End-to-end multi-dimensional holographic metasurface design method and system and electronic equipment

Abstract

The invention provides an end-to-end multi-dimensional holographic metasurface design method and system and electronic equipment. The method comprises the steps of polarization dimension expansion construction of a super-atom library, continuous microprocessing of the super-atom library, multi-dimensional randomization construction of an initial metasurface, holographic image reconstruction of a dual-polarization light field, gradient solution and optimization of multi-dimensional parameters, and design of a polarization sensitive loss function. And dynamically adjusting the adaptive weight of the channel and carrying out full-dimensional end-to-end reverse optimization. According to the method, the direct multi-dimensional mapping relation between the metasurface and the reconstructed image is established, multi-dimensional parameter updating of the metasurface is guided through the loss function, dependence on traditional hologram calculation is thoroughly eliminated, and a multi-dimensional design link is greatly simplified. Meanwhile, the spatial dimension distribution of the metasurface is accurately optimized, multi-wavelength and multi-channel multi-dimensional holographic image coding can be completed only by adopting a simple rectangular structure, dependence on a complex super-atom structure is not needed, and high performance of multi-dimensional information processing is ensured while the manufacturing complexity is reduced.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optics and optical holography, and more specifically, to an end-to-end multidimensional holographic metasurface design method, system, and electronic device. Background Technology

[0002] Multidimensional holographic display technology, with its outstanding advantages in multidimensional security, intuitive multidimensional visualization, and low power consumption, is bringing revolutionary progress to next-generation multidimensional information storage and encryption technologies. The core value of this technology lies in breaking the limitations of traditional single-dimensional information processing, enabling the parallel carrying and interaction of multidimensional information on the same physical medium. In the innovation process of next-generation information storage and encryption technologies, multidimensional holographic display technology is occupying a key position due to its unique advantages. It not only achieves cross-dimensional security protection and intuitive multidimensional information presentation, but also possesses low power consumption characteristics, effectively overcoming the performance bottlenecks of traditional single-dimensional technologies.

[0003] However, current holographic metasurface reuse methods based on traditional physics knowledge face significant challenges in multidimensional expansion due to their high requirements for design expertise, computational resources, and fabrication technology. Traditional solutions employ a multi-metaatomic structure spatial reuse mode, which not only requires the design of a corresponding metaatomic structure for each working wavelength, leading to an exponential increase in structural complexity with dimensional expansion, but also generates severe crosstalk in multi-wavelength, multidimensional superposition scenarios, greatly limiting the efficient transmission and storage of multidimensional information.

[0004] Currently, holographic metasurface reuse technology based on traditional physical theories encounters significant obstacles when expanding to multiple dimensions. On the one hand, this technology places extremely high demands on the professional capabilities of designers, the computing power of computing systems, and precision manufacturing processes. On the other hand, traditional multi-meta-atom spatial reuse strategies require the design of dedicated metaatoms for different wavelengths and polarization states. This not only causes the structural complexity to increase explosively with the increase of dimensions, but also causes strong crosstalk in multi-dimensional scenarios with multiple wavelengths and dual polarizations, which seriously restricts the transmission efficiency and storage security of multi-dimensional information. Summary of the Invention

[0005] This invention addresses the technical problems existing in the prior art by providing an end-to-end multidimensional holographic metasurface design method, system, and electronic device. By precisely optimizing the spatial dimension distribution of metasurface metaatoms, this invention can complete multi-wavelength, multi-channel multidimensional holographic image encoding using only a simple rectangular structure, without relying on complex metaatomic structures. This reduces manufacturing complexity while ensuring high performance in multidimensional information processing.

[0006] According to a first aspect of the present invention, an end-to-end multidimensional holographic metasurface design method is provided, comprising the following steps: Using silicon nanorods on a silica substrate as basic units, the phase and transmittance corresponding to different wavelengths were extracted to construct a superatomic library with wavelength-polarization-phase-transmittance response. By correlating the length and width parameters of the superatom with the phase and transmittance response, the superatom is made continuously differentiable. Within a preset range, initial values ​​for length and width are assigned to each superatom, and the nanostructures are arranged randomly to generate a random initial metasurface. Starting with the initialization of the metasurface, a reconstructed image of the dual-polarization light field is constructed by utilizing the diffraction behavior of the metasurface; Calculate the partial derivatives of the reconstructed image with respect to the length and width parameters of each superatom, determine the direction of parameter adjustment, and complete the directional optimization of the metasurface parameters; Based on the root mean square error between the target image and the reconstructed image, the structural similarity index and polarization isolation loss term are fused to construct a total loss function with multi-dimensional constraints; The weights of each branch are optimized in real time based on the total loss function value, and dynamic adaptive weight adjustment is performed. By minimizing the total loss function to drive the update of metasurface structure parameters, an end-to-end inverse optimization from the target image to the metasurface physical structure is established.

[0007] Based on the above technical solution, the present invention can also be improved as follows.

