Method for identifying high-order continuous OAM modes based on diffraction deep neural network

Abstract

The application discloses a method for identifying high-order continuous OAM modes based on a diffraction deep neural network, and comprises the following steps: step 1, obtaining a light field complex amplitude matrix after an atmospheric turbulence disturbance through numerical simulation, and establishing a data set; step 2, designing and building a basic diffraction deep neural network structure, performing data preprocessing on the training data obtained in step 1, and sending the data into the basic diffraction deep neural network designed in the step to perform model training; and step 3, designing and building a diffraction deep neural network for identifying high-order continuous OAM modes, and testing the effect by using a test set. The method solves the problem of insufficient OAM mode identification under atmospheric turbulence in the prior art related to optical and deep learning methods.

Description

Technical Field

[0001] This invention belongs to the field of wireless optical communication technology, and relates to a system based on a diffractive deep neural network (DNN). 2 A method for identifying high-order continuous OAM patterns using NN. Background Technology

[0002] Orbital Angular Momentum (OAM) is a new degree of freedom carried by vortex beams (VBs), characterized by its complex electric field amplitude containing an exp(ilθ) term, where θ is the azimuth angle and l is the topological charge. In optical communication, VBs of different OAM modes are orthogonal to each other, and theoretically, the value of l is infinite, giving OAM a new physical dimension for improving communication capacity density. Accurate detection of VBs in the receiver is crucial for efficient signal demodulation and ensuring the overall communication quality of the system. However, the lack of effective methods for recognizing high-order continuous OAM patterns severely hinders the development and application of OAM communication.

[0003] In recent years, deep learning has developed rapidly, especially in the field of image classification, where it has shown unparalleled advantages. Methods using deep learning to identify OAM patterns typically treat the OAM pattern recognition problem as a classification problem, using OAM intensity images acquired by CCDs as the basis for classification, which is difficult to detect in real time. In practical applications, the direction of phase rotation is difficult to represent using intensity images, making identification impossible. Furthermore, higher-order OAM patterns are more affected by turbulence than lower-order OAM patterns, resulting in more severe pattern crosstalk and making detection even more difficult. In addition, traditional D... 2 NNs have difficulty recognizing high-order continuous OAM patterns due to their fixed layer size. Summary of the Invention

[0004] The purpose of this invention is to provide a method for identifying high-order continuous OAM modes based on a diffraction deep neural network. This method is capable of identifying the structure of a diffraction deep neural network for high-order continuous OAM modes, thus solving the problem that existing optical and deep learning methods are insufficient for identifying OAM modes under atmospheric turbulence.

[0005] The technical solution adopted in this invention is a method for recognizing high-order continuous OAM patterns based on a diffraction deep neural network, comprising the following steps:

[0006] Step 1: Obtain the complex amplitude matrix of the optical field after atmospheric turbulence disturbance through numerical simulation, and establish a dataset;

[0007] Step 2: Design and build a basic diffraction deep neural network structure. Perform data preprocessing on the training data obtained in Step 1 and feed it into the basic diffraction deep neural network designed in this step for model training.

[0008] Step 3: Design and build a diffraction deep neural network to recognize high-order continuous OAM patterns, and test the effect using a test set.

[0009] The invention is further characterized in that:

[0010] Step 1 shall be carried out according to the following specific steps:

[0011] Step 1.1: Based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of atmospheric turbulence;

[0012] Step 1.2, in cylindrical coordinates, determine the light field expression of the Laguerre-Gaussian beam, specifically:

[0013]

[0014] In the formula, r, φ, z are cylindrical coordinates, and z R =πw0 / λ is the Rayleigh distance (w0 is the waist radius of the Laguerre-Gaussian beam), λ is the wavelength, and w(z) is the beam radius of the Laguerre-Gaussian beam at z; For the associated Laguerre polynomial, k is the space wave number, p is the radial exponent, l is the topological charge, and i is the imaginary number;

[0015] Step 1.3, according to Fresnel's principle, after a beam with electric field U(x,y,z) propagates a distance Δz in atmospheric turbulence, the electric field function U(z+Δz,x,y) is expressed as:

[0016]

[0017] In the formula, x, y, z represent the rectangular coordinate system, and IFFT represents the inverse Fourier transform. Let i be the Fresnel transmission coefficient, i be the imaginary number, and k be the space wavenumber. x and k y Represents spatial frequencies in the x and y directions. For atmospheric turbulence random phase screen;

[0018] Step 1.4: Substitute the light field expression of the Laguerre-Gaussian beam in Step 1.2 as U(x,y,z) in Step 1.3 into Formula (4) to obtain the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance; by changing the magnitude of the topological charge l in the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance, generate a complex amplitude matrix of the light field with a topological charge l of -50 to +50 and not including 0 after atmospheric turbulence disturbance to construct a dataset.

[0019] Step 1.1 shall be implemented according to the following specific steps:

[0020] Step 1.1.1: Select the modified Hill atmospheric refractive index power spectral density function Φ n (k), whose expression is:

[0021]

[0022] In the formula, k is the space wavenumber, k = 2π / λ, λ is the wavelength, and the range of k is 0 ≤ k ≤ ∞; The atmospheric refractive index structure constant. The value is 1×10 -16 m -2 / 3 1×10 -15 m -2 / 3 1×10 -14 m -2 / 3 The time corresponds to weak, moderate, and strong atmospheric turbulence, respectively; the other parameters in equation (1) are: k l =3.3 / l0, where l0 is the internal scale turbulence; k0 = 1 / L0 or 2π / L0, where L0 is the external scale turbulence; a1 = 1.802, a2 ​​= 0.254;

[0023] Step 1.1.2, obtaining the atmospheric turbulence random phase screen based on the power spectrum inversion method, specifically:

[0024] First, generate a complex Gaussian random matrix C. N×N Then, the modified Hill atmospheric refractive index power spectral density function Φ was used. n (k) Filter the filter and finally obtain the atmospheric turbulence random phase screen through inverse Fourier transform. This process can be expressed by the following formula:

[0025]

[0026] In the formula, x, y are position coordinates, IFFT is the inverse Fourier transform, N and Δx represent the number of sampling points and the sampling interval of the phase screen, respectively, and C N×N It is a complex Gaussian random matrix with a mean of 0 and a variance of 1, where k is the spatial wavenumber, Δd is the phase screen spacing, and Φ is the distance between the phase screens. n(k) is the modified Hill atmospheric refractive index power spectral density function.

[0027] In step 1.4, the constructed dataset is divided into a training set and a test set in an 8:2 ratio, and both the test set and the training set are saved in .mat format.

[0028] Step 2 shall be carried out in accordance with the following specific steps:

[0029] Step 2.1: Design and build a diffraction deep neural network. The network structure includes L diffraction layers, each diffraction layer contains w×w nodes, and each node in each diffraction layer is connected to the next layer.

