High-order deterministic vortex generation method and device based on coherent structure regulation and control

Abstract

The invention relates to the technical field of optics, in particular to a high-order deterministic vortex generation method and device based on coherent structure regulation, and the method comprises the steps: coding the angular and radial order characteristics of a Laguerre-Gaussian beam to a random beam through fractional Fourier transform; constructing a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance; converting into controllable random electric field distribution through mode decomposition to obtain a cross spectral density function; completely coherent plane waves are introduced as reference light to interfere with random field signal light of a specified transmission distance, interference intensity light spots are obtained, and a random electric field is recovered from the interference intensity light spots by using an off-axis holographic method; based on the cross spectral density function and the random electric field, the high-order vortex beam with controllable order is generated, and flexible generation of the high-order vortex beam at a specified transmission distance is realized.

Description

Technical Field

[0001] The present invention relates to the field of optical technology, and in particular to a method and device for generating high-order deterministic vortices based on coherent structure regulation. Background Art

[0002] Vortex beams, also known as beams carrying orbital angular momentum (OAM), have a unique phase structure that shows a hollow intensity distribution with a phase singularity at the center of the intensity. With these unique properties, OAM beams can not only be used to rotate particles, but also provide strong support for high-capacity information transmission.

[0003] Optical coherence is another key degree of freedom in the field of light field control. Studies have shown that reducing the spatial coherence of the light field can largely suppress phase-sensitive speckle noise. At the same time, partially coherent beams are more robust against the negative effects of optical turbulence than fully coherent beams. In recent years, partially coherent vortex beams, that is, beams that combine optical vortices with partial coherence properties, have shown many unique advantages and have been widely used in optical imaging, sensing, detection, and computing.

[0004] However, there is an inherent contradiction between optical vortices and partial coherence. In a fully coherent light field, the vortex phase has a definite structure; while in a partially coherent vortex light field, the amplitude and phase fluctuate randomly in both space and time. Previous studies have found that during the propagation of a partially coherent vortex beam, its phase will evolve into a singularity related to the correlation function between two points in space, that is, a coherent singularity or a coherent vortex, while the intensity singularity (or phase singularity) will disappear. Recently, Miao et al. proposed that by combining optical vortices and coherence regulation, a deterministic optical vortex can be constructed at a specified transmission distance.

[0005] However, the existing technology for generating deterministic vortices from random beams at a specified transmission distance is still only at the theoretical level. Moreover, the existing technology can only achieve deterministic vortices with a minimum angular order, that is, an angular order of l = 1 and radial order p =0 Laguerre-Gaussian (LG) beam, which greatly limits the application of vortex beams in practical production fields such as information transmission. Studies have shown that in high-dimensional communications, high-order angular and radial orders play a vital role in the multiplexing and demultiplexing of signals. Therefore, how to generate high-order vortices with controllable orders through random beams at a specified distance remains an urgent problem to be solved. In addition, the correlation function of partially coherent light at a specific transmission distance is a four-dimensional (4D) distribution function related to the spatial position of the two points. Experimentally, the complete measurement and characterization of its four-dimensional correlation function and its inherent coherent vortex is also a scientific problem that has not yet been overcome. Summary of the invention

[0006] Based on the above background technology, the technical problem to be solved by the present invention is to realize the generation of high-order vortex beams in random beams, and to complete the complete characterization of the four-dimensional (4D) distribution correlation function of partially coherent light at a specific transmission distance related to the spatial positions of two points. In order to solve the above technical problems, the present invention provides a method and device for generating high-order deterministic vortices based on coherent structure regulation, and the method comprises the following steps: Step S1: encoding the angular and radial order characteristics of the Laguerre-Gaussian beam into a random beam by fractional Fourier transform, and constructing a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified transmission distance; Step S2: using mode decomposition to transform the theoretical model into a random electric field distribution that can be actually controlled, and obtaining a cross spectral density function of the deterministic vortex beam; Step S3: introducing a beam of fully coherent plane waves as reference light, interfering the reference light with the random field signal light at a specified transmission distance, and obtaining a series of interference intensity spots; Step S4: recovering a series of random electric fields from the series of interference intensity spots, and obtaining a deterministic vortex beam with controllable angular order and radial order based on the cross spectral density function and the random electric field.

