Polarization-insensitive diffractive unit structure library construction and indexing method

Abstract

The application discloses a polarization-insensitive diffraction unit structure library construction and indexing method, relates to the technical field of diffraction optical device design, and comprises the following steps: collecting diffraction response data under irradiation of multiple polarization states of incident light, extracting frequency domain amplitude and phase distribution characteristics through Fourier transform, and constructing a three-dimensional geometric model of a candidate diffraction unit through parameterized modeling. The model is imported into full-wave electromagnetic simulation software to strictly solve in a wide spectral range, simulation scattering field data containing polarization state information are generated, polarization-sensitive configurations are removed through post-processing, polarization-insensitive unit sets are formed by retaining structures with consistent responses in multiple polarization channels, a mapping relationship table of unit geometric parameters and optical performance parameters is established, and the table is stored in a library. The method can weaken the polarization dependence of the optical performance of the structure, guarantee the response stability in multiple polarization channels, realize accurate correlation of parameters, and improve the directivity and adaptability of structure library indexing.

Description

Technical Field

[0001] This invention belongs to the field of diffractive optical device design technology, specifically a method for constructing and indexing a polarization-insensitive diffractive unit structure library. Background Technology

[0002] Conventional diffraction unit structure design often focuses on modeling and simulation for a single polarization state, obtaining scattered field data through conventional electromagnetic simulation. However, it does not conduct structure screening for response consistency under multiple polarization channels. Structure library construction often directly summarizes geometric models without eliminating polarization-sensitive configurations. The structure library only stores geometric parameter information and does not establish a corresponding mapping relationship between geometric parameters and optical performance parameters. Structure indexing often relies on geometric parameters for retrieval.

[0003] Conventional simulations do not cover a wide spectral range and multiple polarization states. Scattered field data cannot fully reflect the structural response under different polarization states, and cannot distinguish between polarization-sensitive and polarization-insensitive configurations. The structure library contains unit structures sensitive to polarization changes, and the stability of optical response under multiple polarization channels cannot be guaranteed. Geometric parameters and optical performance parameters are independent and have no direct correlation. Structure retrieval and retrieval within the library cannot be matched based on optical performance requirements, resulting in insufficient indexing efficiency and adaptability of the structure library.

[0004] The three-dimensional geometric models of candidate diffraction unit structures need to be imported into full-wave electromagnetic simulation software. Simulated scattering field data containing polarization state information is generated through rigorous solving over a wide spectral range. Polarization-sensitive geometric configurations are then eliminated through post-processing, retaining candidate structures with consistent responses across multiple polarization channels to form a set of polarization-insensitive unit structures. A mapping table between the geometric parameters and optical performance parameters of each unit structure in the set of polarization-insensitive unit structures needs to be established, and this mapping table needs to be stored in a structure library for accurate indexing. Summary of the Invention

[0005] This invention aims to solve at least one of the technical problems existing in the prior art; To this end, this invention proposes a method for constructing and indexing a polarization-insensitive diffraction unit structure library, including: Diffraction response datasets under incident light with various preset polarization states are collected, and Fourier transform processing is performed on the diffraction response datasets to extract frequency domain amplitude and phase distribution features. Based on the extracted frequency domain amplitude and phase distribution features, a set of three-dimensional geometric models covering candidate diffraction unit structures with different diffraction efficiencies and angular bandwidths are constructed using parametric modeling techniques. The three-dimensional geometric model of the candidate diffraction unit structure is imported into the full-wave electromagnetic simulation software and rigorously solved over a wide spectral range to generate simulated scattering field data containing polarization state information. The simulated scattering field data is post-processed to eliminate geometric configurations that are sensitive to changes in polarization state, and retain candidate structures that respond consistently in multiple polarization channels to form a set of polarization-insensitive units. Establish a mapping table between the geometric parameters and optical performance parameters of each unit structure in the polarization-insensitive unit set, and store the mapping table in the polarization-insensitive diffraction unit structure library.

[0006] Furthermore, the process of collecting diffraction response datasets under incident light with multiple preset polarization states and performing Fourier transform processing on the diffraction response datasets to extract frequency domain amplitude and phase distribution features specifically includes: The incident light source is configured with three basic modes: linear polarization, circular polarization, and elliptical polarization, and the incident angle of each mode is controlled to perform step scanning within a preset field of view. A photodetector array is set up at the receiving end to record the spatial distribution matrix of the light field intensity under different polarization states and different incident angle combinations, which serves as the original diffraction response dataset. For each frame of light intensity image in the original diffraction response dataset, a two-dimensional fast Fourier transform algorithm is applied to transform it to the frequency domain. In the frequency domain, the complex amplitude value at the center diffraction order under the working condition corresponding to the current frame light intensity image is calculated, and the real part and imaginary part are separated, which are respectively used as the frequency domain amplitude feature and phase distribution feature under the working condition corresponding to the current frame light intensity image. The extracted frequency domain amplitude features and phase distribution features are categorized according to their corresponding operating condition labels to form a structured feature input set.

