. an OAM optical comb, carrying a series of equal mode intervals and equal mode intensities is of great significance for the current practical application scenario. For example, information is loaded in a fundamental mode Gaussian beam and then converted into an OAM optical comb, so that single-channel to multi-channel broadcasting of transmission signals can be realized; the OAM optical comb may also act as a flexible key for holographic encryption and decryption. However, the existing OAM spectrum clipping technology or OAM optical comb generation scheme often has the problems of long grating calculation time, complex system or low diffraction efficiency. Therefore, it is one of the problems to be solved in the art to develop a simple, flexible and practical method for selectively generating an OAM comb.
The invention content is as follows:
in view of this, the invention discloses an OAM optical comb generating method and system based on an angular binarization phase.
According to the OAM optical comb generation method based on the angular binarization phase, a beam of fundamental mode Gaussian beam can be modulated into a multimode multiplexing OAM beam carrying a series of equal OAM mode intervals and equal OAM mode intensities through reasonably designing the diffraction grating, namely the OAM optical comb.
The diffraction grating is a 0-pi angular binarization phase grating, a phase turning point is introduced for the pure phase grating along the angular coordinate direction, and a phase jump from 0 to pi or pi to 0 exists at the turning point. By setting the appropriate number of phase turning points and the angular position coordinates thereof, when a fundamental mode Gaussian beam is incident, a series of OAM optical combs containing different OAM mode ranges and different OAM mode intervals can be generated.
The OAM optical comb generation system based on the angular binarization phase comprises a laser, a polarizer, a liquid crystal spatial light modulator, a plano-convex lens and an area array detector.
The laser is used for generating a fundamental mode Gaussian beam;
the polarizer is arranged in a laser light path behind the laser and is used for generating a horizontal line polarization fundamental mode Gaussian beam;
the liquid crystal spatial light modulator is arranged in a laser light path behind the polarizer, is loaded with the angular binarization phase grating, and converts a horizontal line polarization fundamental mode Gaussian beam into a multimode multiplexing OAM beam which comprises a series of different OAM modes, and has equal OAM mode interval and equal OAM mode intensity, namely an OAM optical comb;
the focal length of the plano-convex lens is f, the plano-convex lens is arranged in a laser light path which is behind the liquid crystal spatial light modulator and has a distance f from the liquid crystal spatial light modulator, and the plano-convex lens is used for performing Fourier transform on a light field so as to facilitate the observation of a far-field OAM optical comb by an area array detector;
the area array detector is arranged in a laser light path behind the plano-convex lens, is spaced from the plano-convex lens by a distance f, and is used for observing the generated OAM optical comb.
The invention has the following beneficial effects:
(1) the OAM optical comb generation method based on the angular binarization phase introduces the phase turning points for the pure phase grating along the angular coordinate direction, and can modulate the incident fundamental mode Gaussian beam into a multimode multiplexing OAM beam which comprises a series of different OAM modes, and has equal OAM mode interval and equal OAM mode intensity, namely the OAM optical comb, by reasonably setting the number of the angular phase turning points and the angular position coordinate, so that the OAM optical comb generation method has wide application prospect in the fields of polymorphic orbital angular momentum keying communication, holographic information encryption and the like;
(2) in the OAM optical comb generation system based on the angular binarization phase, the generation of the OAM optical comb is realized by a series of angular binarization phase gratings which are specially designed according to the OAM mode range and the mode interval requirement of the needed OAM optical comb, and the system has simple structure and strong stability.
Description of the drawings:
FIG. 1 is a diagram illustrating an angular phase distribution of an angular binarization phase grating of the present invention in a single period;
fig. 2 is an angular binarization phase grating designed based on the present invention, and the intensity distribution and OAM spectrum of the OAM optical comb generated thereby;
fig. 3 is a schematic device diagram of an angular binarization phase-based OAM optical comb generation system of the present invention, wherein 1-a laser, 2-a single mode fiber, 3-a collimating mirror, 4-a polarizer, 5-a liquid crystal spatial light modulator, 6-a plano-convex lens, and 7-a planar array detector;
fig. 4 is an OAM comb actually generated based on the method and system of the present invention, which is composed of 64 OAM modes, the OAM mode range is-63- +63, and the OAM mode interval is Δ l ═ 2;
fig. 5 is an OAM comb actually generated based on the method and system of the present invention, which is composed of 32 OAM modes, the OAM mode range is-62- +62, and the OAM mode interval is Δ l-4.
