A method for phase control of a multi-mode vortex beam of an angularly filtered reconstruction neural network

Abstract

The application discloses a kind of angular filter reconstruction neural network multi-mode vortex light beam phase control methods.By explicitly introducing angular restriction physical information in neural network training to filter to realize the consistency constraint of phase distribution, the quality of multi-mode vortex light beam control phase generated by network can be effectively improved, and the training optimization of network is enabled.The explicit angular physical filter refers to the uniform angular sampling of the two-dimensional phase distribution of the neural network feature fusion output along the circumference of the set radius, which is expanded into an angle-phase curve, and then the one-dimensional angular information is reconstructed into a global two-dimensional phase diagram through mapping interpolation.This process is equivalent to applying a filter based on angular prior to phase information, retaining the angular main features and effectively suppressing redundant information, making the multi-mode vortex light beam spectrum information more significant, effectively improving the training speed and accuracy of neural network.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic technology, and more specifically to a multimode vortex beam phase modulation method for angular filtering reconstruction neural networks. Background Technology

[0002] Vortex beams carrying orbital angular momentum (OAM) represent a novel type of laser optical field. Due to the high-dimensionality resulting from the orthogonality of their OAM degrees of freedom, they hold broad application prospects in fields such as optical communication, quantum information, precision detection, and optical manipulation. Among the methods for generating vortex optical fields, pure phase manipulation is one of the simplest, most direct, and most commonly used techniques. However, the phase manipulation design for multimode vortex beams is highly complex, requires extensive iterative calculations, and struggles to obtain a standard reference phase distribution, thus limiting the practical application of phase manipulation for multimode vortex beams.

[0003] In recent years, deep learning technologies such as neural networks have been applied to optical field manipulation, directly generating pure phase patterns for spatial light modulation by inputting the complex amplitude visual information of the target light field. However, within the basic framework of deep learning based on image convolution, the phase distribution output by the neural network after feature extraction and feature fusion often contains local noise, randomness, or discontinuities. The large amount of redundant information introduced by inter-pixel convolution does not take into account the angular consistency of the modulation phase of multimode vortex beams, which seriously affects the beam modulation efficiency and the accuracy of its OAM mode spectrum characterization.

[0004] To improve the quality of pure phase-controlled gratings generated by neural networks, existing methods often require extensive data training to enhance feature map quality, relying on convolutional networks to learn local pixel correlations in image space, while failing to fully utilize the physical structural characteristics of multimode OAM beams in their angular distribution. Therefore, how to introduce constraint mechanisms conforming to the physical laws of OAM during neural network training, while ensuring network expressive power and improving the continuity of the controlled phase and the fidelity of the mode spectrum, has become an urgent technical problem to be solved. Summary of the Invention

[0005] In view of this, the present invention discloses a neural network multimode vortex beam phase control method based on angular filtering reconstruction.

[0006] This invention discloses a neural network-based multimode vortex beam phase modulation method based on angular filtering reconstruction, characterized by the following steps: S1. Acquiring the complex amplitude information corresponding to the target multimode vortex beam and inputting it into a phase modulation neural network, obtaining a phase distribution through feature extraction; S2. Performing angular filtering on the phase distribution to obtain an angular-phase sequence; S3. Performing two-dimensional phase reconstruction based on the acquired angular-phase sequence to obtain the reconstructed phase distribution, and calculating the orbital angular momentum spectrum of the corresponding modulated light field; S4. Determining a loss function based on the orbital angular momentum mode spectrum and the target orbital angular momentum mode spectrum, and updating the neural network parameters according to the loss function. Specifically, the complex amplitude information corresponding to the target multimode vortex beam is acquired, and the complex amplitude information is input into the phase modulation neural network. A phase modulation grating generation neural network is used to perform convolution feature extraction and dynamic weighted fusion on the complex amplitude light field of the multimode vortex beam to obtain a two-dimensional phase distribution output by a deep learning model based on visual information. Based on this, the two-dimensional phase distribution is subjected to angular filtering to introduce physical information. The two-dimensional phase distribution output by the neural network is transformed from a Cartesian coordinate system to a polar coordinate system. Phase sampling is performed along the angular direction on a circle corresponding to a preset radius to obtain phase information corresponding to different angular positions, forming an angle-phase sequence. This extracts the angular structure information in the two-dimensional phase distribution, realizing the physical prior constraint based on the angular symmetry of OAM. Two-dimensional phase reconstruction is then performed based on the angle-phase sequence. Specifically, a polar angle mapping relationship is established based on the angle-phase sequence, and interpolation calculations are performed on the angle-phase sequence to obtain the two-dimensional phase distribution in polar coordinates. Furthermore, based on the transformation relationship between polar and Cartesian coordinates, the reconstructed phase is mapped to a global two-dimensional plane to obtain the angularly filtered and reconstructed control phase distribution. Finally, the orbital angular momentum mode spectrum of the corresponding modulated light field is calculated based on the angularly filtered and reconstructed control phase distribution. The mode spectrum is compared with the target orbital angular momentum mode spectrum, and a network training loss function is constructed based on the error between the two. The neural network parameters are updated through backpropagation to achieve optimized generation of the control phase of the multimode vortex beam.

