A method and device for generating high-order deterministic vortices based on coherent structure regulation

Abstract

The present invention relates to the field of optical technologies, and in particular to a method and device for generating high-order deterministic vortices based on coherent structure regulation. The method includes: encoding the angular and radial order characteristics of a Laguerre-Gaussian beam into a random beam through fractional Fourier transform, constructing a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified propagation distance; transforming it into a manipulable random electric field distribution through mode decomposition to obtain the cross-spectral density function; introducing a completely coherent plane wave as a reference light to interfere with the random field signal light at the specified propagation distance to obtain an interference intensity spot, and using the off-axis holographic method to recover the random electric field therefrom; generating a high-order vortex beam with controllable order based on the cross-spectral density function and the random electric field, realizing the flexible generation of a high-order vortex beam at the specified propagation distance.

Description

Technical Field

[0001] The present invention relates to the field of optical technologies, and particularly 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), exhibit a hollow intensity distribution due to their unique phase structure, and there is a phase singularity at the intensity center. 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 optical field regulation. Research shows that reducing the spatial coherence of the optical field can largely suppress speckle noise sensitive to phase. At the same time, partially coherent beams are more robust than fully coherent beams in resisting the negative effects of optical turbulence. In recent years, partially coherent vortex beams, that is, beams combining optical vortices and partial coherence characteristics, have shown many unique advantages and have been widely used in fields such as optical imaging, sensing, detection, and computing.

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

[0005] But currently, the existing technology for generating deterministic vortices from random beams at a specified propagation distance only remains at the theoretical level. Moreover, the existing technology can only achieve deterministic vortices with the minimum angular order, that is, the Laguerre-Gaussian (LG) beam with angular order l = 1 and radial order p = 0, which greatly limits the application of vortex beams in practical production fields such as information transmission. Research shows that in high-dimensional communication, high-order angular and radial orders play a crucial role in signal multiplexing and demultiplexing. Therefore, how to generate high-order vortices with controllable orders from random beams at a specified distance is still an urgent problem to be solved. In addition, the correlation function of partially coherent light at a specific propagation distance is a four-dimensional (4D) distribution function related to the spatial positions of two points, and it is also an unsolved scientific problem to completely measure and characterize its four-dimensional correlation function and its inherent coherent vortices experimentally. Summary of the Invention

[0006] Based on the above background art, the technical problems to be solved by the present invention are to generate a high-order vortex beam in a random beam, and to complete the complete characterization of the four-dimensional (4D) distribution correlation function related to two spatial positions of a partially coherent light at a specific propagation distance. To solve the above technical problems, the present invention provides a method and device for generating high-order deterministic vortices based on coherent structure control. The method includes the following steps:

[0007] Step S1: Encode the angular and radial order characteristics of a Laguerre-Gaussian beam into a random beam through a fractional Fourier transform, and construct a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at an arbitrarily specified propagation distance;

[0008] Step S2: Use mode decomposition to transform the theoretical model into an actually controllable random electric field distribution, and obtain the cross-spectral density function of the deterministic vortex beam;

[0009] Step S3: Introduce a completely coherent plane wave as a reference light, and interfere the reference light with the random field signal light at a specified propagation distance to obtain a series of interference intensity spots;

[0010] Step S4: 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 fields, obtain a deterministic vortex beam with controllable angular and radial orders.

[0011] In an embodiment of the present invention, in S1, the method for constructing a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at an arbitrarily specified propagation distance is as follows:

[0012] S11: Consider a deterministic vortex beam with arbitrary radial and angular orders as an incoherent superposition of an infinite number of wave modes, which is characterized by a cross-spectral density function at the source plane, as follows:

[0013] S11: Consider a deterministic vortex beam with arbitrary radial and angular orders as an incoherent superposition of an infinite number of wave modes, which is characterized by a cross-spectral density function at the source plane, as follows:

