A full dielectric metasurface polarization beam splitter and a design method thereof

Abstract

The application discloses a kind of full medium metasurface polarization beam splitter, comprising: silica substrate, rectangular silicon nanocolumn array being arranged on the upper surface of the silica substrate and air medium being located above the rectangular silicon nanocolumn array;The design method of the polarization beam splitter includes obtaining unit electromagnetic response dataset;A plurality of forward agent models are trained to obtain predicted response and uncertainty;Candidate unit sampling is selected and RCWA is reviewed;According to the RCWA review result, a multi-level polarization phase library is established;Assemble complete multi-level phase gradient supercell and calculate each propagation diffraction order;Check each propagation diffraction order to meet the constraints;High-precision electromagnetic review is performed;If all meet, output its structure parameters and corresponding electromagnetic evidence record.The design method is gradually admitted by layering through, so that the same trace record is bound in each step in the design process, so that the source of performance loss is effectively identified to improve the structure.

Description

Technical Field

[0001] This invention relates to the field of polarization beam splitter technology, and specifically discloses an all-dielectric metasurface polarization beam splitter and its design method. Background Technology

[0002] Polarization beamsplitters are used to separate two mutually orthogonal input polarization states into different spatial channels, and are fundamental devices in optical communication, integrated photonics, quantum optics, polarization imaging, and optical sensing systems. Traditional polarization beamsplitters typically employ birefringent crystals, prisms, thin-film multilayer structures, or waveguide coupling structures. While these devices can achieve polarization separation, they often suffer from problems such as large size, long propagation distance, integration difficulties, or sensitivity to assembly and adjustment precision.

[0003] In recent years, all-dielectric metasurfaces composed of subwavelength dielectric structures have been able to achieve wavefront control within a planar device by locally propagating phase and polarization-dependent responses. Existing metasurface polarization beam splitting schemes typically involve periodically scanning the geometric parameters of individual nanopillars or nanofins to obtain the transmission amplitude and phase under two orthogonal polarizations; then, according to the target linear phase gradient, selecting the structure closest to the target phase point by point from a cell library; finally, these cells are spliced ​​together into a phase gradient supercell and periodically replicated to form the device. Another type of existing design scheme uses neural networks to learn the mapping between "geometric parameters and optical response," or attempts to directly invert the geometric structure from the target spectrum, phase, or efficiency. A common approach is to randomly divide the cell-level simulation samples into training, validation, and test sets, use a forward or inverse neural network to replace part of the full-wave calculation, and then select the structure based on the network output.

[0004] However, a core problem with existing polarization beamsplitters is that good unit-level performance does not equate to good device-level beam splitting performance. When units are stitched together into a supercell, near-field coupling occurs between adjacent structures, and discrete phase errors accumulate throughout the supercell. Ultimately, the energy not only enters the target diffraction order but may also enter the reverse first, zero, and other propagable orders. Therefore, ranking structures solely based on unit transmittance and phase error easily leads to combinations that appear excellent at the unit level but are inefficient at the target order at the supercell level.

[0005] Furthermore, if conventional neural networks are used directly as the final reverse engineer, they will face issues of multiple solutions and reliability. The optical response of the same target may correspond to multiple sets of geometric structures, and the predictions given by the network may fall in sparse regions of the training data. This leads to the prediction structure satisfying the unit-level fitting error, but failing to guarantee the target diffraction order efficiency, extinction ratio, zero-order suppression, and energy conservation of the entire device.

[0006] Furthermore, existing polarizer design methods often mistakenly equate total transmittance with the target order efficiency. Total transmittance is the sum of the energy of all transmitted propagation orders; high total transmittance does not necessarily mean that energy is concentrated at the target output port. Simply assuming total transmittance as the target order efficiency often leads to an inability to identify the true source of performance loss, thus hindering targeted structural improvements.

[0007] Furthermore, a single low-precision or single numerical method may be affected by Fourier truncation, mesh density, boundary conditions, order projection, and normalization methods. Without high-precision supercell calculations, convergence checks, energy balance checks, and verification of directional consistency among different full-wave methods, the reliability of the final performance data is insufficient.

[0008] Therefore, there is an urgent need to propose an all-dielectric metasurface polarization beamsplitter and its design method, so that the polarization beamsplitter can not only select structural combinations with high target order efficiency at the supercell level during the design process, but also effectively guarantee the target diffraction order efficiency, extinction ratio and zero-order suppression of the entire device. At the same time, it can effectively identify the real source of performance loss during the design process and improve the structure accordingly. Summary of the Invention

[0009] (a) Technical problems to be solved

[0010] To address the aforementioned issues, this invention provides an all-dielectric metasurface polarization beamsplitter and its design method. This all-dielectric metasurface polarization beamsplitter and its design method employ a hierarchical admission relationship: surrogate prediction evidence—unit RCWA verification evidence—complete supercell diffraction order screening evidence—high-precision modeling evidence. This allows the design process of the polarization beamsplitter to not only screen for structural combinations with high target order efficiency at the supercell level, but also effectively guarantee the target diffraction order efficiency, extinction ratio, and zero-order suppression of the entire device. Furthermore, the design process can effectively identify the true sources of performance loss for targeted structural improvements.

[0011] (II) Technical Solution

[0012] To address the aforementioned technical problems, this invention proposes a design method with a traceable electromagnetic evidence chain. This method is used to determine the structural parameters of an all-dielectric metasurface polarization beam splitter. The design method with a traceable electromagnetic evidence chain includes:

[0013] S1. Obtain the unit electromagnetic response dataset;

[0014] S2. Train multiple forward surrogate models with different random seeds, obtain the predicted response of candidate geometric parameters and the uncertainty represented by the prediction divergence between models, and record the predicted response and uncertainty as prediction-level evidence used only for candidate ranking.