[0007] The phase-controlled grating generating neural network consists of a convolutional feature extraction module and a dynamic weighted fusion module. The convolutional feature extraction module comprises three multilayer perceptrons. Each perceptron has a 3×3 convolutional layer connected to a ReLU activation function, followed by another 3×3 convolutional layer, enabling pixel-level nonlinear feature extraction from the input complex amplitude image information. The dynamic weighted fusion module uses a set of parallel branches containing N dynamic transformation modules to fuse feature outputs at different scales. Each branch is equipped with a 1×1 perceptron, which consists of two 1×1 convolutional layers connected via a ReLU activation function for feature fusion. The weight coefficients of each dynamic transformation module are initialized and trained with the network. Finally, a weighted sum is performed with the fused feature outputs at each scale to obtain the dynamic feature fusion result. The angular filtering and reconstruction module, located after the phase-controlled grating generating neural network, consists of two parts: angular filtering and phase reconstruction. The angular filtering includes: converting the phase distribution into polar coordinates; acquiring phase data along the angular direction on a circle corresponding to a preset radius; and forming an angle-phase sequence based on the acquired phase data. This allows for the explicit introduction of angular sampling-based filtering and reconstruction during neural network training, significantly improving the effectiveness of multimode vortex beam spectrum information used for supervisory constraints. The two-dimensional phase reconstruction includes: establishing a polar angle mapping relationship based on the angle-phase sequence; interpolating the angle-phase sequence to obtain a polar coordinate phase distribution; and obtaining the reconstructed phase distribution based on the coordinate mapping relationship between polar and rectangular coordinates, effectively suppressing redundant information while preserving the angular principal features.

[0008] The beneficial effects of this invention include: 1. The angular filtering reconstruction neural network multimode vortex beam phase control method provided by the present invention explicitly introduces the angular consistency prior of phase control in the neural network training. It is an information filtering mechanism with physical consistency constraints. Compared with the prior art, the initial value of the optimized parameters obtained is more effective, thereby improving the accuracy of the generated phase control.

[0009] 2. By reconstructing the two-dimensional phase information generated by the neural network through angular filtering, the local noise and discontinuities caused by convolution are effectively suppressed. Spectral measurements have shown that it can remove redundant information to the maximum extent and improve the effectiveness of the initial value information of the OAM mode spectrum.

[0010] 3. This invention can significantly improve the accuracy of the generated beam OAM mode spectrum and increase the network training convergence speed without increasing network complexity. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of a multimode vortex beam phase modulation method for an angular filtering reconstruction neural network according to an embodiment of the present invention; Figure 2 This is a diagram of the neural network structure for generating phase-controlled gratings based on angular filtering reconstruction optimization in an embodiment of the present invention. Figure 3 To utilize the angular filtering of this invention to reconstruct the two-dimensional phase distribution and its modulated optical field spectrum distribution before and after optimization, i.e. the initial values ​​of the network constraint parameters, the order of the modulated target optical field OAM mode is [-9, -7, -5, -3, 1, 3, 5, 7, 9]; Figure 4 To generate an equal-intensity multimode vortex beam pure phase control grating and its modulated light field spectrum distribution before and after optimization using a multimode vortex beam phase control method for reconstructing a neural network using an angular filtering method of the present invention, the order of the modulated target light field OAM mode is [-9, -7, -5, -3, 1, 3, 5, 7, 9], and the relative intensity of each OAM mode is equal. Figure 5 To generate the pure phase control grating of the non-uniform intensity multimode vortex beam and its modulation optical field spectrum distribution before and after optimization using the multimode vortex beam phase control method of the present invention for reconstructing a neural network by angular filtering, the OAM mode order of the modulation target optical field is [-8, -6, -4, -2, 2, 4, 6, 8], and the corresponding normalized relative intensity is set to [0.12, 0.11, 0.15, 0.12, 0.16, 0.10, 0.09, 0.15]. Detailed Implementation