The specific implementation mode is as follows:
the invention is described in detail below with reference to the accompanying drawings and examples.
The principle of the method for generating the angular binarization-phase-based OAM optical comb according to the present invention is briefly described as follows.
A dammann grating is a phase-only grating with a periodic 0-pi binary change of the phase in the x or y direction in a cartesian coordinate system. By reasonably setting the number of phase turning points and the position coordinates corresponding to the change direction, the incident beam can be expanded on a space position, and one path of incident beam is divided into multiple paths of beams with equal intensity and equal diffraction angle intervals, so that a laser beam array is formed. Similar to dammann grating, 0-pi alternation is introduced in an angular coordinate system for the phase in the angular direction, as shown in fig. 1, by setting a proper number of phase turning points and angular position coordinates thereof, an incident fundamental mode gaussian beam can be modulated into a multimode multiplexing OAM beam including a series of equal OAM mode intervals and equal OAM mode intensities, i.e., an OAM optical comb.
Such a pure phase grating with a phase varying in a polar coordinate system along an angular 0-pi binarization is called an angular binarization phase grating, and its phase distribution function can be expressed as:
Figure BDA0003185215390000021
wherein K represents the number of corner points of the angular phase in the range of 0-2 pi,
Figure BDA0003185215390000022
in the form of an angular coordinate, the angular position,
Figure BDA0003185215390000023
indicating the angular position coordinates of the k-th phase inflection point. Setting the transmittance function of the angular binarization phase grating as
Figure BDA0003185215390000024
Diffraction integral calculation is carried out on the transmittance function, and far-field diffraction distribution of the plane wave after the plane wave passes through the angular binarization phase grating under an ideal condition can be obtained as follows:
Figure BDA0003185215390000025
wherein l represents the OAM mode order; c. ClIs a complex coefficient which is an array of angular phase inflection points
Figure BDA0003185215390000026
Represents the complex amplitude, | c, of the l-order OAM mode componentl|2I.e. the strength of the OAM mode component of order l. The formula shows that the multimode mixed OAM light beam can be effectively generated by introducing the angular binary phase, and the intensity of each OAM component contained in the light beam is determined by the angular phase turning point array
Figure BDA0003185215390000027
To determine.
Angular phase turning point array
Figure BDA0003185215390000028
The numerical solution can be obtained by an iterative optimization algorithm such as a GS algorithm, a random parallel gradient descent algorithm and the like. At the best
Figure BDA0003185215390000029
In the solving process, two evaluation parameters are needed to be set, namely efficiency eta and uniformity U. Where efficiency is defined as η ═ (Σ)l∈L|cl|2)/Σl∈Z|cl|2Wherein, L represents an OAM mode set of the needed OAM optical comb, and Z represents an integer set; uniformity is defined as U ═ 2min { | cl|2}/(max{|cl|2}+min{|cl|2) }, where L ∈ L, min { } and max { } represent taking the minimum value and taking the maximum value, respectively. The numerical solution of the angular phase turning point coordinates when the diffraction efficiency eta is maximum and the uniformity U is maximum is found through iterative optimization, and then the angular phase turning point array is obtained
Figure BDA00031852153900000210
Furthermore, the method can also be used according to the literature [ appl.Opt.34(26),5961(2995)]And giving a numerical solution of the phase turning point of the 0-pi binary Dammann grating, and obtaining the phase turning point by constructing a mapping relation from a rectangular coordinate system to a polar coordinate system.
And the 0-pi angular binarization phase grating is used for generating the OAM optical comb and is obtained by constructing a numerical solution of the corresponding phase turning point number and the angular position coordinate thereof through a computer according to the OAM mode range and the mode interval of the needed OAM optical comb. After the diffraction grating is obtained through calculation, far-field diffraction of the incident fundamental mode Gaussian beam can be obtained through numerical simulation calculation. Fig. 2 shows an angular binarization phase grating designed according to the method, and intensity distribution and an OAM spectrum of an OAM optical comb generated by the angular binarization phase grating. As can be seen from the OAM spectrum shown in fig. 2, after the incident plane wave is diffracted by the angular binarization phase grating, an OAM optical comb including 9 kinds of equal-intensity OAM modes is generated, in which the OAM mode order range is-4 to 4 and the OAM mode interval is 1. The angular binary phase grating generating the OAM optical comb has 6 phase turning points in total, and the corresponding angular position coordinates are 0, 0.4190, 0.8087, 1.7963, 2.8693 and 3.7127, respectively. At this time, the efficiency and uniformity of the generated OAM optical comb were 78.32% and 99.61%, respectively.
