Light beam orbital angular momentum spectrum measurement method based on diffraction neural network

Abstract

The invention discloses a diffraction neural network-based light beam orbital angular momentum spectrum measurement method, which comprises the following steps of: mapping photons of different orbital angular momentum states contained in a light beam to be measured to different spatial positions on a target surface of an area array detector by constructing a multi-layer diffraction neural network model and utilizing diffraction propagation characteristics of a light field; and mapping the intensity information of each orbital angular momentum mode to the intensity distribution of the bright spots at the corresponding spatial position. The orbital angular momentum spectrum of the light beam to be detected can be obtained by analyzing the position and intensity information of the bright spots on the target surface of the detector. The method has the advantages of simple structure, high operation speed and the like, and has wide application prospects in the fields of new-system optical communication, quantum information processing and the like.

Description

Technical Field

[0001] The present invention relates to the field of laser technology, and particularly to a method for measuring the beam orbital angular momentum spectrum based on a diffractive neural network. Background Art

[0002] Orbital angular momentum (OAM) is a new type of high-dimensional degree of freedom of a laser. Previous studies have shown that if the complex amplitude expression of a beam contains a helical phase term then each photon in the beam carries an OAM value of where l is the OAM state, also known as the angular quantum number or topological charge number, which can be any integer and is the eigenvalue of OAM; is the angular coordinate; is the reduced Planck constant. The OAM modes corresponding to different OAM states are orthogonal to each other and can form an infinite-dimensional Hilbert space, which means that a beam of light can carry multiple different OAM modes simultaneously. These peculiar properties make OAM have great application value in the fields of laser communication, laser detection, optical tweezers, quantum information processing, etc.

[0003] The OAM spectrum of a beam refers to the intensity ratio of different OAM modes in the beam, which directly determines the mode field distribution of the beam. Therefore, the measurement of the beam OAM spectrum is the key basis for OAM applications. However, currently commonly used methods for measuring the beam OAM spectrum, such as the interference method and the diffraction method, still face challenges such as limited OAM mode recognition range and poor real-time performance. In recent years, with the development of artificial intelligence technology, domestic and foreign scholars have developed a method for measuring the beam OAM spectrum based on an electrical deep neural network. Although this method has improved the above limitations to a certain extent, problems such as the "black box" characteristic, high computational complexity, and insufficient generalization ability of this method limit its further application.

[0004] A diffractive neural network (DNN) is a machine learning model that combines optical diffraction theory and neural networks, and it has advantages such as high accuracy, fast operation speed, and low energy consumption when processing optical field data. By introducing DNN into the measurement of the beam OAM spectrum, it is expected to solve the bottlenecks such as limited OAM mode recognition range and poor real-time performance, and achieve efficient measurement of the OAM spectrum of a multi-mode hybrid vortex beam. Summary of the Invention

[0005] In view of this, the present invention discloses a method for measuring the beam OAM spectrum based on DNN, which is characterized in that, by utilizing the diffraction propagation characteristics of the optical field, a multi-layer DNN model is constructed, and the DNN is trained by using the backpropagation and gradient descent algorithms to establish a strict correspondence between different OAM modes in the beam to be measured and the spatial positions on the target surface of the area array detector, so as to map the photons with different OAM states in the beam to be measured to different spatial positions on the target surface of the area array detector; and map the intensity information of each OAM mode to the intensity distribution of the bright spot at the corresponding spatial position. According to the phase transmittance function of each DNN layer, a diffractive optical device is fabricated as the carrier of each DNN layer to form a DNN system for measuring the beam OAM spectrum. When the beam to be measured is incident, a spatial laser array can be observed on the target surface of the area array detector, thereby obtaining the OAM spectrum of the beam to be measured.

[0006] The core mechanism of the present invention lies in the mapping relationship between the discrete light intensity distribution on the target surface of the area array detector and the OAM spectrum. Specifically, in the spatial dimension, the position of the bright spot on the target surface of the area array detector corresponds to different OAM mode orders, and in the intensity dimension, the intensity information of the bright spots at different positions characterizes the light intensity value of the OAM mode. By using the trained and optimized DNN model to extract the optical field characteristics, the accurate identification of the OAM mode order and the quantitative analysis of the intensity information can be realized, and finally the high-precision real-time reconstruction of the OAM spectrum can be achieved.

