OAM mode multiplication and division operation method and system based on optical diffraction neural network

Abstract

The invention discloses an OAM mode multiplication and division operation method and system based on an optical diffraction neural network, and relates to the field of orbital angular momentum. Digital signals are represented through OAM mode coding, any 2n times of digital multiplication / division operation can be achieved, the operation function has the advantages of being high in expandability, flexible, controllable and the like, and the method and system can be applied to the field of orbital angular momentum. A basic framework is expected to be established for complex arithmetic operation in a high-dimensional optical space, and a potential solution is provided for practical application of optical digital calculation; the OAM mode serves as an operation physical dimension, mode parallel independent transformation is completed through the optical diffraction neural network to achieve OAM mode numerical value shifting, and therefore digital multiplication / division operation is completed, and the obtained output array has high mode purity.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of orbital angular momentum, and particularly relates to an OAM mode multiplication and division operation method and system based on an optical diffraction neural network. BACKGROUND

[0002] Optical digital computing takes photons as information carriers and can realize a series of general-purpose computing by combining digital logic operation and numerical operation, and has advantages such as super-high speed, low power consumption and natural parallelism, and is expected to provide strong computing power support for new-generation computing and communication technologies and other fields. Among them, optical digital multiplication / division operation, which discretizes the digital control of a specific physical dimension through optical modulation of signal coding, is one of the key technologies of optical digital computing. However, the current research on optical digital computing mainly focuses on basic logic units, and the multiplication / division operation module is relatively less studied, mainly due to the lack of efficient digital signal representation of physical dimensions and numerical shift technology. Traditional optical digital multiplication / division operation represents digital signals with light field intensity and mainly relies on polarization modulation technology for operation and control. Through the design of a polarization switch, the regionally selective amplitude of the input digital coded optical signal is controlled, and binary multiplication operation can be realized. However, the inherent energy attenuation and error accumulation in the operation process can easily lead to confusion of the operation rules, resulting in reduced operation performance. In addition, the regional reflection of the polarizing plate can destroy the light field structure, and there are problems such as poor scalability and resource waste. The orbital angular momentum (OAM) mode carried by a vortex beam has infinite orthogonality in theory, can form an infinite-dimensional Hilbert space, and has obvious mode distinguishability and sufficient degrees of freedom, so it can be used as a physical dimension to represent digital signals. Representing digital signals with OAM modes for digital multiplication / division operation not only can utilize the strong contrast between modes to improve operation accuracy and robustness, but also can solve the problems of poor scalability and high energy consumption in traditional methods that use intensity as the operation dimension. However, how to independently transform multiple input OAM modes in parallel to realize numerical shift operation is the key to realizing OAM mode digital multiplication / division operation, and is also an important problem to be solved for promoting the further development of optical computing. SUMMARY

[0003] In view of the problems in the related art, the application provides an OAM mode multiplication and division operation method and system based on an optical diffraction neural network to overcome the above technical problems existing in the prior art.

[0004] To solve the above technical problems, the application is implemented by the following technical scheme: The application is an OAM mode multiplication and division operation method based on an optical diffraction neural network, comprising the following steps: S1, passing the Gaussian light signal through a first optical coupler to obtain three beams of energy-balanced sub-Gaussian light beams; then passing the three beams of energy-balanced sub-Gaussian light beams through a second optical coupler, a third optical coupler and a fourth optical coupler respectively, and then through a first spiral phase plate, a second spiral phase plate and a third spiral phase plate to obtain three beams of OAM light beams; S2, two of the three beams of OAM light beams pass through a first plane mirror and a first non-polarization beam splitter to form a spatial domain distributed composite OAM light beam; and the other one of the three beams of OAM light beams passes through a second plane mirror and a second non-polarization beam splitter to form a light beam array containing three beams of OAM light beams; S3, combining an optical diffraction neural network to perform mode-parallel independent transformation on the light beam array containing three beams of OAM light beams to output an OAM mode array after numerical shift, and detecting and analyzing by a photoelectric detector and an electronic computer.

