An integrated photonic device electromagnetic field simulation method based on propagation physical priori and physical information constraint

Abstract

The application discloses a kind of integrated photonic device electromagnetic field simulation methods based on propagation physical priori and physical information constraint, belong to integrated photonics, artificial intelligence and the cross technical field of computational electromagnetics.For the problem that existing neural simulation method is difficult to consider whole field prediction accuracy and local output area response accuracy, the method obtains the relative permittivity distribution of the device to be simulated, input port excitation information and working wavelength parameters, and constructs spatial discretization input data;Through direction decoupling feature extraction, neural modal projection, state space propagation and cross-modal coherent coupling, the complex electromagnetic field distribution is reconstructed, and the electromagnetic response parameters such as output port power, light splitting ratio and relative phase are output;In the training stage, the network parameters are optimized by combining data supervision loss and physical constraint loss based on electromagnetic field control equation.The application can be used for the rapid simulation and performance evaluation of directional propagation type integrated photonic device.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of integrated photonics, artificial intelligence and computational electromagnetics, and specifically to a method for simulating the electromagnetic field of integrated photonic devices based on propagation physics priors and physical information constraints. Background Technology

[0002] The design and optimization of integrated photonic devices (such as multimode interferometer beam splitters and directional couplers) rely on extensive simulations of electromagnetic field distributions under different structures and excitation conditions.

[0003] Existing electromagnetic field simulation methods suffer from the following main problems: First, traditional numerical solution methods, such as the finite-difference time-domain (FDTD) and frequency-difference frequency-domain (FDFD) methods, typically solve Maxwell's equations through spatial discretization. While these methods offer high simulation accuracy, their computational complexity increases significantly with grid size, leading to high computational costs during large-scale parameter scanning and device optimization. Second, existing surrogate modeling methods based on neural networks, such as neural operator models based on frequency-domain feature learning, while improving inference speed, are prone to mismatches between global field accuracy and local port responses due to a lack of targeted modeling of electromagnetic wave directional propagation, multimode coupling, and boundary discontinuities. Furthermore, while existing physical information neural network methods enhance the physical consistency of the model by introducing physical control equations, they are still prone to propagation error accumulation in propagation-dominant electromagnetic field modeling tasks and have limited ability to model local port responses, failing to simultaneously balance computational efficiency, global field consistency, and the prediction accuracy of local port performance.

[0004] Therefore, there is an urgent need in this field for an integrated photonic device electromagnetic field simulation method that can balance computational efficiency, overall prediction accuracy, and local output region response accuracy. Summary of the Invention

[0005] In view of the above-mentioned problems in the existing technology, the purpose of this invention is to provide an electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints. This method addresses the problems of high computational cost and long computation cycle of existing numerical electromagnetic simulation methods, which make it difficult to meet the needs of rapid design and optimization of integrated photonic devices. It also solves the problem that existing neural network surrogate models lack targeted modeling of physical mechanisms such as electromagnetic wave propagation, multimode coupling, and boundary response, resulting in a difficulty in simultaneously achieving global field prediction accuracy and local output region response accuracy. Furthermore, it addresses the problem that existing intelligent simulation methods that introduce physical constraints are prone to propagation error accumulation during long-range propagation modeling, thereby achieving efficient and high-precision simulation of the electromagnetic field of integrated photonic devices and prediction of local output parameters.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for simulating the electromagnetic field of integrated photonic devices based on propagation physics priors and physical information constraints is proposed. This method integrates electromagnetic wave directional propagation physics priors into the network structure and performs joint training combined with physical information constraints to achieve efficient simulation of the electromagnetic field of integrated photonic devices. The specific steps include:

[0008] S100, Data Preprocessing: Obtain the spatial distribution of the relative permittivity, input port excitation information, and operating wavelength parameters of the integrated photonic device to be simulated, and construct spatially discretized input data;

[0009] S200, Directional Decoupling Feature Extraction: The input data is input into the wave field simulation network. Through the directional decoupling multi-scale anisotropic feature extraction structure, the long-range propagation features along the electromagnetic wave propagation direction and the lateral local boundary features perpendicular to the propagation direction are extracted to obtain the initial spatial feature map.

[0010] S300, Neural Modal Projection: Based on the initial spatial feature map, the transverse spatial features perpendicular to the electromagnetic wave propagation direction are weighted and aggregated through a trainable transverse modal basis, and the aggregated features are mapped to the modal representation space to obtain a modal feature sequence representing different propagation modes.

[0011] S400, Directed Causal Propagation Modeling: Based on the state-space propagation model, independent hidden state variables are established for each propagation mode at each discrete propagation position. Directed causal recursive calculation is performed from the input end to the output end along the electromagnetic wave physical propagation axis to obtain the propagation state characteristics corresponding to each propagation position.