[0007] Furthermore, based on the extracted frequency domain amplitude and phase distribution features, a set of three-dimensional geometric models covering candidate diffraction unit structures with different diffraction efficiencies and angular bandwidths is constructed using parametric modeling methods, specifically including: The dielectric constant and thickness of the substrate material of the diffraction unit are defined as fixed constraints, and the micro-nano relief profile of the unit surface is defined as an adjustable degree of freedom. Based on the frequency domain amplitude and phase distribution characteristics of the structured feature input set, the target phase delay and target amplitude modulation curve are deduced and transformed into a surface fitting objective function. A genetic algorithm is used to perform global optimization in the space of freedom, and the coordinates of the control points of the micro-nano relief contour are iteratively adjusted until the response of the generated unit structure in the forward simulation matches the objective function. By changing the weight ratio of diffraction efficiency and bandwidth in the fitness function of the genetic algorithm, a batch of candidate diffraction unit structures with different performance focuses are generated. The 3D modeling kernel is invoked to convert the optimized control point coordinates into a solid mesh and export the 3D geometric model file of the candidate diffraction unit structure.

[0008] Furthermore, the three-dimensional geometric model of the candidate diffraction unit structure is imported into full-wave electromagnetic simulation software for rigorous solution over a wide spectral range, generating simulated scattering field data containing polarization state information, specifically including: Read the three-dimensional geometric model file of the candidate diffraction unit structure and convert it into a mesh generation format suitable for calculation using the finite-difference time-domain method; The wavelength range of the incident light is set to the visible light band to the near-infrared band, and it is discretized into multiple monochromatic light sources with a fixed step size; For each monochromatic light source, under both transverse electric field polarization and transverse magnetic field polarization modes, the model is loaded into the mesh-division format and iteratively solved under the boundary conditions. Collect the electric field component data after convergence and obtain the power diffraction efficiency distribution under different polarization states by calculating the time average value of the Poynting vector; The power diffraction efficiency distributions under different wavelengths and polarization states are integrated and assembled into a multi-dimensional simulated scattering field data cube.

[0009] Furthermore, the simulated scattering field data is post-processed to remove geometric configurations sensitive to polarization state changes, retaining candidate structures with consistent responses across multiple polarization channels. Specifically, this includes: Traverse the records of all candidate diffraction unit structures in the simulated scattering field data cube, extract the peak value of the principal diffraction efficiency in the transverse electric field polarization mode, and record it as the first peak value. The peak value of the main diffraction efficiency of the same candidate diffraction unit structure in the transverse magnetic field polarization mode is retrieved and recorded as the second peak value. The percentage of relative deviation between the first peak value and the second peak value is calculated. A polarization sensitivity tolerance threshold is set, and candidate diffraction unit structures whose relative deviation percentage is greater than the polarization sensitivity tolerance threshold are marked as polarization sensitive and eliminated. For candidate structures that pass the polarization sensitivity test, their response data under diagonal polarization is further read to verify their robustness under arbitrary polarization incident conditions. Candidate structures that pass all polarization consistency verifications are moved from the temporary simulation list in memory to the set of polarization-insensitive cells.

[0010] Furthermore, a mapping table is established between the geometric parameters and optical performance parameters of each unit structure in the polarization-insensitive unit set, specifically including: Traverse each unit structure in the polarization-insensitive unit set and analyze several key dimensional parameters used to define the shape in its three-dimensional geometric model; The diffraction efficiency, full width at half maximum (FWHM) bandwidth, and root mean square error within the operating bandwidth of the corresponding unit structure are retrieved from the simulated scattering field data and used as optical performance indicators. The key size parameters and the optical performance indicators are paired by key values ​​to construct a multidimensional vector, where the first half of the vector is the independent variable and the second half is the dependent variable. All multidimensional vectors corresponding to the unit structures are entered into the cache database, and a hash index based on geometric parameters is established. The data snapshots in the cache database are solidified to generate the final mapping table of the polarization-insensitive diffraction unit structure library.

[0011] Furthermore, it also includes the step of building an index, specifically: In the mapping table of the polarization-insensitive diffraction unit structure library, the dominant geometric parameters with the highest weights affecting optical performance indicators are identified; Based on the numerical distribution range of the dominant geometric parameters, the polarization-insensitive diffraction unit structure library is divided into several non-overlapping subspace index blocks. For each subspace index block, calculate a cluster center point that represents the average performance of the cell structure within the subspace index block, and record the coordinate values ​​of the cluster center point; When an external retrieval request is received, the distance metric between the target optical performance index in the retrieval request and each cluster center point is first calculated. Select the subspace index block corresponding to the nearest cluster center point as the coarse screening result and return it to the subsequent fine comparison process.

[0012] Furthermore, after selecting the subspace index block corresponding to the nearest cluster center point, a retrieval and comparison step is also included, specifically: Retrieve the multidimensional vectors of all unit structures within the subspace index block obtained from the coarse screening, and load them into local memory for parallel access. The target optical performance index in the search request is broken down into specific threshold constraints to form a multidimensional inequality screening rule. Traverse all multidimensional vectors within the subspace index block and remove vector entries that do not satisfy the multidimensional inequality filtering rules; For the remaining vector entries, sort them in descending order according to their diffraction efficiency values, and extract a number of entries from the top of the sorted list. The unit structure identifier codes corresponding to the extracted entries are packaged and output as the final search results.

[0013] Furthermore, before establishing the mapping table of the polarization-insensitive diffraction unit structure library, a data cleaning step is also included, specifically: For each candidate structure in the polarization-insensitive unit set, check whether there are error logs of mesh divergence or convergence failure during the simulation process; If an error log exists, the process is traced back to the corresponding 3D geometric model generation step, and the edge sharpness of the micro-nano relief contour is fine-tuned to repair topological defects. Resubmit the repaired 3D geometric model to the simulation queue until a set of error-free simulated scattering field data is obtained. Check the degree of agreement between the simulated scattering field data and the original frequency domain amplitude and phase distribution characteristics. If the degree of agreement is lower than the lower limit, discard the candidate structure and restart the modeling process. Only candidate structures confirmed through the data cleaning process are allowed to proceed to the stage of establishing the mapping relationship table.

