A method for generating a vector vortex light based on a polarization encoding diffraction neural network

Abstract

The application belongs to the field of optics and photonics, and discloses a vector vortex light generation method based on a polarization encoding diffraction neural network. A linear uncontrolled polarization array layer is added to the traditional diffraction neural network to change the characteristic that the traditional diffraction neural network cannot modulate polarization information. The input Gaussian light beam is converted into the output vector vortex light beam through the phase modulation layer of the polarization diffraction neural network, the independent modulation of the x and y direction vector light beams is realized, the output result is optimized through the error back propagation algorithm to match the expected value, and finally the vector vortex light beams with different orbital angular momentum (OAM) modes are generated in the x and y polarization directions. The application has the flexibility and low power consumption of the diffraction neural network, and is expected to be applied to the fields of optical communication, quantum information, optical calculation and the like, and provides a new solution for the generation of vector light fields.

Description

Technical Field

[0001] This invention belongs to the fields of optics and photonics, specifically relating to a method for generating vector vortex light based on a polarization-encoded diffraction neural network. Background Technology

[0002] Vector vortex beams (VVBs) combine the characteristics of vortex beams and vector beams, possessing a helical phase wavefront carrying orbital angular momentum (OAM). -ilθ Both the OAM mode and polarization state can carry information, and the different OAM modes are orthogonal to each other, providing a new degree of freedom for realizing high-capacity, high-speed, and large-scale optical communication. In recent years, the main methods for generating vector vortex light are: liquid crystal phase plate method (S-LCD), spatial light modulator method (SLM), and metasurface generation method. These have been widely used to generate vector vortex light. The first two methods have high control flexibility but often have high optical loss, resulting in low efficiency. While metasurface technology has outstanding advantages in integration and efficiency, it is difficult to adjust flexibly and has high cost. Therefore, traditional generation methods cannot combine flexibility and efficiency.

[0003] In summary, existing vector vortex light generation techniques have limitations, and traditional D... 2 NNs are not sensitive to the polarization state of light and cannot perform light modulation in the polarization dimension. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a vector vortex light generation method based on a polarization-encoded diffraction neural network. This invention adds a linearly untunable polarization array layer to the traditional diffraction neural network, which helps D... 2 NNs enable independent modulation in the x and y directions, possessing the control flexibility and low power consumption of diffractive neural networks. They hold promise for applications in optical communication, quantum information, optical computing, and other fields, providing a new solution for the generation of vector light fields.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] This invention is a method for generating vector vortex light based on a polarization-encoded diffraction neural network (PDN). 2 NNs include implementations of polarization-coded diffraction neural networks (PDs). 2 The polarization array layer (NNs) performs independent polarization modulation in the x and y directions. Specifically, the vector vortex light generation method includes the following steps:

[0007] Step 1: Induce a Gaussian beam with wavelength λ into a polarization-coded diffraction neural network (PD). 2 On the input plane of NNs;

[0008] Step 2: Arrange the incident points on the input plane according to the MPSK constellation diagram, which includes n different incident points, representing vector vortex light with different topological charge values;

[0009] Step 3: Pre-set the polarization array layer;

[0010] Step 4: Place the polarization array layer pre-set in Step 3 onto the diffraction depth neural network (D... 2 The distance between the NNs) diffraction layers and the distance between the NNs and the previous diffraction layer is d. p ;

[0011] Step 5: Input the Gaussian beam into the polarization-encoded diffraction neural network (PD) at different spatial locations. 2 In a polarization-coded diffraction neural network (PDNNs), each input position corresponds to a specific input location. 2 The vector vortex light output of orbital angular momentum (OAM) modes with different topological charges on the output plane of NNs can be multiplied with the Jones matrix of the polarization array layer to obtain vector light fields with different polarization modulations in the x and y directions on the output plane.

[0012] Step 6: In the polarization-encoded diffraction neural network (PD) 2 During training of the polarization-encoded diffraction neural network (PDNN), the mean square error loss function is used to calculate the difference between the predicted vector light field output and the target beam, i.e., the vector vortex light. The difference is evaluated by minimizing the mean square error loss function (MSE). 2 The stochastic gradient descent algorithm is used to apply the polarization-encoded diffraction neural network (PDNNs). 2 Optimize using NNs;

[0013] Step 7: Generate different vector vortex beams by combining the vector light fields in the x and y directions;

[0014] Step 8: Perform Stokes operation on the generated vector vortex beam to obtain the light field distribution in each polarization direction and verify the generated vector vortex beam;

[0015] Step 9: Use the normalized overlap integral and the average structural similarity index (SSIM) to measure the quality of the vector vortex beam generated in Step 7.