[0005] Preferably, the S1 comprises the following steps: S11, a Gaussian light signal emitted by a light source passes through a 1x3 first optical coupler with a splitting ratio of 1:1:1 to generate three beams of energy-balanced sub-Gaussian light beams; S12, the sub-Gaussian light beams in S11 pass through a second optical coupler, a third optical coupler and a fourth optical coupler, and then are converted into three beams of OAM light beams by a first spiral phase plate, a second spiral phase plate and a third spiral phase plate.

[0006] Preferably, the S2 comprises the following steps: S21, one of the three beams of OAM light beams in S12 passes through a first plane mirror to form a spatial domain distributed composite OAM light beam with another beam of OAM light beam by a first non-polarization beam splitter; S22, a third beam of OAM light beams in S12 passes through a second plane mirror, passes through a second non-polarization beam splitter and forms a light beam array containing three beams of OAM light beams with the spatial domain distributed composite OAM light beam in S21.

[0007] Preferably, the S3 comprises the following steps: S31, the light beam array containing three beams of OAM light beams passes through a mode-parallel independent transformation-equivalent numerical shift device obtained by iterative optimization of an optical diffraction neural network to perform mode-parallel independent transformation, and then outputs an OAM mode array after numerical shift, to complete OAM mode multiplication / division operation and obtain an output OAM mode array; The mode-parallel independent transformation-equivalent numerical shift device comprises a first phase diffraction screen, a second phase diffraction screen and a third phase diffraction screen. S32, the output OAM mode array is detected and analyzed by a photodetector and an electronic computer.

[0008] Preferably, the light beam array containing three OAM beams in S31 is iteratively optimized by an optical diffraction neural network, including the following steps: S311, the input light field represented by OAM mode order and spatial position is converted into an output light field after sequentially passing through an optical diffraction neural network with a multi-layer phase structure; wherein the error is back-propagated and the phase matrix is updated to minimize the loss function by using the stochastic gradient descent algorithm and selecting Adam as the optimizer through supervised data labels; S312, the simulation parameters matching the experimental conditions are set, the OAM mode array is generated as the complex amplitude light field input of the model according to the digital signal coding, and the complex amplitude light field is output after passing through the alternating modulation of three-layer phase screens and free-space diffraction propagation; the initial phase screen is a random Gaussian distribution, the phase value is set as the optimization object, the loss function is designed to evaluate the error according to the target light field and the predicted output light field, and the Adam optimizer is selected to back-propagate the error and update the optimized three-layer phase at the same time, and finally the optimal phase distribution is obtained; Preferably, the loss function in S312 is calculated by the predicted output complex amplitude light field and the target complex amplitude light field, as follows,

[0009]

[0010] wherein is the loss field, is the predicted output complex amplitude light field, Loss is the loss function, is the target complex amplitude light field, N × M is the detection area size of the output light field, =1 is a constant factor; Relu and Tanh are activation functions.

[0011] Preferably, for the light beam array containing three OAM beams in S31, two circular rings of different sizes are used to represent two different OAM modes, and the logical states "0" and "1" are encoded as different OAM modes; and the three dashed circles located in different spatial positions represent the bits of the value, from left to right, from high bit to low bit. Preferably, the mode parallel independent transformation formula in S31 is as follows, ;

[0012] wherein , These are the input and output optical fields, respectively, and U is the modulation matrix; and singular value decomposition is used to decompose its modulation matrix into an alternating product of multiple phase and diffraction transmission matrices; Based on the Fresnel diffraction principle, the diffraction transfer matrix is ​​as follows.

[0013] Where H is the diffraction matrix. for spatial frequency, It is the operating wavelength. , It is the lateral distance between floors. It is an imaginary number; The transformation of the OAM mode is represented as follows.

[0014] In the formula, Indicates the first n There are several phase modulation matrices, and the parameter optimization range of the matrices is [0, 2π].

[0015] Preferably, the optical diffraction neural network described in S31 uses the phase matrix as the neural layer, and the interlayer neuron links are completed by the diffraction matrix. Specifically, the structure is a multi-layer network architecture in which the phase modulation matrix and the diffraction matrix are alternately cascaded.

[0016] The OAM mode multiplication and division operation system based on optical diffraction neural network includes an orbital angular momentum mode-digital signal generation module, an orbital angular momentum mode multiplication / division operation module, and a digital signal detection module. The orbital angular momentum mode-digital signal generation module is used to generate an orbital angular momentum mode array based on the input digital signal; The orbital angular momentum mode multiplication / division operation module is used to perform mode parallel independent transformation—equivalent numerical shift—on the OAM mode array; The digital signal detection module is used to detect and analyze the processed pattern signal.