[0030] According to Rayleigh-Sommers diffraction theory, each node in each layer of a diffraction deep neural network is considered a secondary light source, and the point light source satisfies the following formula:

[0031]

[0032] Where x, y, z are Cartesian coordinates, L is the number of network layers, λ is the wavelength, i is an imaginary number, and s represents the s-th node out of w×w nodes in the layer. Let the coordinates of the s-th node be (x, y, z) s ,y s ,z s ), r s Let be the distance from the light source to the s-th node, denoted as . Output of the s-th node in layer L Input light and transmission coefficient from the node The joint decision is expressed as follows:

[0033]

[0034] in, Let be the superposition of the light field from the previous incident light layer (L-1 layer) reaching the s-th node of layer L, v be the v-th node in the w×w nodes of layer L-1, |A| be the relative amplitude modulated by the transmission coefficient of the second wave, Δθ be the phase delay added by the transmission coefficient, and the transmission coefficient be... It consists of two parts: amplitude and phase, and is represented as:

[0035]

[0036] in, For amplitude, Designed D for phase term 2 The NN network structure is a pure phase-type network. To simplify the notation of the above forward propagation model, Eq.(6) is rewritten as:

[0037]

[0038] Where q represents the q-th node in the next layer. For L-layer input, For the Rayleigh-Sommers diffraction theory satisfied by the L-layer point source, The complex amplitude of the network input layer is represented as the superposition of the light field of the incident light from the previous layer reaching the s-th node of layer L. After diffraction transmission, the first layer input is obtained. After transmission through layer M, the received light field intensity on the detector plane of layer M+1 is expressed as:

[0039]

[0040] D 2 The loss function for the neural network is set to the mean square error between the received light intensity and the ideal light intensity.

[0041]

[0042] Where K is the number of measurement points on the output plane. Assuming an ideal light intensity distribution, the network is trained using loss backpropagation and gradient descent algorithms. The training aims to solidify the transmission coefficients at each point in the diffraction layer, expressed as:

[0043]

[0044] Step 2.2: Before starting training, load the training and test sets established in Step 1.4 as required. Set the .mat dataset containing all training and test data with topological loads l ranging from -50 to +50 (excluding 0) obtained after atmospheric turbulence perturbation to one class of 10 topological loads each, i.e., l ranging from -50 to -41, -40 to -31, -30 to -21, -20 to -11, -10 to -1, 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 41 to 50, for a total of 10 classes. Set the size of the atmospheric turbulence perturbation light field complex amplitude matrix dataset to 250×250 and convert it to tensor format. Save the training and test data and labels in .npy format. The data processed above is called coarse classification data.

[0045] In step 2.1, the measurable points K = 10, meaning that 10 categories can be detected at once. Specifically, three rows are set on the same plane, with three measurement points at the top and bottom and four measurement points in the middle. Following a top-down, left-to-right order, each group of ten topological loads (excluding 0) is designated as a single category. These ten topological loads are ultimately displayed at the same measurement point. The first measurement point represents topological load l from -50 to -41, the second from -40 to -31, and so on, with the last measurement point representing topological load l from 41 to 50. The coarse classification data processed in step 2.2 is input into the diffraction deep neural network model from step 2.1 for training. The batch size is set to 128, and the learning rate to 0.003. The mean squared error loss function (MSELoss) is used to calculate the error between the network's output and target values. The network model parameters are iteratively optimized. After 20-30 iterations, the trained coarse classification weight model is saved. The network model using the coarse classification data as the training dataset is called the coarse classification model.

[0046] Step 2.3: Before starting training, load the training and test sets (with topological charges l ranging from -50 to -41 obtained after atmospheric turbulence disturbance) established in Step 1.4 as required. Set the size of the dataset to 250×250 and convert it to tensor format, saving the training and test data and labels in .npy format. This processed data is called the fine-classification data D1. Set the measurable points K = 10 in Step 2.1, meaning 10 categories can be detected at once. Specifically, set three rows on the same plane: three measurement points at the top and bottom, and four in the middle. Each measurement point represents a topological charge, arranged from top to bottom and left to right. The first measurement point represents a topological charge l of -50, the second represents a topological charge l of -49, and so on. Input the processed fine-classification data D1 into the diffraction deep neural network model in Step 2.1 for training, setting the batch size to 128 and the learning rate to [missing value]. With a rate of 0.003, the mean square error loss function MSELoss is used to calculate the error between the network's output value and the target value (received light intensity and ideal light intensity). The network model parameters are continuously optimized through iteration. After 90 to 100 iterations, the trained fine classification weight model is saved. The network model that uses the fine classification data D1 as the training dataset is called the fine classification model F1.

[0047] For the training and test sets established in step 1.4, which are obtained after atmospheric turbulence disturbance and have topological loads l of -40~-31, -30~-21, -20~-11, -10~-1, 1~10, 11~20, 21~30, 31~40, and 41~50 respectively, both sets are set to a size of 250×250 and converted to tensor format. The training and test data and labels are saved in .npy format. The processed data are referred to as the fine classification data D2–D10. The output plane of each fine classification data sets sets the measurable point K in step 2.1 to 10, that is, 10 categories can be detected at one time. Specifically, three rows are set on the same plane, with three measurement points at the top and bottom and four measurement points in the middle. Each measurement point represents a topological load in the order from top to bottom and from left to right. The processed fine-classification data D2–D10 are sequentially input into the diffraction deep neural network model in step 2.1 for training. The batch size is set to 128, and the learning rate to 0.003. The mean squared error loss function (MSELoss) is used to calculate the error between the network's output value and the target value (received light intensity and ideal light intensity). The network model parameters are iteratively optimized. For fine-classification data D5 and D6, the iterations are performed 40–50 times; for fine-classification data D1–D4 and D7–D10, the iterations are performed 90–100 times. The trained fine-classification weight models are then saved. The network model using fine-classification data D2 as the training dataset is called fine-classification model F2; the network model using fine-classification data D3 as the training dataset is called fine-classification model F3; different fine-classification data correspond to different fine-classification models, and so on. The network model using fine-classification data D10 as the training dataset is called fine-classification model F10.

[0048] Step 3 shall be carried out in accordance with the following specific steps:

[0049] Step 3.1: Design and build a diffraction deep neural network for recognizing high-order continuous OAM patterns, which includes two modules: a coarse classifier and a fine classifier.

[0050] Step 3.2: Load the test set divided in step 1.4, set the size of the test set of all the light field complex amplitude matrices after atmospheric turbulence disturbance to 250×250, and convert it to tensor format;

[0051] Step 3.3: Load the coarse classification weight model from step 2.2 and the 10 fine classification weight models from step 2.3. Input the test data from step 3.2 into the network model designed in step 3.1 to identify the OAM pattern, and use the average test accuracy as the evaluation index. The higher the average test accuracy, the better the recognition effect of the network.

[0052] In step 3.1, the specific process of the diffraction deep neural network for high-order continuous OAM modes is as follows: input the complex amplitude matrix of the LG beam field obtained after atmospheric turbulence perturbation in step 3.2—pass through a coarse classifier—determine which fine classifier to use next based on the classification result of the coarse classifier—select the corresponding fine classifier—input the complex amplitude matrix of the LG beam field obtained after atmospheric turbulence perturbation in step 3.2 again—pass through the fine classifier selected above—finally determine the specific OAM mode based on the classification result of the fine classifier.

[0053] In step 3.1, the coarse classifier includes the L-layer diffraction layer of the coarse classification model and 10 light intensity detectors on the output plane. Its specific function is to place 10 light intensity detectors on the output plane to detect the light intensity. The light beam is phase-modulated by the L-layer diffraction layer of the coarse classification model. Finally, the mode range to which the light beam belongs is determined based on which light intensity detector on the output plane has the strongest light intensity.

[0054] The fine classifier contains 10 fine classification models F1 to F10. Each fine classification model contains an L-layer diffraction layer and 10 light intensity detectors on the output plane. The specific function is as follows: 10 light intensity detectors are placed on the output plane to detect the light intensity. The light beam is phase-modulated by the L-layer diffraction layer of the fine classification model. Finally, the specific mode of the light beam is determined based on which light intensity detector on the output plane has the strongest light intensity.