[0013] This invention proposes a neural network multimode vortex beam phase modulation method for angular filtering reconstruction, such as... Figure 1 As shown, the process begins with inputting the amplitude, phase, and OAM mode spectrum of the target beam. Based on this input information, a preliminary modulation grating phase is generated via a neural network convolutional feature extraction module and a dynamic weighted fusion module. Physical information, specifically angular consistency constraints, is introduced into the generated feature-fused two-dimensional phase distribution. An angular filtering reconstruction module is then used to optimize this distribution. The optimized phase grating's modulation OAM mode spectrum is calculated and compared with the target OAM mode spectrum. The neural network parameters are then jointly optimized based on the OAM mode spectrum error. Specifically, the process involves the following steps: 1. Dataset Preparation: A series of multiplexed beams with multiple OAM modes are randomly generated according to the set mode and amplitude. Their phases are read, and the light field distribution after phase modulation is calculated using scalar diffraction and angular spectral transmission theory, represented as follows: Y 0∈ R 1080 ×1080 Here, 1080 and 1080 represent the height and width of the optical field data, respectively. These values ​​are equal to the size of the spatial light modulator used in the experiment. The complex amplitude data of the multi-OAM mode optical field are preprocessed to obtain a learnable real-valued intensity image and phase image for the network. Specifically, the relative intensity is obtained by taking the modulus square of the complex amplitude, and the relative phase is obtained by taking the argument of the complex amplitude and then taking the remainder after dividing by 2π. The data is normalized to [0,1] for intensity and [0,2π] for phase. Each complex amplitude data point and its corresponding modulation phase constitute a pair of training data, constructing a data set between the modulation phase and the complex amplitude of the complex modulated optical field.

[0014] 2. Neural Network Modeling: The neural network structure based on angular filtering reconstruction is as follows... Figure 2 As shown, the system consists of three parts: a convolutional feature extraction module, a dynamic weighted feature fusion module, and an angular filtering reconstruction module. The convolutional feature extraction module comprises three multilayer perceptrons. Each perceptron consists of a 3×3 convolutional layer connected to a ReLU activation function followed by another 3×3 convolutional layer, enabling pixel-level nonlinear feature extraction from the input complex amplitude image information. A 2×2 max-pooling layer is used between the perceptrons to change the receptive field size for feature extraction, and residual connections are introduced to prevent gradient vanishing. The dynamic weighted fusion module uses a set of parallel branches containing N dynamic transformation modules to fuse feature outputs at different scales. Each branch is equipped with a 1×1 perceptron, which is formed by connecting two 1×1 convolutional layers connected by a ReLU activation function for feature fusion. The weight coefficients of each dynamic transformation module are initialized and trained with the network. Finally, the weighted sum of these weighted coefficients with the feature fusion outputs at each scale yields the dynamic feature fusion result.

[0015] 3. Angular Filtering Reconstruction: The angular filtering reconstruction module is located after the dynamic weighted fusion module. It can explicitly introduce angular sampling-based filtering reconstruction during neural network training to significantly improve the effectiveness of multimode vortex beam spectrum information used for supervision constraints. It includes two steps: S1. Extracting the angle-phase curve and performing angular filtering; that is, uniformly sampling phase data along the angular direction on the set radius circle of the two-dimensional phase distribution map output by the neural network to form an angle-phase sequence, realizing phase consistency constraints based on angular priors; specifically, firstly, performing polar coordinate transformation on the dynamic weighted fusion output to convert the phase distribution... Transform to polar coordinates ,in, Indicates radial direction, Indicate the angular direction; then, in Angle-phase curve sampling is performed in the direction of angular direction, with a sampling change angle of 0.01 and a sampling radius of 266, resulting in an angle-phase sequence. Angle filtering is then applied to retain angle information while suppressing other redundant components and noise. S2. Mapping to the global two-dimensional plane achieves reconstruction; that is, based on the polar angle mapping relationship, the angle-phase sequence is interpolated and reconstructed to the global two-dimensional phase distribution, preserving the main angular features while effectively suppressing redundant information. Specifically, the filtered angle-phase curve is interpolated and reconstructed globally to obtain the optimized... Finally, the results are mapped back to a Cartesian coordinate system as the final phase distribution of the control grating.