[0007] In one embodiment of the present invention, in S1, a method for constructing a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance is as follows: S11: A deterministic vortex beam of arbitrary radial and angular order is regarded as an incoherent superposition of infinite wave modes, which is characterized by the cross-spectral density function at the source plane as follows: S11: A deterministic vortex beam of arbitrary radial and angular order is regarded as an incoherent superposition of infinite wave modes, which is characterized by the cross-spectral density function at the source plane as follows: , in, are represented by any two lateral position vectors at the light source surface, is an arbitrary non-negative function, is a spatial two-dimensional frequency variable, express of x Directional component, express of y Directional component; is an arbitrary kernel function, * indicates conjugation, represents the lateral position vector at the light source surface; S12: In order to generate a deterministic vortex beam with controllable order at a specified transmission distance, a coherence length-related constant is introduced, that is, , The theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified transmission distance is obtained. : , in, is a real constant related to the coherence length of the beam, is the electric field expression of the Laguerre-Gaussian beam at the focal plane z = 0, represents the fractional Fourier transform function, represents the fractional Fourier transform domain coordinates; and are the two lateral position vectors of the output plane; Represents light wave mode The kernel function of the system propagates from the source plane to the z plane, Represents the spatial coordinates of the transmission surface.

[0008] In one embodiment of the present invention, the electric field expression of the Laguerre-Gaussian beam on the focal plane z=0 is: In cylindrical coordinates The following expression is as follows: , in, r represents the radial distance in the cylindrical coordinate system, represents the azimuth, z Indicates the free space transmission distance; The radial order is expressed as , the angular order is Laguerre polynomials of ; and are the width and wavefront curvature of the beam at the distance z from the focal plane, respectively; It is the Gouy phase; is the wave number, is the wavelength; The angular order is l The vortex phase term, i Is an imaginary unit.

[0009] In one embodiment of the present invention, the fractional Fourier transform function for: , in, is a variable related to the fractional Fourier transform order, is the fractional order, is the waist width of the Laguerre-Gaussian beam in the focal plane.

[0010] In one embodiment of the present invention, the system kernel function for: , in, is the Fresnel diffraction integral function, .

[0011] In one embodiment of the present invention, in S2, the method for obtaining the cross spectral density function of the deterministic vortex beam is as follows: Using the cross spectral density function in the mode decomposition formula (1), we get: , Where N is the total number of modes, are non-negative weights; is the instantaneous electric field in the source plane; The weights of all electric field modes are , the real and imaginary parts of each electric field mode are randomly distributed in space and satisfy Gaussian statistics, which can be expressed as , where IFT stands for inverse Fourier transform, is a complex Gaussian random number with mean zero and variance 1; and The product of is fractional Fourier transform, and the result is z A random electric field with a controllable high-order vortex source is generated at: , After the random electric field is transmitted in free space, the cross spectral density function at the propagation distance z is obtained as follows: , in, .

[0012] In one embodiment of the present invention, in S3, the method for obtaining a series of interference intensity spots is: A completely coherent plane wave is introduced as the reference light. The plane wave reference light in the reference light path is coherently superimposed with the instantaneous random electric field of the generated deterministic vortex beam to obtain the intensity of a series of interference intensity spots. It is expressed by the following formula: , in, is the random light field at the propagation distance z; is the electric field of the reference light, and Wave vector The angles with the x and y axes, and is a constant phase; represents the real part, i Is an imaginary unit.