[0055] The beneficial effects of this invention are:

[0056] (1) This invention provides a method for identifying high-order continuous OAM modes based on a diffraction deep neural network. It primarily utilizes the theoretical knowledge of diffraction deep neural networks, combined with the theory of beam propagation in atmospheric turbulence, to train a network model. This model enables the identification of OAM modes using the complex amplitude matrix of the light field after transmission disturbance. The results demonstrate that the OAM modes can be identified using the complex amplitude matrix of the light field after transmission disturbance. Compared to existing methods, this method can detect OAM modes in real time and simultaneously identify positive and negative (different phase rotation directions) high-order OAM modes. This addresses the shortcomings of existing optical and deep learning methods in identifying OAM modes and has significant reference value for improving communication capacity.

[0057] (2) The key to solving the problem of not being able to identify positive and negative OAM modes and the difficulty in identifying higher-order OAM modes using light intensity maps in deep learning lies in the input complex amplitude data of the light field and whether the network can directly process the complex amplitude information of the light field. Deep diffraction neural networks, developed from complex-valued neural networks, directly use light as input and diffraction devices such as reflective or transmissive screens as network layers, achieving zero-delay detection at the output. This invention provides a method for identifying higher-order continuous OAM modes based on a diffraction deep neural network. To better identify higher-order OAM modes, it utilizes D... 2 The ability of a neural network to directly process optical field information allows it to use the complex amplitude of the optical field of a Laguerre-Gaussian (LG) beam subjected to turbulence disturbance as the basis for D. 2 The input to the neural network is optimized with the goal of maximizing the intensity of one of the 10 detection points in the last layer. After supervised training on a massive sample set, a model that can automatically recognize high-order continuous OAM patterns is finally obtained. Attached Figure Description

[0058] Figure 1 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -1;

[0059] Figure 2 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -30;

[0060] Figure 3 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -48;

[0061] Figure 4 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -1;

[0062] Figure 5 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -30;

[0063] Figure 6 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -48;

[0064] Figure 7 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -1;

[0065] Figure 8 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -30;

[0066] Figure 9 In the atmospheric refractive index structure constant Distorted LG intensity map when topological charge l = + / -48;

[0067] Figure 10 This is a diagram of a diffraction deep neural network structure for recognizing high-order continuous OAM patterns;

[0068] Figure 11 It is a graph showing the accuracy of the fine-classification model and the coarse-classification model during the training process;

[0069] Figure 12 This is a simulation diagram of the output results of the coarse classification model in Example 1 when the topological load l = -46;

[0070] Figure 13 This is a simulation diagram of the output results of the fine-classification model in Example 1 when the topological load l = -46;

[0071] Figure 14 This is a simulation diagram of the output results of the coarse classification model in Example 2 when the topological load l = +1;

[0072] Figure 15 This is a simulation diagram of the output results of the fine classification model in Example 2 when the topological load l = +1. Detailed Implementation

[0073] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0074] This invention provides a method for identifying high-order continuous OAM patterns based on a diffraction deep neural network, specifically including the following steps:

[0075] Step 1: Obtain the complex amplitude matrix of the optical field after atmospheric turbulence disturbance through numerical simulation, and establish a dataset;

[0076] Step 1 shall be carried out according to the following specific steps:

[0077] Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of atmospheric turbulence, specifically as follows:

[0078] Step 1.1.1: Select the modified Hill atmospheric refractive index power spectral density function Φ n (k), whose expression is:

[0079]

[0080] In the formula, k is the space wavenumber, k = 2π / λ, λ is the wavelength, and the range of k is 0 ≤ k ≤ ∞; The atmospheric refractive index structure constant is a constant whose value increases closer to the ground. It is typically used as a primary measure of turbulence intensity. The value is 1×10 -16 m -2 / 3 1×10 -15 m -2 / 3 1×10 -14 m -2 / 3 The time corresponds to weak, moderate, and strong atmospheric turbulence, respectively; the other parameters in equation (1) are: k l = 3.3 / l0, where l0 is internal-scale turbulence; k0 = 1 / L0 or 2π / L0, where L0 is external-scale turbulence; a1 = 1.802, a2 ​​= 0.254. Atmospheric turbulence can be considered to be formed by the cyclical motion of countless turbulent vortices of different sizes. Based on the size of the turbulent vortices, turbulence can be divided into external-scale turbulence (L0) and internal-scale turbulence (l0). It is generally believed that external-scale turbulence exhibits anisotropy within a given space, and the size of L0 can reach tens to hundreds of meters. When the turbulence size is smaller than that of internal-scale turbulence, it is considered to be isotropic within a local space, and the size of internal-scale turbulence (l0) is generally a few millimeters.

[0081] Step 1.1.2, obtaining the atmospheric turbulence random phase screen based on the power spectrum inversion method, specifically:

[0082] First, generate a complex Gaussian random matrix C. N×N Then, the modified Hill atmospheric refractive index power spectral density function Φ was used. n (k) Filter the filter and finally obtain the atmospheric turbulence random phase screen through inverse Fourier transform. This process can be expressed by the following formula:

[0083]

[0084] In the formula, x, y are position coordinates, IFFT is the inverse Fourier transform, N and Δx represent the number of sampling points and the sampling interval of the phase screen, respectively, and C N×N It is a complex Gaussian random matrix with a mean of 0 and a variance of 1, where k is the spatial wavenumber, Δd is the phase screen spacing, and Φ is the distance between the phase screens. n (k) is the modified Hill atmospheric refractive index power spectral density function;

[0085] Step 1.2, in cylindrical coordinates, determine the light field expression of the Laguerre-Gaussian beam, specifically:

[0086]

[0087] In the formula, r, φ, z are cylindrical coordinates, and z R=πw0 / λ is the Rayleigh distance (w0 is the waist radius of the Laguerre-Gaussian beam), λ is the wavelength, and w(z) is the beam radius of the Laguerre-Gaussian beam at z; For the associated Laguerre polynomial, k is the space wave number, p is the radial exponent, l is the topological charge, and i is the imaginary number;

[0088] Step 1.3, according to Fresnel's principle, after a beam with electric field U(x,y,z) propagates a distance Δz in atmospheric turbulence, the electric field function U(z+Δz,x,y) is expressed as:

[0089]

[0090] In the formula, x, y, z represent the rectangular coordinate system, and IFFT represents the inverse Fourier transform. Let i be the Fresnel transmission coefficient, i be the imaginary number, and k be the space wavenumber. x and k y Represents spatial frequencies in the x and y directions. For atmospheric turbulence random phase screen;

[0091] Step 1.4: Substitute the light field expression of the Laguerre-Gaussian beam in Step 1.2 into formula (4) as U(x,y,z) in Step 1.3 to obtain the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance; by changing the magnitude of the topological charge l in the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance, generate a complex amplitude matrix of the light field with a topological charge l of -50 to +50 (excluding 0) after atmospheric turbulence disturbance, and construct a dataset with a total of 93,800 samples of the complex amplitude matrix of the light field (938 of each topological charge); divide the constructed dataset into a training set and a test set in an 8:2 ratio, of which 7,500 samples are used as D 2 The training set for the neural network (750 samples per topology load) and the test set (188 samples per topology load) consist of 18,800 samples. 2 The recognition performance of the NN model, both the test set and the training set are saved in .mat format.