[0015] S3. Construct a candidate ranking based on the prediction-level evidence, select candidate geometric parameters with high prediction performance or large prediction discrepancies between models, re-execute the unit RCWA calculation, and associate and record the solution configuration, solution status and dual polarization transmission response as backtesting-level evidence; the RCWA response in the backtesting-level evidence replaces the corresponding surrogate prediction response and serves as the response data allowed to enter the multi-level polarization phase library;

[0016] S4. Establish a multi-level polarization phase library based only on the candidate cells that have been successfully solved and meet the cell admission conditions in the backtesting evidence.

[0017] S5. Select candidate units from the multi-level polarization phase library to assemble a complete multi-level phase gradient supercell, calculate all propagable diffraction orders using the screening precision RCWA, and record the solution configuration, efficiency of each order and solution status as screening level evidence.

[0018] S6. Using the locked reference supercell as a retained candidate, compare the candidate supercell to be replaced with the locked reference supercell under the same screening accuracy RCWA configuration; only when the average target order efficiency of the candidate supercell to be replaced is higher than that of the locked reference supercell, the decrease in ERx and ERy relative to the locked reference supercell is not more than 0.5 dB, the average zero-order residue of the two polarizations is not more than that of the locked reference supercell plus 0.002, the sum of other transmission orders of the two polarizations is not more than that of the locked reference supercell plus 0.005, and the difference in the target order efficiency of the two polarizations is not more than 1.10 times the corresponding difference of the locked reference supercell, is the candidate supercell to be replaced determined to meet the constraints; otherwise, record the unmet constraints and the reason for rejection, and retain the locked reference supercell or return to step S3 or S4 to select an alternative candidate unit;

[0019] S7. Using a Fourier order and a denser spatial grid with a higher screening accuracy than in step S5, perform a high-precision RCWA verification on candidate supercells that meet the constraints of step S6, recalculate all propagable diffraction orders and energy balance. If the verification fails, reduce the evidence level and return to step S3 or S4.

[0020] S8. If the high-precision RCWA verification is passed, then the finalized evidence is formed and the structural parameters of the multi-level phase gradient supercell and the corresponding electromagnetic evidence record are output. The electromagnetic evidence record includes at least the evidence level, candidate identifier, geometric parameters, source identifier, solution configuration, output physical quantity, solution status and the correlation between upstream and downstream evidence.

[0021] Preferably, step S1 includes:

[0022] S101. Establish a periodic unit model of a silicon dioxide substrate, air, and rectangular silicon nanopillars, and use periodic lateral boundary conditions and normal incident plane wave excitation.

[0023] S102. Scan rectangular silicon nanopillars within the processable Lx, Ly, and height parameter space;

[0024] S103. Solve for the complex transmission coefficients for x-linear polarization and y-linear polarization respectively, and record Tx, Ty, φx and φy. To eliminate the learning discontinuity caused by the phase jump at -π and π, retain Tx and Ty, and encode φx and φy as sinφx, cosφx, sinφy and cosφy respectively.

[0025] S104. The geometric input for each sample is Lx, Ly, H, and the response output is Tx, Ty, sinφx, cosφx, sinφy, cosφy.

[0026] S105. After marking and removing samples with abnormal calculations, energy gaps, or geometrically unmanufacturable characteristics, a dataset of unit electromagnetic responses is formed.

[0027] Preferably, in step S2, to reduce the bias caused by random initialization of a single network, multiple forward models with the same structure but random seeds are trained. The normalized Lx, Ly, and H are input into the integrated forward proxy model, and the output ensemble mean is used as the prediction response. The prediction discrepancy between the models is used as an uncertainty signal.

[0028] Preferably, the backbone network of the integrated forward proxy model includes 5 fully connected hidden layers, each with 256 neurons. The hidden layers use the GELU activation function and have a Dropout value of 0.05.

[0029] The output of the integrated forward proxy model includes two parts: transmittance and phase components. Tx and Ty are output using Sigmoid to constrain their numerical range. The four phase components are output using linearity. The loss function is the weighted mean square error of each output component, and a phase unit circle constraint is added to make the predicted sinφ and cosφ satisfy sin²φ+cos²φ≈1 and the weight of the unit circle penalty term is 0.05.

[0030] Preferably, step S3 includes:

[0031] S301. The candidate geometric parameters are predicted forward using multiple integrated forward models to obtain the mean values ​​of dual-polarization transmission and phase response.

[0032] S302. Construct a candidate ranking based on the transmittance, phase error, geometric manufacturability, and model uncertainty of the X-polarization channel and the Y-polarization channel;

[0033] S303. Prioritize candidate points with high prediction performance or large model divergence, and re-execute RCWA calculation;

[0034] S304. Add the newly added RCWA calculation results to the forward model training set in step S2;

[0035] S305. Repeat steps S301-S304 until each target phase level has at least one candidate cell that has been verified by the cell RCWA and meets the requirements for transmittance, phase error and geometric spacing.

[0036] Preferably, step S4 includes:

[0037] S401. Divide 0 to 2π into multiple target phase levels, with each level evenly spaced.

[0038] S402. For each phase level, select rectangular silicon nanopillars that simultaneously satisfy the following conditions from the candidates after RCWA verification: x and y polarization target phase, Tx and Ty are both greater than 0.70, phase error is lower than the preset upper limit, and geometric manufacturability. Establish a multi-level polarization phase library.

[0039] Preferably, step S5 includes:

[0040] S501. Based on the multi-level polarization phase library established in step S4, multiple selected units are arranged sequentially according to the principle that the x-polarization phase increases along the supercell direction and the y-polarization phase decreases along the supercell direction.

[0041] S502, Supercell-level screening: Perform screening precision RCWA on a complete supercell composed of multiple selected units, solve all propagable diffraction orders, and calculate the target order efficiency, reverse first-order leakage, zero-order residue, and the sum of other transmission orders for x and y polarization.

[0042] Preferably, in step S7, based on the high-precision supercell RCWA, three types of checks are performed on the structural parameters of the multi-level phase gradient supercell:

[0043] S701. Calculate all propagable transmission diffraction orders and reflection power, and set T+R+A=1 within the preset numerical tolerance kernel.