[0013] In one embodiment of the present invention, in S4, the method for recovering a series of random electric fields from the series of interference intensity spots is as follows: The intensity data of the series of interference intensity spots are subjected to Fourier transformation to obtain multiple separated frequency domain components in the frequency domain, including random electric field The first separated frequency domain component is proportional to the random electric field A second separated frequency domain component proportional to the complex conjugate of After the first separated frequency domain component is moved to the center of the zero value matrix, an inverse Fourier transform is performed to obtain a complex valued electric field corresponding to the instantaneous interference light intensity.

[0014] Based on the same inventive concept, the present invention also provides a high-order deterministic vortex generating device based on coherent structure regulation, which is used to implement the steps of the high-order deterministic vortex generating method based on coherent structure regulation, and the device includes an interference intensity spot generating module and a control system; The interference intensity spot generating module is used to introduce a beam of completely coherent plane waves as reference light, interfere the reference light with the random field signal light at a specified transmission distance, and obtain a series of interference intensity spots; The control system is used to encode the angular and radial order characteristics of a Laguerre-Gaussian beam into a random beam through fractional Fourier transform, construct a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance, and use mode decomposition to transform the theoretical model into a random electric field distribution that can be actually controlled to obtain a cross-spectral density function of the deterministic vortex beam; and recover a series of random electric fields from the series of interference intensity spots, and obtain a deterministic vortex beam with controllable angular order and radial order based on the cross-spectral density function and the random electric field.

[0015] In one embodiment of the present invention, the interference intensity spot generation module includes: a light source module, a beam modulation module, a beam processing module, a free space transmission module, a reference light generation module and a detection and interference module Wherein, the light source module comprises a laser, a first attenuation plate, a first beam expander and a first beam splitter which are placed in sequence, and the first beam splitter divides the light beam propagation path of the first beam expander into a first branch and a second branch; The beam modulation module comprises a phase spatial light modulator, and the phase spatial light modulator is arranged on the first branch; The light beam processing module includes a first lens, a single-hole filter, and a second lens arranged on the first branch, and screens the light beam modulated by the phase spatial light modulator to obtain a random field signal light in a specified diffraction order range; The free space transmission module comprises a first reflector, a second reflector, a third reflector, a fourth reflector and a movable displacement platform, wherein the first reflector and the second reflector are mounted on a fixed end of the movable displacement platform, and the fixed end is located behind the second lens, and the third reflector and the fourth reflector are mounted on a movable end of the movable displacement platform to adjust the light beam transmission distance and generate a random field signal light at a specified transmission distance; The reference light generation module comprises a fifth reflector, a second attenuation plate, a second beam expander and a sixth reflector which are sequentially arranged on the second branch to generate a plane wave reference light; The detection and interference module includes a second beam splitter and a CCD detector, which is used to interfere the plane wave reference light with the random field signal light at the specified transmission distance to obtain a series of interference intensity spots and acquire their intensity distribution.

[0016] The above technical solution of the present invention has the following advantages compared with the prior art: 1. The present invention utilizes light field coherent structure control and fractional Fourier transform to achieve coded hiding of high-order deterministic vortices at the light source, and to achieve flexible construction of high-order vortices with precisely controllable order at a specified transmission distance.

[0017] 2. The device provided by the present invention only needs to use a single spatial light modulator and an off-axis holographic interferometer system. Without changing the optical experimental system, by pre-planning the key parameters such as the order of the high-order vortex beam and specifying the transmission distance, and generating a computer-generated hologram based on this, the transmission and measurement of the controllable high-order vortex partially coherent beam at any target distance can be achieved.