[0012] S500, cross-modal coherent coupling: at the same propagation position, the propagation state features corresponding to each propagation mode are combined along the modal dimension and input into the modal interaction network for intermodal feature interaction and information fusion to obtain coherent coupling features that characterize multimodal coherent interference;

[0013] S600, Field Reconstruction and Output: The coherent coupling features are mapped back to the spatial feature domain, and the complex electromagnetic field distribution inside the integrated photonic device to be simulated is reconstructed through a field decoding network; based on the reconstructed complex electromagnetic field distribution, the electromagnetic response parameters of the corresponding output region of the integrated photonic device are calculated and output.

[0014] S700, Joint Training Optimization: During the training phase, the field distribution error between the predicted complex electromagnetic field and the target complex electromagnetic field is used as the data supervision loss function. At the same time, a physical constraint loss function based on the electromagnetic field control equation is introduced to construct a joint loss function to iteratively optimize the network parameters. In a preferred embodiment, the electromagnetic field control equation adopts the Helmholtz equation. In other embodiments, the electromagnetic field control equation may also adopt Maxwell's equations or the equivalent propagation control equations derived from Maxwell's equations.

[0015] Furthermore, the multi-scale anisotropic feature extraction structure with directional decoupling described in step S200 adopts a serial independent extraction architecture, specifically including: performing initial feature mapping on the spatially discretized input data to obtain high-dimensional spatial features; firstly, extracting long-range propagation features and interference response features on the continuous propagation path inside the device through an axial feature extraction branch set along the electromagnetic wave propagation direction; then, extracting local spatial features of the dielectric boundary region and structural discontinuity region through a transverse feature extraction branch set perpendicular to the electromagnetic wave propagation direction; after channel compression and nonlinear activation of the features output by the transverse feature extraction branch, performing residual connection with the high-dimensional spatial features, and performing normalization processing to obtain the initial spatial feature map.

[0016] Furthermore, in step S300, the trainable lateral modal basis is a propagation modal representation basis obtained through adaptive learning of training data, which reduces the dependence on solving fixed physical eigenmodes in advance through electromagnetic equations and reduces the pre-calculation process of device eigenmodes.

[0017] Furthermore, in step S400, the state space propagation module adaptively adjusts the state transition parameters between adjacent propagation positions based on the local medium distribution characteristics and the current modal characteristics, in order to characterize the phase evolution, energy coupling, and self-imaging effect of electromagnetic waves during propagation within the device.

[0018] Furthermore, in step S500, the modal interaction network is implemented using a residual multilayer perceptron. Under the condition of keeping the spatial dimension information unchanged, feature interaction and feature update are performed only along the modal dimension to achieve information fusion between different propagation modalities.

[0019] Furthermore, the wave field simulation network also includes a reverse residual compensation path corresponding to the main propagation path, specifically including: extracting the initial spatial feature map output by the direction-decoupled multi-scale anisotropic feature extraction structure; in the reverse residual compensation path, updating the initial spatial feature map in reverse along the propagation sequence opposite to the electromagnetic wave propagation direction to obtain spatial residual features; mapping the cross-modal coherent coupling features to the spatial feature domain and fusing them with the spatial residual features to obtain a compensated spatial feature map; inputting the compensated spatial feature map into the field decoding network to reconstruct the corresponding complex electromagnetic field distribution inside the integrated photonic device to be simulated; the reverse residual compensation path is used to compensate for the output-side medium discontinuity, weak reflection components, and local propagation deviations generated during electromagnetic wave propagation.

[0020] Further, in step S700, the physical constraint loss function is constructed by substituting the predicted complex electromagnetic field distribution output by the field decoding network into the electromagnetic field control equation corresponding to the integrated photonic device to be simulated, and calculating the control equation residual within the propagation region; in a preferred embodiment, the electromagnetic field control equation adopts the Helmholtz equation.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] Firstly, by incorporating the physical prior of electromagnetic wave directional propagation into the wave field simulation network and combining it with physical information constraint training, this invention can achieve rapid inference of the electromagnetic field of integrated photonic devices. Compared with traditional numerical solution methods, it can improve simulation efficiency and is suitable for large-scale parameter scanning and device optimization design.

[0023] Secondly, this invention improves the prediction accuracy of the fully complex electromagnetic field and enhances the response prediction capability of the local output region by using directional decoupling feature extraction, neural modal projection, state space propagation modeling, and cross-modal coupling mechanism.

[0024] Third, this invention further combines the reverse residual compensation mechanism and the physical constraint training mechanism to improve the physical consistency of the model under complex propagation scenarios and its generalization ability under cross-device conditions.