[0014] ,

[0015] where, respectively represent any two transverse position vectors at the source plane, is an arbitrary non-negative function, is the two-dimensional spatial frequency variable, represents of x direction component, denote of y direction component; is an arbitrary kernel function, * denotes conjugate, denotes the transverse position vector at the light source plane;

[0016] S12: To generate a deterministic vortex beam with controllable order at a specified propagation distance, a coherence length-related constant is introduced, i.e., let ,

[0017] A theoretical model for generating a deterministic vortex beam with controllable angular order and radial order at any specified propagation distance is obtained :

[0018] ,

[0019] wherein, is a real constant related to the coherence length of the beam, is the electric field expression of the Laguerre-Gaussian beam on the focal plane z = 0, denotes the fractional Fourier transform function, denotes the fractional Fourier transform domain coordinates; and are two transverse position vectors of the output plane; denotes the optical wave mode The system kernel function for the propagation of the light wave mode from the source plane to the z plane, denotes the space coordinates of the transmission plane.

[0020] In an embodiment of the present invention, the electric field expression of the Laguerre-Gaussian beam on the focal plane z = 0 In the cylindrical coordinate system The expression is as follows:

[0021] ,

[0022] wherein, r denotes the radial distance in the cylindrical coordinate system, denotes the azimuth angle, z denotes the free space propagation distance; is denoted as the Laguerre polynomial with a radial order of , and an angular order of ; and are respectively the width and wavefront curvature of the beam at a distance z from the focal plane; is the Gouy phase; is the wave number, is the wavelength; denotes the vortex phase term with an angular order of l ​i is the imaginary unit.

[0023] In one embodiment of the present invention, the fractional Fourier transform function is:

[0024] ,

[0025] where is a variable related to the order of the fractional Fourier transform, is the fractional order, is the waist width of the Laguerre-Gaussian beam at the focal plane.

[0026] In one embodiment of the present invention, the system kernel function is:

[0027] ,

[0028] where is the Fresnel diffraction integral function, .

[0029] 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:

[0030] Using the cross-spectral density function in the mode decomposition formula (1), we get:

[0031] ,

[0032] where N is the total number of modes, is the non-negative weight; is the instantaneous electric field at the source plane;

[0033] The weights of all electric field modes are , and the real and imaginary parts of each electric field mode are randomly distributed in space and satisfy Gaussian statistics, expressed as , where IFT represents the inverse Fourier transform, is a complex Gaussian random number with a mean of zero and a variance of 1; taking the fractional Fourier transform of the product of and , we obtain the random electric field at the position of the high-order vortex light source with a controllable order at a specified distance z :

[0034] ,

[0035] After free-space propagation of the random electric field, the cross-spectral density function at the propagation distance z is obtained as:

[0036] ,

[0037] Among them, .

[0038] In one embodiment of the present invention, in S3, the method for obtaining a series of interference intensity spots is as follows:

[0039] Introduce a completely coherent plane wave as the reference light. The plane wave reference light in the reference optical path is coherently superposed 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 represented by the following formula:

[0040] ,

[0041] Among them, is the random optical field at the propagation distance z; is the electric field of the reference light, and are the angles between the wave vector and the x and y axes respectively, and are constant phases; denotes taking the real part, i is the imaginary unit.

[0042] 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:

[0043] Perform Fourier transform on the intensity data of the series of interference intensity spots to obtain multiple separated frequency domain components in the frequency domain, including a first separated frequency domain component proportional to the random electric field and a second separated frequency domain component proportional to the complex conjugate of the random electric field ;

[0044] After moving the first separated frequency domain component to the center of the zero value matrix, perform inverse Fourier transform to obtain the complex-valued electric field corresponding to the instantaneous interference light intensity.