[0018] 3. The present invention does not require pre-designed mask plates, does not rely on optical hardware such as scattering media, has high flexibility, low cost, and has broad application prospects in various fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein: Figure 1 It is a schematic flow chart of a high-order deterministic vortex generation method based on coherent structure regulation provided in an embodiment of the present invention; Figure 2 The present invention is a process for recovering a series of random electric fields from the series of interference intensity spots by using the off-axis holographic method, wherein (a) represents a series of interference intensity spots, (b) represents the Fourier transform result of the interference intensity spots, (c) represents moving the separated frequency domain components proportional to the random electric field to the center of the zero value matrix, and (d) represents the complex value electric field corresponding to the instantaneous interference light intensity; Figure 3 is a schematic structural diagram of a high-order deterministic vortex generating device based on coherent structure regulation provided in an embodiment of the present invention; Figure 4 yes Figure 3 A schematic diagram of the structure of the interference intensity spot generating module in the device; Figure 5 (a) to (e) are the experimental results of vortex beams generated at different transmission distances z of 0mm, 250mm, 500mm, 750mm, and 1000mm respectively; Figure 6 (a) to (e) are the experimental results of vortex beams generated at different transmission distances z of 0mm, 250mm, 500mm, 750mm, and 1000mm respectively; Explanation of the reference numerals in the specification: 100, interference intensity spot generating module; 10, light source module; 101, laser; 102, first attenuation plate; 103, first beam expander; 104, first beam splitter; 20, beam modulation module; 201, phase spatial light modulator; 30, beam processing module; 301, first lens; 302, single-hole filter; 303, second lens; 40, free space transmission module; 401, first reflector; 402, second reflector; 403, third reflector; 404, fourth reflector; 405, movable displacement platform; 50, reference light generating module; 501, fifth reflector; 502, second attenuation plate; 503, second beam expander; 504, sixth reflector; 60, detection and interference module; 601, second beam splitter; 602, CCD detector; 200, control system. DETAILED DESCRIPTION

[0020] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0021] Embodiment 1

[0022] like Figure 1 As shown, the present invention provides a high-order deterministic vortex generation method based on coherent structure regulation, the method comprising the following steps: Step S1: encoding the angular and radial order characteristics of the Laguerre-Gaussian beam into a random beam by fractional Fourier transform, and constructing a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified transmission distance; Step S2: using mode decomposition to transform the theoretical model into a random electric field distribution that can be actually controlled, and obtaining a cross spectral density function of the deterministic vortex beam; Step S3: introducing a beam of fully coherent plane waves as reference light, interfering the reference light with the random field signal light at a specified transmission distance, and obtaining a series of interference intensity spots; Step S4: recovering a series of random electric fields from the series of interference intensity spots, and obtaining a deterministic vortex beam with controllable angular order and radial order based on the cross spectral density function and the random electric field.

[0023] Furthermore, in S1, a method for constructing a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance is as follows: S11: According to the generalized van Sietszenic theorem, a deterministic vortex beam of arbitrary radial and angular order is regarded as an incoherent superposition of infinite wave modes, which is characterized by the cross-spectral density function at the source plane as follows: , in, are represented by any two lateral position vectors at the light source surface, is an arbitrary non-negative function, is a spatial two-dimensional frequency variable, express of x Directional component, express of y Directional component; is an arbitrary kernel function, * indicates conjugation, represents the lateral position vector at the light source surface; S12: In order to generate a deterministic vortex beam with controllable order at a specified transmission distance, a coherence length related constant is introduced, that is, , , in, is a real constant related to the coherence length of the beam, is the electric field expression of the Laguerre-Gaussian beam at the focal plane z = 0, which is expressed in the cylindrical coordinate system The following expression is as follows: , in, , r represents the radial distance in the cylindrical coordinate system, represents the azimuth, z Indicates the free space transmission distance; The radial order is expressed as , the angular order is Laguerre polynomials of ; and are the width and wavefront curvature of the beam at the distance z from the focal plane, respectively; It is the Gouy phase; is the wave number, is the wavelength; The angular order is l The vortex phase term; Represents the fractional Fourier transform function as follows: , in, is a variable related to the fractional Fourier transform order, is a fractional order, and its value is . is the waist width of the Laguerre-Gaussian beam in the focal plane, i Is an imaginary unit.