[0025] This invention can be widely applied to the rapid simulation and performance evaluation of various directional propagation integrated photonic devices such as waveguides, directional couplers, and multimode interferometers, and can provide simulation analysis support for the design of optical computing and on-chip optical network chips. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints, as implemented in this invention.

[0027] Figure 2 This is a schematic diagram of a multi-scale anisotropic feature extraction structure for directional decoupling provided in an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram of the structure of the neural modal projection and state space propagation module provided in an embodiment of the present invention;

[0029] Figure 4 A schematic diagram illustrating the details of state space propagation provided for an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Based on the technical solutions disclosed in this invention, equivalent substitutions or modifications made by those skilled in the art without departing from the spirit and substance of this invention should fall within the protection scope of this invention.

[0031] like Figure 1 As shown, the electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints provided in this embodiment includes a simulation inference stage and a training stage.

[0032] Experimental Environment and Dataset Preparation: The training and inference processes in this embodiment can be implemented on general-purpose computing devices or high-performance computing servers. These devices may include processors, memory, and graphics processing units (GPUs). Deep learning frameworks such as PyTorch, JAX, or other frameworks capable of automatic differentiation and tensor computation can be used. The true reference values ​​for the electromagnetic field can be pre-calculated using the finite difference frequency domain method, the finite element method, or other electromagnetic numerical solution methods.

[0033] This embodiment selects a 3×3 multimode interferometric beamsplitter under 15 different operating wavelengths as the verification object. The dataset contains a total of 23,040 samples, of which 18,432 samples are used as the training set and 4,608 samples are used as the test set, covering the operating wavelength range of 1.530 μm to 1.565 μm and different device lengths, widths, and input / output waveguide position parameters. For each sample, the relative permittivity distribution is... and input excitation field The data is discretized into a two-dimensional grid tensor of 80×384 and used as input data for the wave field simulation network.

[0034] The specific implementation process of the electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints is as follows:

[0035] Step S100: Obtain the spatial distribution of the relative permittivity, input port excitation information, and operating wavelength parameters of the integrated photonic device to be simulated, and construct spatially discretized input data.

[0036] Specifically, in order to enable the physical structure information and excitation conditions of integrated photonic devices to be processed by the wave field simulation network, this embodiment converts the continuous physical computation domain and its corresponding physical parameters into spatially discretized tensor data.

[0037] First, the physical computation domain of the integrated photonic device to be simulated is determined. Taking the cross-sectional simulation of a two-dimensional multimode interferometric beam splitter (MMI) as an example, the main propagation direction of the electromagnetic wave is defined as the axial direction, denoted as the z-axis; the cross-sectional direction perpendicular to the propagation direction is defined as the transverse direction, denoted as the y-axis. For a three-dimensional simulation scenario, the transverse direction can be extended to the x−y plane, and the z-axis can be taken as the axial propagation direction.

[0038] The horizontal spatial grid step size is set according to the device geometry and simulation resolution requirements. And axial spatial grid step size And divide the continuous physical space into resolutions of The discretized spatial grid. Wherein, Indicates the number of horizontal grid nodes. This indicates the number of grid nodes along the propagation axis.

[0039] Subsequently, the spatial distribution of the relative permittivity of the integrated photonic device to be simulated within the physical computation domain is obtained. Based on the discrete spatial grid, each grid node is extracted. Construct a relative permittivity mapping matrix for the corresponding relative permittivity values. It is used to characterize the refractive index distribution, waveguide boundary, and structural region distribution inside the device.

[0040] Furthermore, the excitation information of the input port and the operating wavelength parameters of the current simulation are obtained. For a specified input port, the excitation electromagnetic field distribution at the input end face can be calculated, such as the transverse electric fundamental mode. The transverse field distribution under a mode or other specific mode is denoted as .

[0041] In a preferred embodiment, the input excitation field can be replicated and extended along the electromagnetic wave propagation direction to form an excitation feature channel with the same size as the discrete spatial grid; in another embodiment, the excitation injection channel can be constructed only at the input end face. Further, the current operating wavelength is obtained. And calculate the free space wavenumber based on the operating wavelength. The operating wavelength parameter or free space wavenumber can be mapped to a parameter feature map with the same size as the discrete space grid.

[0042] Subsequently, the relative permittivity mapping matrix, the excitation feature channel, and the wavelength parameter feature map are combined along the feature channel dimension to obtain spatially aligned input feature data. Preferably, before inputting the directional decoupling multi-scale anisotropic feature extraction structure in step S200, each input physical channel is normalized to improve the numerical stability of the network training process.

[0043] Finally, the input feature tensor corresponding to the physical space grid is generated. In a preferred embodiment, the input feature tensor adopts a channel-first tensor organization form, and the number of channels is determined by the type of input physical parameters.