[0014] Furthermore, it also includes a step of incrementally updating the polarization-insensitive diffraction unit structure library, specifically: Monitor the latest micro / nano fabrication process design rules, extract newly added manufacturable morphological features, and use them as input variables for incremental design; The input variables of the incremental design are hybridized and recombined with high-performance unit structures in the existing polarization-insensitive diffraction unit structure library to generate the next generation of candidate geometric models. The newly generated candidate geometric models are sequentially subjected to parametric modeling verification, full-wave electromagnetic simulation solution, polarization sensitivity screening, and multi-polarization channel response consistency verification processes to obtain a batch of new polarization-insensitive unit structures. This batch of new polarization-insensitive unit structures is merged with the existing polarization-insensitive diffraction unit structure library, and duplicate and redundant entries are removed. The mapping table of the polarization-insensitive diffraction unit structure library is updated, the index range is expanded, and an incremental update iteration is completed.

[0015] Compared with the prior art, the beneficial effects of the present invention are: The three-dimensional geometric model of the candidate diffraction unit structure is imported into the full-wave electromagnetic simulation software. Rigorous solution operations are performed over a wide spectral range to generate simulated scattering field data carrying complete polarization state information. Oriented post-processing is performed on the simulated scattering field data to screen out geometric configurations that exhibit response fluctuations to changes in the polarization state of the incident light. Candidate structures with consistent optical responses across multiple polarization channels are retained, forming a dedicated set of polarization-insensitive unit structures. The spectral coverage and polarization dimension of the simulation solution are expanded, and the scattering field data can fully reflect the structural response state under different polarization states. Polarization-sensitive configurations are directionally excluded, and the structures within the unit set all possess response stability under multiple polarization channels. The polarization dependence of the structural optical performance is effectively weakened.

[0016] For the established set of polarization-insensitive unit cells, the geometric parameters and optical performance parameters corresponding to each unit cell structure are matched one by one, and a direct mapping table between the two types of parameters is built. The mapping table is synchronously stored in the polarization-insensitive diffraction unit cell structure library. The geometric parameters and optical performance parameters form a one-to-one correspondence. The information storage format in the structure library changes from single geometric parameter storage to parameter association storage. The indexing logic of the structure library can directly match the corresponding geometric configuration based on the optical performance parameters. The parameter association can directly support the targeted retrieval and calling of structures in the library. The adaptability and retrieval direction of the structure library are enhanced. Attached Figure Description

[0017] Figure 1 This is a step diagram illustrating the method for constructing and indexing a polarization-insensitive diffraction unit structure library as described in this invention; Figure 2 This is a flowchart of diffraction response data acquisition and frequency domain feature extraction. Figure 3 A flowchart for parameterized modeling and optimization of candidate diffraction unit structures; Figure 4 Box plot comparing the full width at half height (WHM) bandwidth distribution before and after incremental update; Figure 5 This is a heatmap showing the linear correlation between geometric parameters and optical performance. Detailed Implementation

[0018] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. 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.

[0019] See Figure 1Diffraction response datasets under incident light with various preset polarization states were collected, and Fourier transforms were performed on these datasets to extract frequency domain amplitude and phase distribution features. Based on the extracted frequency domain amplitude and phase distribution features, a set of three-dimensional geometric models of candidate diffraction unit structures covering different diffraction efficiencies and angular bandwidths were constructed using parametric modeling techniques. These three-dimensional geometric models of the candidate diffraction unit structures were imported into full-wave electromagnetic simulation software for rigorous solving over a wide spectral range, generating simulated scattering field data containing polarization state information. Post-processing of the simulated scattering field data eliminated geometric configurations sensitive to polarization state changes, retaining candidate structures with consistent responses across multiple polarization channels, forming a set of polarization-insensitive unit structures. A mapping table between the geometric parameters and optical performance parameters of each unit structure in the set of polarization-insensitive unit structures was established and stored in a polarization-insensitive diffraction unit structure library.

[0020] In one embodiment of the present invention, see [reference] Figure 2 This study focuses on the acquisition and processing of diffraction response data under incident light with various preset polarization states. The basic incident light source modes include linear, circular, and elliptical polarization. The incident angle for each basic polarization mode is controlled within a preset field of view, for example, a preset field of view range of -10 degrees to +10 degrees, with an incident angle increment of 1 degree. A photodetector array, consisting of 2048x2048 pixel units with a pixel pitch of 2.5 micrometers, is used at the receiving end to record data under each preset polarization state. The incident direction of the light is sequentially changed according to the set incident angle step value, and the photodetector array synchronously records the spatial distribution matrix of the light field intensity formed at each specific incident angle. All recorded two-dimensional light intensity matrices together constitute the original diffraction response dataset.