[0017] The present invention has the following beneficial effects: 1. In this invention, digital signals are represented by OAM mode encoding, which can realize arbitrary 2 n This method enables multiple digital multiplication / division operations, and its computational functions are highly scalable, flexible, and controllable. It is expected to establish a basic framework for complex arithmetic operations in high-dimensional optical space and provide potential solutions for the practical application of optical digital computing. Using the OAM mode as the physical dimension of the operation, the OAM mode numerical shift is achieved by completing parallel independent transformation of the mode through an optical diffraction neural network, thereby completing the digital multiplication / division operation. The resulting output array has high mode purity.

[0018] 2. In the present application, through the synergistic effect of multi-stage optical coupler and spiral phase plate, efficient energy distribution and orbital angular momentum mode conversion of Gaussian light signal are realized, generating three OAM beams with equal energy; using spatial domain distributed composite technology, two OAM beams and the third OAM beam are combined into an OAM beam array containing three OAM beams through the combination of plane mirror and non-polarized beam splitter, significantly improving the spatial distribution flexibility and mode diversity of the beam.

[0019] 3. In the present application, by combining optical diffraction neural network, the mode of the beam array is transformed in parallel and independently, realizing efficient output of the OAM mode array after numerical shift, and through the synergistic detection and analysis of photodetector and electronic computer, real-time processing and analysis of complex OAM mode are completed; not only the generation and regulation efficiency of OAM beam is optimized, but also the data processing capacity is greatly improved through the mode parallel independent transformation technology, providing efficient and flexible optical regulation means for optical communication, quantum information processing and other fields.

[0020] Of course, any product implementing the present application does not necessarily need to achieve all the advantages described above. BRIEF DESCRIPTION OF DRAWINGS

[0021] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0022] Figure 1 It is a schematic diagram of the device structure corresponding to the OAM mode multiplication and division operation method based on optical diffraction neural network of the present application. Figure 2 It is a schematic diagram of digital signal-orbital angular momentum mode encoding representation of the OAM mode multiplication and division operation method based on optical diffraction neural network of the present application. Figure 3 It is a working process schematic diagram of the optical diffraction neural network model corresponding to the OAM mode multiplication and division operation method based on optical diffraction neural network of the present application. Figure 4 It is a module schematic diagram of the OAM mode multiplication and division operation system based on optical diffraction neural network of the present application.

[0023] In the figure: 1, light source; 2, first optical coupler; 3, second optical coupler; 4, third optical coupler; 5, fourth optical coupler; 6, first spiral phase plate; 7, second spiral phase plate; 8, third spiral phase plate; 9, first plane mirror; 10, first non-polarizing beam splitter; 11, second non-polarizing beam splitter; 12, second plane mirror; 13, first phase diffraction screen; 14, second phase diffraction screen; 15, third phase diffraction screen; 16, photodetector; 17, electronic computer. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the application. In order to make the working principles, technical solutions and advantages of the application more clear and explicit, the application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application, and cannot be used to limit the application. In the description of the application, it should be understood that the relationship indicated by the orientation or position terms is based on the orientation or position relationship shown in the drawings, and is only for the convenience of describing the application and simplifying the description, and cannot be understood as a limitation on the application. The "multiple layers" in the "multiple layer phase modulation" do not specifically refer to a fixed number of layers, but refer to a suitable number of layers according to the mode conversion effect, and the three-layer phase modulation shown in the application cannot be understood as limiting the number of layers of the phase modulation in the application to a fixed number of layers.