[0045] Based on the same inventive concept, the present invention also provides a high-order deterministic vortex generation device based on coherent structure regulation for implementing the steps of the high-order deterministic vortex generation method based on coherent structure regulation. The device includes an interference intensity spot generation module and a control system;

[0046] Among them, the interference intensity spot generation module is used to introduce a completely coherent plane wave as the reference light, interfere the reference light with the random field signal light at a specified transmission distance to obtain a series of interference intensity spots;

[0047] The control system 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 and radial orders at an arbitrarily specified transmission distance, convert the theoretical model into an actually manipulable random electric field distribution by mode decomposition, and obtain the 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 and radial orders based on the cross-spectral density function and the random electric field.

[0048] In an 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

[0049] Among them, the light source module includes a laser, a first attenuation sheet, a first beam expander, and a first beam splitter arranged in sequence. The first beam splitter divides the beam propagation path of the first beam expander into a first branch and a second branch;

[0050] The beam modulation module includes a phase spatial light modulator, and the phase spatial light modulator is arranged on the first branch;

[0051] The beam processing module includes a first lens, a single-hole filter sheet, and a second lens arranged on the first branch, and screens the beam modulated by the phase spatial light modulator to obtain a random field signal light within a specified diffraction order range;

[0052] The free space transmission module includes 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 installed at the 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 installed at the movable end of the movable displacement platform to adjust the beam transmission distance and generate a random field signal light at a specified transmission distance;

[0053] The reference light generation module includes a fifth reflector, a second attenuation sheet, a second beam expander, and a sixth reflector arranged in sequence on the second branch to generate a plane wave reference light;

[0054] The detection and interference module includes a second beam splitter and a CCD detector, which are 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 distributions.

[0055] The above technical solutions of the present invention have the following advantages compared with the prior art:

[0056] 1. The present invention utilizes the coherent structure regulation of the optical field and the fractional Fourier transform to achieve the encoding and hiding of high-order deterministic vortices at the light source, and flexibly constructs high-order vortices with precisely adjustable orders at a specified transmission distance.

[0057] 2. The device provided by the present invention only needs to utilize a single spatial light modulator and an off-axis holographic interference system. Without changing the optical experimental system, by pre-planning key parameters such as the order of the high-order vortex beam and the specified transmission distance, and generating a computer-generated hologram accordingly, it is possible to achieve the transmission and measurement of a controllable high-order vortex partially coherent beam at any target distance.

[0058] 3. The present invention does not require pre-designing a mask plate and does not rely on optical hardware such as scattering media. It has high flexibility and low cost, and has broad application prospects in various fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the drawings, wherein,

[0060] Figure 1 is a schematic flow chart of a method for generating high-order deterministic vortices based on coherent structure regulation provided in an embodiment of the present invention;

[0061] Figure 2 is a flow chart for recovering a series of random electric fields from the series of interference intensity spots by using the off-axis holographic method, where (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-valued electric field corresponding to the instantaneous interference light intensity;

[0062] Figure 3 is a schematic structural diagram of a device for generating high-order deterministic vortices based on coherent structure regulation provided in an embodiment of the present invention;

[0063] Figure 4 is Figure 3 a schematic structural diagram of the interference intensity spot generation module in the said device;

[0064] Figure 5 In (a)-(e) are the experimental results of the vortex beams generated at different transmission distances z of 0 mm, 250 mm, 500 mm, 750 mm, and 1000 mm in sequence;

[0065] Figure 6Among (a)-(e) are the experimental results of the vortex beam generated at different transmission distances z of 0mm, 250mm, 500mm, 750mm, and 1000mm in sequence;

[0066] Explanation of the reference numerals in the drawings of the specification: 100, interference intensity spot generation module; 10, light source module; 101, laser; 102, first attenuation sheet; 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 mirror; 402, second mirror; 403, third mirror; 404, fourth mirror; 405, movable displacement platform; 50, reference light generation module; 501, fifth mirror; 502, second attenuation sheet; 503, second beam expander; 504, sixth mirror; 60, detection and interference module; 601, second beam splitter; 602, CCD detector; 200, control system. Detailed implementation manners

[0067] The present invention will be 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 be able to implement it, but the embodiments cited are not intended to limit the present invention.