[0016] A further improvement of the present invention is that step 5 specifically includes the following steps:

[0017] Step 5.1: Using a Gaussian beam as input, at the input plane spatial position (x... m ,y m ,z m The optical field of the input polarized electromagnetic wave on the input is represented as:

[0018]

[0019] Among them, E x (represents) the light field in the x-direction and E y Represents the light field in the y direction, (x m ,y m ,z m ) represents the spatial location, m represents the m-th incident Gaussian point, E x and E y Polarization-encoded diffraction neural network (PD) 2 Parallel computation within NNs;

[0020] Step 5.2: Generate the same complex-valued modulation for the two orthogonal polarization states. The propagation between the diffraction layers is based on the Rayleigh-Sommerfeld diffraction equation. If the distance from the input to the diffraction layer and the distance between the diffraction layers are both denoted as d, then the modulated light field reaching the (l+1)th layer after passing through the l-th diffraction layer is expressed as:

[0021]

[0022] Where p represents the polarization state of the modulated light field E located at (x,y,z), S represents all pixels in the l-th layer, and t l+1 This represents the modulation of the (l+1)th diffraction layer. The modulation can be phase modulation, amplitude modulation, or amplitude-phase modulation. Let m be the diffraction propagation function between the l-th layer and the (l+1)-th layer at point m;

[0023] Step 5.3: Using the Jones matrix J θ Let θ represent each polarization unit in the polarization array layer, and let θ represent the angle between the polarization axis and the x-axis. Then, the modulation of the input vector light field by the polarization unit located at (x, y, z) in the polarization array layer can be expressed as:

[0024] E out (x,y,z)=J θ (x,y,z)E in (x,y,z)

[0025] Among them, E in and E out These represent the vector optical fields before and after polarization modulation, respectively. For each vector optical field, there are two directional components, x and y. After passing through the Jones matrix J of the polarization array layer... θThis resulted in different modulations of the x and y components.

[0026] A further improvement of this invention is that, in step 8, the Stokes parameters can effectively display the vector characteristics of the output vector vortex light field on the output plane, showing that the intensity distribution of the vector light field is different in different polarization directions. The Stokes parameters are a four-dimensional vector containing S0, S1, S2, and S3, used to describe any vector light field, and their expression is:

[0027]

[0028] Among them, I H I V I represents the horizontal and vertical intensities, respectively. 45° I 135° I represents the polarization intensities at 45° and 135° angles to the x-axis, respectively. R I L The polarization intensities of the right and left circles are represented respectively. For each mode of vector vortex light field, the corresponding polarization direction light field is obtained after Stokes operation. When the light field intensity distribution in each polarization direction has different petal distributions, it is verified that the generated light field is a vector vortex light field.

[0029] A further improvement of the present invention is that, in step 9, the quality of the vector vortex beam generated in step 7 is verified using the normalized overlap integral and the average structural similarity index (SSIM). Specifically, the overlap integral is normalized to the range [0,1], where 1 represents complete overlap and 0 represents complete non-overlap, expressed as:

[0030]

[0031] Where E1[n] and E2[n] represent the light field values ​​of the nth pixel on the target light field and the predicted light field output plane, respectively, and E2... * [n] indicates taking the conjugate of E2[n]. Represents the square of the sum of overlaps. It is the product of the light field intensity, used for normalization;

[0032] The Structural Similarity Index (SSIM) is calculated as follows:

[0033]

[0034] Where μ1 represents the mean amplitude of the target light field E1[n], μ2 represents the mean amplitude of the predicted light field E2[n], and σ1 2 σ2 represents the variance of the amplitude of E1[n]. 2 σ represents the variance of the amplitude of E2[n]. 12The covariance of the amplitudes of E1[n] and E2[n] is represented by C1 and C2, which are constants to prevent division by zero errors.