[0092] Since the atmospheric refractive index structure constant is usually used as the main measure of turbulence intensity, this section studies the atmospheric refractive index structure constant. And the influence of the magnitude of the topological charge l on beam propagation. The atmospheric refractive index structure constants are respectively... (Weak turbulence) (Medium turbulence) (Strong turbulence), with a radial exponent of p = 2, the distorted light intensity diagrams under different topological charges are as follows: Figure 1-9 As shown, from Figure 1-9 It can be seen from this that as the atmospheric refractive index structure constant changes... As the intensity increases, the distortion of the transmitted light intensity also increases, which is consistent with the fact that stronger atmospheric turbulence leads to more severe beam distortion in reality, confirming the accuracy of the simulation model. Furthermore, the intensity diagrams under positive and negative topological charges are identical (this is because light intensity is obtained from the conjugate of the light field, and the sign of the topological charge does not affect the final result), which also confirms that the sign (phase rotation direction) of the OAM mode cannot be directly determined from the intensity diagram.

[0093] Step 2: Design and build a basic diffraction deep neural network structure. Perform data preprocessing on the training data obtained in Step 1 and feed it into the basic diffraction deep neural network designed in this step for model training.

[0094] Step 2 shall be carried out in accordance with the following specific steps:

[0095] Step 2.1: Design and build a diffraction deep neural network. This network structure includes L diffraction layers, each containing w×w nodes. Each node in each diffraction layer (corresponding to each neuron in the neural network layer) is connected to the next layer. K light intensity detectors can be placed on the output plane of this network to detect the output light field intensity. The K measurement points on the output plane represent the number of categories that the basic structure of the diffraction deep neural network can identify at one time.

[0096] According to Rayleigh-Sommers diffraction theory, each node in each layer of a diffraction deep neural network is considered a secondary light source, and the point light source satisfies the following formula:

[0097]

[0098] Where x, y, z are Cartesian coordinates, L is the number of network layers, λ is the wavelength, i is an imaginary number, and s represents the s-th node out of w×w nodes in the layer. Let the coordinates of the s-th node be (x, y, z) s ,y s ,z s ), r s Let be the distance from the light source to the s-th node, denoted as . Output of the s-th node in layer L Input light and transmission coefficient from the node The joint decision is expressed as follows:

[0099]

[0100] in, Let be the superposition of the light field from the previous layer (i.e., layer L-1) reaching the s-th node of layer L, v be the v-th node in layer L-1 with a total of w×w nodes, |A| be the relative amplitude modulated by the transmission coefficient of the second wave, Δθ be the phase delay added by the transmission coefficient, and the transmission coefficient be... It consists of two parts: amplitude and phase, and is represented as:

[0101]

[0102] in, For amplitude, For the phase term, D varies depending on the type of trainable parameter chosen for the transmission coefficient. 2 Networks (NNs) can be classified into three types: pure amplitude type, pure phase type, and hybrid type. If the amplitude is constant, the network is a pure phase type; if the phase is constant, the network is a pure amplitude type; and if both amplitude and phase are variables, the network is a hybrid type. The D network designed in this invention... 2 The NN network structure is a pure phase-type network. To simplify the notation of the above forward propagation model, Eq.(6) is rewritten as:

[0103]

[0104] Where q represents the q-th node in the next layer. For L-layer input, For the Rayleigh-Sommers diffraction theory satisfied by the L-layer point source, The complex amplitude of the network input layer is represented as the superposition of the light field of the incident light from the previous layer reaching the s-th node of layer L. After diffraction transmission, the first layer input is obtained. After transmission through layer M, the received light field intensity on the detector plane of layer M+1 is expressed as:

[0105]

[0106] D 2 The loss function for the neural network is set to the mean square error between the received light intensity and the ideal light intensity.

[0107]

[0108] Where K is the number of measurement points on the output plane. Assuming an ideal light intensity distribution, the network is trained using loss backpropagation and gradient descent algorithms. The training aims to solidify the transmission coefficients at each point in the diffraction layer, expressed as:

[0109]

[0110] Step 2.2: Before starting training, load the training and test sets established in Step 1.4 as required. Set the .mat dataset containing all training and test data with topological loads l ranging from -50 to +50 (excluding 0) obtained after atmospheric turbulence perturbation to one class of 10 topological loads each, i.e., l ranging from -50 to -41, -40 to -31, -30 to -21, -20 to -11, -10 to -1, 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 41 to 50, for a total of 10 classes. Set the size of the atmospheric turbulence perturbation light field complex amplitude matrix dataset to 250×250 and convert it to tensor format. Save the training and test data and labels in .npy format. The data processed above is called coarse classification data.

[0111] In step 2.1, the measurable points K = 10, meaning that 10 categories can be detected at once. Specifically, three rows are set on the same plane, with three measurement points at the top and bottom and four measurement points in the middle. Following a top-down, left-to-right order, each group of ten topological loads (excluding 0) is designated as a single category. These ten topological loads are ultimately displayed at the same measurement point. The first measurement point represents topological load l from -50 to -41, the second from -40 to -31, and so on, with the last measurement point representing topological load l from 41 to 50. The coarse classification data processed in step 2.2 is input into the diffraction deep neural network model from step 2.1 for training. The batch size is set to 128, and the learning rate to 0.003. The mean square error loss function MSELoss is used to calculate the error between the network's output value and the target value (received light intensity and ideal light intensity). The network model parameters are continuously optimized through iteration. After 20-30 iterations, the trained coarse classification weight model is saved. The network model using the coarse classification data as the training dataset is called the coarse classification model.

[0112] Step 2.3: Before starting training, load the training and test sets (with topological charges l ranging from -50 to -41 obtained after atmospheric turbulence disturbance) established in Step 1.4 as required. Set the size of the dataset to 250×250 and convert it to tensor format, saving the training and test data and labels in .npy format. This processed data is called the fine-classification data D1. Set the measurable points K = 10 in Step 2.1, meaning 10 categories can be detected at once. Specifically, set three rows on the same plane: three measurement points at the top and bottom, and four in the middle. Each measurement point represents a topological charge, arranged from top to bottom and left to right. The first measurement point represents a topological charge l of -50, the second represents a topological charge l of -49, and so on. Input the processed fine-classification data D1 into the diffraction deep neural network model in Step 2.1 for training, setting the batch size to 128 and the learning rate to [missing value]. With a rate of 0.003, the mean square error loss function MSELoss is used to calculate the error between the network's output value and the target value (received light intensity and ideal light intensity). The network model parameters are continuously optimized through iteration. After 90 to 100 iterations, the trained fine classification weight model is saved. The network model that uses the fine classification data D1 as the training dataset is called the fine classification model F1.

[0113] For the training and test sets established in step 1.4, which are obtained after atmospheric turbulence disturbance and have topological loads l of -40~-31, -30~-21, -20~-11, -10~-1, 1~10, 11~20, 21~30, 31~40, and 41~50 respectively, both sets are set to a size of 250×250 and converted to tensor format. The training and test data and labels are saved in .npy format. The processed data are referred to as the fine classification data D2–D10. The output plane of each fine classification data sets sets the measurable point K in step 2.1 to 10, that is, 10 categories can be detected at one time. Specifically, three rows are set on the same plane, with three measurement points at the top and bottom and four measurement points in the middle. Each measurement point represents a topological load in the order from top to bottom and from left to right. The processed fine-classification data D2–D10 are sequentially input into the diffraction deep neural network model in step 2.1 for training. The batch size is set to 128, and the learning rate to 0.003. The mean squared error loss function (MSELoss) is used to calculate the error between the network's output value and the target value (received light intensity and ideal light intensity). The network model parameters are iteratively optimized. For fine-classification data D5 and D6, the iterations are performed 40–50 times; for fine-classification data D1–D4 and D7–D10, the iterations are performed 90–100 times. The trained fine-classification weight models are then saved. The network model using fine-classification data D2 as the training dataset is called fine-classification model F2; the network model using fine-classification data D3 as the training dataset is called fine-classification model F3; different fine-classification data correspond to different fine-classification models, and so on. The network model using fine-classification data D10 as the training dataset is called fine-classification model F10.