[0068] Embodiment 1

[0069] As Figure 1 shown, the present invention provides a method for generating high-order deterministic vortices based on coherent structure regulation, and the method includes the following steps:

[0070] Step S1: Encode the angular and radial order characteristics of the Laguerre-Gaussian beam into a random beam through fractional Fourier transform, and construct a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified transmission distance;

[0071] Step S2: Use mode decomposition to transform the theoretical model into an actually controllable random electric field distribution, and obtain the cross-spectral density function of the deterministic vortex beam;

[0072] Step S3: Introduce a completely coherent plane wave as a 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;

[0073] Step S4: Recover a series of random electric fields from the series of interference intensity spots, and obtain a deterministic vortex beam with controllable angular and radial orders based on the cross-spectral density function and the random electric field.

[0074] Further, in S1, the method for constructing a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at an arbitrarily specified transmission distance is as follows:

[0075] S11: According to the generalized van Cittert-Zernike theorem, a deterministic vortex beam with arbitrary radial and angular orders is regarded as an incoherent superposition of an infinite number of wave modes, which is characterized by the cross-spectral density function at the source plane as follows:

[0076] ,

[0077] where, respectively represent any two transverse position vectors at the source plane, is an arbitrary non-negative function, is the two-dimensional spatial frequency variable, represents 's x direction component, represents 's y direction component; is an arbitrary kernel function, * represents conjugation, represents the transverse position vector at the source plane;

[0078] S12: To generate a deterministic vortex beam with controllable order at the specified transmission distance, a coherence length-related constant is introduced, that is, let:

[0079] ,

[0080] ,

[0081] where, is a real constant related to the coherence length of the beam, is the electric field expression of the Laguerre-Gaussian beam on the focal plane z = 0, and its expression in the cylindrical coordinate system is as follows:

[0082] ,

[0083] where, , r represents the radial distance in the cylindrical coordinate system, represents the azimuth angle, z represents the free space transmission distance; is expressed as the Laguerre polynomial with radial order and angular order ; and are the width and wavefront curvature of the beam at a distance z from the focal plane respectively; is the Gouy phase; is the wave number, is the wavelength; represents the vortex phase term with an angular order of l ; represents the fractional Fourier transform function, as follows:

[0084] ,

[0085] where is a variable related to the fractional Fourier transform order, is the fractional order, taking values in . is the beam waist width of the Laguerre-Gaussian beam at the focal plane, i is the imaginary unit.

[0086] By organizing the above formulas, the theoretical model for the propagation of a deterministic vortex beam from the source plane to the plane with an axial coordinate of z is obtained :

[0087] ,

[0088] where and are two transverse position vectors in the output plane; represents the optical wave mode The system kernel function for the propagation of the optical wave mode from the source plane to the z plane is obtained from the Huygens-Fresnel principle. The system kernel function for the propagation of the optical wave mode from the source plane to the z plane is as follows:

[0089] ,

[0090] where is the transverse position vector in the output plane, including and ; is the Fresnel diffraction integral function, as follows:

[0091] ,

[0092] Substituting formulas (3), (5), and (8) into formula (7), we get The final analytical expression of is:

[0093] ,

[0094] where:

[0095] ,

[0096] where , is the Gamma function, represents the binomial coefficient, is the Kronecker delta function. From the final analytical expression, it can be seen that the vortex phase structure is only determined by the term .

[0097] It is found through research that at the off-axis position , a vortex phase will be generated, and the determination of this position depends on . However, at the critical distance , regardless of taking any value, the generated vortices will coincide, and the vortex center will be fixed at the origin. Finally, a deterministic vortex structure will be presented at the critical distance . In addition, is a value independent of the radial and angular orders, and can vary with from and take any value from zero to positive infinity. Therefore, by adjusting the value of , a deterministic vortex beam can be generated at any desired distance.