[0044] Step S200: Input the input data into the wave field simulation network, and extract the long-range propagation features along the electromagnetic wave propagation direction and the lateral local boundary features perpendicular to the propagation direction through the multi-scale anisotropic feature extraction structure with directional decoupling, to obtain the initial spatial feature map.

[0045] like Figure 2 As shown, the directionally decoupled multi-scale anisotropic feature extraction structure includes an initial feature mapping layer, a multi-scale directionally decoupled feature extraction structure, a feature fusion and enhancement unit, and a residual connection and normalization unit.

[0046] Specifically, in directional propagation integrated photonic devices, electromagnetic waves exhibit continuous propagation and phase accumulation along the propagation direction. However, within the transverse section perpendicular to the propagation direction, variations in the refractive index of the medium create local boundary features. To mitigate the impact of premature mixing of physical features from different directions during the initial feature extraction stage on the representation of propagation and boundary features, this embodiment employs a directionally decoupled multi-scale anisotropic feature extraction structure at the front end of the wave field simulation network.

[0047] First, the input feature tensor obtained in step S100 is input into the initial feature mapping layer. The input physical features are mapped to a hidden feature space of a preset dimension through pointwise convolution to obtain high-dimensional space features.

[0048] Subsequently, based on the high-dimensional spatial features, multiple directional decoupling feature extraction branches with different receptive field scales are constructed to extract spatial propagation features at different scales.

[0049] For any scale of feature extraction branch, the high-dimensional spatial features are first subjected to directional convolution along the electromagnetic wave propagation direction using an axial feature extraction unit to extract long-range propagation features and coherent interference features along the continuous propagation path inside the device. Preferably, the axial feature extraction unit uses a size of 1× Channel-wise convolution, where The length of the convolution kernel along the propagation axis can be set according to the device structure size and propagation distance, such as, but not limited to, 3, 5, and 7.

[0050] Subsequently, the axial feature extraction results are subjected to directional convolution processing perpendicular to the electromagnetic wave propagation direction by a lateral feature extraction unit to extract local spatial features of the medium boundary region, refractive index abrupt change region, and structural discontinuity region. Preferably, the lateral feature extraction unit uses a size of [missing information - likely a unit size]. ×1 channel-wise convolution, where is the length of the horizontal convolution kernel, and >1.

[0051] Next, the features output from the feature extraction branches at different scales are fused. This fusion process includes concatenation, summation, weighted fusion, or combinations thereof. The fused features are then further processed by pointwise convolution for channel mapping and enhanced using nonlinear activation functions, including but not limited to GELU, SiLU, or ReLU.

[0052] Finally, the enhanced feature result is residually connected to the high-dimensional spatial features output by the initial feature mapping layer to retain the physical spatial location information and medium distribution information in the input data; then the residually connected features are normalized to obtain the initial spatial feature map, and the initial spatial feature map is used as the input for neural modality projection in step S300.

[0053] Step S300: Based on the initial spatial feature map, perform neural modal projection on the lateral spatial features perpendicular to the electromagnetic wave propagation direction using a trainable lateral modal basis to obtain modal feature sequences characterizing different propagation modes.

[0054] Specifically, in order to achieve a compact representation of the electromagnetic wave propagation process, this embodiment maps the initial spatial feature map output in step S200 to the neural modal representation space to obtain a modal feature expression suitable for subsequent propagation state modeling.

[0055] like Figure 3 As shown, the neural modality projection module maps the initial spatial feature map into a modality feature sequence, and inputs the modality feature sequence into the state space propagation module for directional causal recursion.

[0056] First, the initial spatial feature map output in step S200 is obtained. The initial spatial feature map includes the internal dielectric distribution characteristics of the device, the boundary response characteristics, and the initial field distribution characteristics formed by the input excitation.

[0057] Subsequently, the initial spatial feature map is segmented position by position along the electromagnetic wave propagation direction, and the lateral spatial features corresponding to each propagation position are extracted. Each lateral spatial feature is used to characterize the local response information of each discrete spatial node within the corresponding propagation cross section.

[0058] Furthermore, a trainable lateral modal basis is constructed. This lateral modal basis is adaptively learned from the training data during the training process, and its number of modes is a preset value M, used to compress and represent the lateral spatial features. This lateral modal basis differs from the fixed physical eigenmode basis obtained beforehand by solving the electromagnetic control equations; it can learn propagation mode representations suitable for different device structures based on the propagation field distribution characteristics in the training samples.

[0059] Subsequently, a neural modality projection operation is performed on the lateral spatial features at each propagation location. Specifically, the lateral spatial features are weighted and projected using the trainable lateral modality basis, mapping the discrete node features in the spatial feature domain to the modality representation space, thereby obtaining modality feature components corresponding to multiple propagation modalities.