[0025] Embodiment one

[0026] Please refer to Figure 1 , the embodiment is an OAM mode multiplication and division operation method based on an optical diffraction neural network, including a Gaussian light signal emitted by a light source 1, the light source 1 is a laser with an output wavelength of 1550 nm, and three beams of energy-balanced sub-Gaussian light beams are generated after passing through a 1x3 first optical coupler 2 with a splitting ratio of 1:1:1. After passing through a second optical coupler 3, a third optical coupler 4 and a fourth optical coupler 5, the three beams of sub-Gaussian light beams are converted into three beams of OAM light beams by a first spiral phase plate 6, a second spiral phase plate 7 and a third spiral phase plate 8. At this time, the OAM light beams can be approximately expressed as Laguerre-Gaussian beams LG :

[0027] wherein r is a radial component, is an angular component, is a beam waist radius, isz waist size of the beam, is the associated Laguerre polynomial, l is the orbital angular momentum topological charge, p is the radial parameter, is the Rayleigh distance, z is the beam propagation distance, k is the wave vector, phase factor indicates that the light beam has a spiral structure, i is the imaginary unit.

[0028] One of the three generated OAM beams passes through the first plane mirror 9 and the other OAM beam is composed of two spatial domain distributed composite OAM beams by the first non-polarization beam splitter 10, and the light field distribution is the superposition of the light fields of two different position OAM beams.

[0029] The third beam of sub-Gaussian beams passes through the second plane mirror 12 and is integrated with the OAM light field to form a beam array containing three OAM beams by the second non-polarization beam splitter 11, and the light field distribution is the superposition of the light fields of three different position OAM beams.

[0030] The beam array containing three OAM beams passes through the mode parallel independent transformation-equivalent numerical shift device (the first phase diffraction screen 13, the second phase diffraction screen 14 and the third phase diffraction screen 15) obtained by iterative optimization of optical diffraction neural network to perform mode parallel independent transformation, and outputs the OAM mode array after numerical shift, and completes the OAM mode multiplication / division operation.

[0031] The obtained output OAM mode array is detected and analyzed by the photodetector 16 and the electronic computer 17.

[0032] The present application uses OAM mode array to represent binary numerical value, and the encoding representation mapping relationship is as follows Figure 2The logical states "0" and "1" are encoded as different OAM modes (OAM1 represents logical state "0" and OAM2 represents logical state "1"). Three dotted circles in different spatial positions represent the bits of the numerical value, from left to right, high bits to low bits. Therefore, different OAM modes combined with different spatial positions constitute the OAM mode array of the digital signal coding. For example, the input binary numerical value "010" is encoded into three OAM modes (OAM1, OAM2, OAM1) arranged in order from left to right, each mode being located in the corresponding dotted circle. The generated OAM mode array is subjected to mode parallel independent transformation-equivalent numerical value shift device to complete mode parallel independent transformation, realize spatial shift of the OAM mode array to equivalent binary numerical value shift, and thus realize OAM mode multiplication / division operation.

[0033] The OAM mode array parallel independent transformation described in the application can be expressed as:

[0034] wherein are input and output optical fields respectively, and U is a modulation matrix. The key to realizing OAM mode multiplication / division lies in successfully completing mode parallel independent transformation of the OAM mode array, that is, solving the unknown modulation matrix U. In order to improve the solving accuracy and reduce the difficulty, the singular value decomposition can be used to decompose the modulation matrix into multiple phase and diffraction transmission matrixes. Among them, based on the Fresnel diffraction principle, the diffraction matrix can be expressed as:

[0035] wherein H is a diffraction matrix, is the spatial frequency of , is the working wavelength, , is the interlayer lateral distance, is an imaginary number. According to these parameters, the transformation of the OAM mode can be expressed as:

[0036] wherein represents the nth phase modulation matrix, and the parameter optimization interval of the matrix is [0, 2π].

[0037] Therefore, the main challenge of solving the modulation matrix U is to solve the unknown phase matrix parameters. To solve this problem, an optical diffraction neural network based on deep learning is constructed to build a photonic guiding physical model for inputting OAM mode array. The model takes the phase matrix as the neural layer, and the inter-layer neuron link is completed by the diffraction matrix. The specific structure is a multi-layer network architecture with alternating cascading of phase modulation matrix and diffraction matrix. The input light field represented by OAM mode order and spatial position is converted into the output light field after passing through the optical diffraction neural network with multi-layer phase structure in turn. By supervised data label, the random gradient descent algorithm is adopted, and Adam is selected as the optimizer to back-propagate the error and update the phase matrix to minimize the loss function, so as to ensure that the output light field closely matches the target light field, thereby obtaining the optimal phase distribution. The workflow is as shown in Figure 3 The simulation parameters of the matching experiment condition are set, the OAM mode array is generated as the complex amplitude light field input of the model according to the digital signal coding, and the complex amplitude light field is output after the alternating modulation of three layers of phase screens and free space diffraction propagation. The initial phase screen is a random Gaussian distribution. In order to make the phase distribution meet the required parallel independent transformation-equivalent numerical shift modulation, the phase value is set as the optimization object, the loss function is designed to evaluate the error according to the target light field and the predicted output light field, and the Adam optimizer is selected to back-propagate the error and update the optimization of the three layers of phase at the same time, and finally the optimal phase distribution is obtained.