[0008] Optionally, the step of extracting the phase and transmittance at different wavelengths based on silicon nanorods on a silicon dioxide substrate includes: A full-dimensional simulation was conducted using the finite-time difference method. The simulation simultaneously introduced the perpendicular incident conditions of X-polarization and Y-polarization. Wavelength and polarization state were used as primary indices, and superatomic structure parameters were used as secondary indices. The electric field distribution, magnetic field distribution and light propagation characteristics of the two polarized lights under different wavelengths were analyzed, and the phase response and transmittance data of each wavelength-polarization combination were accurately extracted.

[0009] Optionally, the continuous differentiability processing of superatoms includes: Using the length and width of the superatoms as two-dimensional structural coordinates and mapping the wavelength and polarization state as additional dimensional parameters, a four-dimensional function space of "structural parameters-wavelength-polarization" is constructed. With phase and transmittance as function output values, a bicubic interpolation polynomial is constructed through the phase, transmittance, and first-order partial derivatives corresponding to adjacent wavelength points and different polarizations.

[0010] Optionally, the step of arranging the nanostructures in a random manner to generate a random initial metasurface includes: For each superatom in the metasurface array, a pseudo-random number generator is used to assign initial values ​​for length and width within a preset range, and then an initial polarization response tendency is assigned through random tags. Optionally, the process of constructing a reconstructed image of a dual-polarization light field, starting from the initialization of the metasurface and utilizing its diffraction behavior, includes: The polarization-sensitive angular spectral method is adopted, and the polarization state propagation matrix is ​​introduced to simulate the diffraction behavior of X-polarized and Y-polarized light fields respectively. The light field distribution of X-polarized and Y-polarized wavelength-polarization combination is calculated by fast Fourier transform, and the light field distribution is converted into intensity distribution to obtain the reconstructed image of the dual-polarized light field.

[0011] Optionally, the calculation of the partial derivatives of the reconstructed image with respect to each superatomic length and width parameter, and the determination of the parameter adjustment direction, includes: Based on the root mean square error between the target image and the reconstructed image, the partial derivatives of the total loss function of the reconstructed image with respect to the length and width parameters of each superatom are calculated to determine the direction of parameter adjustment. The influence of small changes in structural parameters on the phase matching degree in the dual polarization state is quantitatively analyzed, thereby achieving directional optimization of metasurface parameters.

[0012] Optionally, the calculation of the partial derivatives of the reconstructed image with respect to each superatom's aspect ratio includes: A two-dimensional automatic differentiation technique based on the backpropagation algorithm is adopted. First, the derivative of the loss function of each channel with respect to the structural parameters is solved separately. Then, the derivatives are fused according to the weight allocation to obtain the total derivative. Based on the total derivative, the length, width and polarization response adaptation parameters of the superatom are synchronously adjusted along the gradient in the opposite direction.

[0013] According to a second aspect of the present invention, an end-to-end multidimensional holographic metasurface design system is provided, comprising: The polarization dimension extension construction module of the superatomic library is used to extract the phase and transmittance corresponding to different wavelengths based on silicon nanorods on a silicon dioxide substrate, and construct a superatomic library with wavelength-polarization-phase-transmittance response. The continuous differentiable processing module of the superatom library is used to correlate the length and width parameters of superatoms with phase and transmittance response, and to perform continuous differentiable processing on superatoms. The multidimensional randomization construction module of the initial metasurface is used to assign initial values ​​of length and width to each superatom within a preset range, arrange the nanostructures in a random form, and generate a random initial metasurface. The holographic image reconstruction module for dual-polarized light fields is used to construct a reconstructed image of a dual-polarized light field by starting with the initialization of the metasurface and utilizing the diffraction behavior of the metasurface. The gradient calculation and optimization module for multi-dimensional parameters is used to calculate the partial derivatives of the reconstructed image with respect to the length and width parameters of each superatom, determine the direction of parameter adjustment, and complete the directional optimization of the metasurface parameters. The polarization-sensitive loss function construction module is used to construct a total loss function with multi-dimensional constraints by fusing the structural similarity index and polarization isolation loss term based on the root mean square error between the target image and the reconstructed image. The channel adaptive weight dynamic adjustment module is used to optimize the weights of each branch in real time based on the total loss function value and perform dynamic adaptive weight adjustment. The full-dimensional end-to-end inverse optimization module is used to drive the update of metasurface structure parameters by minimizing the total loss function, and to establish an end-to-end inverse optimization from the target image to the metasurface physical structure.

[0014] According to a third aspect of the present invention, an electronic device is provided, including a memory and a processor, the processor being configured to execute a computer program stored in the memory to implement the steps of an end-to-end multidimensional holographic metasurface design method.