[0044] S702. Use wavelength-correlated real part refractive index to check the dispersion sensitivity of materials;

[0045] S703. Use Lumerical FDTD and COMSOL / FEM to check whether the diffraction direction and field distribution of the dominant energy are consistent with the high-precision RCWA. FDTD and COMSOL / FEM are only used as evidence of consistency in direction and trend, and do not replace the quantitative results of high-precision RCWA.

[0046] The present invention also provides an all-dielectric metasurface polarization beamsplitter for polarization separation in the 1550 nm near-infrared band. The structural parameters of the all-dielectric metasurface polarization beamsplitter are determined based on the above-mentioned design method with a traceable electromagnetic evidence chain. The all-dielectric metasurface polarization beamsplitter includes: a silicon dioxide substrate, a rectangular silicon nanopillar array disposed on the upper surface of the silicon dioxide substrate, and an air medium located above the rectangular silicon nanopillar array.

[0047] The rectangular silicon nanopillar array comprises multiple rectangular silicon nanopillars arranged sequentially along the x-direction. The cross-section of each rectangular silicon nanopillar is set along the x-axis and y-axis respectively, and the corresponding lateral dimensions are Lx and Ly respectively. The same group of rectangular silicon nanopillars forms a discrete linear phase gradient that increases along the supercell direction for x-linear polarization, causing the main transmitted energy to enter the +1 diffraction order, and forms a discrete linear phase gradient that decreases along the same supercell direction for y-linear polarization, causing the main transmitted energy to enter the -1 diffraction order.

[0048] Preferably, the rectangular silicon nanopillar array comprises twelve rectangular silicon nanopillars with different lateral dimensions Lx and Ly, and the twelve rectangular silicon nanopillars are arranged sequentially along the x-direction to form a twelve-level phase gradient supercell; the height H of the rectangular silicon nanopillars is 800 nm, the center distance P between adjacent rectangular silicon nanopillars is 650 nm, the period Λ of the twelve-level phase gradient supercell is 12P and equal to 7800 nm, and the target phase interval between adjacent phase levels is 2π / 12.

[0049] (III) Beneficial Effects

[0050] Compared with existing technologies, the all-dielectric metasurface polarization beam splitter and its design method of the present invention have the following advantages:

[0051] 1. This all-dielectric metasurface polarization beam splitter uses a twelve-level phase gradient supercell that varies along the x-direction to ensure that normally incident x-polarized light mainly enters the +1 transmission diffraction order and normally incident y-polarized light mainly enters the -1 transmission diffraction order, thereby achieving spatial separation of two orthogonal polarizations on the same planar device.

[0052] 2. The design method with a traceable electromagnetic evidence chain sets up a hierarchical admission relationship of "proxy prediction evidence - unit RCWA verification evidence - complete supercell diffraction order screening evidence - high-precision modeling evidence". This allows the design process of the polarization beam splitter to not only screen out structural combinations with high target order efficiency at the supercell level, but also effectively ensure the target diffraction order efficiency, extinction ratio and zero-order suppression of the entire device. At the same time, each step in the design process is bound to the same traceability record, which enables it to effectively identify the real source of performance loss and improve the structure in a targeted manner. Attached Figure Description

[0053] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 A schematic diagram of the overall process of the traceable electromagnetic evidence chain design method of the present invention;

[0055] Figure 2 This is a schematic diagram showing the module composition and data transmission relationship of the metasurface polarization beam splitter of the present invention;

[0056] Figure 3 This is a schematic diagram illustrating the electromagnetic evidence levels, evidence-level conditions, and data access permissions for each level in this invention.

[0057] Figure 4 This is a schematic diagram illustrating the hierarchical relationship between the metasurface unit structure, the multi-level polarization-dependent phase library, and the complete phase gradient supercell of the present invention.

[0058] Figure 5 This is a schematic diagram of the process of performing constraint rejection, soft scoring sorting, and high-precision modeling verification on supercell candidates according to the present invention. Detailed Implementation

[0059] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0060] The following is in conjunction with the appendix Figure 1-5 The all-dielectric metasurface polarization beam splitter and its design method of the present invention will be further described.

[0061] Please refer to Figure 4This invention discloses an all-dielectric metasurface polarization beamsplitter for polarization separation in the 1550 nm near-infrared band. It comprises: a silicon dioxide substrate, a rectangular silicon nanopillar array disposed on the upper surface of the silicon dioxide substrate, and an air medium located above the rectangular silicon nanopillar array. The rectangular silicon nanopillar array includes multiple rectangular silicon nanopillars arranged sequentially along the x-direction. The cross-section of each rectangular silicon nanopillar is arranged along the x-axis and y-axis respectively, with corresponding lateral dimensions Lx and Ly. The same group of rectangular silicon nanopillars forms a discrete linear phase gradient increasing along the supercell direction for x-linear polarization, causing the main transmitted energy to enter the +1 diffraction order, and forms a discrete linear phase gradient decreasing along the same supercell direction for y-linear polarization, causing the main transmitted energy to enter the -1 diffraction order.

[0062] In one specific embodiment, as shown in Table 1, the cross-section of the silicon nanopillar is a rectangle with sides set along the x-axis and y-axis respectively, and its lateral dimensions are denoted as Lx and Ly. The pillar height H is 800 nm; the center distance between adjacent units, i.e., the unit period P, is 650 nm.

[0063] Twelve rectangular silicon nanopillars with different Lx and Ly values ​​are arranged sequentially to form a twelve-level phase gradient supercell that varies along the x-direction. The supercell period Λ = 12P = 7800 nm. The target phase interval of the twelve phase levels is 2π / 12. Due to the different effective refractive indices and propagation phases of the rectangular nanopillars in the x and y directions, the same geometric unit can simultaneously generate independent transmission amplitudes and transmission phases for x-linear polarization and y-linear polarization.