[0060] In a preferred embodiment, the neural modality projection operation includes: weighting and aggregating the lateral spatial features at each propagation location with the trainable lateral modality basis, and performing linear mapping and nonlinear feature transformation on the aggregation result through a trainable feature mapping matrix to obtain the modality feature components.

[0061] Each of the modal feature components is used to characterize the complex field propagation response characteristics under different propagation modes at the corresponding propagation position.

[0062] Finally, the modal feature components obtained at each propagation location are organized along the electromagnetic wave propagation direction to form a modal feature sequence, and output to the state space propagation module in step S400.

[0063] Through the above-described neural modal projection process, this embodiment can achieve modal compression representation of spatial features while preserving lateral propagation information, thereby reducing the computational complexity of subsequent propagation state recursion and improving propagation modeling efficiency.

[0064] Step S400: Based on the state-space propagation model, perform directional causal recursive calculations on the modal feature sequence obtained in step S300 along the electromagnetic wave propagation direction to obtain the propagation state features corresponding to each propagation position.

[0065] Specifically, within integrated photonic devices, the evolution of electromagnetic waves along the propagation direction exhibits directionality and sequence correlation. The field distribution at the current propagation position is related not only to the local medium distribution at the current position but also to the propagation state at the previous propagation position. To describe the aforementioned propagation laws, this embodiment sets up a state-space propagation module in the wave field simulation network to perform directional recursive modeling of the modal feature sequence.

[0066] First, the modal feature sequence output in step S300 is received, and the corresponding hidden state variables are initialized for each propagation mode. The hidden state variables are used to characterize the historical propagation state information of the corresponding propagation mode during the propagation process.

[0067] Subsequently, state update calculations are performed sequentially for each discrete propagation position along the electromagnetic wave propagation direction from the input end to the output end. For the current propagation position, its propagation state is jointly determined by the hidden state passed from the previous propagation position and the modal input characteristics of the current position.

[0068] In a preferred embodiment, the state update process can be represented as follows:

[0069]

[0070]

[0071] Where j represents the discrete position index along the propagation direction ( ); This indicates the current position obtained in step S300. Initial modal feature input at the location; Indicates the previous position Hidden state variables passed down from elsewhere; This represents the hidden state variable indicating the updated current position. This represents the current position propagation state feature output after recursive calculation; , These represent the discretized state transition parameter matrix and the input control parameter matrix, respectively. This represents the output mapping parameter matrix.

[0072] Furthermore, in a preferred embodiment, the state space propagation module employs a selective state update mechanism. The state transition parameters, input control parameters, and output mapping parameters are adaptively generated based on the local medium distribution characteristics and modal input characteristics at the current location, thereby enabling dynamic propagation modeling in different propagation regions.

[0073] When the electromagnetic wave is in a propagation region with a relatively uniform medium distribution, the state space propagation module is used to characterize the phase accumulation and stable propagation state during continuous propagation. When the electromagnetic wave propagates to a region of abrupt change in refractive index, a structural boundary region, or a mode coupling region, the state space propagation module adaptively adjusts the state update parameters to characterize local propagation disturbances, mode conversions, and energy coupling behavior.

[0074] Finally, the propagation state features corresponding to each propagation position are organized according to the propagation order to form a propagation state feature sequence, and output to the cross-modal coupling module in step S500.

[0075] Through the above-described directional causal propagation modeling process, this embodiment can model the long-range evolution of electromagnetic waves along the propagation direction and improve the ability to express the propagation state of local structural disturbance regions.

[0076] Step S500: At the same propagation position, combine the propagation state features corresponding to each propagation mode along the modal dimension and input them into the modal interaction network for intermodal feature interaction and information fusion to obtain coherent coupling features that characterize multimodal coherent interference.

[0077] Specifically, after the directional causal recursion in step S400, each propagation mode obtains its propagation state characteristics along the electromagnetic wave propagation direction. Since different propagation modes may have mode coupling, phase interference, and energy exchange relationships during propagation within the integrated photonic device, this embodiment introduces a cross-mode coupling mechanism at the same discrete propagation position to establish the characteristic correlation relationship between different propagation modes.

[0078] At each discrete propagation location At this point, the propagation state features corresponding to multiple propagation modes output in step S400 are obtained and combined along the modality dimension to form a full-modality aggregated feature. The combination method includes splicing, stacking, weighted combination, or a combination thereof.

[0079] Subsequently, the full-modal aggregated features are input into a modal interaction network for inter-modal feature interaction and information fusion. Preferably, the modal interaction network is implemented using a residual multilayer perceptron, which includes a first linear mapping layer, a nonlinear activation layer, and a second linear mapping layer connected in sequence, used to model the feature associations between different propagation modalities while keeping the propagation position dimension unchanged.