[0007] A DNN-based beam OAM spectrum measurement system of the present invention includes a DNN diffraction layer and an area array detector. Among them, the DNN has three layers in total, and each layer is a diffractive optical device. The second diffraction layer is located in the laser optical path behind the first diffraction layer, the third diffraction layer is located in the laser optical path behind the second diffraction layer, and the area array detector is located in the laser optical path behind the third diffraction layer; all three diffraction layers include 200×200 optical neurons, and the neuron size is 8μm×8μm, and the distance between adjacent diffraction layers is set to 2 cm; the distance from the target surface of the area array detector to the third diffraction layer is 4 cm.

[0008] The beneficial effects of the present invention include:

[0009] 1. Based on DNN, the present invention uses optical diffraction phenomena to perform calculations, avoiding the high computational complexity and energy consumption problems of traditional electrical neural networks, and having the characteristics of high efficiency and energy saving. At the same time, DNN realizes real-time calculation through optical field propagation, and the operation speed is significantly better than traditional methods, which can meet application scenarios with high real-time requirements. Moreover, the present invention adopts a pure optical calculation method, without the need for complex electronic computing devices, the system structure is simple, and it is easy to be integrated into existing optical systems, having high practicality and scalability.

[0010] 2. By introducing intensity as the observable quantity of the target surface of the area array detector, the present invention can effectively extract the intensity distribution information of different modes in the multi-mode hybrid vortex beam, solve the problem of limited pattern recognition range of the traditional method, and achieve high-precision measurement of the OAM spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0012] Figure 1 FIG. 1 is a schematic diagram of a beam OAM spectrum measurement system based on DNN in an embodiment of the present invention, where 1 - the first diffraction layer, 2 - the second diffraction layer, 3 - the third diffraction layer, 4 - the area array detector, 5 - the computer;

[0013] Figure 2 FIG. 2 is a DNN training flow chart for beam OAM spectrum measurement of the present invention;

[0014] FIG. 3(a) shows the intensity distribution of the input optical field when measuring a five-OAM mode hybrid beam with a mode interval of 1 using the DNN-based beam OAM spectrum measurement method of the present invention;

[0015] FIG. 3(b) shows the intensity distribution of the output optical field measured by the area array detector when measuring a five-OAM mode hybrid beam with a mode interval of 1 using the DNN-based beam OAM spectrum measurement method of the present invention;

[0016] FIG. 3(c) shows the correspondence between the position of the sub-spot in the optical field of FIG. 3(b) and the OAM mode;

[0017] FIG. 3(d) shows the measurement result of the OAM spectrum of a five-OAM mode hybrid beam with a mode interval of 1 measured using the DNN-based beam OAM spectrum measurement method of the present invention;

[0018] FIG. 4(a) shows the intensity distribution of the input optical field when measuring a six-OAM mode hybrid beam using the DNN-based beam OAM spectrum measurement method of the present invention;

[0019] FIG. 4(b) shows the intensity distribution of the output optical field measured by the area array detector when measuring a six-OAM mode hybrid beam using the DNN-based beam OAM spectrum measurement method of the present invention;

[0020] FIG. 4(c) shows the correspondence between the position of the sub-spot in the optical field of FIG. 4(b) and the OAM and mode;

[0021] FIG. 4(d) shows the measurement result of the OAM spectrum of a six-OAM-mode mixed beam measured by the DNN-based OAM spectrum measurement method of the present invention. Detailed implementation manners