[0015] The technical effects and advantages of this invention are as follows: This invention provides an end-to-end multidimensional holographic metasurface design method, system, and electronic device. This method, through synergistic optimization of the spatial arrangement and polarization response characteristics of metasurface metaatoms, can efficiently encode 24-channel multidimensional holographic images under multi-wavelength and dual-polarization combinations, even using simple rectangular metaatoms. Furthermore, by establishing a direct multidimensional mapping relationship between the metasurface and the reconstructed image, and guiding the multidimensional parameter updates of the metasurface through a loss function, it completely eliminates the dependence on traditional hologram calculations, significantly simplifying the multidimensional design process. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the operation of the multidimensional holographic metasurface provided in an embodiment of the present invention; Figure 2 A schematic diagram of superatoms and superatomic libraries provided in an embodiment of the present invention; Figure 3 The superatomic initialization arrangement provided in the embodiments of the present invention constitutes a random metasurface pattern; Figure 4 This is a flowchart of the end-to-end multidimensional holographic metasurface algorithm optimization provided in an embodiment of the present invention; Figure 5 The loss value curves of the two polarizations and the total loss during the optimization stage of the model provided in the embodiment of the present invention; Figure 6 This is a diagram showing the target image and the reconstructed image after model optimization, provided in an embodiment of the present invention. Figure 7This is a schematic diagram of the metasurface structure output by the model provided in an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Understandably, given the deficiencies in the background technology, this invention proposes an end-to-end multidimensional holographic metasurface design method, comprising the following steps: Step 1: Using silicon nanorods on a silica substrate as basic units, extract the phase and transmittance corresponding to different wavelengths to construct a superatomic library with wavelength-polarization-phase-transmittance response; In this embodiment, silicon nanorods on a silica substrate are used as the basic unit to determine the periodic parameters, height specifications, and length and width parameter ranges of the superatoms. For X / Y dual-polarized light in multi-wavelength scenarios, the corresponding phase response and transmittance characteristics are extracted and integrated to form a superatomic library covering the two-dimensional "wavelength-polarization" dimension.

[0019] Specifically, in this embodiment of the invention, a 24-channel information carrier is used as the basic unit. To obtain the complete optical response of superatoms under multiple wavelengths and dual polarizations, the extraction of phase and transmittance corresponding to different wavelengths using silicon nanorods on a silicon dioxide substrate as the basic unit includes: A full-dimensional simulation was conducted using the finite-time difference method. The simulation simultaneously introduced X-polarization (transverse electric wave TE mode) and Y-polarization (transverse magnetic wave TM mode) perpendicular incident conditions to ensure coverage of practical application scenarios with 24 channels (multi-wavelength × 2 polarization).

[0020] like Figure 1 The diagram shows a schematic of the operation of a multidimensional holographic metasurface. The metasurface can generate holographic images with multiple channels under multiple wavelengths and polarizations. By precisely controlling simulation parameters, the electric field distribution, magnetic field distribution, and light propagation characteristics corresponding to two polarized lights at different wavelengths are analyzed, and the phase response and transmittance data for each wavelength-polarization combination are accurately extracted.

[0021] In wavelength selection, representative discrete wavelengths were chosen based on the spectral coverage requirement of 24 channels to ensure coverage of the full spectral range expected for metasurface operation. The polarization dimension strictly distinguishes response differences under different phases to avoid polarization crosstalk. The extracted four-dimensional data of "wavelength-polarization-phase-transmittance" are integrated to construct a metaatom library with a two-dimensional index.

[0022] Using wavelength and polarization state as primary indexes and superatomic structure parameters as secondary indexes, a storage structure for efficient querying and retrieval is formed, providing basic unit support for 24-channel information encoding.

[0023] like Figure 2 The diagram shows the superatoms and superatomic library. The superatoms are based on a SiO2 substrate, and the overall structure is a rectangular Si structure, where W is the width, L is the length, and H is the height. A phase and transmittance database is constructed by scanning W and L.

[0024] Step 2: Correlate the length and width parameters of the superatom with the phase and transmittance response to perform continuous differentiability processing on the superatom; It should be noted that although the discrete superatomic library contains multi-wavelength and dual-polarization information, its discreteness can cause interruptions in the calculation of derivatives between the polarization and wavelength dimensions during gradient optimization, affecting the continuity of the 24-channel optimization. Therefore, a bi-dimensional bicubic interpolation method is employed to simultaneously process the wavelength- and polarization-related superatomic parameters for continuity.

[0025] In this embodiment, the length and width parameters of the superatom are mapped to a two-dimensional coordinate grid, and the phase and transmittance responses are used as correlation function values ​​to perform continuous-differentiable processing on the superatom. This continuous-differentiable processing eliminates computational gaps caused by discrete characteristics, ensuring the differentiability of parameter changes under dual-polarization states and providing a continuous mathematical foundation for multi-dimensional gradient optimization.