[0098] Furthermore, in S2, in order to generate a deterministic vortex beam using a liquid crystal spatial light modulator (SLM) or a digital micromirror device, the theoretical model is transformed into a practically manipulable random electric field distribution by mode decomposition, and the method for obtaining the cross-spectral density function of the deterministic vortex beam is as follows:

[0099] Using the cross-spectral density function in the mode decomposition formula (1), we get:

[0100] ,

[0101] where N is the total number of modes, is a non-negative weight; is the instantaneous electric field in the source plane; in this case, if the random mode set is given, all the information about the cross-spectral density can be known.

[0102] Here, for the random mode set , the weights of all the electric field modes are all , and the real and imaginary parts of each electric field mode are randomly distributed in space and satisfy Gaussian statistics, expressed as , where IFT represents the inverse Fourier transform, is a complex Gaussian random number with a mean of zero and a variance of 1, for and Perform a fractional Fourier transform on the product to obtain the random electric field at a specified propagation distance z at a position where a high-order vortex light source with controllable order is generated:

[0103] ,

[0104] By repeating the above process multiple times, a set of random patterns of the cross-spectral density function at the source plane is obtained. Subsequently, using the Fresnel diffraction integral theorem, after free-space propagation of the random electric field, the cross-spectral density function at a specified propagation distance z is:

[0105] ,

[0106] where, .

[0107] Furthermore, in S3, a completely coherent plane wave is introduced as a reference light, and the method for interfering the reference light with the random field signal light at a specified transmission distance to obtain a series of interference intensity spots is:

[0108] Introduce a completely coherent plane wave as a reference light, and the plane wave reference light in the reference optical path is coherently superposed with the instantaneous random electric field of the generated deterministic vortex beam to obtain the intensity of a series of interference intensity spots which is expressed by the following formula:

[0109] ,

[0110] where, is the random optical field at the propagation distance z; is the electric field of the reference light, and are the angles between the wave vector and the x and y axes respectively, and are constant phases; denotes taking the real part, i is the imaginary unit.

[0111] As Figure 2 shown, in S4, the method for recovering a series of random electric fields from the series of interference intensity spots using the off-axis holography principle is as follows:

[0112] S41: Perform a Fourier transform on the intensity data of the series of interference intensity spots shown in (a) of Figure 2 to obtain multiple separated frequency-domain components in the frequency domain, including a first separated frequency-domain component proportional to the random electric field and a second separated frequency-domain component proportional to the random electric field and a second separated frequency-domain component proportional to the random electric field a second separated frequency-domain component proportional to the complex conjugate, as Figure 2 shown in (b) of

[0113] S42: As Figure 2 shown in (c) of move the separated frequency-domain component proportional to the random electric field to the center of the zero-value matrix, and then perform an inverse Fourier transform to obtain the complex-valued electric field corresponding to the instantaneous interference light intensity , as Figure 2 shown in (d) of

[0114] Use an optoelectronic signal detector (such as a CCD detector) to record a series of continuous interference intensity spot images and save them. After that, each image will undergo the processing of steps S41 and S42, and finally obtain a set of random electric field patterns .

[0115] Substitute the set of random electric field patterns into the cross-spectral density function shown in formula (13) to measure and characterize the four-dimensional cross-spectral density signal at a specified propagation distance z , and then obtain a deterministic vortex beam with controllable angular and radial orders. Embodiment 2

[0116] Based on the same inventive concept as in Embodiment 1, the present invention also provides a high-order deterministic vortex generation device based on coherent structure regulation for implementing the steps of the high-order deterministic vortex generation method based on coherent structure regulation described in Embodiment 1. As Figure 3 and Figure 4 shown, the device includes an interference intensity spot generation module 100 and a control system 200;

[0117] Among them, the interference intensity spot generation module 100 is used to introduce a completely coherent plane wave as a reference light, and interfere the reference light with the random field signal light at a specified propagation distance to obtain a series of interference intensity spots;

[0118] The control system 200 is used to encode the angular and radial order characteristics of the Laguerre-Gaussian beam into the random beam through a fractional Fourier transform, construct a theoretical model for generating a deterministic vortex beam with controllable angular and radial orders at any specified propagation distance, convert the theoretical model into an actually controllable random electric field distribution by using mode decomposition 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 obtain a deterministic vortex beam with controllable angular and radial orders based on the cross-spectral density function and the random electric field.