[0114] Step 3: Design and build a diffraction deep neural network to recognize high-order continuous OAM patterns, and test the effect using a test set;

[0115] Step 3 shall be carried out in accordance with the following specific steps:

[0116] Step 3.1: Design and build a diffraction deep neural network for recognizing high-order continuous OAM patterns. The theoretical construction of the diffraction deep neural network for recognizing high-order continuous OAM patterns established in this invention is as follows: Figure 10 As shown. The network consists of two modules: a coarse classifier and a fine classifier;

[0117] The specific process of the diffraction deep neural network for high-order continuous OAM modes is as follows: Input the complex amplitude matrix of the LG beam field obtained after atmospheric turbulence perturbation in step 3.2 — pass through a coarse classifier — determine which fine classifier to use next based on the classification result of the coarse classifier — select the corresponding fine classifier — input the complex amplitude matrix of the LG beam field obtained after atmospheric turbulence perturbation in step 3.2 again — pass through the fine classifier selected above — finally determine the specific OAM mode based on the classification result of the fine classifier;

[0118] The coarse classifier includes an L-layer diffraction layer of the coarse classification model and 10 light intensity detectors on the output plane. Its specific function is to place 10 light intensity detectors on the output plane to detect the light intensity. The light beam is phase-modulated by the L-layer diffraction layer of the coarse classification model. Finally, the beam is determined to be of which mode range based on which light intensity detector on the output plane has the strongest light intensity.

[0119] The fine classifier contains 10 fine classification models F1 to F10. Each fine classification model contains an L-layer diffraction layer and 10 light intensity detectors on the output plane. The specific function is as follows: 10 light intensity detectors are placed on the output plane to detect the light intensity. The light beam is phase-modulated by the L-layer diffraction layer of the fine classification model. Finally, the specific mode of the light beam is determined based on which light intensity detector on the output plane has the strongest light intensity.

[0120] Step 3.2: Load the test set divided in step 1.4, set the size of the test set of all the light field complex amplitude matrices after atmospheric turbulence disturbance to 250×250, and convert it to tensor format;

[0121] Step 3.3: Load the coarse classification weight model from step 2.2 and the 10 fine classification weight models from step 2.3. Input the test data from step 3.2 into the network model designed in step 3.1 to identify the OAM pattern, and use the average test accuracy as the evaluation index. The higher the average test accuracy, the better the recognition effect of the network.

[0122] Example 1

[0123] Step 1: Unless otherwise specified, set the MATLAB simulation parameters as follows: wavelength λ = 632 nm, beam waist radius w0 = 0.01, transmission distance Δz = 1000 m, phase screen size 0.4, outer scale L0 = 1, inner scale l0 = 0.01, radial exponent p = 2, atmospheric refractive index structure constant. (Medium turbulence), topological load l from -50 to +50 (excluding 0), construct a dataset and divide it into training and test sets in an 8:2 ratio.

[0124] Step 2, unless otherwise specified, sets D. 2 The simulation parameters of the NN network are as follows: the spacing between diffraction layers is 100nm, the input light field will pass through 5 diffraction layers, each diffraction layer has 250×250 nodes, which is equivalent to 250×250 neurons; the input dataset of the network is set as follows: the entire training dataset with topological charge l of -50 to +50 (excluding 0) is used as the input dataset of the coarse classification model (every 10 kinds of topological charge are set as one class), and the training datasets with topological charge l of -50 to -41, -40 to -31, -30 to -21, -20 to -11, -10 to -1, 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 41 to 50 are used as the input datasets of 10 fine classification models - F1 to F10 respectively. The training set is input into the constructed basic diffraction deep neural network for training. The batch size is set to batch_size = 128. The input data is passed through the network forward propagation to obtain the output data. The mean squared error loss function MSELoss is used to calculate the error between the network's output value and the target value. Optimization is performed with the goal of maximizing the intensity of one of the 10 measurement points in the last layer. The weights are updated through backpropagation. After iterating according to steps 2.2 and 2.3 for the corresponding number of times, the trained coarse and fine classification weight models are saved. The training accuracy is as follows: Figure 11 As shown. From Figure 11 It can be seen that the training accuracy function value generally increases monotonically, and gradually stabilizes after a certain number of iterations, indicating that after a certain number of training iterations, D... 2 The NN model can effectively identify OAM patterns. Furthermore, it can be observed that although the initial training accuracy gradually decreases with increasing topological load (absolute value) (this indicates that the larger the topological load, the greater the influence of turbulence on the recognition probability, and the greater the crosstalk between OAM patterns), the accuracy can still remain above 96.5% after a certain number of training rounds. This demonstrates that D... 2 NN models can effectively identify high-order continuous OAM patterns.

[0125] Step 3: Load the test set (188 types) with topological load l = -46 set in Step 3.2, and input it into the network model built in Step 3.1. Use the built model to identify higher-order OAM patterns, and output the average test accuracy of the network model. The output results of the network model in identifying higher-order OAM patterns are as follows: Figures 12-13 As shown in the diagram (the settings for each measurement point are as described in step 2 above). The average test accuracy is: test_accuracy = 94.1%, which shows that the diffraction deep neural network performs well in recognizing high-order OAM patterns.

[0126] Example 2

[0127] Step 1: Unless otherwise specified, set the MATLAB simulation parameters as follows: wavelength λ = 632 nm, beam waist radius w0 = 0.01, transmission distance Δz = 1000 m, phase screen size 0.4, outer scale L0 = 1, inner scale l0 = 0.01, radial exponent p = 2, atmospheric refractive index structure constant. (Medium turbulence), topological load l from -50 to +50 (excluding 0), construct a dataset and divide it into training and test sets in an 8:2 ratio.

[0128] Step 2, unless otherwise specified, sets D. 2 The simulation parameters of the NN network are as follows: the spacing between diffraction layers is 100nm, the input light field will pass through 5 diffraction layers, each diffraction layer has 250×250 nodes, which is equivalent to 250×250 neurons; the input dataset of the network is set as follows: the entire training dataset with topological charge l of -50 to +50 (excluding 0) is used as the dataset of the coarse classification model (every 10 kinds of topological charge are set as one class), and the training datasets with topological charge l of -50 to -41, -40 to -31, -30 to -21, -20 to -11, -10 to -1, 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 41 to 50 are used as the input datasets of 10 fine classification models - F1 to F10 respectively. The training set is input into the constructed basic diffraction deep neural network for training. The batch size is set to batch_size = 128. The input data is passed through the network forward propagation to obtain the output data. The mean square error loss function MSELoss is used to calculate the error between the network output value and the target value. The optimization is performed with the goal of maximizing the intensity of one of the 10 detection points in the last layer. The weights are updated through backpropagation. After iterating for the corresponding number of times according to steps 2.2 and 2.3, the trained coarse and fine classification weight models are saved.

[0129] Step 3: Load the test set (188 types) with topological load l = -46 set in Step 3.2, and input it into the network model built in Step 3.1. Use the built model to identify higher-order OAM patterns, and output the average test accuracy of the network model. The output results of the network model in identifying higher-order OAM patterns are as follows: Figures 14-15 As shown (the settings for each measurement point are as described in step 2 above). The average test accuracy is: test_accuracy = 100%, which shows that the diffraction deep neural network performs well in recognizing higher-order OAM patterns. Comparing the test accuracy result of Example 1 with topological charge l = -46 (test_accuracy = 94.1%), it can be seen that as the absolute value of OAM decreases, the accuracy of the network in recognizing the order of OAM also increases.