[0026] The continuous differentiable processing of superatoms includes: By using the length and width of superatoms as two-dimensional structural coordinates and mapping wavelength and polarization state as additional dimensional parameters, a four-dimensional function space of "structural parameters-wavelength-polarization" is constructed. With phase and transmittance as function outputs, a bicubic interpolation polynomial is constructed using four sets of superatomic data (phase, transmittance, and first-order partial derivatives corresponding to different polarizations) at adjacent wavelengths and in dual polarization modes. This bicubic interpolation polynomial can calculate the superatomic optical response under any combination of "length-width-wavelength-polarization," realizing the continuity and differentiability of the superatomic library in the three dimensions of structure, wavelength, and polarization, laying the mathematical foundation for 24-channel collaborative gradient optimization.

[0027] Step 3: Assign initial values ​​for length and width to each superatom within a preset range, arrange the nanostructures randomly, and generate a random initial metasurface; It should be noted that the initial metasurface construction needs to consider the structural diversity in both the "wavelength-polarization" dimensions, providing sufficient parameter exploration space for 24-channel optimization. The random arrangement of nanostructures to generate a random initial metasurface includes: For each superatom in the metasurface array, a pseudo-random number generator is used to assign initial values ​​for length and width within a preset range. By enhancing the randomness of the spatial distribution of the initial parameters, a full exploration of the "wavelength-polarization-space" three-dimensional parameter space is achieved, thereby improving the search efficiency for the global optimum.

[0028] In the assignment of superatomic parameters, the random value ranges for length and width are set to be consistent with the phase and transmittance database constructed by scanning W and L in step 1. Simultaneously, considering the dual polarization characteristics, a pseudo-random number generator is used to attach a "polarization response adaptability tag" to each superatom. This ensures that the initial structure can quickly adapt to the response requirements of X and Y polarization in subsequent optimizations.

[0029] Figure 3 illustrates the random arrangement of nanostructures to generate randomized initial metasurfaces. Specifically, for each superatom in the metasurface array, initial length and width values ​​are first randomly generated within a preset range, and then its initial polarization response tendency is assigned through random tags. This dual random allocation method of "structural parameters + polarization tendency" can fully explore the metasurface structural parameter space and cover the polarization dimension requirements of 24 channels, avoiding the initial structure being limited to a single polarization characteristic, and providing more starting points for subsequent 24-channel crosstalk-free optimization.

[0030] Step 4: Starting with the initialization of the metasurface, construct a reconstructed image of the dual-polarization light field through the diffraction behavior of the metasurface; In this embodiment, the initial metasurface is introduced into the gradient descent optimization framework to accurately simulate the diffraction behavior of beams with different polarization states on the metasurface, generating a reconstructed image of the dual polarization light field.

[0031] Specifically, the light field propagation process was calculated for each of the 24 channels (multi-wavelength × dual-polarization combination). By combining the angular spectrum method and Fresnel propagation theory, the diffraction behavior of beams with different polarization states on the metasurface was accurately simulated, generating reconstructed images for each channel.

[0032] In the optimization process, to accurately calculate the propagation and transformation of multi-wavelength, dual-polarized light fields on the metasurface, the process of constructing a reconstructed image of the dual-polarized light field, starting from the initialization of the metasurface and utilizing its diffraction behavior, includes: A polarization-sensitive angular spectral method is adopted. Based on the traditional angular spectral method, a polarization state propagation matrix is ​​introduced to separate the independent propagation processes of X-polarized and Y-polarized light fields, thus avoiding polarization crosstalk.

[0033] Furthermore, after inputting the initial metasurface structure parameters into the optimization algorithm, the optical field distribution for each wavelength-polarization combination was calculated using Fast Fourier Transform (FFT) for each of the 24 channels (multi-wavelength × TE / TM). First, the phase modulation of the metasurface to specific polarized light was solved, and then Fresnel propagation was used to supplement the optical field attenuation and phase delay, ultimately obtaining the optical field distribution for each channel. The optical field distribution of each channel was converted into an intensity distribution, forming 24 independent reconstructed images. Simultaneously, the influence of the superatom length, width, and polarization response parameters on the image quality of each channel was analyzed, providing a directional basis for subsequent parameter optimization.

[0034] Step 5: Calculate the partial derivatives of the reconstructed image with respect to the length and width parameters of each metaatom, determine the direction of parameter adjustment, and complete the directional optimization of metasurface parameters; In this embodiment, calculating the partial derivatives of the reconstructed image with respect to each superatom's length and width parameters, and determining the direction of parameter adjustment, includes: Based on the root mean square error between the target image and the reconstructed image, the partial derivatives of the total loss function of the reconstructed image with respect to the length and width parameters of each superatom are calculated to determine the direction of parameter adjustment. The influence of small changes in structural parameters on the phase matching degree in the dual polarization state is quantitatively analyzed, thereby achieving directional optimization of metasurface parameters.