[0024] By reorganizing the above formulas, we can obtain the theoretical model of the deterministic vortex beam propagating from the source plane to the plane with the axis coordinate z. : , in, and are the two lateral position vectors of the output plane; Represents light wave mode The kernel function of the system propagating from the source plane to the z plane is used to obtain the light wave mode according to the Huygens-Fresnel principle. The kernel function of the system propagating from the source plane to the z plane as follows: , in, is the lateral position vector of the output plane, including and ; is the Fresnel diffraction integral function, as follows: , Substituting formulas (3), (5) and (8) into formula (7), we obtain The final analytical expression is: , in: , in, , is the Gamma function, represents the binomial coefficient, is the Kronecker delta function. The final analytical expression of Determined.

[0025] The study found that in the off-axis position The vortex phase will be generated at the position where the vortex phase is determined by However, at the critical distance No matter where For any value of , the generated vortices will overlap and the vortex center will be fixed at the origin. Eventually, the coherent vortex will be at the critical distance A deterministic vortex structure is presented at . In addition, is a value that is independent of radial and angular order, and Can follow from changes, taking any value from zero to positive infinity. Therefore, by adjusting By adjusting the value of , a deterministic vortex beam can be generated at any desired distance.

[0026] Furthermore, in S2, in order to generate a deterministic vortex beam using a liquid crystal phase spatial light modulator (SLM) or a digital micromirror device, the theoretical model is converted into a random electric field distribution that can be actually controlled by mode decomposition, and the method for obtaining the cross spectral density function of the deterministic vortex beam is as follows: Using the cross spectral density function in the mode decomposition formula (1), we get: , Where N is the total number of modes, are non-negative weights; is the instantaneous electric field in the source plane; in this case, if the random pattern set Given, we can know all the information about the cross spectral density.

[0027] Here, for the random pattern set , the weights of all electric field modes Both , the real and imaginary parts of each electric field mode are randomly distributed in space and satisfy Gaussian statistics, which can be expressed as , where IFT stands for inverse Fourier transform, is a complex Gaussian random number with mean zero and variance 1. and The product of is subjected to fractional Fourier transform to obtain the value at the specified propagation distance. z A random electric field with a controllable high-order vortex source is generated at: , By repeating the above process multiple times, a random pattern set of the cross-spectral density function at the source plane is obtained. Then, using the Fresnel diffraction integral theorem, the random electric field is transmitted in free space, and the cross-spectral density function at the specified propagation distance z is obtained as: , in, .

[0028] Furthermore, in S3, a beam of completely coherent plane waves is introduced as reference light, and the reference light is interfered with the random field signal light at a specified transmission distance to obtain a series of interference intensity spots. A completely coherent plane wave is introduced as the reference light. The plane wave reference light in the reference light path is coherently superimposed with the instantaneous random electric field of the generated deterministic vortex beam to obtain the intensity of a series of interference intensity spots. It is expressed by the following formula: , in, is the random light field at the propagation distance z; is the electric field of the reference light, and Wave vector The angles with the x and y axes, and is a constant phase; represents the real part, i Is an imaginary unit.

[0029] like Figure 2 As shown, in S4, the method of recovering a series of random electric fields from the series of interference intensity spots using the off-axis holographic principle is as follows: S41: For Figure 2 Intensity data of a series of interference intensity spots shown in (a) Perform Fourier transform to obtain multiple separated frequency domain components in the frequency domain, including random electric field The first separated frequency domain component is proportional to the random electric field The complex conjugate of is proportional to the second separated frequency domain component, such as Figure 2 As shown in (b); S42: Figure 2As shown in (c), the random electric field After the separated frequency domain components proportional to each other are moved to the center of the zero value matrix, an inverse Fourier transform is performed to obtain the complex valued electric field corresponding to the instantaneous interference light intensity. ,like Figure 2 As shown in (d).

[0030] A series of continuous interference intensity spot images are recorded and saved using a photoelectric signal detector (such as a CCD detector). Each image is then processed through steps S41 and S42 to finally obtain a random electric field pattern set. .