[0130] Example 3

[0131] The method for identifying high-order continuous OAM patterns based on diffraction deep neural networks includes the following steps:

[0132] Step 1: Obtain the complex amplitude matrix of the optical field after atmospheric turbulence disturbance through numerical simulation, and establish a dataset;

[0133] Step 2: Design and build a basic diffraction deep neural network structure. Perform data preprocessing on the training data obtained in Step 1 and feed it into the basic diffraction deep neural network designed in this step for model training.

[0134] Step 3: Design and build a diffraction deep neural network to recognize high-order continuous OAM patterns, and test the effect using a test set.

[0135] Example 4

[0136] The method for identifying high-order continuous OAM patterns based on diffraction deep neural networks includes the following steps:

[0137] Step 1: Obtain the complex amplitude matrix of the optical field after atmospheric turbulence disturbance through numerical simulation, and establish a dataset;

[0138] Step 1 shall be carried out according to the following specific steps:

[0139] Step 1.1: Based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of atmospheric turbulence;

[0140] Step 1.2, in cylindrical coordinates, determine the light field expression of the Laguerre-Gaussian beam, specifically:

[0141]

[0142] In the formula, r, φ, z are cylindrical coordinates, and z R =πw0 / λ is the Rayleigh distance (w0 is the waist radius of the Laguerre-Gaussian beam), λ is the wavelength, and w(z) is the beam radius of the Laguerre-Gaussian beam at z; For the associated Laguerre polynomial, k is the space wave number, p is the radial exponent, l is the topological charge, and i is the imaginary number;

[0143] Step 1.3, according to Fresnel's principle, after a beam with electric field U(x,y,z) propagates a distance Δz in atmospheric turbulence, the electric field function U(z+Δz,x,y) is expressed as:

[0144]

[0145] In the formula, x, y, z represent the rectangular coordinate system, and IFFT represents the inverse Fourier transform. Let i be the Fresnel transmission coefficient, i be the imaginary number, and k be the space wavenumber. x and k y Represents spatial frequencies in the x and y directions. For atmospheric turbulence random phase screen;

[0146] Step 1.4: Substitute the light field expression of the Laguerre-Gaussian beam in Step 1.2 as U(x,y,z) in Step 1.3 into Formula (4) to obtain the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance; by changing the magnitude of the topological charge l in the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance, generate a complex amplitude matrix of the light field with a topological charge l of -50 to +50 and not including 0 after atmospheric turbulence disturbance to construct a dataset.

[0147] Step 2: Design and build a basic diffraction deep neural network structure. Perform data preprocessing on the training data obtained in Step 1 and feed it into the basic diffraction deep neural network designed in this step for model training.

[0148] Step 3: Design and build a diffraction deep neural network to recognize high-order continuous OAM patterns, and test the effect using a test set.

[0149] Example 5

[0150] The method for identifying high-order continuous OAM patterns based on diffraction deep neural networks includes the following steps:

[0151] Step 1: Obtain the complex amplitude matrix of the optical field after atmospheric turbulence disturbance through numerical simulation, and establish a dataset;

[0152] Step 1 shall be carried out according to the following specific steps:

[0153] Step 1.1: Based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of atmospheric turbulence;

[0154] Step 1.1 shall be implemented according to the following specific steps:

[0155] Step 1.1.1: Select the modified Hill atmospheric refractive index power spectral density function Φ n (k), whose expression is:

[0156]

[0157] In the formula, k is the space wavenumber, k = 2π / λ, λ is the wavelength, and the range of k is 0 ≤ k ≤ ∞; The atmospheric refractive index structure constant. The value is 1×10 -16 m -2 / 3 1×10 -15m -2 / 3 1×10 -14 m -2 / 3 The time corresponds to weak, moderate, and strong atmospheric turbulence, respectively; the other parameters in equation (1) are: k l =3.3 / l0, where l0 is the internal scale turbulence; k0 = 1 / L0 or 2π / L0, where L0 is the external scale turbulence; a1 = 1.802, a2 ​​= 0.254;

[0158] Step 1.1.2, obtaining the atmospheric turbulence random phase screen based on the power spectrum inversion method, specifically:

[0159] First, generate a complex Gaussian random matrix C. N×N Then, the modified Hill atmospheric refractive index power spectral density function Φ was used. n (k) Filter the filter and finally obtain the atmospheric turbulence random phase screen through inverse Fourier transform. This process can be expressed by the following formula:

[0160]

[0161] In the formula, x, y are position coordinates, IFFT is the inverse Fourier transform, N and Δx represent the number of sampling points and the sampling interval of the phase screen, respectively, and C N×N It is a complex Gaussian random matrix with a mean of 0 and a variance of 1, where k is the spatial wavenumber, Δd is the phase screen spacing, and Φ is the distance between the phase screens. n (k) is the modified Hill atmospheric refractive index power spectral density function.

[0162] Step 1.2, in cylindrical coordinates, determine the light field expression of the Laguerre-Gaussian beam, specifically:

[0163]

[0164] In the formula, r, φ, z are cylindrical coordinates, and z R =πw0 / λ is the Rayleigh distance (w0 is the waist radius of the Laguerre-Gaussian beam), λ is the wavelength, and w(z) is the beam radius of the Laguerre-Gaussian beam at z; For the associated Laguerre polynomial, k is the space wave number, p is the radial exponent, l is the topological charge, and i is the imaginary number;

[0165] Step 1.3, according to Fresnel's principle, after a beam with electric field U(x,y,z) propagates a distance Δz in atmospheric turbulence, the electric field function U(z+Δz,x,y) is expressed as:

[0166]

[0167] In the formula, x, y, z represent the rectangular coordinate system, and IFFT represents the inverse Fourier transform. Let i be the Fresnel transmission coefficient, i be the imaginary number, and k be the space wavenumber. x and k y Represents spatial frequencies in the x and y directions. For atmospheric turbulence random phase screen;

[0168] Step 1.4: Substitute the light field expression of the Laguerre-Gaussian beam in Step 1.2 as U(x,y,z) in Step 1.3 into Formula (4) to obtain the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance; by changing the magnitude of the topological charge l in the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance, generate a complex amplitude matrix of the light field with a topological charge l of -50 to +50 and not including 0 after atmospheric turbulence disturbance to construct a dataset.

[0169] Step 2: Design and build a basic diffraction deep neural network structure. Perform data preprocessing on the training data obtained in Step 1 and feed it into the basic diffraction deep neural network designed in this step for model training.

[0170] Step 3: Design and build a diffraction deep neural network to recognize high-order continuous OAM patterns, and test the effect using a test set.