[0035] In this embodiment, by calculating the partial derivative of the total loss function of the 24-channel reconstructed image with respect to the length and width parameters of each superatom, the direction of parameter adjustment is determined by the sign of the derivative, and the influence of small changes in structural parameters on the phase matching degree in the dual polarization state is quantitatively analyzed, thereby achieving directional optimization of metasurface parameters.

[0036] To achieve 24-channel wavelength-polarization co-optimization, it is necessary to calculate the total loss function for all channel reconstructed images, including the partial derivatives with respect to the length, width, and polarization response parameters of each superatom. The total loss function comprehensively reflects the differences between the 24 reconstructed images and the target image, and its derivatives must simultaneously reflect the direction and extent of the influence of structural parameter changes on different wavelengths and polarization channels.

[0037] During the calculation, a two-dimensional automatic differentiation technique was employed. Based on the backpropagation algorithm, the derivative of the loss function of each channel with respect to the structural parameters was first calculated separately. Then, the derivatives were fused according to the weight allocation of the 24 channels (subsequent step 7) to obtain the total derivative. Based on the total derivative, the length, width, and polarization response adaptation parameters of the superatom were synchronously adjusted along the gradient in the opposite direction. For regions with large errors in the TE mode channels, the TE polarization response parameters of the superatom were optimized in particular. For channels with significant wavelength shifts, the size of the superatom was adjusted to match the target wavelength phase, achieving crosstalk-free optimization of the 24 channels.

[0038] Optimize the flowchart as follows Figure 4As shown, the initial metasurface can generate a multidimensional hologram. The multidimensional hologram is compared with the target image, and a loss function is used to comprehensively reflect the differences between the reconstructed image and the target image. Gradient descent is used to update the W and L values ​​of each superatom, forming a new metasurface. This process continues until the error requirement is met, generating the final metasurface structure.

[0039] Step 6: Based on the root mean square error between the target image and the reconstructed image, fuse the structural similarity index and the polarization isolation loss term to construct a total loss function with multi-dimensional constraints; In this embodiment, the root mean square error (RMSE) between the target image and the 24-channel reconstructed image within the region of interest is used as a basis, and the structural similarity index (SSIM) is fused to enhance the image detail matching. A polarization isolation loss term is specifically introduced (through L1+L2 regularization) to suppress crosstalk noise between different polarization channels, constructing a multi-dimensional constrained total loss function.

[0040] Adjusting the superatomic parameters may affect the phase of a certain wavelength channel in the TE mode, while simultaneously avoiding crosstalk to other wavelength channels in the TM mode. Therefore, this embodiment of the invention reduces external noise by minimizing the output intensity in non-target regions. This ensures effective suppression of background noise, improves the overall sharpness of the reconstructed image, and reduces crosstalk. By combining the Structural Similarity Index (SSIM) and Root Mean Square Error (RMSE) for complementarity, the RMSE quantifies objective errors at the pixel level, while the SSIM measures structural similarity consistent with human vision. This combination overcomes the limitations of a single metric.

[0041] In this embodiment, the total loss function formula for multi-dimensional constraints can be expressed as:

[0042] Where α, β, and γ are the weighting factors for each loss. It is the root mean square error. It is a structural similarity error. It is noise loss.

[0043] To address the multidimensional characteristics of the 24-channel image with both wavelength and polarization, a polarization-wavelength dual-constraint loss function is designed. The core objective is not only to minimize the differences in single-channel images, but also to suppress polarization crosstalk and wavelength crosstalk between channels.

[0044] The polarization-wavelength dual-constraint loss function includes: the base layer, the intermediate layer, and the top layer; more specifically, The base layer is based on the root mean square error (RMSE) of the region of interest for 24 channels: for each wavelength-polarization channel, the RMSE of the reconstructed image Ir (λ,pol,x,y) and the target image It (λ,pol,x,y) is calculated separately (λ is the wavelength and pol is the polarization state) to ensure the accuracy of the single-channel values.

[0045] The intermediate layer introduces a polarization-sensitive structural similarity index (SSIM): based on the traditional SSIM, a polarization state matching weight is added. If the polarization state of the reconstructed image deviates significantly from the polarization state of the target image, the P-SSIM value will still decrease even if the brightness and contrast are similar, thus guiding the optimization process to focus on polarization state fidelity.

[0046] Top-level channel isolation noise loss is added: Through L1+L2 regularization, optical field leakage from non-target polarization channels (such as crosstalk between polarization channels) is suppressed on the one hand, and energy interference from non-target wavelength channels is reduced on the other hand, ensuring the independent operation of 24 channels. This ultimately forms a total loss function of "single-channel RMSE + SSIM + channel isolation loss," achieving comprehensive constraint on multi-dimensional errors. The loss curves output by the model during the optimization phase, and the loss curves for each polarization after 5000 iterations, are shown below. Figure 5 As shown.