[0031] The random electric field pattern set Substituting into the cross spectral density function shown in formula (13) To achieve the specified transmission distance z The four-dimensional cross-spectral density signal at is measured and characterized, and then a deterministic vortex beam with controllable angular order and radial order is obtained. Embodiment 2

[0032] Based on the same inventive concept as that of the first embodiment, the present invention further provides a high-order deterministic vortex generating device based on coherent structure regulation, which is used to implement the steps of the high-order deterministic vortex generating method based on coherent structure regulation described in the first embodiment. Figure 3 and Figure 4 As shown, the device includes an interference intensity spot generating module 100 and a control system 200; The interference intensity spot generating module 100 is used to introduce a beam of completely coherent plane waves as reference light, and interfere the reference light with the random field signal light at a specified transmission distance to obtain a series of interference intensity spots; The control system 200 is used to encode the angular and radial order characteristics of the Laguerre-Gaussian beam into a random beam through fractional Fourier transform, construct a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance, and use mode decomposition to convert the theoretical model into a random electric field distribution that can be actually controlled to obtain the cross-spectral density function of the deterministic vortex beam; and use the off-axis holographic principle to recover a series of random electric fields from the series of interference intensity spots, and based on the cross-spectral density function and the random electric field, obtain a deterministic vortex beam with controllable angular order and radial order.

[0033] Further, the interference intensity spot generation module 100 includes: a light source module 10, a beam modulation module 20, a beam processing module 30, a free space transmission module 40, a reference light generation module 50 and a detection and interference module 60; The light source module 10 includes a laser 101, a first attenuation plate 102, a first beam expander 103 and a first beam splitter 104 which are placed in sequence; the laser 101 emits a beam of fully coherent laser light with a wavelength of 532 nm, passes through the first attenuation plate 102 and the first beam expander 103, and the first beam splitter 104 is used to divide the light beam propagation path of the first beam expander 103 into a first branch and a second branch; The beam modulation module 20 includes a phase spatial light modulator 201, which is arranged on the first branch. The light beam passing through the first beam splitter 104 is uniformly transmitted to the phase spatial light modulator 201, and the phase spatial light modulator 201 is used to load a computer generated hologram (CGHs) of the electric field of the synthetic controllable high-order vortex partially coherent beam light source; The beam processing module 30 includes a first lens 301, a single-hole filter 302, and a second lens 303 arranged on the first branch. The focal lengths of the first lens 301 and the second lens 303 are equal, and the focal lengths f =250mm, forming a 4f imaging system, the light beam modulated by the phase spatial light modulator 201 enters the 4f imaging system for screening, and the single-hole filter 302 is placed between the first lens 301 and the second lens 303 to obtain the required +1-order diffraction random field signal light, shielding the unnecessary diffraction order and background noise; The free space transmission module 40 includes a first reflector 401, a second reflector 402, a third reflector 403, a fourth reflector 404 and a movable displacement platform 405. The first reflector 401 and the second reflector 402 are installed at a fixed end of the movable displacement platform 405, and the fixed end is located behind the second lens 303. The third reflector 403 and the fourth reflector 404 are installed at a movable end of the movable displacement platform 405 to adjust the free space transmission distance of the light beam and generate a random field signal light at a specified transmission distance. The reference light generating module 50 comprises a fifth reflecting mirror 501, a second attenuation plate 502, a second beam expander 503 and a sixth reflecting mirror 504 which are sequentially arranged on the second branch to generate a plane wave reference light; The detection and interference module 60 includes a second beam splitter 601 and a CCD detector 602, which is used to interfere the plane wave reference light with the random field signal light at the specified transmission distance to obtain a series of interference intensity spots and acquire their intensity distribution.

[0034] When the moving end of the movable displacement platform 405 is located at the dotted line segment, the distance between the second lens 303 and the CCD detector 602 is exactly the focal length of the second lens 303, that is, the CCD detector 602 is located at the source plane of the light beam. z 0 When the light beam detected by the CCD detector 602 is at a distance At this time, the CCD detector 602 detects the instantaneous light intensity of a series of signal lights interfering with the reference light.