[0080] In a preferred embodiment, the feature update process of the modal interaction network can be represented as follows:

[0081]

[0082] in, This represents the full-modal aggregation feature at the j-th propagation position; This indicates a normalization operation; This represents a parameterized modal interaction network; This represents the coherent coupling features after the intermodal feature interaction is completed.

[0083] Through the above residual update method, the modal interaction network introduces coupling correction information between different propagation modes while retaining the original propagation state characteristics, thereby obtaining coherent coupling characteristics for characterizing multimode coherent interference relationships.

[0084] Finally, the coherent coupling features obtained at each discrete propagation location are organized according to the electromagnetic wave propagation direction to form a coherent coupling feature sequence, and output to the field reconstruction and output module in step S600.

[0085] Step S600: Map the coherent coupling features back to the spatial feature domain, and reconstruct the corresponding complex electromagnetic field distribution inside the integrated photonic device to be simulated through a field decoding network; based on the reconstructed complex electromagnetic field distribution, calculate and output the electromagnetic response parameters of the corresponding output region of the integrated photonic device.

[0086] Specifically, after the cross-modal coupling in step S500, coherent coupling features containing multimode coherent propagation information are obtained. To recover the spatial electromagnetic field distribution inside the device, the coherent coupling features are first mapped to the spatial feature domain through a trainable lateral spatial decoding basis. The mapping relationship can be expressed as:

[0087]

[0088] in, This represents the coherent coupling feature sequence output in step S500; The spatial decoding basis matrix is ​​used to map features in the modality representation space back to the spatial feature domain; This represents the spatial feature map obtained after mapping.

[0089] Furthermore, in a preferred embodiment, the wavefield simulation network further includes a reverse residual compensation path corresponding to the main propagation path. The reverse residual compensation path is used to introduce a feature update process opposite to the electromagnetic wave propagation direction to compensate for output-side boundary disturbances, weak reflection components, and local propagation deviations generated during electromagnetic wave propagation.

[0090] Specifically, the initial spatial feature map output by the reverse residual compensation path extraction step S200 is updated in reverse order along the propagation sequence opposite to the electromagnetic wave propagation direction to obtain spatial residual features. Subsequently, the spatial feature map With the aforementioned spatial residual features Feature fusion is performed to obtain a compensated spatial feature map, thereby enhancing the characterization ability of the local boundary response and weak reflection components of the output region. The feature fusion method includes at least one of addition, splicing, or weighted fusion.

[0091] Subsequently, the compensated spatial feature map is input into the field decoding network. Preferably, the field decoding network includes multiple convolutional layers and nonlinear activation layers to perform a nonlinear mapping from spatial features to physical field distribution, outputting the complex electromagnetic field distribution E(y, z) corresponding to the interior of the integrated photonic device to be simulated. In a preferred embodiment, the complex electromagnetic field distribution represents the real and imaginary parts of the electromagnetic field through two output channels; in other embodiments, the complex electromagnetic field distribution can also be represented by amplitude and phase.

[0092] Finally, based on the preset output region location, the reconstructed complex electromagnetic field distribution is locally read out to calculate the electromagnetic response parameters of the integrated photonic device. Specifically, a local observation window corresponding to the output port can be selected at the device output end face, and the electromagnetic response parameters of the output port can be calculated by discrete integration or mode overlap integration based on the distribution state of the complex electromagnetic field within this local observation window.

[0093] In a preferred embodiment of the two-dimensional simulation, for the i-th output port, its port transmission power is... The calculation formula is:

[0094]

[0095] in, E(y, L) represents the lateral observation window range of the i-th output port; E(y, L) represents the reconstructed electromagnetic field distribution at the output end face z=L of the device.

[0096] In addition to port transmission power, the splitting ratio, relative phase, mode transmission characteristics, or coupling response parameters can be further calculated based on the complex electromagnetic field distribution for performance evaluation of integrated photonic devices.

[0097] Step S700: During the training phase, the field distribution error between the predicted complex electromagnetic field and the target complex electromagnetic field is used as the data supervision loss function. At the same time, a physical constraint loss function based on the electromagnetic field control equation is introduced to construct a joint loss function to iteratively optimize the network parameters. In a preferred embodiment, the electromagnetic field control equation adopts the Helmholtz equation.

[0098] Specifically, this embodiment employs a joint training mechanism that combines data-driven supervision and physical constraint supervision to optimize the network parameters in the wave field simulation network. The network parameters include convolution parameters in the direction-decoupled feature extraction structure, neural modality projection basis parameters, state space propagation parameters, and field decoding network parameters.