[0035] A further improvement of the present invention is that the polarization-coded diffraction neural network includes an input plane, an output plane, a diffraction layer, and a method for implementing the polarization-coded diffraction neural network (PD). 2 NNs) is a polarization array layer that performs independent polarization modulation in the x and y directions.

[0036] A further improvement of the present invention is that the polarization array layer in step 3 includes multiple polarization units, and each polarization unit includes two polarization angles, 0° and 90°.

[0037] The beneficial effects of this invention are: Based on the traditional diffraction neural network, this invention adds a linearly untunable polarization array layer, which can help D... 2 Neural networks (NNs) achieve independent modulation in the x and y directions. Specifically, x- and y-polarized light of the same intensity produces the same modulation in the polarization-insensitive diffraction layer, but when passing through the polarization array layer, multiplication with the Jones matrix of the polarization array layer produces different polarization modulations in the x and y directions, thus resulting in different predicted vector light fields. By matching the network's prediction results with the output target, vector vortex light is generated.

[0038] Meanwhile, the vector beam generated by this invention underwent optical field similarity analysis, and the vector vortex beam with the required indicators was obtained.

[0039] This invention provides a new approach for the efficient and flexible generation of vector vortex light under all-optical computing.

[0040] The polarization diffraction network design proposed in this invention is not based on birefringence, anisotropy, or polarization-sensitive materials, but rather on a standard isotropic diffraction material with the addition of a linear polarizer layer. This simplifies the material selection, manufacturing, and scaling up of this invention. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the polarization-encoded diffractive nerve model proposed in this invention.

[0042] Figure 2 This is a schematic diagram of the polarization array layer.

[0043] Figure 3 The intensity diagrams of the output vector vortex light in the x and y polarization directions and the intensity diagrams represented by Stokes parameters are obtained through simulation.

[0044] Figure 4 This is a schematic diagram of the input plane division. Detailed Implementation

[0045] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not essential.

[0046] like Figure 1 and Figure 4 As shown, this invention is a vector vortex light generation method based on a polarization-encoded diffraction neural network (PDN). 2 NNs include implementations of polarization-coded diffraction neural networks (PDs). 2 The polarization array layer (NNs) performs independent polarization modulation in the x and y directions. Specifically, the vector vortex light generation method includes the following steps:

[0047] Step 1: Induce a Gaussian beam of red light with a wavelength of 633.8 nm into a polarization-coded diffraction neural network (PD). 2 On the input plane of NNs;

[0048] Step 2: To obtain vortex beams of different modes and avoid inter-mode crosstalk, the incident points on the input plane are arranged according to the MPSK constellation diagram, containing a total of 8 input Gaussian beams. Each input Gaussian beam at a different spatial location corresponds to the output of a different mode, such as... Figure 4 As shown. For example, if the center of the image is taken as the origin, then the first Gaussian point is directly above the origin, corresponding to an output vector vortex beam with l=1. The output vector vortex beam with l value increases sequentially as the Gaussian point rotates counterclockwise.

[0049] The polarization-coded diffraction neural network comprises an input plane, an output plane, four diffraction layers, and a polarization array layer. The polarization array layer is crucial for achieving independent modulation in the x and y directions. Specifically, this invention... 2 The neural networks incorporate a non-trainable, pre-defined polarization array layer, such as... Figure 2 As shown in the diagram. The polarization array layer consists of multiple polarization units, each containing two polarization angles: 0° and 90°. The polarization array layer is placed on D... 2 The distance between the NNs diffraction layers and the distance between the NNs and the previous diffraction layer is 0.

[0050] Step 3: Input the Gaussian beam into the polarization-encoded diffraction neural network (PD) at different spatial locations. 2 In a polarization-coded diffraction neural network (PDNNs), each input position corresponds to a specific input location. 2The vector vortex light output of orbital angular momentum (OAM) modes with different topological charges on the output plane of NNs can be multiplied with the Jones matrix of the polarization array layer to obtain vector light fields with different polarization modulations in the x and y directions on the output plane.