[0022] A DNN-based OAM spectrum measurement system of the present invention consists of three diffraction layers and a planar array detector, as Figure 1 shown. Each DNN layer contains 200×200 optical neurons, and the neuron size is 8μm×8μm. Each layer is a diffractive optical device. The second diffraction layer is located in the laser optical path behind the first diffraction layer, the third diffraction layer is located in the laser optical path behind the second diffraction layer, and the planar array detector is located in the laser optical path behind the third diffraction layer. The distance between adjacent diffraction layers is set to 2 cm, and the distance from the target surface of the planar array detector to the third diffraction layer is 4 cm. Each diffraction layer modulates the input optical field through phase modulation and light field diffraction propagation, and finally forms an intensity distribution on the target surface of the planar array detector. By calculating its intensity value and performing normalization processing, the OAM spectrum is obtained. Specifically, the phase distribution of each diffraction layer is obtained through training optimization for modulating the input optical field. After the optical field is modulated by multiple diffraction layers, it propagates through the propagation layer to the target surface of the planar array detector, forming a bright spot distribution. The position of the bright spot on the target surface of the planar array detector corresponds to different OAM mode orders, and the intensity of the bright spot characterizes the intensity value of the OAM mode of that order. By analyzing the position and intensity distribution of the bright spots, the intensity distribution of each OAM mode can be accurately calculated, and then the OAM spectrum of the beam to be measured can be obtained.

[0023] A DNN-based OAM spectrum measurement method of the present invention has a training process as Figure 2 shown. During the training process, the optical field to be measured is input into the DNN and sequentially passes through the first diffraction layer, the second diffraction layer, and the third diffraction layer, and the output optical field distribution, that is, a series of bright spots on the planar array detector, can be obtained. By calculating the position and intensity distribution of the bright spots and performing normalization processing, the OAM spectrum of the beam to be measured can be obtained. Comparing it with the actual OAM spectrum and being constrained by the loss function, the phase values of the first diffraction layer, the second diffraction layer, and the third diffraction layer are continuously optimized, so that the MSE between the OAM spectrum calculated by the DNN and the actual OAM spectrum gradually decreases until it finally converges.

[0024] The network training process of the DNN for OAM spectrum measurement of the present invention includes the following steps:

[0025] First step, set different mode ranges, mode intervals, and mode relative intensity distributions to generate the complex amplitude data E of the multi-mode hybrid vortex beam. The size of E is 200×200, where 200 and 200 represent the height and width of the optical field data respectively. Generate the output data E' of the true value surface array detector target surface according to the intensity distribution. The size of E' is 200×200, where 200 and 200 represent the height and width of the output optical field data respectively;

[0026] Second step, construct a data set. Each complex amplitude data and its output data of the true value surface array detector target surface form a pair of training data, generating a total of 27,000 pairs of samples, where the training set contains 24,000 pairs of samples and the test set contains 3,000 pairs of samples. By presetting the correspondence between the spatial position coordinates of the bright spots at the target surface of the surface array detector and the orbital angular momentum, and assigning the normalized relative intensity values to the intensities of the bright spots at different spatial positions, the output data of the true value surface array detector target surface is obtained;

[0027] Third step, input the complex amplitude data of the beam to be measured into the DNN model for training. For the selection of hyperparameters, the AdamW optimizer is used to optimize the gradient during the training process. The learning rate is 0.01, the batch training quantity is 128, and 300 rounds of iteration are performed on the entire training set. During the iterative training process, the Mean Squared Error (MSE) is used as the loss function to constrain the difference between the model prediction value and the true value. MSE can effectively measure the difference between the model prediction value and the true value, and is a good evaluation method for the OAM spectrum measurement effect.

[0028] After training, the trained DNN model can be directly used for the OAM spectrum measurement of the beam without retraining. The DNN model of the present invention shows high measurement accuracy on the test set and can meet the requirements of various practical applications.

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely below.

[0030] Example 1: Measure the OAM spectrum of a five-OAM mode hybrid beam with a mode interval of 1

[0031] In this embodiment, the OAM spectrum of a five-OAM-mode hybrid beam with a measurement mode interval of 1 is measured. Fig. 3(a) shows the intensity distribution of the beam to be measured, Fig. 3(b) shows the intensity distribution of the optical field output by the DNN measured by the area array detector, Fig. 3(c) shows the correspondence between the positions of the sub-spots in the optical field of Fig. 3(b) and the OAM modes, and Fig. 3(d) shows the OAM spectrum measurement result. The OAM mode orders are -2, -1, 0, +1, and +2 respectively, and the relative intensity ratios of each mode are {0.1417:0.2392:0.3286:0.1956:0.0949}. The OAM spectrum of this five-mode hybrid beam is measured by using the DNN-based beam OAM spectrum measurement method proposed by the present invention. The obtained result is basically consistent with the true value OAM spectrum, and the measurement error MSE value is 3.48×10 -7 .