[0064] Table 1: Specific Structural Parameters of Metasurface Polarization Beam Splitter

[0065]

[0066] In this embodiment, the rectangular silicon nanopillar can be equivalent to a subwavelength waveguide with different effective refractive indices for x and y polarizations. As incident light passes through the nanopillar, a polarization-dependent propagation phase accumulates. By jointly changing Lx and Ly, the desired phases can be selected for the x and y polarization channels respectively while maintaining high transmittance. When the supercell phase varies along the x-direction in fixed steps, the Fourier components of the transmitted field coherently superimpose at specific diffraction orders. The x-polarization channel uses a phase sequence pointing to the +1st order, and the y-polarization channel uses a phase sequence pointing to the -1st order. Thus, the two orthogonal polarizations propagate in opposite directions in the far field. For normal incident conditions, the first-order deflection direction is determined by the grating equation and the supercell period.

[0067] Furthermore, this invention defines the +1st order efficiency ηx, +1 under x-polarization and the -1st order efficiency ηy, -1 under y-polarization as the target order efficiency; the opposite order ηx, -1 and ηy, +1 as reverse leakage; m=0 as the zeroth order; and the sum of the remaining propagable transmission orders as other transmission orders. The total transmittance Ttot is the sum of all propagating transmission orders and cannot replace the target order efficiency. The extinction ratios of the two polarization channels are defined as: ERx = 10log10(ηx, +1 / ηx, -1) and ERy = 10log10(ηy, -1 / ηy, +1). By simultaneously examining the target order efficiency, reverse leakage, zeroth order, other transmission orders, total reflectance, and T+R+A energy balance, it is determined whether the device truly achieves high-quality polarization beam splitting.

[0068] like Figure 1 , Figure 2 , Figure 3 and Figure 5 As shown, the present invention also provides a design method with a traceable electromagnetic evidence chain, which is used to determine the structural parameters of the above-mentioned all-dielectric metasurface polarization beam splitter. The design method with a traceable electromagnetic evidence chain includes:

[0069] S1. Obtain the unit electromagnetic response dataset;

[0070] S2. Train multiple forward surrogate models with different random seeds, obtain the predicted response of candidate geometric parameters and the uncertainty represented by the prediction divergence between models, and record the predicted response and uncertainty as prediction-level evidence used only for candidate ranking.

[0071] S3. Construct a candidate ranking based on the prediction-level evidence, select candidate geometric parameters with high prediction performance or large prediction discrepancies between models, re-execute the unit RCWA calculation, and associate and record the solution configuration, solution status and dual polarization transmission response as backtesting-level evidence; the RCWA response in the backtesting-level evidence replaces the corresponding surrogate prediction response and serves as the response data allowed to enter the multi-level polarization phase library;

[0072] S4. Establish a multi-level polarization phase library based only on the candidate cells that have been successfully solved and meet the cell admission conditions in the backtesting evidence.

[0073] S5. Select candidate units from the multi-level polarization phase library to assemble a complete multi-level phase gradient supercell, calculate all propagable diffraction orders using the screening precision RCWA, and record the solution configuration, efficiency of each order and solution status as screening level evidence.

[0074] S6. Using the locked reference supercell as a retained candidate, compare the candidate supercell to be replaced with the locked reference supercell under the same screening accuracy RCWA configuration; only when the average target order efficiency of the candidate supercell to be replaced is higher than that of the locked reference supercell, the decrease in ERx and ERy relative to the locked reference supercell is not more than 0.5 dB, the average zero-order residue of the two polarizations is not more than that of the locked reference supercell plus 0.002, the sum of other transmission orders of the two polarizations is not more than that of the locked reference supercell plus 0.005, and the difference in the target order efficiency of the two polarizations is not more than 1.10 times the corresponding difference of the locked reference supercell, is the candidate supercell to be replaced determined to meet the constraints; otherwise, record the unmet constraints and the reason for rejection, and retain the locked reference supercell or return to step S3 or S4 to select an alternative candidate unit;

[0075] In this step, a comparison with the locked reference supercell using the same configuration is employed. Candidates for replacement enter high-precision verification only if all of the following conditions are met: ① The average target order efficiency of both polarizations is higher than the locked reference; ② The decrease in ERx and ERy relative to the reference does not exceed 0.5 dB, thus limiting reverse first-order leakage; ③ The average zero-order residual of both polarizations does not exceed the reference value plus 0.002; ④ The sum of other transmission orders of both polarizations does not exceed the reference value plus 0.005; ⑤ The difference in target efficiency between the two polarizations does not exceed 1.10 times the corresponding difference in the reference. If any condition is not met, the specific reason for rejection is recorded, the locked reference is retained, or the candidate selection / phase library is updated. The above criteria are derived from the Type A hard constraints in the actual supercell screening code.

[0076] S7. Using a higher Fourier order and denser spatial grid than the RCWA configuration in step S5, perform a high-precision RCWA verification on candidate supercells that meet the constraints of step S6, recalculate all propagating diffraction orders and energy balance. If the verification fails, reduce the evidence level and return to step S3 or S4. S8. If the high-precision RCWA verification passes, form a type-level evidence and output the structural parameters of the multi-level phase gradient supercell and the corresponding electromagnetic evidence record. The electromagnetic evidence record includes at least the evidence level, candidate identifier, geometric parameters, source identifier, solution configuration, output physical quantities, solution status, and the correlation between upstream and downstream evidence.

[0077] Further, step S1 includes:

[0078] S101. Establish a periodic unit model of a silicon dioxide substrate, air, and rectangular silicon nanopillars, and use periodic lateral boundary conditions and normal incident plane wave excitation.

[0079] S102. Scan rectangular silicon nanopillars within the processable Lx, Ly and height parameter space, with a reference height of 800 nm and a fixed unit period of 650 nm.

[0080] S103. Solve for the complex transmission coefficients for x-linear polarization and y-linear polarization respectively, and record Tx, Ty, φx and φy. To eliminate the learning discontinuity caused by the phase jump at -π and π, retain Tx and Ty, and encode φx and φy as sinφx, cosφx, sinφy and cosφy respectively.