[0051] Specifically, this invention uses a Gaussian beam as input, at a spatial position (x m ,y m ,z m The optical field of the input polarized electromagnetic wave in () is represented as:

[0052]

[0053] Among them, E x Polarization-encoded diffraction neural network (PD) 2 The light field in the direction of NNs)x, E y Polarization-encoded diffraction neural network (PD) 2 The light field in the y direction of NNs)x m ,y m ,z m Indicates spatial location, m represents the m-th incident Gaussian point, E x and E y Polarization-encoded diffraction neural network (PD) 2 Parallel computation within NNs;

[0054] Since the trainable diffraction layers are insensitive to polarization states, they produce the same complex-valued modulation for two orthogonal polarization states. Propagation between diffraction layers is based on the Rayleigh-Sommerfeld diffraction equation. If the distance from the input to the diffraction layer and the distance between the diffraction layers are both set to 3 cm, then the modulated light field reaching the (l+1)th layer after passing through the l-th diffraction layer can be expressed as:

[0055]

[0056] Where p represents the polarization state of the modulated light field E located at (x,y,z), S represents all pixels in the l-th layer, t represents the diffraction layer modulation, and W represents the diffraction propagation function between layers. For the linear polarization element used, i.e., the polarization array layer, the Jones matrix J is used. θ Modeling each polarization unit in the polarization array layer, where θ represents the angle between the polarization axis and the x-axis, the replicated modulation of the optical field at (x,y,z) by a polarization unit in the polarization array layer is represented as:

[0057] E out (x,y,z)=J θ (x,y,z)E in (x,y,z)

[0058] Among them, E in and E out Let J represent the vector complex fields before and after polarization modulation, respectively. Each vector complex field has two orthogonal components, x and y. Then, after passing through the Jones matrix J of the polarization array layer... θ This produces different modulations on the two orthogonal polarization states.

[0059] To address the insensitivity of the diffraction layer to polarization, this invention models the polarization array layer within the diffraction network. This polarization array layer can modulate the x and y polarization components differently. Figure 2 As shown. For the polarization array layer used, each polarization unit in the polarization array layer is mathematically modeled using the Jones matrix:

[0060]

[0061] Here, θ takes values ​​of 0° and 90°. The polarization array layer consists of multiple polarization units, each containing two polarization angles: 0° and 90°. These two different polarizations are spatially combined into a 2x2 period, repeating four times in each direction, extending into a square region, such as... Figure 2 As shown. The linear polarizer is placed between the second and third diffraction layers, and at a distance d from the second layer. p A value of 0 indicates that the light is attached to the third layer. Physically, this polarization array layer can be modeled using a linear polarizer. At this point, each Jones matrix is ​​multiplied by the light field modulated by the previous layer, thus the PD... 2 NNs can modulate vector beams in the polarization dimension, solving the problem of traditional D 2 The shortcomings of NNs.

[0062] Step 4: On the output plane, in the polarization-encoded diffraction neural network (PD) 2 During training of the polarization-encoded diffraction neural network (PDNN), the mean square error loss function is used to calculate the difference between the predicted vector light field output and the target beam, i.e., the vector vortex light. The difference is evaluated by minimizing the mean square error loss function (MSE). 2 The stochastic gradient descent algorithm is used to apply the polarization-encoded diffraction neural network (PDNNs). 2 Optimize using NNs;

[0063] The loss function during backpropagation is defined as follows:

[0064]

[0065] Where E1[n] and E2[n] represent PD respectively. 2Complex amplitude distributions of the target and predicted light fields of NNs, E 1x [n]、E 2x [n] and E 1y [n]、E 2y [n] represents the x and y polarization components of the light field, respectively. The total loss function can be decomposed into the sum of the light field losses in the x and y polarization directions. n is the number of pixels in the diffraction layer, and b represents the number of samples in a batch during network training.

[0066] The structure of the polarization-encoded diffraction deep neural network is built using four diffraction layers, each with a size of 128×128. The distances between the input plane and the diffraction layers, as well as between the diffraction layers, are all set to 3 cm. The polarization layer, also with a size of 128×128, is placed between the second and third layers.

[0067] The input and output datasets are prepared as follows: the input dataset consists of 1600 sample data points generated by the fundamental mode Gaussian function; the output dataset is generated by superimposing two Laguerre-Gaussian beams with opposite topological charges l and opposite circular polarization states, producing a total of 1600 sample data points. This data is only used during the training phase. For the testing phase of this embodiment, one sample is generated for each phase.