[0032] Embodiment 2: Measuring the OAM spectrum of a six-OAM-mode hybrid beam

[0033] In this embodiment, the OAM spectrum of a large-range six-OAM-mode hybrid beam is measured. Fig. 4(a) shows the intensity distribution of the beam to be measured, Fig. 4(b) shows the intensity distribution of the optical field output by the DNN measured by the area array detector, Fig. 4(c) shows the correspondence between the positions of the sub-spots in the optical field of Fig. 4(b) and the OAM modes, and Fig. 4(d) shows the OAM spectrum measurement result. The OAM mode orders are -10, -8, -5, -2, 3, 7, and 8 respectively, and the relative intensity ratios of each mode are {0.0312:0.3456:0.2638:0.0140:0.2988:0.0075:0.0390}. The OAM spectrum of this five-mode hybrid beam is measured by using the DNN-based beam OAM spectrum measurement method proposed by the present invention. The obtained result is basically consistent with the true value OAM spectrum, and the measurement error MSE value is 1.669×10 -5 .

[0034] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for measuring the beam orbital angular momentum spectrum based on a diffraction neural network, characterized in that By utilizing the diffraction propagation characteristics of the optical field, a multi-layer diffraction neural network model is constructed, and the backpropagation and gradient descent algorithms are used to train the diffraction neural network to establish a strict correspondence between different orbital angular momentum modes in the beam to be measured and the spatial positions on the target surface of the area array detector, mapping the photons with different orbital angular momentum states contained in the beam to be measured to different spatial positions on the target surface of the area array detector; mapping the intensity information of each orbital angular momentum mode to the intensity distribution of the bright spot at the corresponding spatial position; processing a diffractive optical device according to the phase transmittance function of each diffraction neural network layer as the carrier of each diffraction neural network layer to form a diffraction neural network system for measuring the orbital angular momentum spectrum of the beam. When the beam to be measured is incident, a spatial laser array can be observed on the target surface of the area array detector, thereby obtaining the orbital angular momentum spectrum of the beam to be measured.

2. The method according to claim 1, wherein, The training process of the diffraction neural network for orbital angular momentum spectrum measurement is as follows: In the first step, different mode ranges, mode intervals, and mode relative intensity distributions are set to generate the complex amplitude data E of the multi-mode hybrid vortex beam. The size of E is 200×200, where 200 and 200 are the height and width of the input optical field data; according to the intensity distribution, its true value detector target surface output data E' is generated. The size of E' is 200×200, where 200 and 200 are the height and width of the output optical field data. In the second step, a data set is constructed. Each complex amplitude data and its true value area array detector target surface output data form a pair of training data, generating a total of 27,000 pairs of samples, where the training set contains 24,000 pairs of samples and the test set contains 3,000 pairs of samples; by presetting the correspondence between the spatial position coordinates of the bright spots at the target surface of the area array detector and the orbital angular momentum, and assigning the normalized relative intensity values to the intensities of the bright spots at different spatial positions, the true value area array detector target surface output data is obtained. In the third step, the optical field to be measured is input into the diffraction neural network model for training; for the selection of hyperparameters, the AdamW optimizer is used to optimize the gradient during the training process, the learning rate is 0.01, the batch training quantity is 128, and 300 rounds of iteration are performed on the entire training set. During the training process, the mean square error is used as the loss function to constrain the difference between the model prediction value and the true value. The loss function is realized by calculating the mean square error between the predicted light intensity distribution and the true value light intensity distribution on the target surface of the detector.

3. A beam orbital angular momentum spectrum measurement system based on a diffraction neural network, comprising a diffraction layer of the diffraction neural network and a planar array detector, wherein, The diffraction neural network has three layers, and each layer is a diffractive optical device. The second diffraction layer is located in the laser optical path behind the first diffraction layer, the third diffraction layer is located in the laser optical path behind the second diffraction layer, and the area array detector is located in the laser optical path behind the third diffraction layer; all three diffraction layers contain 200×200 optical neurons, and the neuron size is 8μm×8μm. The distance between adjacent diffraction layers is set to 2 cm; the distance from the target surface of the area array detector to the third diffraction layer is 4 cm.

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