[0021] In some embodiments, for each frame of light intensity image in the original diffraction response dataset, a two-dimensional fast Fourier transform algorithm needs to be applied to transform it from the spatial domain to the frequency domain. For each frame, the corresponding condition label contains the polarization state type of the incident light and the specific incident angle value. After completing the Fourier transform, the coordinate position corresponding to the central diffraction order is located in the generated frequency domain image, and the complex value at that coordinate position is extracted. This complex value is separated into two parts: a real part and an imaginary part. The value of the real part is recorded as the frequency domain amplitude feature under the current condition, and the value of the imaginary part is recorded as the phase distribution feature under the current condition. It can be understood that for linearly polarized light incident, its frequency domain amplitude feature reflects the intensity information of the diffraction efficiency under that polarization direction. Optionally, after separating the real and imaginary parts, the response intensity can be quantized, for example, by calculating the modulus of the complex value or performing a specific combination operation on the real and imaginary parts. One operational relationship can be expressed as: in: This indicates the overall response intensity under this operating condition. This represents the extracted real part, i.e., the frequency domain amplitude feature. This represents the extracted imaginary part, i.e., the phase distribution characteristics.

[0022] In practical implementation, all extracted frequency domain amplitude features and phase distribution features are systematically categorized according to their corresponding operating condition labels, forming a structured feature input set. The categorization process creates an independent data entry for each combination of incident angle and polarization state. This entry stores the frequency domain amplitude feature value, phase distribution feature value, and operating condition label as an index, calculated from the corresponding light intensity image. For example, for an operating condition with linear polarization at 0 degrees and an incident angle of 5 degrees, its feature data is stored in a specific row or specific data structure within the feature input set. In some embodiments, the ellipticity parameter and azimuth parameter of elliptically polarized light are also encoded within the operating condition label. Optionally, the structured feature input set can be organized in the form of a database table or a multidimensional array, where the row index corresponds to different scan step numbers, and the column index corresponds to the polarization state encoding, incident angle value, calculated frequency domain amplitude feature value, and phase distribution feature value, respectively. This organization ensures that subsequent parametric modeling processes can accurately and efficiently access and utilize the optical response feature data corresponding to each specific illumination condition.

[0023] In one embodiment of the present invention, see [reference] Figure 3 Parametric modeling is developed based on a structured feature input set. The first step is to define the dielectric constant and thickness of the substrate material of the diffraction unit as fixed constraints. For example, the substrate material is selected as fused silica, with its dielectric constant set to a fixed value at the target wavelength, and the substrate thickness set to 500 micrometers. The micro-nano relief profile of the unit surface is defined as an adjustable degree of freedom, which can be parametrically described by the coordinates of the control points of a set of non-uniform rational B-spline curves. Based on the frequency domain amplitude and phase distribution characteristics of the structured feature input set, the desired target phase delay distribution and target amplitude modulation curve need to be derived. This inversion process can be regarded as a phase recovery problem. It can be understood that the mathematical combination of the inverted target phase delay distribution and target amplitude modulation curve can be transformed into a surface fitting objective function to guide the generation of three-dimensional geometry.

[0024] In some embodiments, a genetic algorithm is used to perform global optimization within a degree-of-freedom space defined by the coordinates of the control points of the micro / nano relief contour. The initial population of the genetic algorithm contains 200 randomly generated individuals, each representing an encoding of a set of control point coordinates. In each generation of evolution, the algorithm calculates the optical response of the unit structure corresponding to each individual in forward simulation and compares this response with the aforementioned surface fitting objective function; the difference is used to calculate the fitness value. The genetic algorithm iteratively adjusts the control point coordinates of the micro / nano relief contour, generating a new population through selection, crossover, and mutation operations. This optimization loop continues until the matching error between the optical response calculated in forward simulation and the surface fitting objective function of a certain unit structure generated by the algorithm is lower than a preset convergence threshold. It can be understood that by changing the weight ratio of the two performance indicators, diffraction efficiency and bandwidth, in the fitness function of the genetic algorithm, the search can be guided towards different performance focuses. For example, one way to construct a fitness function can be expressed as: in: Represents the fitness value. This indicates the diffraction efficiency at the target wavelength and angle. This represents the angular bandwidth of the main diffraction peak. and It is a positive weighting coefficient used to adjust the trade-off between diffraction efficiency and bandwidth.

[0025] In practice, this is achieved by systematically adjusting the weighting coefficients. and By combining numerical values ​​and rerunning the genetic algorithm optimization process, a batch of candidate diffraction unit structures with differences in their emphasis on diffraction efficiency and angular bandwidth performance can be generated. For example, a set of optimization runs will... Set to a larger value One set of weights is set to a smaller value to prioritize unit structures with high diffraction efficiency; the other set of optimization runs uses the opposite weight configuration to prioritize unit structures with large angular bandwidth. Optionally, after the genetic algorithm optimization process is complete, for the optimization results obtained under each weight configuration, i.e., the final set of control point coordinates, a 3D modeling kernel needs to be invoked. The 3D modeling kernel reconstructs a non-uniform rational B-spline curve surface based on the provided control point coordinates and converts this parameterized surface into a solid triangular mesh model with a specific resolution. Finally, the 3D modeling kernel exports the solid triangular mesh model of each candidate diffraction unit structure in a standard file format, generating an independent 3D geometric model file.