[0119] 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;

[0120] Among them, the light source module 10 includes a laser 101, a first attenuation sheet 102, a first beam expander 103, and a first beam splitter 104 arranged in sequence; the laser 101 emits a completely coherent laser beam with a wavelength of 532 nm. Through the first attenuation sheet 102 and the first beam expander 103, the first beam splitter 104 divides the beam propagation path of the first beam expander 103 into a first branch and a second branch;

[0121] The beam modulation module 20 includes a phase spatial light modulator 201. The phase spatial light modulator 201 is arranged on the first branch. The beam passing through the first beam splitter 104 is uniformly transmitted onto the phase spatial light modulator 201. The phase spatial light modulator 201 is used to load a computer-generated hologram (CGHs) that synthesizes a controllable high-order vortex partially coherent beam light source electric field;

[0122] 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 length f = 250 mm, forming a 4f imaging system. The beam modulated by the phase spatial light modulator 201 enters the 4f imaging system for screening. 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, blocking the unwanted diffraction orders and background noise;

[0123] The free space transmission module 40 includes a first mirror 401, a second mirror 402, a third mirror 403, a fourth mirror 404, and a movable displacement platform 405. The first mirror 401 and the second mirror 402 are installed at the fixed end of the movable displacement platform 405, and the fixed end is located behind the second lens 303. The third mirror 403 and the fourth mirror 404 are installed at the movable end of the movable displacement platform 405 to adjust the free space transmission distance of the beam and generate a random field signal light at a specified transmission distance;

[0124] The reference light generation module 50 includes a fifth mirror 501, a second attenuation sheet 502, a second beam expander 503, and a sixth mirror 504 arranged in sequence on the second branch to generate a plane wave reference light;

[0125] The detection and interference module 60 includes a second beam splitter 601 and a CCD detector 602, which are used to interfere the plane wave reference light with the random field signal light at the specified transmission distance, obtain a series of interference intensity spots and acquire their intensity distributions.

[0126] When the mobile end of the movable displacement platform 405 is located at the virtual 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 where the light beam is generated. When the mobile end of the movable displacement platform 405 moves a distance z 0 from the virtual line segment, the light beam detected by the CCD detector 602 is located at a distance at which time the CCD detector 602 detects a series of instantaneous light intensities of the interference between the signal light and the reference light.

[0127] By presetting the order of the high-order vortex and the specified transmission distance required for the generation of the high-order vortex z c , the electric field of the controllable high-order vortex partially coherent beam light source is encoded to generate a computer-generated hologram, thereby achieving the encoding and concealment of the controllable high-order vortex partially coherent beam. With the precise controllability of the distance by the displacement platform, the transmission and measurement of the controllable high-order vortex partially coherent beam at any distance are further realized.

[0128] Figure 5 and Figure 6 The experimental results of c show that only at the specified distance z Figure 5 can a deterministic vortex with controllable angular and radial orders be generated, that is, z c a deterministic vortex beam with an angular order of 2 and a radial order of 0 is generated at Figure 6 = 500 mm in (c) of z c = 500 mm, and a deterministic vortex beam with an angular order of 1 and a radial order of 1 is generated at Figure 5 = 500 mm in (c) of Figure 6 , while non-deterministic vortex beams are obtained at other distances in (a), (b), (d) of

[0129] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take 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.) that contain computer-usable program code.

[0130] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or blocks.

[0131] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means implement the functions specified in Figure 1 one or more of the flows Figure 1 or blocks.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Therefore, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one or more of the flows Figure 1 or blocks.