[0038] The loss function is calculated by the predicted output complex amplitude light field and the target complex amplitude light field, and is designed as:

[0039]

[0040] In the formula is the loss field, is the predicted output complex amplitude light field, Loss is the loss function, is the target complex amplitude light field, N is the output light field, M is the detection area size of the output light field, =1 is a constant factor. Among them, Relu and Tanh are two common activation functions in neural networks:

[0041]

[0042] In summary, the application discloses an OAM mode multiplication / division device based on an optical diffraction neural network, which comprises an OAM mode-digital signal generation module, an OAM mode multiplication / division operation module and a digital signal detection module. In the device, the OAM mode-digital signal generation module generates a plurality of OAM modes at different spatial positions according to a digital signal, the OAM mode multiplication / division operation module performs mode value shift to complete numerical multiplication / division operation, and the digital signal detection module detects and analyzes the operated OAM mode signal. The device is characterized in that the OAM mode is used as the operation physical dimension, the numerical shift based on the mode parallel independent transformation is completed through the optical diffraction neural network, and the OAM mode multiplication / division operation can be realized. The OAM mode multiplication / division operation module of the application can realize arbitrary 2n times of digital multiplication / division operation, and has the characteristics of strong scalability and flexible controllability, and is expected to establish a basic framework for complex arithmetic operation in high-dimensional optical space and provide a potential solution for the practical application of optical digital calculation.

[0043] Embodiment two Please refer to Figure 4 The embodiment discloses an OAM mode multiplication / division operation system based on an optical diffraction neural network, which can realize the method of the above embodiment and comprises an OAM mode-digital signal generation module, an OAM mode multiplication / division operation module and a digital signal detection module. The OAM mode-digital signal generation module is used to generate an OAM mode array according to an input digital signal. The OAM mode multiplication / division operation module is used to perform mode parallel independent transformation-equivalent numerical shift on the OAM mode array. The digital signal detection module is used to detect and analyze the operated mode signal.

[0044] In the description of the specification, the description of the terms "one embodiment", "example", "specific example" and the like means that the specific features, structures, materials or characteristics described in combination with the embodiment or example are contained in at least one embodiment or example of the application. In the specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0045] The preferred embodiments of the application disclosed above are only to facilitate the elucidation of the application. The preferred embodiments do not describe all the details of the application and limit the application to the specific embodiments described. Obviously, many modifications and variations can be made in light of the teachings above. The description is chosen and described in order to provide the best illustration of the application principles and their practical application, so that those skilled in the art can well understand and utilize the application.

Claims

1. A method for OAM mode multiplication and division based on optical diffractive neural networks, characterized in that, The method comprises the following steps: S1, passing the Gaussian light signal through a first optical coupler to obtain three beams of energy-balanced sub-Gaussian light beams; then passing the three beams of energy-balanced sub-Gaussian light beams through a second optical coupler, a third optical coupler and a fourth optical coupler respectively, and then converting through a first spiral phase plate, a second spiral phase plate and a third spiral phase plate to obtain three beams of OAM light beams; S2, two of the three beams of OAM light beams pass through a first plane mirror and a first non-polarization beam splitter to form a spatial domain distributed composite OAM light beam; the spatial domain distributed composite OAM light beam and the other one of the three beams of OAM light beams pass through a second plane mirror and a second non-polarization beam splitter to form a light beam array containing three beams of OAM light beams; S3, combining an optical diffraction neural network, performing mode parallel independent transformation on the light beam array containing three beams of OAM light beams to output an OAM mode array after numerical shift, and detecting and analyzing by a photoelectric detector and an electronic computer.

2. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 1, wherein, The S1 comprises the following steps: S11, the Gaussian light signal emitted by a light source passes through a first optical coupler to generate three beams of energy-balanced sub-Gaussian light beams; S12, the sub-Gaussian light beams in S11 pass through a second optical coupler, a third optical coupler and a fourth optical coupler, and then are converted into three beams of OAM light beams by a first spiral phase plate, a second spiral phase plate and a third spiral phase plate.

3. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 2, wherein, The S2 comprises the following steps: S21, one of the three beams of OAM light beams in S12 passes through a first plane mirror to form a spatial domain distributed composite OAM light beam with another beam of OAM light beam by a first non-polarization beam splitter; S22, the third beam of OAM light beams in S12 passes through a second plane mirror, passes through a second non-polarization beam splitter and forms a light beam array containing three beams of OAM light beams with the spatial domain distributed composite OAM light beam in S21.

4. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 3, wherein, The S3 comprises the following steps: S31, the light beam array containing three beams of OAM light beams in S31 passes through a mode parallel independent transformation-equivalent numerical shift device obtained by iterative optimization of an optical diffraction neural network to perform mode parallel independent transformation, and then outputs an OAM mode array after numerical shift, completes OAM mode multiplication / division operation and obtains an output OAM mode array; The mode parallel independent transformation-equivalent numerical shift device comprises a first phase diffraction screen, a second phase diffraction screen and a third phase diffraction screen; S32, the output OAM mode array is detected and analyzed by a photoelectric detector and an electronic computer.

5. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 4, wherein, The S31 comprises the following steps: S311, an input light field represented by an OAM mode order and a spatial position is converted into an output light field after sequentially passing through an optical diffraction neural network with a multi-layer phase structure; wherein a random gradient descent algorithm is adopted by supervised data labels, and Adam is selected as an optimizer to back-propagate errors and update a phase matrix to minimize a loss function; S312, set the simulation parameters matching the experimental conditions, generate OAM mode array as the model of complex amplitude light field input according to the digital signal coding, after a distance of free space diffraction propagation, output the complex amplitude light field through the alternative modulation of three layers of phase screen and free space diffraction propagation; the initial phase screen is random Gaussian distribution, the phase value is set as the optimization object, the loss function is designed to evaluate the error according to the target light field and the predicted output light field, and the Adam optimizer is selected to update the optimization three layers of phase by backpropagating the error, and finally the optimal phase distribution is obtained.

6. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 5, wherein, The loss function in S312 is calculated by predicting the output complex amplitude light field and the target complex amplitude light field, as follows, ； ； wherein is the loss field, is the predicted output complex amplitude light field, Loss is the loss function, is the target complex amplitude light field, N x M is the size of the detection region of the output light field, =1 is a constant factor; Relu and Tanh are activation functions.

7. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 4, wherein: For the light beam array containing three OAM beams in S31, two circular rings of different sizes are used to represent two different OAM modes, and the logical states "0" and "1" are encoded as different OAM modes; and the three dotted circles located in different spatial positions represent the bits of the value, from left to right, from high bit to low bit.

8. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 4, wherein, The formula for parallel independent transformation of modes in S31 is as follows, ； wherein , are input and output optical fields, respectively, U is a modulation matrix; and using singular value decomposition to decompose the modulation matrix into an alternating product of phase and diffractive transmission matrices; Based on the principle of Fresnel diffraction, the diffraction transmission matrix is as follows, ； where H is the diffraction matrix, is the spatial frequency, is the operating wavelength, , is the interlayer lateral distance, is an imaginary number; The transformation of OAM mode is represented as follows, ； In the formula, represents the first n phase modulation matrix, and the parameter optimization interval of the matrix is [0, 2π].

9. The OAM mode multiplication and division method based on optical diffractive neural network according to claim 4, wherein, The optical diffraction neural network in S31 uses a phase matrix as a neural layer, and the inter-layer neuron link is completed by a diffraction matrix. The specific structure is a multi-layer network architecture with phase modulation matrix and diffraction matrix alternatingly cascaded.

10. A system for implementing the OAM mode multiplication and division operation method based on the optical diffraction neural network according to any one of claims 1-9.

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