[0171] Example 6

[0172] The method for identifying high-order continuous OAM patterns based on diffraction deep neural networks is characterized by the following steps:

[0173] Step 1: Obtain the complex amplitude matrix of the optical field after atmospheric turbulence disturbance through numerical simulation, and establish a dataset;

[0174] Step 1 shall be carried out according to the following specific steps:

[0175] Step 1.1: Based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of atmospheric turbulence;

[0176] Step 1.1 shall be implemented according to the following specific steps:

[0177] Step 1.1.1: Select the modified Hill atmospheric refractive index power spectral density function Φ n (k), whose expression is:

[0178]

[0179] In the formula, k is the space wavenumber, k = 2π / λ, λ is the wavelength, and the range of k is 0 ≤ k ≤ ∞; The atmospheric refractive index structure constant. The value is 1×10 -16 m -2 / 3 1×10-15 m -2 / 3 1×10 -14 m -2 / 3 The time corresponds to weak, moderate, and strong atmospheric turbulence, respectively; the other parameters in equation (1) are: k l =3.3 / l0, where l0 is the internal scale turbulence; k0 = 1 / L0 or 2π / L0, where L0 is the external scale turbulence; a1 = 1.802, a2 ​​= 0.254;

[0180] Step 1.1.2, obtaining the atmospheric turbulence random phase screen based on the power spectrum inversion method, specifically:

[0181] First, generate a complex Gaussian random matrix C. N×N Then, the modified Hill atmospheric refractive index power spectral density function Φ was used. n (k) Filter the filter and finally obtain the atmospheric turbulence random phase screen through inverse Fourier transform. This process can be expressed by the following formula:

[0182]

[0183] In the formula, x, y are position coordinates, IFFT is the inverse Fourier transform, N and Δx represent the number of sampling points and the sampling interval of the phase screen, respectively, and C N×N It is a complex Gaussian random matrix with a mean of 0 and a variance of 1, where k is the spatial wavenumber, Δd is the phase screen spacing, and Φ is the distance between the phase screens. n (k) is the modified Hill atmospheric refractive index power spectral density function.

[0184] Step 1.2, in cylindrical coordinates, determine the light field expression of the Laguerre-Gaussian beam, specifically:

[0185]

[0186] In the formula, r, φ, z are cylindrical coordinates, and z R =πw0 / λ is the Rayleigh distance (w0 is the waist radius of the Laguerre-Gaussian beam), λ is the wavelength, and w(z) is the beam radius of the Laguerre-Gaussian beam at z; For the associated Laguerre polynomial, k is the space wave number, p is the radial exponent, l is the topological charge, and i is the imaginary number;

[0187] Step 1.3, according to Fresnel's principle, after a beam with electric field U(x,y,z) propagates a distance Δz in atmospheric turbulence, the electric field function U(z+Δz,x,y) is expressed as:

[0188]

[0189] In the formula, x, y, z represent the rectangular coordinate system, and IFFT represents the inverse Fourier transform. Let i be the Fresnel transmission coefficient, i be the imaginary number, and k be the space wavenumber. x and k y Represents spatial frequencies in the x and y directions. For atmospheric turbulence random phase screen;

[0190] Step 1.4: Substitute the light field expression of the Laguerre-Gaussian beam in Step 1.2 as U(x,y,z) in Step 1.3 into Formula (4) to obtain the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance; by changing the magnitude of the topological charge l in the specific light field expression of the Laguerre-Gaussian beam after atmospheric turbulence disturbance, generate a complex amplitude matrix of the light field with a topological charge l of -50 to +50 and not including 0 after atmospheric turbulence disturbance to construct a dataset.

[0191] In step 1.4, the constructed dataset is divided into a training set and a test set in an 8:2 ratio, and both the test set and the training set are saved in .mat format.

[0192] Step 2: Design and build a basic diffraction deep neural network structure. Perform data preprocessing on the training data obtained in Step 1 and feed it into the basic diffraction deep neural network designed in this step for model training.

[0193] Step 3: Design and build a diffraction deep neural network to recognize high-order continuous OAM patterns, and test the effect using a test set.

Claims

1. A method for identifying high-order continuous OAM modes based on a diffractive deep neural network, characterized in that, Comprise the following steps: Step 1, obtain the light field complex amplitude matrix after atmospheric turbulence disturbance by numerical simulation, and establish a data set; Step 2, design and build a basic diffractive deep neural network structure, preprocess the training data obtained in step 1, and send it to the basic diffractive deep neural network designed in this step for model training; Step 2 includes the following steps: Step 2.1, design and build a diffractive deep neural network, which includes L layers of diffractive layers, each layer of diffractive layers contains w x w nodes, and each node in each diffractive layer is connected to the next layer; Wherein, according to the Rayleigh-Sommerfeld diffraction theory, each node in each layer of the diffractive deep neural network is regarded as a quadratic light source, and the point light source satisfies the following formula: where x, y, z are the rectangular coordinate system, L is the number of network layers, λ is the wavelength, i is the imaginary number, s represents the s-th node in the w x w nodes of the layer, and the coordinates of the s-th node are set as (x s ,y s ,z s ), r s is the distance from the light source to the s-th node, and the output of the s-th node in the L layer is represented as . The output of the s-th node in the L layer is jointly determined by the node input light and the transmission coefficient , and the expression is as follows: wherein, is the superposition of the light field of the previous layer, i.e. layer L-1, arriving at the s-th node of layer L, v is the v-th node of the w x w nodes of layer L-1, |A| is the relative amplitude of the transmission coefficient modulation of the secondary wave, Δθ is the phase delay added by the transmission coefficient, and T is the transmission coefficient contains both amplitude and phase parts and is expressed as: where, is the amplitude term, is the phase term, and the designed D 2 The NN network structure is a pure phase type network, in order to simplify the above forward propagation model symbol, Eq. (6) is rewritten as: where q represents the qth node of the next layer, for the Lth layer input, Rayleigh-Sommerfeld diffraction theory satisfied by the Lth layer point light source, is the light field superposition of the incident light reaching the sth node of the Lth layer, and the network input layer complex amplitude is represented as After diffraction transmission, the first layer input is obtained After M layers of transmission, the received light field intensity on the M+1 layer detection plane is represented as: D 2 The NN loss function is set as the mean square error between the received light intensity and the ideal light intensity: where K is the number of measurement points on the output plane, is the ideal light intensity distribution; the network is trained by back propagation through the loss and gradient descent algorithm, and the purpose of training is to fix the transmission coefficients of each point of the diffraction layer, which is represented as: Step 3, design and build a diffractive deep neural network for identifying high-order continuous OAM modes, and test the effect using the test set.

2. The method of identifying high-order continuous OAM modes based on a diffractive deep neural network according to claim 1, wherein, Step 1 is implemented according to the following specific steps: Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of atmospheric turbulence random phase screen; Step 1.2, in the cylindrical coordinate system, determine the light field expression of Laguerre-Gaussian beam, specifically: where r, φ, z are cylindrical coordinates, z R = πw0 / λ is the Rayleigh range, λ is the wavelength, and w(z) is the beam radius of the Laguerre-Gaussian beam at z; are the associated Laguerre polynomials, k is the spatial wave number, p is the radial index, l is the topological charge, and i is the imaginary unit. Step 1.3, according to the Fresnel principle, the light beam with electric field U(x,y,z) propagates in atmospheric turbulence for a distance Δz, and the electric field function U(z+Δz,x,y) is expressed as: where x, y, z are the rectangular coordinates, IFFT is the inverse Fourier transform, is the Fresnel transmission coefficient, i is the imaginary unit, k is the spatial wave number, k x and k y represent the spatial frequencies in the x and y directions, is the atmospheric turbulence random phase screen; Step 1.4, the light field expression of the Laguerre-Gaussian beam in step 1.2 is substituted into formula (4) as U(x,y,z) in 1.3, and the specific Laguerre-Gaussian beam light field expression after atmospheric turbulence disturbance is obtained; By changing the size of the topological charge l in the specific Laguerre-Gaussian beam light field expression after atmospheric turbulence disturbance, the light field complex amplitude matrix with topological charge l from-50 to +50 and excluding 0 is generated to form a data set.