[0081] S104. The geometric input for each sample is Lx, Ly, H, and the response output is Tx, Ty, sinφx, cosφx, sinφy, cosφy.

[0082] S105. After marking and removing samples with abnormal calculations, energy gaps, or geometrically unmanufacturable characteristics, a dataset of unit electromagnetic responses is formed.

[0083] In a specific embodiment, rectangular silicon nanopillars with a height of 800 nm were disposed on a silicon dioxide substrate, with air as the upper medium. The unit cell period was fixed at 650 nm. Under normal incident conditions and a center wavelength of 1550 nm, RCWA scans were performed on different combinations of Lx and Ly to obtain the transmittance and phase under x and y polarization, respectively. The 0–2π phase range was divided into 12 phase levels, and 12 rectangular pillars that balance high transmittance, dual polarization target phase, and manufacturability were selected to form a supercell with a period of 7800 nm.

[0084] During the arrangement, the x-polarization phase is varied stepwise by +π / 6, and the y-polarization phase is varied stepwise by -π / 6. High-precision RCWA is used to solve the complete supercell. The results show that the x-polarization +1st order efficiency is 0.788151, reverse leakage is 0.004688, and ERx = 22.26 dB; the y-polarization -1st order efficiency is 0.910945, reverse leakage is 0.001911, and ERy = 26.78 dB, achieving separation of the two orthogonal polarizations in opposite first-order diffraction directions.

[0085] See Figure 2 , Figure 3 In step S2, the forward surrogate model is used to quickly predict dual-polarization transmission and phase response from geometric parameters, rather than bypassing physical solutions to directly claim the final device performance. To reduce the bias caused by random initialization of a single network, five forward models with identical structures but random seeds are trained. The normalized Lx, Ly, and H are input into the ensemble forward surrogate model, and the ensemble mean of the output is used as the predicted response. The prediction discrepancies between the models are used as uncertainty signals.

[0086] The backbone network of the integrated forward proxy model consists of 5 fully connected hidden layers, each with 256 neurons. The hidden layers use the GELU activation function and are set to 0.05 for Dropout (Dropout is a regularization technique to prevent overfitting in deep neural networks, which increases the generalization ability of the model by randomly shutting down some neurons during training).

[0087] The output of the integrated forward proxy model includes two parts: transmittance and phase components. Tx and Ty are output using Sigmoid to constrain their numerical range. The four phase components are output using linear output. The loss function is the weighted mean square error of each output component, and a phase unit circle constraint is added to make the predicted sinφ and cosφ satisfy sin²φ+cos²φ≈1 and the weight of the unit circle penalty term is 0.05.

[0088] Specifically, as shown in Table 2, the feedforward model uses the AdamW optimizer with an initial learning rate of 0.001, weight decay of 0.0001, and a batch size of 64. The baseline data is divided into 1172 training samples, 251 validation samples, and 251 test samples. To reduce the bias caused by random initialization of a single network, five models with identical structures but random seeds of 42, 43, 44, 45, and 46 are trained. The ensemble mean is used as the predicted response, and the prediction discrepancy between models is used as an uncertainty signal.

[0089] Table 2: Forward Integration Proxy Model

[0090]

[0091] In step s2, the design method employs a forward surrogate model with three geometric inputs and six optical outputs, encodes the phase in sin / cos, and maintains physical phase consistency through a unit circle penalty.

[0092] In a preferred embodiment, step S3 includes:

[0093] S301. The candidate geometric parameters are predicted forward using five integrated forward models to obtain the mean values ​​of dual-polarization transmission and phase response.

[0094] S302. Construct a candidate ranking based on the transmittance, phase error, geometric manufacturability, and model uncertainty of the X-polarization channel and the Y-polarization channel;

[0095] S303. Prioritize candidate points with high prediction performance or large model divergence, and re-execute RCWA calculation;

[0096] S304. Add the newly added RCWA calculation results to the forward model training set in step S2; the expanded ensemble model is recorded as 1226 training samples, 260 validation samples, 251 fixed benchmark test samples and 3 active learning hold-out samples.

[0097] S305. Repeat steps S301-S304 until each target phase level has at least one candidate cell that has been verified by the cell RCWA and meets the requirements for transmittance, phase error and geometric spacing.

[0098] In step S3, based on the integrated model assembled in step S2, uncertainty is represented by model divergence, and RCWA supplementary calculations are guided by this uncertainty. Through an active learning process, limited high-precision electromagnetic calculations are prioritized for regions with higher information content or better potential performance. This invention does not consider surrogate model predictions as the final performance conclusion; all candidates entering the final twelve-level phase library must undergo RCWA verification. In the specific embodiment described above, this step uses the mean of five model predictions to rank candidate geometries and uses inter-model divergence to identify sparse training regions. Selected candidates undergo RCWA calculations again and are added to the expanded training set. The final candidates are still confirmed through complete supercell RCWA, effectively preventing surrogate prediction errors from being directly transmitted to device performance.

[0099] Further, step S4 includes:

[0100] S401. Divide 0 to 2π into 12 target phase levels, with each level evenly spaced and the level interval being π / 6;

[0101] S402. For each phase level, select rectangular silicon nanopillars that simultaneously satisfy the following conditions from the candidates after RCWA verification: x and y polarization target phase, Tx and Ty are both greater than 0.70, phase error is lower than the preset upper limit, and geometric manufacturability. Establish a 12-level polarization phase library.

[0102] like Figure 5 As shown, step S5 includes: S501, based on the 12-level polarization phase library established in step S4, arranging the 12 selected units sequentially according to the principle that the x-polarization phase increases along the supercell direction and the y-polarization phase decreases along the supercell direction;

[0103] S502, Supercell-level screening: Perform RCWA screening with a precision of 12 selected units on a complete supercell, solve for all propagable diffraction orders, and calculate the target order efficiency, reverse first-order leakage, zero-order residue, and the sum of other transmission orders for x and y polarization. If a candidate supercell to be replaced does not meet any of the constraints in step S6, record the corresponding rejection reason and eliminate it, even if its unit-level score is higher.