[0016] 4. Joint Optimization Training: The network inputs the amplitude, phase, and corresponding OAM mode spectrum of the target beam. The network output is the phase distribution of the modulation grating, with dimensions consistent with the input light field. The optimized modulation phase grating distribution, after diagonal filtering and reconstruction, is input into the diffraction propagation model to calculate its modulated light field OAM spectrum distribution. The error between the obtained mode spectrum and the target mode spectrum is measured and used as a loss function constraint for network training. Gradient descent is adopted, with the following hyperparameter settings. The Adam optimizer is used to optimize the gradient and momentum during training, with a learning rate of 0.01 cycles, a batch size of 8, and 800 iterations on the entire training set. An early stopping mechanism is introduced. During iterative training, an early termination callback function is used to monitor the model training status in real time to prevent overfitting. This invention uses mean square error (MSE) as the loss function to constrain the difference between the model's predicted values ​​and the true values.

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0018] Example 1: Equal-intensity multimode vortex beam manipulation using the method of the present invention In this embodiment, a target multimode vortex beam is randomly selected, with OAM mode orders of [-9, -7, -3, -1, 3, 5, 7, 9], and the relative intensity ratios of each OAM mode are equal. The two-dimensional phase distribution and its modulated optical field spectrum distribution before and after optimization using the angular filtering reconstruction of this invention, i.e., the initial values ​​of the network constraint parameters, are as follows: Figure 3 As shown. The OAM spectrum of its modulated optical field was measured and compared with the target OAM spectrum, as shown. Figure 4As shown, the optimized OAM mode orders measured by the modulated light field are [-9, -7, -3, -1, 3, 5, 7, 9]. After training, the OAM mode spectrum measured by the modulated light field has high consistency with the target mode spectrum, and each target mode can be accurately reconstructed. The mean square error (MSE) of the mode spectrum is 1.31 × 10⁻⁶. -5 This embodiment demonstrates that the present invention effectively improves the initial value of the network constraint for phase modulation, thereby significantly enhancing the generation accuracy of pure phase modulation gratings.

[0019] Example 2: Modulation of non-uniform intensity multimode vortex beam using the method of the present invention In this embodiment, a target multi-OAM mode multiplexed beam is randomly selected, with OAM mode orders of [-8, -6, -4, -2, 2, 4, 6, 8] and corresponding normalized relative intensities of [0.12, 0.11, 0.15, 0.12, 0.16, 0.10, 0.09, 0.15]. The sum of the relative intensities of each mode is 1, and the energy distributions of each mode are different. The proposed angular filtering reconstruction neural network is used for training. After training, the generated pure phase modulation grating is used to modulate the target beam, and the OAM mode spectrum of the resulting light field is calculated. Figure 5 As shown, after angular filtering reconstruction optimization, the relative intensities of each orbital angular momentum mode can be well recovered to the target value, and the generated mode spectrum maintains a high degree of consistency with the target mode spectrum. Compared with the network without the angular filtering reconstruction module, the leakage of non-target modes in the mode spectrum is further reduced, the mean square error of the mode spectrum is significantly reduced, and the mean square error (MSE) between the generated OAM spectrum and the target OAM spectrum is 4.07 × 10⁻⁶. -5 The results further demonstrate that the angular filtering reconstruction method proposed in this invention can effectively improve the learning ability of neural networks for energy distributions of different modes and has good generalization performance. This embodiment shows that this invention is not only applicable to equal-intensity mode multiplexing, but also applicable to phase modulation of multimode vortex beams with arbitrary energy distributions.

[0020] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A neural network-based multimode vortex beam phase modulation method based on angular filtering reconstruction, characterized in that, The process includes the following steps: S1. Acquire the complex amplitude information corresponding to the target multimode vortex beam and input it into a phase modulation neural network to obtain the phase distribution through feature extraction; S2. Perform angular filtering on the phase distribution to obtain an angular-phase sequence; S3. Perform two-dimensional phase reconstruction based on the acquired angular-phase sequence to obtain the reconstructed phase distribution and calculate the orbital angular momentum spectrum of the corresponding modulated light field. S4. Determine the loss function based on the orbital angular momentum pattern spectrum and the target orbital angular momentum pattern spectrum, and update the neural network parameters according to the loss function.

2. The method according to claim 1, characterized in that, The angular filtering includes: converting the phase distribution into polar coordinates; acquiring phase data along the angular direction on a circle corresponding to a preset radius; and forming an angle-phase sequence based on the acquired phase data. This can significantly improve the effectiveness of multimode vortex beam spectrum information used for supervision and constraint by explicitly introducing angular sampling-based filtering reconstruction in neural network training.

3. The method according to claim 1, characterized in that, The two-dimensional phase reconstruction includes establishing a polar angle mapping relationship based on the angle-phase sequence; interpolating the angle-phase sequence to obtain a polar coordinate phase distribution; and obtaining the reconstructed phase distribution based on the coordinate mapping relationship between polar coordinates and rectangular coordinates, effectively suppressing redundant information while retaining the angular principal features.

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