3. The method of claim 2, wherein, Step 1.1 is implemented according to the following specific steps: Step 1.1.1, selection of the modified Hill atmospheric refractive index power spectral density function Φ n (k), which is expressed as: In the formula, k is a spatial wave number, k = 2π / λ, λ is a wavelength, and k has a value range of 0≤k≤∞; is an atmospheric refractive index structure constant, has a value of 1×10 -16 m -2 / 3 , 1×10 -15 m -2 / 3 , 1×10 -14 m -2 / 3 , respectively, correspond to weak, medium, and strong atmospheric turbulence; in formula (1), other parameters are as follows: k l =3.3 / l0, l0 is an inner scale turbulence; k0=1 / L0 or 2π / L0, L0 is an outer scale turbulence; a1=1.802, a2=0.254; Step 1.1.2, obtain the atmospheric turbulence random phase screen based on the power spectrum inversion method, specifically: First, a complex Gaussian random matrix C is generated N×N Then, the modified Hill atmospheric refractive index power spectral density function Φ n (k) is filtered, and finally the atmospheric turbulence random phase screen is obtained by inverse Fourier transform This process can be expressed as: where x, y are position coordinates, IFFT is the inverse Fourier transform, N and Δx represent the number of sampling points and sampling interval of the phase screen, respectively, C N×N is a complex Gaussian random matrix with mean 0 and variance 1, k is the spatial wave number, Δd is the phase screen interval, Φ n (k) is the modified Hill atmospheric refractive index power spectral density function.

4. The method of claim 2, wherein, In step 1.4, the data set constructed is divided into training set and test set according to the ratio of 8:2, and the test set and the training set are saved in.mat format.

5. The method of claim 2, wherein, Step 2 further includes the following steps: Step 2.2, before starting training, load the training set and test set established in step 1.4 as required, set all the training and test.mat data sets obtained after atmospheric turbulence disturbance with topological charge I from -50 to +50 and excluding 0 as one large class every 10 topological charges I, that is, topological charge I from -50 to -41 as one class, -40 to -31 as one class, -30 to -21 as one class, -20 to -11 as one class, -10 to -1 as one class, 1 to 10 as one class, 11 to 20 as one class, 21 to 30 as one class, 31 to 40 as one class, 41 to 50 as one class, a total of 10 classes; set the size of the above set classification light field complex amplitude matrix data set after atmospheric turbulence disturbance to 250x250, and convert it to tensor format, save the training and test data and labels in.npy format, and call the above processed data as coarse classification data; Set the measurable point K in step 2.1 to 10, that is, detect 10 categories at a time, and specifically set it as follows: a total of three rows are set in the same plane, three measuring points above and below, and four measuring points in the middle; according to the order from top to bottom and from left to right, each ten topological charges I excluding 0 is defined as one large class, that is, the ten topological charges I is one category, which is finally displayed on the same measuring point, the first measuring point represents topological charge I from -50 to -41, the second measuring point represents topological charge I from -40 to -31, each measuring point represents ten topological charges I, and so on, and the last measuring point represents topological charge I from 41 to 50; input the coarse classification data processed in step 2.2 into the diffraction deep neural network model in step 2.1 for training, set the batch size batch_size = 128, the learning rate learning rate = 0.003, use the mean square error loss function MSELoss to calculate the error between the output value and the target value of the network, optimize the network model parameters through continuous iteration, save the trained coarse classification weight model after 20-30 iterations, and call the network model using coarse classification data as the training data set as the coarse classification model; Step 2.3, before starting training, load the training set and test set of topological charge l from -50 to -41 obtained after atmospheric turbulence disturbance established in step 1.4 as required, set the size of the above data set to 250x250, and convert it to tensor format, save the training and test data and labels in.npy format, and call the above processed data fine classification data D1; set the measurable points K=10 in step 2.1, that is, detect 10 categories at a time, and specifically set: a total of three rows in the same plane, three measuring points above and below, and four measuring points in the middle; according to the order from top to bottom and from left to right, each measuring point represents a topological charge l, the first measuring point represents topological charge l=-50, the second measuring point represents topological charge l=-49, and so on; input the above processed fine classification data D1 into the diffraction deep neural network model in step 2.1 for training, set the batch size batch_size=128, the learning rate learning rate=0.003, use the mean square error loss function MSELoss to calculate the error between the output value and the target value of the network, and optimize the network model parameters through continuous iteration, save the fine classification weight model after 90-100 iterations of training, and call the network model using fine classification data D1 as the training data set as fine classification model F1; For the training set and test set of topological charge l established in step 1.4 after atmospheric turbulence disturbance, the size is set to 250x250, and the training and test data and labels are saved in.npy format after conversion to tensor format. The above processed data are referred to as fine classification data D2-D10; the output plane of each fine classification data is set to 10 in step 2.1, that is, 10 categories are detected at a time, and the specific setting is as follows: a total of three rows are set in the same plane, three measurement points above and below, and four measurement points in the middle; each measurement point represents a topological charge l in the order from top to bottom and from left to right; the above processed fine classification data D2-D10 are input into the diffraction deep neural network model in step 2.1 for training, the batch size is set to 128, the learning rate is set to 0.003, the mean square error loss function MSELoss is used to calculate the error between the output value and the target value of the network, and the network model parameters are optimized by continuous iteration. For fine classification data D5 and D6, iteration is performed for 40-50 times, and for fine classification data D1-D4 and D7-D10, iteration is performed for 90-100 times, and the trained fine classification weight model is saved; the network model using fine classification data D2 as the training data set is referred to as fine classification model F2, and the network model using fine classification data D3 as the training data set is referred to as fine classification model F3. Different fine classification data correspond to different fine classification models, and so on. The network model using fine classification data D10 as the training data set is referred to as fine classification model F10.

6. The method of claim 2, wherein, Step 3 is implemented according to the following specific steps: Step 3.1, design and build a diffraction deep neural network for recognizing high-order continuous OAM modes, which includes two modules: a coarse classifier and a fine classifier; Step 3.2, load the test set divided in step 1.4, set the size of the generated test set of all atmospheric turbulence disturbed light field complex amplitude matrices to 250x250, and convert it to tensor format; Step 3.3, load the coarse classification weight model of step 2.2 and the 10 fine classification weight models of step 2.3, input the test data in step 3.2 into the network model designed in step 3.1 to recognize OAM modes, and use the average test accuracy as an evaluation index. The higher the average test accuracy, the better the recognition effect of the network.

7. The method of claim 6, wherein, In step 3.1, the specific process of the diffraction deep neural network of high-order continuous OAM modes is as follows: input the LG beam optical field complex amplitude matrix obtained after atmospheric turbulence disturbance in step 3.2, pass through the coarse classifier, determine which fine classifier to use next according to the classification result of the coarse classifier, select the corresponding fine classifier, input the LG beam optical field complex amplitude matrix obtained after atmospheric turbulence disturbance in step 3.2 again, pass through the selected fine classifier, and finally determine the specific mode of the OAM according to the classification result of the fine classifier.

8. The method of identifying high-order continuous OAM modes based on a diffractive deep neural network according to claim 7, wherein, In step 3.1, the coarse classifier includes L layers of diffraction layers of the coarse classification model and 10 light intensity detectors on the output plane, and the specific function is as follows: 10 light intensity detectors are placed on the output plane to detect light intensity, the light beam is phase-modulated by the L layers of diffraction layers of the coarse classification model, and finally it is determined which mode range the light beam belongs to according to which light intensity detector on the output plane has the strongest light intensity. The fine classifier includes 10 fine classification models F1-F10, each of which includes L layers of diffraction layers and 10 light intensity detectors on the output plane, and the specific function is as follows: 10 light intensity detectors are placed on the output plane to detect light intensity, the light beam is phase-modulated by the L layers of diffraction layers of the fine classification model, and finally it is determined which specific mode the light beam belongs to according to which light intensity detector on the output plane has the strongest light intensity.

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