[0104] In step S5, a complete twelve-cell supercell screening is set between cell phase matching and final high-precision verification to avoid mismatch between cell-level scoring and device-level diffraction performance. Furthermore, in a specific embodiment, the twelve-cell supercell of Example 1 remains geometrically unchanged, and wavelength scanning is performed. Using ηx, +1 > 0.7 and ηy, -1 > 0.8 as common criteria, a 25 nm initial scan is performed, followed by verification with 10 nm and 5 nm step sizes. Successful RCWA points show a common working window of 1525–1600 nm. Subsequently, the wavelength-dependent real refractive indexes of Si and SiO2 are introduced, yielding an average target efficiency of 0.843084 at 1550 nm, with ERx = 21.944 dB and ERy = 26.241 dB.

[0105] Uniform ±2 nm, ±5 nm, and ±10 nm perturbations were applied to Lx and Ly, along with 20 sets of independent random perturbations of U(-5,+5) nm. Height perturbations were also calculated separately, resulting in a total of 43 configurations. For each configuration, the efficiency and leakage of the two polarization targets were recalculated to identify the impact of dimensional errors on device performance.

[0106] In the small-sample four-candidate analysis, the Pearson correlation coefficient between cell score and supercell average target order efficiency was -0.325, indicating that cell-level scores cannot reliably represent device-level performance. This result is used to illustrate the necessity of setting up the "supercell-level electromagnetic backtesting" step, rather than as a large-sample statistical regularity.

[0107] In one specific implementation, step S7 performs three types of checks on the structural parameters of the multi-level phase gradient supercell based on the high-precision supercell RCWA:

[0108] S701. Calculate all propagable transmission diffraction orders and reflection power, and set T+R+A=1 within the preset numerical tolerance kernel.

[0109] S702. Use wavelength-correlated real part refractive index to check the dispersion sensitivity of materials;

[0110] S703. Use Lumerical FDTD and COMSOL / FEM to check whether the diffraction direction and field distribution of the dominant energy are consistent with the high-precision RCWA. FDTD and COMSOL / FEM are only used as evidence of consistency in direction and trend, and do not replace the quantitative results of high-precision RCWA.

[0111] In this step, the final index is determined by high-precision supercell RCWA and is verified in layers by energy balance, dispersion, band, processing tolerance, and FDTD / COMSOL dominant order direction.

[0112] In specific embodiments, periodic models are established in Lumerical FDTD and COMSOL / FEM, respectively. The dominant direction of transmitted energy is determined by far-field order projection or Fourier projection of the transmission field. Both methods support the directional conclusion that x-polarization mainly points to the +1 order and y-polarization mainly points to the -1 order. Since the normalization and numerical discretization of different methods are not entirely the same, high-precision supercell RCWA is used as the quantitative basis for the final efficiency, leakage, and extinction ratio. The FDTD and COMSOL results serve as evidence of consistency in direction and trend, but do not replace the high-precision RCWA quantitative values.

[0113] Furthermore, based on the above-described design method with a traceable electromagnetic evidence chain, this invention provides a specific fabrication method for the hardware portion of a polarization beam splitter, comprising:

[0114] 1. Select a silicon dioxide substrate and clean it;

[0115] 2. Deposit or grow a silicon functional layer with a thickness of approximately 800 nm on the substrate surface;

[0116] 3. Spin-coating electron beam photoresist, followed by exposure and development according to the twelve-level supercell geometry;

[0117] 4. Deposit a hard mask or use a mask system suitable for silicon etching to transfer the pattern to the mask layer;

[0118] 5. Rectangular silicon nanopillar arrays are formed by reactive ion etching or inductively coupled plasma etching;

[0119] 6. Remove residual mask and clean to obtain an all-dielectric metasurface polarization beamsplitter with an air / silicon nanopillar / silicon dioxide substrate.

[0120] Under the conditions of Example 1, the actual design effect of this metasurface polarization beam splitter is as follows:

[0121] Under the approximation of normal incidence and transparent low-loss materials at 1550 nm, the high-precision supercell RCWA yields the following results: for x-polarized, the +1 target order efficiency is 0.788151, the reverse -1 order leakage is 0.004688, the zero order is 0.006641, the sum of other transmission orders is 0.106039, the total transmittance is 0.905520, and the extinction ratio ERx is 22.26 dB; for y-polarized, the -1 target order efficiency is 0.910945, the reverse +1 order leakage is 0.001911, the zero order is 0.006559, the sum of other transmission orders is 0.043757, the total transmittance is 0.963171, and the extinction ratio ERy is 26.78 dB.

[0122] Table 3: Actual Output Effects of X-Polarization and Y-Polarization

[0123]

[0124] The target transmission orders accounted for 87.04% and 94.58% of the total transmitted power, respectively; other transmission orders accounted for 11.71% and 4.54% of the total transmitted power, respectively. This indicates that the energy concentration is higher in the y-polarization region; the main loss in the x-polarization region is not the reverse first-order leakage, but rather the redistribution of energy to other transmission orders. This energy distribution analysis provides a clear direction for subsequent optimization.

[0125] The energy balance results are: x-polarization Ttot = 0.905520, Rtot = 0.094480, A = 0, T + R + A = 1.000000, and the energy balance error is 3.159 × 10⁻⁶. -14 y-polarization Ttot=0.963171, Rtot=0.036829, A=0, T+R+A=1.000000, error 1.314×10 -14 This eliminates the risk of misjudging numerical energy non-closure as high efficiency.