[0068] The optical field similarity index uses the normalized overlap integral and the average structure similarity index (SSIM) to examine the quality of the generated vector vortex beam. The overlap integral is used to calculate the spatial overlap between two optical fields. Typically, the overlap integral is normalized to the range [0,1], where 1 represents complete overlap and 0 represents no overlap. It can be expressed as:

[0069]

[0070] Where E1[n] and E2[n] represent the light field values ​​of the nth pixel on the target light field and the predicted light field output plane, respectively, and E2... * [n] represents the conjugation of E2[n], the numerator represents the square of the overlap, and the denominator is the product of the light field intensities, used for normalization.

[0071] The Structural Similarity Index (SSIM) is calculated as follows:

[0072]

[0073] Where μ1 represents the mean amplitude of the target light field E1[n], μ2 represents the mean amplitude of the predicted light field E2[n], and σ1 2 σ2 represents the variance of the amplitude of E1[n]. 2 σ represents the variance of the amplitude of E2[n]. 12The covariance of the amplitudes of E1[n] and E2[n] is represented by C1 and C2, which are constants to prevent division by zero errors.

[0074] The final simulation results are used to display PD. 2 The internal generalization ability of neural networks to generate vector vortex light was tested by inputting Gaussian light from different spatial locations into the network according to the 8PSK constellation diagram, and the PD was evaluated. 2 Can NNs generate vector vortex beams of the corresponding mode? The obtained normalized intensity map is as follows. Figure 3 As shown, it can be seen that for each type of OAM mode vector vortex light, PD 2 NNs can generate high-quality signals. To verify the generation quality of the vector vortex beams, the normalized overlap integral and structural similarity index between the output and target light fields were calculated. The normalized overlap integral and the average structural similarity index (SSIM) during the testing phase for each output vector vortex beam and the target value both reached 0.99.

[0075] To verify the vector characteristics of the beam, and to more intuitively describe the polarization state of the generated vector vortex light, the Stokes parameter is used on the output plane to effectively display the vector characteristics of the output vector vortex light field. This is manifested in the fact that the intensity distribution of the vector light field differs in different polarization directions. The Stokes parameter is a four-dimensional vector containing S0, S1, S2, and S3, used to describe any vector light field, and its expression is:

[0076]

[0077] Among them, I H I V I represents the horizontal and vertical intensities, respectively. 45° I 135° I represents the polarization intensities at 45° and 135° angles to the x-axis, respectively. R I L These represent the polarization intensities of the right and left circles, respectively. The resulting normalized intensity map is shown below. Figure 3 As shown. For each mode of vector vortex light field, the corresponding polarization direction light field is obtained after Stokes operation. When the light field intensity distribution in each polarization direction has different petal distribution, it is verified that the generated light field is a vector vortex light field.

[0078] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for generating vector vortex light based on a polarization-encoded diffraction neural network, characterized in that: The polarization-encoded diffraction neural network includes a polarization array layer that enables independent polarization modulation in the x and y directions. The vector vortex light generation method specifically includes the following steps: Step 1: Inject a Gaussian beam with wavelength λ onto the input plane of the polarization-encoded diffraction neural network; Step 2: Arrange the incident points on the input plane according to the MPSK constellation diagram, which includes n different incident points, representing vector vortex light with different topological charge values; Step 3: Pre-set the polarization array layer; Step 4: Place the polarization array layer pre-set in Step 3 between the diffraction layers of the diffraction depth neural network, with a distance d between it and the previous diffraction layer. p ; Step 5: Input the Gaussian beam into the polarization-encoded diffraction neural network at different spatial positions. Each input position corresponds to the vector vortex light output of the orbital angular momentum mode of different topological charges on the output plane of the polarization-encoded diffraction neural network. By multiplying with the Jones matrix of the polarization array layer, vector light fields with different polarization modulations in the x and y directions are obtained on the output plane. Step 6: During the training of the polarization-encoded diffraction neural network, the mean square error loss function is used to calculate the difference between the predicted vector light field output and the target beam, i.e., the vector vortex light. The polarization-encoded diffraction neural network is evaluated by minimizing the mean square error loss function, and the polarization-encoded diffraction neural network is optimized using the stochastic gradient descent algorithm. Step 7: Generate different vector vortex beams by combining the vector light fields in the x and y directions; Step 8: Perform Stokes operation on the generated vector vortex beam to obtain the light field distribution in each polarization direction and verify the generated vector vortex beam; Step 9: Use the normalized overlap integral and the average structural similarity index to measure the quality of the vector vortex beam generated in Step 7.