[0133] Obviously, the above embodiments are merely examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill 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 enumerate all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present 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, including: Performing Fourier transformation on the intensity data of the series of interference intensity spots to obtain a plurality of separated frequency domain components in the frequency domain, including a first separated frequency domain component proportional to the random electric field and a second separated frequency domain component proportional to the complex conjugate of the random electric field; After moving the first separated frequency domain component 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, and finally a random electric field pattern set is obtained; The random electric field pattern set is substituted into the cross spectral density function to achieve the measurement and characterization of the four-dimensional cross spectral density signal at a specified transmission distance z, thereby obtaining a deterministic vortex beam with controllable angular order and radial order.

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 and radial orders 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: W(r1,r2,0)=∫∫p(v)H * (r1,v,0)H(r2,v,0)d 2 in (1) Where r1 and r2 represent any two lateral position vectors at the light source surface, p(v) is an arbitrary non-negative function, v = (v x ,v y ) is the spatial two-dimensional frequency variable, v x represents the x-direction component of v, v y represents the y-direction component of v; H(r,v,0) is an arbitrary kernel function, * represents conjugation, and r 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 W(ρ1, ρ2, z) for generating a deterministic vortex beam with controllable angular order and radial order at any specified transmission distance is obtained: W(ρ1,ρ2,z)=∫∫p(v)H * (ρ1,v,z)H(ρ2,v,z)d 2 v (2) Among them, δ0 is a real constant related to the coherence length of the beam, U pl (r′,0) is the electric field expression of the Laguerre-Gaussian beam at the focal plane z = 0, F θ (r,r′) represents the fractional Fourier transform function, r′ represents the fractional Fourier transform domain coordinates; ρ1 and ρ2 are the two lateral position vectors of the output plane; H(ρ,v,z) represents the system kernel function of the light wave mode H(r,v,0) propagating from the source plane to the z plane, and ρ represents the spatial coordinates of the transmission plane.

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 U of the Laguerre-Gaussian beam on the focal plane z=0 is pl (r′,0) in cylindrical coordinates The following expression is as follows: Where r represents the radial distance in the cylindrical coordinate system, represents the azimuth, and z represents the free space transmission distance; It is expressed as a Laguerre polynomial with radial order p and angular order l; ω(z) and R(z) are the width and wavefront curvature of the beam at distance z from the focal plane, respectively; ψ(z) is the Gouy phase; k = 2π / λ is the wave number, λ is the wavelength; represents the vortex phase term of angular order l, and 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 F θ (r,r′) is: Where θ = p e π / 2 is a variable related to the fractional Fourier transform order, p e ∈[0,1] is the fractional order, and ω0 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 H(ρ,v,z) is: H(ρ,v,z)=∫∫H(r,v,0)G(ρ,r,z)d 2 r (5) Among them, G(ρ,r,z) 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, λ n is a non-negative weight; E n (r, 0), n = 1, 2, ... N is the instantaneous electric field in the source plane; All electric field modes have a weight of λ n =1 / N, 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, R n (v) is a complex Gaussian random number with mean zero and variance 1; for T n (r′) and U pl The product of (r′,0) is subjected to fractional Fourier transform to obtain the random electric field at the source of high-order vortex with controllable order at the specified distance z: E n (r,0)=∫∫U pl (r′,0)T n (r′)F θ (r,r′)d 2 r′ (7) After the random electric field is transmitted in free space, the cross spectral density function at the propagation distance z is obtained as follows: Among them, E n (ρ,z)=∫∫E n (r,0)G(ρ,r,z)d 2 r.

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 I of a series of interference intensity spots. n (ρ,z) is expressed by the following formula: Among them, E n (ρ,z) is the random light field at the propagation distance z; is the electric field of the reference light, α and β are the angles between the wave vector k and the x and y axes respectively, A0 and φ0 are constant phases; Re represents the real part, and i is the imaginary unit.

8. 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 7, 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.

9. The high-order deterministic vortex generating device based on coherent structure regulation according to claim 8, 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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