[0126] The fixed reference structure has a common threshold window of 1525–1600 nm at successfully calculated RCWA sampling points, categorized by an x-polarized target efficiency greater than 0.7 and a y-polarized target efficiency greater than 0.8. This window is first identified by a 25 nm step scan, and then verified by 10 nm and 5 nm step scans. A repeatable singular matrix failure point appears at 1560 nm, which is not interpolated or replaced with a neighboring value. Therefore, the aforementioned common threshold window only refers to successfully calculated discrete sampling points and does not represent uninterrupted continuous bandwidth.

[0127] By recalculating using the wavelength-dependent real refractive index and the transparency k approximation, the average efficiency of the two polarized targets at 1550 nm was obtained as 0.843084, ERx = 21.944 dB, and ERy = 26.241 dB. The common threshold window remained at 1525–1600 nm, indicating that the design has a certain degree of stability for the real dispersion of the material.

[0128] The fabrication tolerance simulation includes 43 configurations, including the baseline configuration, Lx / Ly uniform ±2 nm, ±5 nm, and ±10 nm perturbations, individual height perturbations, and 20 sets of independent uniformly distributed U(-5,+5) nm random lateral size perturbations; the random seed is 42, and the height remains constant in the random samples. The results of this set are used to evaluate the robustness of numerical manufacturing and are not used as measured fabrication yield.

[0129] Lumerical FDTD confirmed the +1st order of x-polarization and the -1st order of y-polarization as the dominant transmission directions at 1550 nm. Compared to RCWA, its order-type target values ​​showed a difference of +0.063331 (approximately +8.04%) in the x-channel and -0.075970 (approximately -8.34%) in the y-channel. These differences stem from normalization, order projection, boundary conditions, mesh discretization, and the finite computational domain; therefore, it is used for cross-method directional consistency rather than replacing RCWA quantitative data. Fourier projection results from COMSOL / FEM were also used to confirm the dominant order directions.

[0130] Lumerical FDTD confirmed the +1st order of x-polarization and the -1st order of y-polarization as the dominant transmission directions at 1550 nm. Compared to RCWA, its order-type target values ​​showed a difference of +0.063331 (approximately +8.04%) in the x-channel and -0.075970 (approximately -8.34%) in the y-channel. These differences stem from normalization, order projection, boundary conditions, mesh discretization, and the finite computational domain; therefore, it is used for cross-method directional consistency rather than replacing RCWA quantitative data. Fourier projection results from COMSOL / FEM were also used to confirm the dominant order directions.

[0131] In summary, the all-dielectric metasurface polarization beamsplitter designed using this traceable electromagnetic evidence chain approach achieves its design process through a hierarchical admission relationship of "surrogate prediction evidence—unit RCWA verification evidence—complete supercell diffraction order screening evidence—high-precision modeling evidence." This allows the design process to not only screen structural combinations with high target order efficiency at the supercell level but also effectively guarantee the target diffraction order efficiency, extinction ratio, and zero-order suppression of the entire device. Furthermore, each step in the design process is bound to the same traceability record, enabling the effective identification of the true source of performance loss for targeted structural improvements.

Claims

1. A design method for a traceable electromagnetic evidence chain, characterized in that, The design method with a traceable electromagnetic evidence chain is used to determine the structural parameters of an all-dielectric metasurface polarization beam splitter. The design method with a traceable electromagnetic evidence chain includes: S1. Obtain the unit electromagnetic response dataset; S2. Train multiple forward surrogate models with different random seeds, obtain the predicted response of candidate geometric parameters and the uncertainty represented by the prediction divergence between models, and record the predicted response and uncertainty as prediction-level evidence used only for candidate ranking. S3. Construct a candidate ranking based on the prediction-level evidence, select candidate geometric parameters with high prediction performance or large prediction discrepancies between models, re-execute the unit RCWA calculation, and associate and record the solution configuration, solution status and dual polarization transmission response as backtesting-level evidence; the RCWA response in the backtesting-level evidence replaces the corresponding surrogate prediction response and serves as the response data allowed to enter the multi-level polarization phase library; S4. Establish a multi-level polarization phase library based only on the candidate cells that have been successfully solved and meet the cell admission conditions in the backtesting evidence. S5. Select candidate units from the multi-level polarization phase library to assemble a complete multi-level phase gradient supercell, calculate all propagable diffraction orders using the screening precision RCWA, and record the solution configuration, efficiency of each order and solution status as screening level evidence. S6. Using the locked reference supercell as a retained candidate, compare the candidate supercell to be replaced with the locked reference supercell under the same screening accuracy RCWA configuration; only when the average target order efficiency of the candidate supercell to be replaced is higher than that of the locked reference supercell, the decrease in ERx and ERy relative to the locked reference supercell is not more than 0.5 dB, the average zero-order residue of the two polarizations is not more than that of the locked reference supercell plus 0.002, the sum of other transmission orders of the two polarizations is not more than that of the locked reference supercell plus 0.005, and the difference in the target order efficiency of the two polarizations is not more than 1.10 times the corresponding difference of the locked reference supercell, is the candidate supercell to be replaced determined to meet the constraints; otherwise, record the unmet constraints and the reason for rejection, and retain the locked reference supercell or return to step S3 or S4 to select an alternative candidate unit; S7. Using a Fourier order and a denser spatial grid with a higher screening accuracy than in step S5, perform a high-precision RCWA verification on candidate supercells that meet the constraints of step S6, recalculate all propagable diffraction orders and energy balance. If the verification fails, reduce the evidence level and return to step S3 or S4. S8. If the high-precision RCWA verification is passed, then the finalized evidence is formed and the structural parameters of the multi-level phase gradient supercell and the corresponding electromagnetic evidence record are output. The electromagnetic evidence record includes at least the evidence level, candidate identifier, geometric parameters, source identifier, solution configuration, output physical quantity, solution status and the correlation between upstream and downstream evidence.