The OAM optical comb generation system based on the angular binarization phase is shown in figure 3 and comprises a laser, a polarizer, a liquid crystal spatial light modulator, a plano-convex lens and an area array detector. Wherein: the laser is used for generating a fundamental mode Gaussian beam; the polarizer is arranged in a laser light path behind the laser and is used for generating a horizontal line polarization fundamental mode Gaussian beam; the liquid crystal spatial light modulator is arranged in a laser light path behind the polarizer, is loaded with the angular binarization phase grating, and converts a horizontal line polarization fundamental mode Gaussian beam into a multimode multiplexing OAM beam which comprises a series of different OAM modes, equal OAM mode intervals and equal OAM mode intensities, namely an OAM optical comb; the focal length of the plano-convex lens is f, the plano-convex lens is arranged in a laser light path which is behind the liquid crystal spatial light modulator and has a distance f from the liquid crystal spatial light modulator, and the plano-convex lens is used for performing Fourier transform on a light field so as to facilitate the observation of a diffraction light field by the area array detector; the area array detector is arranged in a laser light path behind the plano-convex lens, is away from the plano-convex lens by a distance f and is used for observing the generated OAM optical comb.
The modulation performance of the method and system for generating the OAM optical comb based on the angular binarization phase according to the present invention will be briefly described below with reference to two embodiments.
Example 1: and generating an OAM mode range: OAM optical comb of-63- +63, OAM mode interval Deltal ═ 2
In bookIn the embodiment, according to the OAM state range and the mode interval of the OAM optical comb, the phase distribution of the angular binarization phase grating obtained by computer numerical calculation comprises 70 angular phase turning points
Figure BDA0003185215390000031
The composition of (A) is as follows:
{0,0.0654,0.1095,0.1854,0.2550,0.2996,0.3825,0.4433,0.5277,0.6118,0.6456,0.8074,0.9000,1.3369,1.5495,1.6505,1.7605,1.8155,1.8639,1.9960,2.0368,2.1219,2.2730,2.4053,2.4895,2.5937,2.6624,2.7229,2.7530,2.8186,2.8867,2.9336,2.9799,3.0406,3.0747,3.1416,3.2070,3.2511,3.3270,3.3966,3.4412,3.5241,3.5849,3.6693,3.7534,3.7872,3.9490,4.0416,4.4785,4.6911,4.7921,4.9021,4.9571,5.0055,5.1376,5.1784,5.2635,5.4146,5.5469,5.6311,5.7353,5.8040,5.8645,5.8946,5.9602,6.0283,6.0752,6.1215,6.1822,6.2163}
and loading the angular binarization phase grating on a liquid crystal spatial light modulator to obtain far-field diffraction of the incident fundamental mode Gaussian beam after modulation by the liquid crystal spatial light modulator, namely the generated OAM optical comb. The OAM mode of the OAM optical comb obtained by the experiment is analyzed by the spiral phase inversion method to obtain an OAM spectrum of the OAM optical comb generated in this embodiment, as shown in fig. 4, the generated OAM optical comb includes 64 OAM states (i.e., comb teeth), the uniformity reaches 92.04%, and it is better to match with the theoretical simulation.