[0035] By presetting the order of the high-order vortex and the specified transmission distance required for the high-order vortex generation z c , encode the electric field of the controllable high-order vortex partially coherent beam light source, generate a computer hologram, and achieve the coding hiding of the controllable high-order vortex partially coherent beam. With the precise controllability of the displacement platform over the distance, the transmission and measurement of the controllable high-order vortex partially coherent beam at any distance can be achieved.

[0036] Figure 5 and Figure 6 The experimental results show that only at a specified distance z c Only at this point can a deterministic vortex with controllable angular and radial orders be generated, that is, Figure 5 (c) in z c =500mm produces a deterministic vortex beam with an angular order of 2 and a radial order of 0. Figure 6 (c) in z c =500mm produces a deterministic vortex beam with an angular order of 1 and a radial order of 1. Figure 5 (a), (b), (d) and Figure 6 The beams obtained at other distances in (a), (b) and (d) are all non-deterministic vortex beams.

[0037] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0038] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0039] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0040] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0041] Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from these are still within the protection scope of the invention.

Claims

1. A high-order deterministic vortex generation method based on coherent structure regulation, characterized in that: The following steps are involved: Step S1: encoding the angular and radial order characteristics of the Laguerre-Gaussian beam into a random beam by fractional Fourier transform, and constructing a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified transmission distance; Step S2: using mode decomposition to transform the theoretical model into a random electric field distribution that can be actually controlled, and obtaining a cross spectral density function of the deterministic vortex beam; Step S3: introducing a beam of fully coherent plane waves as reference light, interfering the reference light with the random field signal light at a specified transmission distance, and obtaining a series of interference intensity spots; Step S4: recovering a series of random electric fields from the series of interference intensity spots, and obtaining a deterministic vortex beam with controllable angular order and radial order based on the cross spectral density function and the random electric field.

2. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 1 is characterized in that: In S1, the method for constructing a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance is as follows: S11: A deterministic vortex beam of arbitrary radial and angular order is regarded as an incoherent superposition of infinite wave modes, which is characterized by the cross-spectral density function at the source plane as follows: ， in, are represented by any two lateral position vectors at the light source surface, is an arbitrary non-negative function, is a spatial two-dimensional frequency variable, express of x Directional component, express of y Directional component; is an arbitrary kernel function, * indicates conjugation, represents the lateral position vector at the light source surface; S12: In order to generate a deterministic vortex beam with controllable order at a specified transmission distance, a coherence length-related constant is introduced, that is, , The theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified transmission distance is obtained. : ， in, is a real constant related to the coherence length of the beam, is the electric field expression of the Laguerre-Gaussian beam at the focal plane z = 0, represents the fractional Fourier transform function, represents the fractional Fourier transform domain coordinates; and are the two lateral position vectors of the output plane; Represents light wave mode The kernel function of the system propagates from the source plane to the z plane, Represents the spatial coordinates of the transmission surface.

3. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 2 is characterized in that: The electric field expression of the Laguerre-Gaussian beam on the focal plane z=0 is In cylindrical coordinates The following expression is as follows: ， in, r represents the radial distance in the cylindrical coordinate system, represents the azimuth, z Indicates the free space transmission distance; The radial order is expressed as , the angular order is Laguerre polynomials of ; and are the width and wavefront curvature of the beam at the distance z from the focal plane, respectively; It is the Gouy phase; is the wave number, is the wavelength; The angular order is l The vortex phase term, i Is an imaginary unit.

4. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 2 is characterized in that: The fractional Fourier transform function for: ， in, is a variable related to the fractional Fourier transform order, is the fractional order, is the waist width of the Laguerre-Gaussian beam in the focal plane.

5. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 2 is characterized in that: The system kernel function for: ， in, is the Fresnel diffraction integral function, .

6. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 2 is characterized in that: In S2, the method for obtaining the cross spectral density function of the deterministic vortex beam is as follows: Using the cross spectral density function in the mode decomposition formula (1), we get: ， Where N is the total number of modes, are non-negative weights; is the instantaneous electric field in the source plane; The weights of all electric field modes are , the real and imaginary parts of each electric field mode are randomly distributed in space and satisfy Gaussian statistics, which can be expressed as , where IFT stands for inverse Fourier transform, is a complex Gaussian random number with mean zero and variance 1; and The product of is fractional Fourier transform, and the result is z A random electric field with a controllable high-order vortex source is generated at: ， After the random electric field is transmitted in free space, the cross spectral density function at the propagation distance z is obtained as follows: ， in, .

7. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 1 is characterized in that: In S3, the method for obtaining a series of interference intensity spots is: A completely coherent plane wave is introduced as the reference light. The plane wave reference light in the reference light path is coherently superimposed with the instantaneous random electric field of the generated deterministic vortex beam to obtain the intensity of a series of interference intensity spots. It is expressed by the following formula: ， in, is the random light field at the propagation distance z; is the electric field of the reference light, and Wave vector The angles with the x and y axes, and is a constant phase; represents the real part, i Is an imaginary unit.

8. The high-order deterministic vortex generation method based on coherent structure regulation according to claim 1 is characterized in that: In S4, the method of recovering a series of random electric fields from the series of interference intensity spots is as follows: The intensity data of the series of interference intensity spots are subjected to Fourier transformation to obtain multiple separated frequency domain components in the frequency domain, including random electric field The first separated frequency domain component is proportional to the random electric field A second separated frequency domain component proportional to the complex conjugate of After the first separated frequency domain component is moved to the center of the zero value matrix, an inverse Fourier transform is performed to obtain a complex valued electric field corresponding to the instantaneous interference light intensity.

9. A high-order deterministic vortex generating device based on coherent structure regulation, characterized in that: A method for realizing the high-order deterministic vortex generation method based on coherent structure regulation as claimed in any one of claims 1 to 8, wherein the device comprises an interference intensity spot generation module and a control system; The interference intensity spot generating module is used to introduce a beam of completely coherent plane waves as reference light, interfere the reference light with the random field signal light at a specified transmission distance, and obtain a series of interference intensity spots; The control system is used to encode the angular and radial order characteristics of a Laguerre-Gaussian beam into a random beam through fractional Fourier transform, construct a theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance, and use mode decomposition to transform the theoretical model into a random electric field distribution that can be actually controlled to obtain a cross-spectral density function of the deterministic vortex beam; and recover a series of random electric fields from the series of interference intensity spots, and obtain a deterministic vortex beam with controllable angular order and radial order based on the cross-spectral density function and the random electric field.

10. The high-order deterministic vortex generating device based on coherent structure regulation according to claim 9, characterized in that: The interference intensity spot generating module comprises: A light source module, the light source module comprising a laser, a first attenuation plate, a first beam expander and a first beam splitter which are placed in sequence, wherein the first beam splitter divides a light beam propagation path of the first beam expander into a first branch and a second branch; A beam modulation module, the beam modulation module comprising a phase spatial light modulator, and the phase spatial light modulator is arranged on the first branch; A beam processing module, the beam processing module comprising a first lens, a single-hole filter, and a second lens arranged on the first branch, screening the light beam modulated by the phase spatial light modulator to obtain a random field signal light within a specified diffraction order range; A free space transmission module, the free space transmission module comprising a first reflector, a second reflector, a third reflector, a fourth reflector and a movable displacement platform, the first reflector and the second reflector are mounted on a fixed end of the movable displacement platform, and the fixed end is located behind the second lens, the third reflector and the fourth reflector are mounted on a movable end of the movable displacement platform to adjust the light beam transmission distance and generate a random field signal light at a specified transmission distance; A reference light generation module, the reference light generation module comprising a fifth reflector, a second attenuation plate, a second beam expander and a sixth reflector sequentially arranged on the second branch to generate a plane wave reference light; The detection and interference module includes a second beam splitter and a CCD detector, which is used to interfere the plane wave reference light with the random field signal light at the specified transmission distance to obtain a series of interference intensity spots and acquire their intensity distribution.

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