2. The design method for a traceable electromagnetic evidence chain according to claim 1, characterized in that, Step S1 includes: S101. Establish a periodic unit model of a silicon dioxide substrate, air, and rectangular silicon nanopillars, and use periodic lateral boundary conditions and normal incident plane wave excitation. S102. Scan rectangular silicon nanopillars within the processable Lx, Ly, and height parameter space; S103. Solve for the complex transmission coefficients for x-linear polarization and y-linear polarization respectively, and record Tx, Ty, φx and φy. To eliminate the learning discontinuity caused by the phase jump at −π and π, retain Tx and Ty, and encode φx and φy as sinφx, cosφx, sinφy and cosφy respectively. S104. The geometric input for each sample is Lx, Ly, H, and the response output is Tx, Ty, sinφx, cosφx, sinφy, cosφy. S105. After marking and removing samples with abnormal calculations, energy gaps, or geometrically unmanufacturable characteristics, a dataset of unit electromagnetic responses is formed.

3. The design method for a traceable electromagnetic evidence chain according to claim 2, characterized in that, In step S2, to reduce the bias caused by random initialization of a single network, multiple forward models with the same structure but random seeds are trained. The normalized Lx, Ly, and H are input into the integrated forward proxy model, and the output ensemble mean is used as the prediction response. The prediction discrepancy between the models is used as the uncertainty signal.

4. The design method for a traceable electromagnetic evidence chain according to claim 3, characterized in that, The backbone network of the integrated forward proxy model consists of 5 fully connected hidden layers, each with 256 neurons. The hidden layers use the GELU activation function and have a Dropout value of 0.

05. The output of the integrated forward proxy model includes two parts: transmittance and phase components. Tx and Ty are output using Sigmoid to constrain their numerical range. The four phase components are output using linearity. The loss function is the weighted mean square error of each output component, and a phase unit circle constraint is added to make the predicted sinφ and cosφ satisfy sin²φ+cos²φ≈1 and the weight of the unit circle penalty term is 0.

05.

5. The design method for a traceable electromagnetic evidence chain according to claim 3, characterized in that, Step S3 includes: S301. The candidate geometric parameters are predicted forward using multiple integrated forward models to obtain the mean values ​​of dual-polarization transmission and phase response. S302. Construct a candidate ranking based on the transmittance, phase error, geometric manufacturability, and model uncertainty of the X-polarization channel and the Y-polarization channel; S303. Prioritize candidate points with high prediction performance or large model divergence, and re-execute RCWA calculation; S304. Add the newly added RCWA calculation results to the forward model training set in step S2; S305. Repeat steps S301-S304 until each target phase level has at least one candidate cell that has been verified by the cell RCWA and meets the requirements for transmittance, phase error and geometric spacing.

6. The design method for a traceable electromagnetic evidence chain according to claim 5, characterized in that, Step S4 includes: S401. Divide 0 to 2π into multiple target phase levels, with each level evenly spaced. S402. For each phase level, select rectangular silicon nanopillars from the candidates after RCWA verification that simultaneously satisfy the target phases of x and y polarization, Tx and Ty both greater than 0.70, phase error lower than the preset upper limit, and geometric manufacturability, and establish a multi-level polarization phase library.

7. The design method for a traceable electromagnetic evidence chain according to claim 6, characterized in that, Step S5 includes: S501. Based on the multi-level polarization phase library established in step S4, multiple selected units are arranged sequentially according to the principle that the x-polarization phase increases along the supercell direction and the y-polarization phase decreases along the supercell direction. S502, Supercell-level screening: Perform screening precision RCWA on a complete supercell composed of multiple selected units, solve all propagable diffraction orders, and calculate the target order efficiency, reverse first-order leakage, zero-order residue, and the sum of other transmission orders for x and y polarization.

8. The design method for a traceable electromagnetic evidence chain according to claim 7, characterized in that, In step S7, based on the high-precision supercell RCWA, three types of checks are performed on the structural parameters of the multi-level phase gradient supercell: S701. Calculate all propagable transmission diffraction orders and reflection power, and set T+R+A=1 within the preset numerical tolerance kernel. S702. Use wavelength-correlated real part refractive index to check the dispersion sensitivity of materials; S703. Use Lumerical FDTD and COMSOL / FEM to check whether the diffraction direction and field distribution of the dominant energy are consistent with the high-precision RCWA. FDTD and COMSOL / FEM are only used as evidence of consistency in direction and trend, and do not replace the quantitative results of high-precision RCWA.

9. An all-dielectric metasurface polarization beamsplitter, wherein the all-dielectric metasurface polarization beamsplitter is used for polarization separation in the 1550 nm near-infrared band, characterized in that, The structural parameters of the all-dielectric metasurface polarization beamsplitter are determined based on the design method with a traceable electromagnetic evidence chain as described in any one of claims 1-8. The all-dielectric metasurface polarization beamsplitter includes: a silicon dioxide substrate, a rectangular silicon nanopillar array disposed on the upper surface of the silicon dioxide substrate, and an air medium located above the rectangular silicon nanopillar array. The rectangular silicon nanopillar array comprises multiple rectangular silicon nanopillars arranged sequentially along the x-direction. The cross-section of each rectangular silicon nanopillar is set along the x-axis and y-axis respectively, and the corresponding lateral dimensions are Lx and Ly respectively. The same group of rectangular silicon nanopillars forms a discrete linear phase gradient that increases along the supercell direction for x-linear polarization, causing the main transmitted energy to enter the +1 diffraction order, and forms a discrete linear phase gradient that decreases along the same supercell direction for y-linear polarization, causing the main transmitted energy to enter the -1 diffraction order.

10. The all-dielectric metasurface polarization beam splitter according to claim 9, characterized in that, The rectangular silicon nanopillar array comprises twelve rectangular silicon nanopillars with different lateral dimensions Lx and Ly. The twelve rectangular silicon nanopillars are arranged sequentially along the x-direction to form a twelve-level phase gradient supercell. The height H of the rectangular silicon nanopillars is 800 nm, the center-to-center distance P between adjacent rectangular silicon nanopillars is 650 nm, the period Λ of the twelve-level phase gradient supercell is 12P and equal to 7800 nm, and the target phase interval between adjacent phase levels is 2π / 12.

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