[0026] In one embodiment of the present invention, full-wave electromagnetic simulation software reads the three-dimensional geometric model file and converts it into a mesh format suitable for calculation using the finite-difference time-domain method. The mesh size is set according to the simulation wavelength and structural characteristics, for example, the mesh size is set to one-twentieth of the minimum wavelength. The wavelength range of the incident light is set to the visible light band to the near-infrared band, specifically from 400 nm to 800 nm, and this range is discretized into multiple monochromatic light sources with a fixed step size of 5 nm. For each monochromatic light source, such as monochromatic light with a wavelength of 550 nm, the plane wave light source is loaded into the meshed model under two basic modes: transverse electric field polarization and transverse magnetic field polarization. Iterative solutions are performed under periodic boundary conditions until the calculated field energy residual is less than a preset convergence criterion.

[0027] In some embodiments, electric field component data at various points in space are collected after convergence of the finite-difference time-domain (FDTD) solution. By calculating the time average of the Poynting vector, the power distribution of the light wave at different diffraction orders after passing through the diffraction unit structure under a specific polarization state and given a monochromatic light source is obtained. The above calculation is repeated for each monochromatic light source and each polarization state. The obtained power diffraction efficiency distribution is integrated according to wavelength, polarization state, and diffraction order to form a multi-dimensional simulated scattering field data cube. The records of all candidate diffraction unit structures in the simulated scattering field data cube are traversed, and the principal diffraction efficiency peak value of each structure in the transverse electric field polarization mode is extracted and recorded as the first peak value. The principal diffraction efficiency peak value of the same candidate diffraction unit structure in the transverse magnetic field polarization mode is retrieved and recorded as the second peak value. The relative deviation percentage between the first and second peak values ​​is calculated using the following formula: in: Indicates the percentage of relative deviation. The first peak value represents the principal diffraction efficiency peak under the transverse electric field polarization mode. This represents the peak value of the principal diffraction efficiency under the transverse magnetic field polarization mode, which is also the second peak value. A polarization sensitivity tolerance threshold is set, for example, 5%. Candidate diffraction unit structures with a calculated relative deviation percentage greater than 5% are marked as polarization-sensitive structures and discarded.

[0028] In practical implementation, for candidate structures that pass the aforementioned polarization sensitivity test, their response data under 45-degree diagonal linear polarization is further read from the simulated scattering field data cube to verify the principal diffraction efficiency of the candidate structure under 45-degree linear polarization incident light. Candidate structures verified by transverse electric field polarization, transverse magnetic field polarization, and diagonal polarization are transferred from the temporary simulation list in memory to a separate database or list structure for storing the set of polarization-insensitive elements. Optionally, a data cleaning step is included before storing the candidate structures in the set of polarization-insensitive elements and establishing the mapping table. For each candidate structure in the set of polarization-insensitive elements, the log file generated by the software during the full-wave electromagnetic simulation solution is checked to confirm whether there are error log entries indicating mesh divergence or convergence failure. It is understood that if there are error logs recording mesh divergence, it is necessary to backtrack to the parametric modeling step that generated the 3D geometric model file of this structure.

[0029] In some embodiments, for candidate structures with simulation errors, the edge sharpness of the micro / nano relief contour defining its shape is fine-tuned in the parametric modeling software. For example, sharp corners of the contour are rounded to repair topological defects that may lead to mesh quality degradation. The repaired, new 3D geometric model file is resubmitted to the simulation queue, and the complete full-wave electromagnetic simulation process is executed until a set of simulation scattering field data without error logs is obtained. The newly obtained simulation scattering field data is checked for consistency with the frequency domain amplitude and phase distribution features initially extracted from the structured feature input set to drive the generation of the structure. Optionally, the root mean square error between the simulated principal diffraction efficiency and the feature inversion target value can be calculated as a consistency index. If the root mean square error is lower than a preset lower limit, the candidate structure is discarded and the modeling optimization process from features to 3D geometric model is restarted.

[0030] In one embodiment of the present invention, the three-dimensional geometric model file of each unit structure in the polarization-insensitive unit set is analyzed to extract several key dimensional parameters for defining the unit shape. For example, for a rectangular relief structure, the key dimensional parameters may include the relief height, the width of the top of the relief, the width of the bottom of the relief, and the structural period. These parameters are recorded in micrometers or nanometers. The diffraction efficiency at a specific center wavelength, the full width at half maximum (FWHM) bandwidth of the diffraction main peak, and the root mean square error of the diffraction efficiency curve over the entire target working bandwidth of the corresponding unit structure are retrieved from the post-processed simulated scattering field data. These three quantities are used as core optical performance indicators.

[0031] In practice, the multidimensional vector is constructed by using all key dimension parameters as the first part of the vector as independent variables and all optical performance indicators as the second part as dependent variables. For example, if a unit structure has four key dimension parameters and three optical performance indicators, the constructed multidimensional vector will be a 7-dimensional vector. All multidimensional vectors corresponding to the unit structures are entered into a high-speed cache database, such as Redis, and a hash index based on geometric parameters is created for each vector record. The hash key can be a combination of strings representing the key dimension parameters. A snapshot of the data in the cache database is then exported in tabular form to generate the final mapping table for the polarization-insensitive diffraction unit structure library. See Table 1 for a simplified example of the mapping table.