[0099] First, the data supervision loss function is calculated. After each training forward propagation, the predicted complex electromagnetic field output by the field decoding network is obtained. The target complex electromagnetic field was obtained by high-precision numerical solution. As a supervisory label, a data supervision loss function is constructed by comparing the field distribution errors of the two across the entire spatial computational domain.

[0100] Preferably, the data supervision loss function can be at least one of mean squared error, mean absolute error, normalized mean absolute error, or relative norm error. Taking mean squared error as an example, the data supervision loss function is expressed as follows:

[0101]

[0102] Where N represents the total number of spatial discrete grid nodes; and Let represent the predicted complex field value and the target complex field value at the i-th grid node, respectively.

[0103] Further, the physical constraint loss function is calculated. In a preferred embodiment, for the propagation region of a passive, isotropic integrated photonic device, the predicted complex electromagnetic field can be constrained by the scalar Helmholtz equation. For a given relative permittivity distribution... and free space wavenumber The Helmholtz equation is expressed as:

[0104]

[0105] in, For the Laplace operator; in two-dimensional simulation, ; , This is the operating wavelength.

[0106] The predicted complex electromagnetic field output by the wave field simulation network Substituting directly into the Helmholtz equation above, calculate the residuals of the governing equations within the passive propagation region. :

[0107]

[0108] Spatial derivative information can be obtained through finite difference methods, automatic differentiation methods, or other numerical differentiation methods. Subsequently, the residuals of the governing equations at the physical sampling points are statistically analyzed to construct the physical constraint loss function. :

[0109]

[0110] in, The number of sampling points involved in the physical constraint calculation.

[0111] Finally, a joint loss function is constructed and gradient backpropagation is performed. The data-supervised loss function and the physical constraint loss function are weighted and combined to construct the final joint loss function. :

[0112]

[0113] in, This represents the weighting coefficients of the physical constraint loss function. These weighting coefficients can be set based on training stability, field distribution prediction error, and the magnitude of the physical residuals. Preferably, the weight ratio of the data supervision loss function to the physical constraint loss function can be set to 10:1 to 100:1 to reduce numerical instability caused by excessively large physical residuals in the early stages of training. In a specific preferred embodiment, the weight ratio can be set to 50:1 (i.e., ...). ).

[0114] Based on the joint loss function, a gradient optimization algorithm is used to perform backpropagation and parameter updates on the wave field simulation network until an electromagnetic field simulation model of the integrated photonic device that meets the preset accuracy requirements is obtained. The gradient optimization algorithm can be Adam, AdamW, or other adaptive gradient optimization algorithms.

Claims

1. A method for simulating the electromagnetic field of an integrated photonic device based on propagation physics priors and physical information constraints, characterized in that, For integrated photonic devices with directional electromagnetic propagation characteristics, by incorporating prior knowledge of electromagnetic wave propagation into a wave field simulation network and training it with physical information constraints, the method realizes the prediction of complex electromagnetic fields inside the device and the calculation of output response. The method includes a simulation inference stage and a training stage. The simulation reasoning stage includes the following steps: S100: Obtain the spatial distribution of the relative permittivity, input port excitation information, and operating wavelength parameters of the integrated photonic device to be simulated, and construct spatially discretized input data; S200, The input data is input into the wave field simulation network. Through the direction-decoupled multi-scale anisotropic feature extraction structure, the long-range propagation features along the electromagnetic wave propagation direction and the lateral local boundary features perpendicular to the propagation direction are extracted to obtain the initial spatial feature map. S300, based on the initial spatial feature map, neural modal projection is performed on the lateral spatial features perpendicular to the electromagnetic wave propagation direction through a trainable lateral modal basis to obtain modal feature sequences characterizing different propagation modes. S400, based on the state space propagation module, performs directional causal recursive calculation on the modal feature sequence along the electromagnetic wave propagation direction to obtain the propagation state features corresponding to each propagation position; S500 combines the propagation state features corresponding to each propagation mode along the modal dimension at the same propagation position and inputs them into the modal interaction network for intermodal feature interaction and information fusion to obtain coherent coupling features that characterize multimodal coherent interference. S600, the coherent coupling characteristics are mapped back to the spatial feature domain, and the complex electromagnetic field distribution inside the integrated photonic device to be simulated is reconstructed through the field decoding network; based on the reconstructed complex electromagnetic field distribution, the electromagnetic response parameters of the corresponding output region of the integrated photonic device are calculated and output; The training phase includes: using the field distribution error between the predicted complex electromagnetic field and the target complex electromagnetic field as the data supervision loss function, and simultaneously introducing a physical constraint loss function based on the electromagnetic field control equation to construct a joint loss function to iteratively optimize the parameters of the wave field simulation network.