[0047] Step 7: Optimize the weights of each branch in real time based on the total loss function value, and perform dynamic adaptive weight adjustment; like Figure 6 The images shown are target images at different wavelengths and polarizations, as well as a multidimensional holographic image generated by a metasurface. To address the error differences in different wavelengths and polarization channels across the 24 channels, the dynamic adaptive weight adjustment based on the total loss function value for real-time optimization of each branch weight includes: The weights of each branch are optimized in real time based on the total loss function value. A dynamic balancing strategy is implemented to address the error differences between the dual polarization channels. In the multi-wavelength dimension, weight coefficients are assigned according to the importance of the channels and combined for optimization to ensure a balanced improvement in the overall performance of the 24 channels.

[0048] A three-dimensional adaptive weight adjustment scheme is constructed, with weight dimensions covering "wavelength importance - polarization mode priority - channel error degree"; among which, Wavelength dimension: Assign higher weights to wavelength channels in spectrally sensitive regions (such as wavelengths with high information density) to ensure the optimization priority of core wavelength channels; Polarization dimension: For channels with high risk of polarization crosstalk (such as wavelengths with small response differences under dual polarization), increase the weight of P-SSIM and channel isolation loss to enhance polarization isolation; Error dimension: In the early stage of optimization, the weight of the root mean square error (RMSE) is increased for channels with large RMSE to quickly reduce the basic error; in the later stage of optimization, when the RMSE drops below the threshold, the weight of the structural similarity index (SSIM) and channel isolation loss is automatically increased to improve the visual effect of the image and channel independence.

[0049] Taking actual optimization as an example: In the initial stage, if the root mean square error (RMSE) of a certain wavelength channel reaches 0.3 (threshold 0.1), the weight is automatically increased to 0.6 to prioritize reducing the error of that channel; when the root mean square error (RMSE) drops to 0.08, the weight is reduced to 0.3, and at the same time the channel isolation loss weight is increased from 0.2 to 0.4 to suppress crosstalk between its adjacent wavelength channels.

[0050] Step 8: Drive the metasurface structure parameter update by minimizing the total loss function, and establish an end-to-end inverse optimization from the target image to the metasurface physical structure.

[0051] In this embodiment, the metasurface structure parameters are directly updated by minimizing the total loss function, establishing an end-to-end inverse optimization from the "target image set" to the "metasurface physical structure". This process simultaneously optimizes the dual polarization response characteristics under multiple wavelengths, achieving crosstalk-free information encoding of 24 independent channels, and completing the multi-dimensional inverse design of the holographic metasurface. Specifically, the inverse optimization involves directly outputting the metasurface structure based on a given output image.

[0052] The core of end-to-end inverse optimization is to directly update the "structure-polarization-wavelength" correlation parameters of the metasurface by minimizing the total loss function, thereby achieving a direct mapping from 24 target images to the physical structure of the metasurface.

[0053] The optimization algorithm employs a multi-dimensional Adam optimizer: based on the traditional Adam algorithm, adaptive learning rates are set for wavelength and polarization dimensions respectively. A smaller learning rate is used for wavelength-sensitive parameters (such as superatom size) to avoid wavelength shift; a larger learning rate is used for polarization response parameters (such as the polarization adaptation label of the superatom) to quickly improve polarization fidelity. After calculating the gradient of the total loss function with respect to the superatom length, width, and polarization response parameters, the parameters are updated according to the rule of "wavelength grouping - polarization classification".

[0054] For TE / TM channels at the same wavelength, the metaatomic size is synchronously adjusted to match the wavelength phase, and then the polarization response parameters are fine-tuned to suppress crosstalk. For channels at different wavelengths, the size is adjusted differently according to the weight allocation to avoid phase conflicts between wavelengths. Through iterative updates, the difference between the 24-channel reconstructed image of the metasurface and the target image is gradually reduced, ultimately achieving the reverse design of a 24-channel holographic metasurface with "no wavelength shift, no polarization crosstalk, and high image fidelity." Figure 7 The image shows the overall metasurface structure output by the computational model. The array has 2000x2000 unit structures, with a size of 600 um x 600 um.

[0055] In summary, the end-to-end multi-wavelength holographic metasurface design method proposed in this invention provides a novel path to simplify the multidimensional design process and overcome dimensional limitations. This method, through synergistic optimization of the spatial arrangement and polarization response characteristics of metasurface metaatoms, can efficiently encode 24-channel multidimensional holographic images under multi-wavelength and dual-polarization combinations, even using simple rectangular metaatoms. This design eliminates the need for complex metaatomic structures, significantly reducing manufacturing difficulty while maintaining high stability and accuracy in multidimensional information processing. More importantly, this scheme establishes a three-in-one multidimensional mapping mechanism of "wavelength-polarization-space" between the metasurface and the reconstructed image. By using a loss function to drive the dynamic adjustment of multidimensional parameters of the metasurface, it completely eliminates the traditional hologram calculation step, significantly simplifying the multidimensional design process.