[0032] Table 1: Mapping Table of Structure Parameters and Performance of Polarization-Insensitive Diffraction Unit Optionally, the polarization-insensitive diffraction unit cell library supports incremental updates. It monitors the latest micro / nano fabrication process design rule documents in the semiconductor manufacturing field, extracting new manufacturable topographic features from these documents, such as a new sidewall tilt angle range or minimum fillet radius. These new features are then used as input variables for incremental design. In some embodiments, the incremental update process hybridizes and recombines the input variables of the incremental design with existing polarization-insensitive diffraction unit cell libraries that are identified as high-performance by a mapping table. For example, it selects unit cells with diffraction efficiencies higher than 0.9 from the library, combines their key dimensional parameters with the newly added topographic feature parameters, and generates a series of new candidate geometric model parameter sets that conform to the latest process rules through scripts. For each newly generated candidate geometric model parameter set, the complete process from parametric modeling, full-wave electromagnetic simulation solving, polarization sensitivity screening, and multi-polarization channel response consistency verification is re-executed sequentially to obtain a batch of new polarization-insensitive unit cells that meet current manufacturing capabilities.

[0033] In practice, these new polarization-insensitive unit structures are merged with the existing polarization-insensitive diffraction unit structure library. During the merging process, duplicate and redundant entries need to be removed. For example, if the differences in all key dimensional parameters between two unit structures are within a preset tolerance range, they are considered duplicate entries and only one is retained. After deduplication, multi-dimensional vectors of key dimensional parameters and optical performance parameters need to be generated for the newly added unit structures, and these new vector records are appended to the cache database. The mapping table of the polarization-insensitive diffraction unit structure library is updated to integrate the new records. Simultaneously, the range of the hash index is recalculated and adjusted based on the expanded parameter space to complete a full incremental update iteration. For example, the formula for calculating the root mean square error within the working bandwidth can be defined as: in: This represents the root mean square error. This represents the total number of wavelength points sampled within the operating bandwidth. Indicates at wavelength The diffraction efficiency value obtained from the simulation. Indicates at wavelength The preset target diffraction efficiency value is used to quantify the degree of agreement between the simulation results and the design target.

[0034] See Figure 4 In the comparative analysis of the full width at half maximum (FWHM) bandwidth distribution, the statistical characteristics of the original data and the incrementally updated data showed significant differences. From the box plot distribution, the median FWHM bandwidth of the original data group was approximately 12.5 nm, with the box range concentrated between 12.0 and 13.1 nm, extending to 10.0 nm and 14.2 nm above and below, respectively. Two outliers were also observed, indicating a high degree of dispersion and a large performance fluctuation range. The median FWHM bandwidth of the incrementally updated data group was approximately 11.9 nm, with the box range narrowing to 11.6–12.2 nm, extending to 11.2 nm and 12.7 nm above and below, respectively. Only one outlier was observed. This indicates that after the incremental update process, the FWHM bandwidth distribution of the cell structure was more concentrated, significantly improving performance consistency and stability. Simultaneously, the overall bandwidth level decreased slightly, reflecting the trade-off optimization between process constraints and performance robustness achieved through incremental updates.

[0035] In one embodiment of the present invention, by performing multivariate regression analysis or principal component analysis on the data of all unit structures in the table, it can be determined that parameters such as relief height and structural period have significantly higher weights on diffraction efficiency and bandwidth than other parameters, thus identifying relief height and structural period as the dominant geometric parameters. Based on the numerical distribution range of the dominant geometric parameters, the entire polarization-insensitive diffraction unit structure library is divided into several non-overlapping subspace index blocks. For example, based on the numerical range of relief height (200nm to 400nm), it is divided into 4 intervals, and based on the numerical range of structural period (300nm to 500nm), it is divided into 4 intervals. The Cartesian product of the two divides the parameter space into 16 subspace index blocks.

[0036] In some embodiments, a cluster center point representing the average performance of all unit structures within each partitioned subspace index block is calculated. The coordinates of the cluster center point are formed by the arithmetic mean of all multidimensional vectors within the subspace index block across various optical performance dimensions. For example, for a subspace index block containing 10 unit structures, the average values ​​of these 10 structures across three optical performance metrics—diffraction efficiency, full width at half maximum (FWHM), and root mean square error—are calculated, and the vector formed by these three average values ​​is recorded as the coordinates of the cluster center point of the subspace index block. When an external search request is received, such as a request to search for unit structures with a diffraction efficiency higher than 0.8 and a FWHM greater than 10 degrees, the distance metric between the target optical performance metric in the search request and the coordinates of the cluster center points of each subspace index block needs to be calculated first. It can be understood that the distance metric can be calculated using Euclidean distance, and its calculation formula is: in: This represents the distance between the search target and the cluster center of the k-th subspace index block. This represents the target value of the j-th optical performance index specified in the search request. This represents the coordinate value of the cluster center point of the k-th subspace index block in the j-th optical performance index dimension. This represents the total number of dimensions for the optical performance indicators considered. The calculated distance is selected. The subspace index block corresponding to the cluster center with the smallest median value is returned as the preliminary coarse screening result to the subsequent fine comparison process.

[0037] In practice, the retrieval and comparison process begins by retrieving the multidimensional vectors of all unit structures within the subspace index block obtained from the initial screening. These vector data are loaded from the database into local memory for parallel access to improve processing speed. The target optical performance index in the retrieval request is decomposed into specific threshold constraints, forming a multidimensional inequality screening rule. For example, the above retrieval request can be decomposed into two inequality conditions: "diffraction efficiency > 0.8" and "full width at half maximum (FWHM) bandwidth > 10 degrees". All multidimensional vectors within the subspace index block are traversed, and each vector's recorded optical performance index value is checked to see if it simultaneously satisfies all inequality conditions. Vector entries that do not meet all conditions are eliminated. Optionally, bitmap indexing technology can be used during the traversal and screening to accelerate the elimination of entries that do not meet the conditions. The remaining vector entries after screening are sorted in descending order according to their recorded diffraction efficiency values, and a few entries from the top of the sorted list are selected, for example, the top 5 entries in terms of diffraction efficiency.