2. The electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints as described in claim 1, characterized in that, The directionally decoupled multi-scale anisotropic feature extraction structure includes: performing initial feature mapping on the spatially discretized input data to obtain a spatial feature representation; extracting long-range propagation features and interference response features on the continuous propagation path inside the device through an axial feature extraction branch set along the electromagnetic wave propagation direction; extracting local spatial features of the medium boundary region, refractive index abrupt region, and structural discontinuity region through a transverse feature extraction branch set perpendicular to the electromagnetic wave propagation direction; and fusing and enhancing the spatial features extracted at different scales and in different directions to obtain an initial spatial feature map for subsequent neural modality projection.

3. The electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints as described in claim 1, characterized in that, The neural modal projection includes: inputting the initial spatial feature map into the modal learning module; weighting and aggregating the lateral spatial features perpendicular to the electromagnetic wave propagation direction using a trainable lateral modal basis; mapping the aggregated spatial features to the modal representation space to obtain modal feature components corresponding to multiple propagation modes; wherein each modal feature component is used to characterize the complex field propagation response features under different propagation modes at the corresponding propagation position; organizing each modal feature component along the electromagnetic wave propagation direction to form a modal feature sequence for subsequent propagation state modeling; wherein the lateral modal basis is a trainable propagation modal representation basis obtained through adaptive learning of training data, and the lateral modal basis does not use a pre-solved fixed physical eigenmode as a fixed input.

4. The electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints as described in claim 1, characterized in that, The directed causal recursive calculation includes: inputting the modal feature sequence into the state space propagation module and initializing the corresponding hidden state variables for each propagation mode; sequentially performing state update calculations for each discrete propagation position along the electromagnetic wave propagation direction from the input end to the output end; for the current propagation position, updating the hidden state variables and propagation state features corresponding to the current position based on the hidden state passed from the previous propagation position and the modal input features of the current position; wherein, the state space propagation module adaptively generates or adjusts the state transition parameters, input control parameters, and output mapping parameters according to the local medium distribution characteristics and modal input characteristics at the current position to characterize the propagation state evolution of the electromagnetic wave inside the device; and using the propagation state features corresponding to each propagation position for subsequent cross-modal coupling calculations.

5. The electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints according to claim 4, characterized in that, The cross-modal coherent coupling includes: acquiring the propagation state features corresponding to each propagation mode at the same propagation position, and combining them along the modal dimension to form a full-modal aggregated feature; inputting the full-modal aggregated feature into a modal interaction network for inter-modal feature interaction and information fusion to obtain cross-modal coherent coupling features; wherein, the modal interaction network establishes the coupling relationship between modes based on the feature association relationship between different propagation modes, and completes the information transmission and feature update between different propagation modes; the cross-modal coherent coupling features are used to characterize the coherent coupling relationship between different propagation modes and are used for subsequent field reconstruction.

6. The electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints as described in claim 5, characterized in that, The wave field simulation network also includes a reverse residual compensation path corresponding to the main propagation path. The reverse residual compensation path includes: extracting the initial spatial feature map output by the multi-scale anisotropic feature extraction structure of the direction decoupling; updating the initial spatial feature map in reverse along the propagation order opposite to the electromagnetic wave propagation direction to obtain spatial residual features; mapping the cross-modal coherent coupling features to the spatial feature domain and fusing them with the spatial residual features to obtain a compensated spatial feature map; and inputting the compensated spatial feature map into the field decoding network to reconstruct the corresponding complex electromagnetic field distribution inside the integrated photonic device to be simulated. The reverse residual compensation path is used to compensate for output-side boundary disturbances, weak reflection components, and local propagation deviations generated during electromagnetic wave propagation.

7. The electromagnetic field simulation method for integrated photonic devices based on propagation physics priors and physical information constraints as described in claim 1, characterized in that, The joint training optimization includes: acquiring the predicted complex electromagnetic field output by the field decoding network, and using the target complex electromagnetic field as a supervision label, constructing a data supervision loss function based on the field distribution error between the predicted complex electromagnetic field and the target complex electromagnetic field; substituting the predicted complex electromagnetic field into the electromagnetic field control equation corresponding to the integrated photonic device to be simulated, calculating the control equation residual within the propagation region, and constructing a physical constraint loss function based on the control equation residual; weighting and combining the data supervision loss function and the physical constraint loss function to construct a joint loss function; and performing backpropagation and iterative optimization on the parameters of the wave field simulation network based on the joint loss function; wherein, the electromagnetic field control equation includes at least one of the Helmholtz equation, Maxwell's equations, or equivalent propagation control equations derived from Maxwell's equations.

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