Example 2: and generating an OAM mode range: OAM optical comb of-62- +62, OAM mode interval delta l ═ 4
In this embodiment, according to the OAM state range of the OAM optical comb and its mode interval, the phase distribution of the angular binary phase grating obtained by the computer numerical calculation includes 68 angular phase turning points, and
Figure BDA0003185215390000032
the composition of (A) is as follows:
{0,0.1740,0.2796,0.3459,0.4191,0.5441,0.6151,0.6626,0.7245,0.7813,1.0370,1.0939,1.2598,1.3609,1.3858,1.4618,1.5205,1.5708,1.7448,1.8504,1.9167,1.9899,2.1149,2.1859,2.2334,2.2952,2.3521,2.6078,2.6647,2.8306,2.9317,2.9566,3.0326,3.0913,3.1416,3.3156,3.4212,3.4875,3.5607,3.6857,3.7567,3.8042,3.8660,3.9229,4.1786,4.2355,4.4014,4.5025,4.5273,4.6034,4.6621,4.7124,4.8864,4.9920,5.0583,5.1315,5.2565,5.3275,5.3750,5.4368,5.4937,5.7494,5.8063,5.9722,6.0733,6.0981,6.1742,6.2329}
and loading the angular binarization phase grating on a liquid crystal spatial light modulator to obtain far-field diffraction of the incident fundamental mode Gaussian beam after modulation by the liquid crystal spatial light modulator, namely the generated OAM optical comb. The OAM mode of the OAM optical comb obtained by the experiment is analyzed by the spiral phase inversion method to obtain an OAM spectrum of the OAM optical comb generated in this embodiment, as shown in fig. 5, the generated OAM optical comb includes 32 OAM states (i.e., comb teeth), the uniformity reaches 90.95%, and it is better in agreement with the theoretical simulation.
The embodiment shows that the OAM optical comb generation method and system based on the angular binarization phase have good performance.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. The utility model provides a can generate orbital angular momentum optical comb's angular binarization phase grating which characterized in that:
(1) a phase turning point exists along the angular direction, and a phase jump from 0 to pi or pi to 0 exists at the turning point;
(2) the phase distribution function is:
Figure FDA0003579770040000011
wherein K represents the number of corner points of the angular phase in the range of 0-2 pi,
Figure FDA0003579770040000012
in the form of an angular coordinate, the angular position,
Figure FDA0003579770040000013
angular position coordinates representing the kth phase inflection point;
(3) under ideal conditions, the far field diffraction distribution of the plane wave after being diffracted by the angular binarization phase grating is as follows:
Figure FDA0003579770040000014
wherein l represents the order of orbital angular momentum mode; c. ClIs a complex coefficient which is an array of angular phase inflection points
Figure FDA0003579770040000015
Represents the complex amplitude of the l-order orbital angular momentum mode component;
(4) the light beam of the plane wave after being diffracted by the angular binarization phase grating is a multimode mixed orbital angular momentum light beam, and the intensity of each orbital angular momentum component contained in the light beam is determined by an angular phase turning point array
Figure FDA0003579770040000016
To determine;
(5) by setting the number of phase turning points and the angular position coordinates thereof, the required orbital angular momentum optical comb can be generated.
2. An orbital angular momentum optical comb generation method based on the angular binarization phase grating of claim 1 is characterized in that the angular binarization phase grating of claim 1 is irradiated by a fundamental mode Gaussian beam, and a diffraction field is a multimode multiplexing orbital angular momentum beam carrying a series of equal orbital angular momentum mode intervals and equal orbital angular momentum mode intensities, namely an orbital angular momentum optical comb.
3. An orbital angular momentum optical comb generating system based on the angular binarization phase grating as claimed in claim 1, characterized by comprising a laser, a polarizer, a liquid crystal spatial light modulator, a plano-convex lens and an area array detector:
the laser is used for generating a fundamental mode Gaussian beam;
the polarizer is arranged in a laser light path behind the laser and is used for generating a horizontal line polarization fundamental mode Gaussian beam;
the liquid crystal spatial light modulator is arranged in a laser light path behind a polarizer, is loaded with the angular binarization phase grating as described in claim 1, and converts a horizontal line polarization fundamental mode Gaussian beam into a multimode multiplexing orbital angular momentum beam which comprises a series of different orbital angular momentum modes, and has equal orbital angular momentum mode intervals and equal orbital angular momentum mode intensity, namely an orbital angular momentum comb;
the focal length of the plano-convex lens is f, the plano-convex lens is arranged in a laser light path which is behind the liquid crystal spatial light modulator and has a distance f from the liquid crystal spatial light modulator, and the plano-convex lens is used for performing Fourier transform on a light field so as to facilitate the observation of a far field orbital angular momentum optical comb by an area array detector;
the area array detector is arranged in a laser light path behind the plano-convex lens, is spaced from the plano-convex lens by f and is used for observing the generated orbital angular momentum optical comb.
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