[0038] See Figure 5In the correlation analysis between geometric parameters and optical performance, the quantification of the linear correlation between parameters relies on the Pearson correlation coefficient matrix. Specifically, key geometric parameters (relief height, structural period, aspect ratio) and optical performance indicators (diffraction efficiency, full width at half maximum (FWHM) bandwidth, and root mean square error) in the polarization-insensitive diffraction unit structure library are constructed into a multidimensional feature matrix. A symmetrical correlation heatmap is generated by calculating the Pearson correlation coefficients between each pair of parameters. The diagonal elements in the matrix are always 1.00, representing a perfect positive correlation between the parameter and itself; the off-diagonal elements reflect the strength of the linear correlation between parameters: the correlation coefficient between relief height and diffraction efficiency reaches 0.98, showing a very strong positive correlation; the correlation coefficient between structural period and FWHM bandwidth is 0.97, also showing a strong linear correlation; while the absolute values ​​of the correlation coefficients between aspect ratio, root mean square error, and other parameters are all below 0.12, exhibiting weak correlation or near-independence. The results of this analysis can be directly used to identify dominant geometric parameters, providing a quantitative basis for the subsequent subspace partitioning and indexing of the structure library.

[0039] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A method for constructing and indexing a polarization-insensitive diffraction unit structure library, characterized in that, Includes the following steps: Diffraction response datasets under incident light with various preset polarization states are collected, and Fourier transform processing is performed on the diffraction response datasets to extract frequency domain amplitude and phase distribution features. Based on the extracted frequency domain amplitude and phase distribution features, a set of three-dimensional geometric models covering candidate diffraction unit structures with different diffraction efficiencies and angular bandwidths are constructed using parametric modeling techniques. The three-dimensional geometric model of the candidate diffraction unit structure is imported into the full-wave electromagnetic simulation software and rigorously solved over a wide spectral range to generate simulated scattering field data containing polarization state information. The simulated scattering field data is post-processed to eliminate geometric configurations that are sensitive to changes in polarization state, and retain candidate structures that respond consistently in multiple polarization channels to form a set of polarization-insensitive units. Establish a mapping table between the geometric parameters and optical performance parameters of each unit structure in the polarization-insensitive unit set, and store the mapping table in the polarization-insensitive diffraction unit structure library.

2. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 1, characterized in that, The process of collecting diffraction response datasets under incident light with multiple preset polarization states and performing Fourier transform processing on the diffraction response datasets to extract frequency domain amplitude and phase distribution features specifically includes: The incident light source is configured with three basic modes: linear polarization, circular polarization, and elliptical polarization, and the incident angle of each mode is controlled to perform step scanning within a preset field of view. A photodetector array is set up at the receiving end to record the spatial distribution matrix of the light field intensity under different polarization states and different incident angle combinations, which serves as the original diffraction response dataset. For each frame of light intensity image in the original diffraction response dataset, a two-dimensional fast Fourier transform algorithm is applied to transform it to the frequency domain. In the frequency domain, the complex amplitude value at the center diffraction order under the working condition corresponding to the current frame light intensity image is calculated, and the real part and imaginary part are separated, which are respectively used as the frequency domain amplitude feature and phase distribution feature under the working condition corresponding to the current frame light intensity image. The extracted frequency domain amplitude features and phase distribution features are categorized according to their corresponding operating condition labels to form a structured feature input set.

3. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 2, characterized in that, Based on the extracted frequency domain amplitude and phase distribution features, a set of three-dimensional geometric models covering candidate diffraction unit structures with different diffraction efficiencies and angular bandwidths is constructed using parametric modeling techniques. Specifically, this includes: The dielectric constant and thickness of the substrate material of the diffraction unit are defined as fixed constraints, and the micro-nano relief profile of the unit surface is defined as an adjustable degree of freedom. Based on the frequency domain amplitude and phase distribution characteristics of the structured feature input set, the target phase delay and target amplitude modulation curve are deduced and transformed into a surface fitting objective function. A genetic algorithm is used to perform global optimization in the space of freedom, and the coordinates of the control points of the micro-nano relief contour are iteratively adjusted until the response of the generated unit structure in the forward simulation matches the objective function. By changing the weight ratio of diffraction efficiency and bandwidth in the fitness function of the genetic algorithm, a batch of candidate diffraction unit structures with different performance focuses are generated. The 3D modeling kernel is invoked to convert the optimized control point coordinates into a solid mesh and export the 3D geometric model file of the candidate diffraction unit structure.

4. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 3, characterized in that, The three-dimensional geometric model of the candidate diffraction unit structure is imported into full-wave electromagnetic simulation software, and rigorously solved over a wide spectral range to generate simulated scattering field data containing polarization state information, specifically including: Read the three-dimensional geometric model file of the candidate diffraction unit structure and convert it into a mesh generation format suitable for calculation using the finite-difference time-domain method; The wavelength range of the incident light is set to the visible light band to the near-infrared band, and it is discretized into multiple monochromatic light sources with a fixed step size; For each monochromatic light source, under both transverse electric field polarization and transverse magnetic field polarization modes, the model is loaded into the mesh-division format and iteratively solved under the boundary conditions. Collect the electric field component data after convergence and obtain the power diffraction efficiency distribution under different polarization states by calculating the time average value of the Poynting vector; The power diffraction efficiency distributions under different wavelengths and polarization states are integrated and assembled into a multi-dimensional simulated scattering field data cube.

5. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 4, characterized in that, The simulated scattering field data is post-processed to remove geometric configurations sensitive to polarization state changes, retaining candidate structures with consistent responses across multiple polarization channels. Specifically, this includes: Traverse the records of all candidate diffraction unit structures in the simulated scattering field data cube, extract the peak value of the principal diffraction efficiency in the transverse electric field polarization mode, and record it as the first peak value. The peak value of the main diffraction efficiency of the same candidate diffraction unit structure in the transverse magnetic field polarization mode is retrieved and recorded as the second peak value. The percentage of relative deviation between the first peak value and the second peak value is calculated. A polarization sensitivity tolerance threshold is set, and candidate diffraction unit structures whose relative deviation percentage is greater than the polarization sensitivity tolerance threshold are marked as polarization sensitive and eliminated. For candidate structures that pass the polarization sensitivity test, their response data under diagonal polarization is further read to verify their robustness under arbitrary polarization incident conditions. Candidate structures that pass all polarization consistency verifications are moved from the temporary simulation list in memory to the set of polarization-insensitive cells.

6. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 5, characterized in that, Establish a mapping table between the geometric parameters and optical performance parameters of each unit structure in the polarization-insensitive unit set, specifically including: Traverse each unit structure in the polarization-insensitive unit set and analyze several key dimensional parameters used to define the shape in its three-dimensional geometric model; The diffraction efficiency, full width at half maximum (FWHM) bandwidth, and root mean square error within the operating bandwidth of the corresponding unit structure are retrieved from the simulated scattering field data and used as optical performance indicators. The key size parameters and the optical performance indicators are paired by key values ​​to construct a multidimensional vector, where the first half of the vector is the independent variable and the second half is the dependent variable. All multidimensional vectors corresponding to the unit structures are entered into the cache database, and a hash index based on geometric parameters is established. The data snapshots in the cache database are solidified to generate the final mapping table of the polarization-insensitive diffraction unit structure library.

7. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 6, characterized in that, It also includes the step of building the index, specifically: In the mapping table of the polarization-insensitive diffraction unit structure library, the dominant geometric parameters with the highest weights affecting optical performance indicators are identified; Based on the numerical distribution range of the dominant geometric parameters, the polarization-insensitive diffraction unit structure library is divided into several non-overlapping subspace index blocks. For each subspace index block, calculate a cluster center point that represents the average performance of the cell structure within the subspace index block, and record the coordinate values ​​of the cluster center point; When an external retrieval request is received, the distance metric between the target optical performance index in the retrieval request and each cluster center point is first calculated. Select the subspace index block corresponding to the nearest cluster center point as the coarse screening result and return it to the subsequent fine comparison process.

8. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 7, characterized in that, After selecting the subspace index block corresponding to the nearest cluster center point, the method further includes a retrieval and comparison step, specifically: Retrieve the multidimensional vectors of all unit structures within the subspace index block obtained from the coarse screening, and load them into local memory for parallel access. The target optical performance index in the search request is broken down into specific threshold constraints to form a multidimensional inequality screening rule. Traverse all multidimensional vectors within the subspace index block and remove vector entries that do not satisfy the multidimensional inequality filtering rules; For the remaining vector entries, sort them in descending order according to their diffraction efficiency values, and extract a number of entries from the top of the sorted list. The unit structure identifier codes corresponding to the extracted entries are packaged and output as the final search results.

9. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 8, characterized in that, Before establishing the mapping table for the polarization-insensitive diffraction unit structure library, a data cleaning step is also included, specifically: For each candidate structure in the polarization-insensitive unit set, check whether there are error logs of mesh divergence or convergence failure during the simulation process; If an error log exists, the process is traced back to the corresponding 3D geometric model generation step, and the edge sharpness of the micro-nano relief contour is fine-tuned to repair topological defects. Resubmit the repaired 3D geometric model to the simulation queue until a set of error-free simulated scattering field data is obtained. Check the degree of agreement between the simulated scattering field data and the original frequency domain amplitude and phase distribution characteristics. If the degree of agreement is lower than the lower limit, discard the candidate structure and restart the modeling process. Only candidate structures confirmed through the data cleaning process are allowed to proceed to the stage of establishing the mapping relationship table.

10. The method for constructing and indexing a polarization-insensitive diffraction unit structure library according to claim 9, characterized in that, It also includes the step of incrementally updating the polarization-insensitive diffraction unit structure library, specifically: Monitor the latest micro / nano fabrication process design rules, extract newly added manufacturable morphological features, and use them as input variables for incremental design; The input variables of the incremental design are hybridized and recombined with high-performance unit structures in the existing polarization-insensitive diffraction unit structure library to generate the next generation of candidate geometric models. The newly generated candidate geometric models are sequentially subjected to parametric modeling verification, full-wave electromagnetic simulation solution, polarization sensitivity screening, and multi-polarization channel response consistency verification processes to obtain a batch of new polarization-insensitive unit structures. This batch of new polarization-insensitive unit structures is merged with the existing polarization-insensitive diffraction unit structure library, and duplicate and redundant entries are removed. The mapping table of the polarization-insensitive diffraction unit structure library is updated, the index range is expanded, and an incremental update iteration is completed.

Images