2. The vector vortex light generation method based on polarization-encoded diffraction neural network according to claim 1, characterized in that: Step 5 specifically includes the following steps: Step 5.1: Using a Gaussian beam as input, at the input plane spatial position (x... m ,y m ,z m The optical field of the input polarized electromagnetic wave on the input is represented as: Among them, E x E represents the light field in the x-direction. y Represents the light field in the y direction, (x m ,y m ,z m ) represents the spatial location, m represents the m-th incident point, and E x and E y Parallel computation is performed throughout the entire polarization-encoded diffraction neural network; Step 5.2: Generate the same complex-valued modulation for the two orthogonal polarization states. The propagation between the diffraction layers is based on the Rayleigh-Sommerfeld diffraction equation. If the distance from the input to the diffraction layer and the distance between the diffraction layers are both denoted as d, then the modulated light field reaching the (l+1)th layer after passing through the l-th diffraction layer is expressed as: Where p represents the polarization state of the modulated light field E located at (x,y,z), S represents all pixels in the l-th layer, and t l+1 This indicates the modulation of the (l+1)th diffraction layer. Let m be the diffraction propagation function between the l-th layer and the (l+1)-th layer at point m; Step 5.3: Using the Jones matrix J θ Let θ represent each polarization unit in the polarization array layer, and let θ represent the angle between the polarization axis and the x-axis. Then, the modulation of the input vector light field by the polarization unit located at (x, y, z) in the polarization array layer can be expressed as: E out (x,y,z)=J θ (x,y,z)E in (x,y,z) Among them, E in and E out These represent the vector optical fields before and after polarization modulation, respectively. For each vector optical field, there are two directional components, x and y. After passing through the Jones matrix J of the polarization array layer... θ This resulted in different modulations of the x and y components.

3. The vector vortex light generation method based on polarization-encoded diffraction neural network according to claim 2, characterized in that: In step 8, the Stokes parameters are used to effectively display the vector characteristics of the output vector vortex light field on the output plane. This is manifested in the fact that the intensity distribution of the vector light field differs in different polarization directions. The Stokes parameters are four-dimensional vectors containing S0, S1, S2, and S3, used to describe any vector light field. Their expression is: Among them, I H I V I represents the horizontal and vertical intensities, respectively. 45 °、I 135 o represents the polarization intensity at 45° and 135° to the x-axis, respectively. R I L The polarization intensities of the right and left circles are represented respectively. For each mode of vector vortex light field, the corresponding polarization direction light field is obtained after Stokes operation. When the light field intensity distribution in each polarization direction has different petal distributions, it is verified that the generated light field is a vector vortex light field.

4. The vector vortex light generation method based on polarization-encoded diffraction neural network according to claim 1, characterized in that: In step 9, the quality of the vector vortex beam generated in step 7 is checked using the normalized overlap integral and the average structural similarity index. Specifically, the overlap integral is normalized to the range [0,1], where 1 represents complete overlap and 0 represents no overlap, expressed as: Where E1[n] and E2[n] represent the target light field and the light field value of the nth pixel of the expected output plane, respectively, and E2... * [n] indicates taking the conjugate of E2[n]. Represents the square of the sum of overlaps. It is the product of the light field intensity, used for normalization; The average structural similarity index is calculated as follows: Where μ1 represents the mean amplitude of the target light field E1[n], μ2 represents the mean amplitude of the predicted light field E2[n], and σ1 2 σ2 represents the variance of the amplitude of E1[n]. 2 σ represents the variance of the amplitude of E2[n]. 12 Let C1 and C2 represent the covariance of the amplitudes of E1[n] and E2[n], respectively. C1 and C2 are constants.

5. A vector vortex light generation method based on a polarization-encoded diffraction neural network according to any one of claims 1-4, characterized in that: The polarization-encoded diffraction neural network includes an input plane, an output plane, a diffraction layer, and a polarization array layer that enables independent polarization modulation of the polarization-encoded diffraction neural network in the x and y directions.

6. The vector vortex light generation method based on polarization-encoded diffraction neural network according to claim 5, characterized in that: The polarization array layer in step 3 includes multiple polarization units, and each polarization unit includes two polarization angles: 0° and 90°.

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