[0056] Verification has shown that the multi-wavelength multiplexed holographic metasurface developed based on this scheme successfully achieved stable operation of 24 independent dimensional channels with dual polarization. 24 different sets of information can be loaded in parallel on the same metasurface, and the reconstruction process is free of crosstalk, fully demonstrating the superior performance of simple superatomic structures in the field of multidimensional high-density information multiplexing. This technological achievement not only provides core support for upgrading displays to multidimensional stereoscopic displays, but also promotes a dimensional-level increase in optical data storage capacity. Furthermore, it can create a multidimensional key system of "wavelength + polarization + space" for information encryption, opening up a new direction for innovative development in the field of intelligent photonics.

[0057] According to a second aspect of the present invention, an end-to-end multidimensional holographic metasurface design system is provided, comprising: The polarization dimension extension construction module of the superatomic library is used to extract the phase and transmittance corresponding to different wavelengths based on silicon nanorods on a silicon dioxide substrate, and construct a superatomic library with wavelength-polarization-phase-transmittance response. The continuous differentiable processing module of the superatom library is used to correlate the length and width parameters of superatoms with phase and transmittance response, and to perform continuous differentiable processing on superatoms. The multidimensional randomization construction module of the initial metasurface is used to assign initial values ​​of length and width to each superatom within a preset range, arrange the nanostructures in a random form, and generate a random initial metasurface. The holographic image reconstruction module for dual-polarized light fields is used to construct a reconstructed image of a dual-polarized light field by starting with the initialization of the metasurface and utilizing the diffraction behavior of the metasurface. The gradient calculation and optimization module for multi-dimensional parameters is used to calculate the partial derivatives of the reconstructed image with respect to the length and width parameters of each superatom, determine the direction of parameter adjustment, and complete the directional optimization of the metasurface parameters. The polarization-sensitive loss function construction module is used to construct a total loss function with multi-dimensional constraints by fusing the structural similarity index and polarization isolation loss term based on the root mean square error between the target image and the reconstructed image. The channel adaptive weight dynamic adjustment module is used to optimize the weights of each branch in real time based on the total loss function value and perform dynamic adaptive weight adjustment. The full-dimensional end-to-end inverse optimization module is used to drive the update of metasurface structure parameters by minimizing the total loss function, and to establish an end-to-end inverse optimization from the target image to the metasurface physical structure.

[0058] It is understood that the end-to-end multidimensional holographic metasurface design system provided by the present invention corresponds to the end-to-end multidimensional holographic metasurface design method provided in the foregoing embodiments. The relevant technical features of the end-to-end multidimensional holographic metasurface design system can be referred to the relevant technical features of the end-to-end multidimensional holographic metasurface design method, and will not be repeated here.

[0059] According to a third aspect of the present invention, an electronic device is provided, comprising: a processor, a communications interface, a memory, and a communication bus, wherein the processor, the communications interface, and the memory communicate with each other via the communication bus. The processor can invoke logical instructions in the memory to execute the implementation steps of the end-to-end multidimensional holographic metasurface design method described above.

[0060] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0061] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0062] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An end-to-end multi-dimensional holographic metasurface design method, characterized in that, The method comprises the following steps: Taking silicon nanorods on a silicon dioxide substrate as a basic unit, the phase and transmittance corresponding to different wavelengths are extracted respectively, and an atomic library of wavelength-polarization-phase-transmittance response is constructed; The length and width parameters of the super atom are associated with the phase and transmittance response, and the super atom is continuously processed to be differentiable; Initial values of length and width are assigned to each super atom within a preset range, and the nanometer structure is arranged in a random form to generate a random initial metasurface; Taking the initial metasurface as a starting point, the reconstruction image of the dual-polarized light field is constructed through the diffraction behavior of the metasurface; The partial derivatives of the reconstruction image with respect to the length and width parameters of each super atom are calculated, the parameter adjustment direction is judged, and the directional optimization of the metasurface parameters is completed; Based on the root mean square error between the target image and the reconstruction image, a multi-dimensional constraint total loss function is constructed by fusing the structural similarity index and the polarization isolation loss term; The total loss function value is used to optimize the branch weight in real time, and dynamic adaptive weight adjustment is performed; The total loss function is minimized to drive the update of the metasurface structure parameters, and an end-to-end reverse optimization from the target image to the physical structure of the metasurface is established.

2. The end-to-end metasurface design method of claim 1, wherein, The silicon nanorods on the silicon dioxide substrate are taken as the basic unit, and the phase and transmittance corresponding to different wavelengths are extracted respectively, including: The full-dimensional simulation is carried out by using the finite time domain difference method, and the X-polarized and Y-polarized perpendicular incidence conditions are introduced simultaneously in the simulation. The wavelength and polarization state are used as the first index, and the super atom structure parameters are used as the second index. The electric field distribution, magnetic field distribution and light propagation characteristics of the two polarized lights under different wavelengths are analyzed respectively, and the phase response and transmittance data under each wavelength-polarization combination are accurately extracted.

3. The method of claim 1, wherein, The continuous differentiable processing of the super atom includes: The length and width of the super atom are taken as two-dimensional structure coordinates, the wavelength and polarization state are mapped as additional dimension parameters, a four-dimensional function space of "structure parameter-wavelength-polarization" is constructed, the phase and transmittance are taken as function output values, a bicubic interpolation polynomial is constructed by using the phase, transmittance and first-order partial derivative corresponding to adjacent wavelength points and different polarizations.

4. The method of claim 1, wherein, The nanometer structure is arranged in a random form to generate a random initial metasurface, including: For each super atom in the metasurface array, the pseudo-random number generator is used to assign initial values of length and width within a preset range, and then the initial polarization response tendency is assigned through a random label.

5. The end-to-end metasurface design method of claim 1, wherein, Taking the initial metasurface as a starting point, the reconstruction image of the dual-polarized light field is constructed through the diffraction behavior of the metasurface, including: The polarization-sensitive angular spectrum method is used, the polarization state propagation matrix is introduced, the diffraction behavior of the X-polarized and Y-polarized light fields is simulated, the light field distribution of the X-polarized and Y-polarized wavelength-polarization combinations is calculated through fast Fourier transform, the light field distribution is converted into intensity distribution, and the reconstruction image of the dual-polarized light field is obtained.

6. The end-to-end metasurface design method of claim 1, wherein, The partial derivatives of the reconstruction image with respect to the length and width parameters of each super atom are calculated, and the parameter adjustment direction is judged. The total loss function of the reconstructed image is calculated based on the root mean square error of the target image and the reconstructed image, and the partial derivative of the total loss function of the reconstructed image with respect to each super atom length and width parameter is calculated, the parameter adjustment direction is judged, the influence degree of the slight change of the structure parameter on the phase matching degree in the dual polarization state is quantitatively analyzed, and the directional optimization of the super surface parameter is completed.

7. The end-to-end metasurface design method of claim 6, wherein, The calculation of the partial derivative of the reconstructed image with respect to each super atom length and width parameter comprises: The length, width and polarization response adaptation parameters of the super atom are synchronously adjusted in the reverse direction of the gradient based on the total derivative, by adopting a two-dimensional automatic differentiation technique based on a back propagation algorithm, solving the derivative of each channel loss function with respect to the structure parameter, and then performing derivative fusion according to the weight distribution to obtain the total derivative.

8. The end-to-end metasurface design method of claim 1, wherein, The real-time optimization of the weight of each branch based on the total loss function value comprises: In the wavelength dimension, the weight coefficients are allocated according to the importance of the channels for combination optimization, and the following three-dimensional adaptive weight adjustment scheme is constructed, comprising: Wavelength dimension: higher weight is allocated to the wavelength channel of the spectral sensitive region to ensure the optimization priority of the core wavelength channel; Polarization dimension: the weight of the structure similarity index and the channel isolation loss is increased for the channel with high polarization crosstalk risk to strengthen the polarization isolation; Error dimension: the weight of the root mean square error is increased for the channel with large root mean square error to reduce the basic error; when the root mean square error is below the threshold, the weight of the structure similarity index and the channel isolation loss is automatically increased to improve the image visual effect and channel independence.

9. An end-to-end multi-dimensional holographic metasurface design system, characterized by, Comprise: A polarization dimension extension module of the super atom library is used to take silicon nanorods on a silicon dioxide substrate as a basic unit, extract corresponding phases and transmittances under different wavelengths respectively, and construct a super atom library of wavelength-polarization-phase-transmittance response; A continuous differentiable processing module of the super atom library is used to associate the length and width parameters of the super atom with the phase and transmittance response, and perform continuous differentiable processing on the super atom; A multi-dimensional randomization construction module of the initial super surface is used to allocate initial values of the length and width to each super atom within a preset range, arrange the nano structure in a random form, and generate a random initial super surface; A holographic image reconstruction module of the dual polarization light field is used to take the initial super surface as a starting point, construct a reconstructed image of the dual polarization light field through the diffraction behavior of the super surface, and perform gradient calculation and optimization on the multi-dimensional parameters. A polarization sensitive loss function construction module is used to construct a total loss function with multi-dimensional constraints by fusing the structure similarity index and the polarization isolation loss term based on the root mean square error of the target image and the reconstructed image. A channel adaptive weight dynamic adjustment module is used to real-time optimize the weight of each branch based on the total loss function value, and perform dynamic adaptive weight adjustment. A full-dimensional end-to-end reverse optimization module is used to drive the super surface structure parameter update by minimizing the total loss function, and establish an end-to-end reverse optimization from the target image to the physical structure of the super surface. ​ 10. An electronic device, comprising: The computer program product comprises a memory and a processor, wherein the processor is configured to implement the end-to-end multi-dimensional holographic metasurface design method according to any one of claims 1 to 8 when executing the computer program stored in the memory.

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