Compact asymmetric multimode interference coupler hybrid reverse design method based on pixelated topological optimization
By combining pixelated topology optimization with improved genetic algorithms and boundary refinement, the problem of arbitrary asymmetric splitting ratio of multimode interference couplers in compact size is solved, achieving efficient design and stable performance, and improving computational efficiency and device performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2026-03-26
- Publication Date
- 2026-05-15
AI Technical Summary
Existing multimode interference coupler designs struggle to achieve arbitrary asymmetric splitting ratios within a compact size, and suffer from issues such as the trade-off between algorithm convergence and computational cost, low local search efficiency, and limitations in device physical performance.
A hybrid inverse design method based on pixel-based topology optimization is adopted, which combines an improved genetic algorithm, hash-memory search, and adaptive mutation mechanism. The two-dimensional binary matrix is optimized through a global-local evolution strategy, and the fitness function is calculated using three-dimensional finite difference time-domain simulation to refine the boundary pixel set, thereby achieving efficient design.
Achieving arbitrary asymmetric splitting ratios (such as 1:20) in an extremely compact size while maintaining a transmission efficiency of over 80% significantly improves computational efficiency, suppresses isolated pixel defects, and reduces manufacturing difficulty.
Smart Images
Figure CN122043735A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of integrated photonic device design technology, specifically relating to a hybrid reverse design method for multimode interference couplers. Background Technology
[0002] Multimode interference (MMI) couplers are key photonic integrated devices based on the self-image principle, widely used for power distribution and beam routing in optical communication networks, optical interconnects, and optical signal processing systems. Compared to directional couplers, MMI couplers typically offer wider operating bandwidth, more compact size, and greater manufacturing tolerance. With the increasing integration of photonic integrated circuits (PICs), the demand for couplers capable of achieving arbitrary power distribution ratios (especially asymmetric splitting ratios with large dynamic ranges, such as 1:20) in extremely compact sizes is growing.
[0003] Traditional multimode interference coupler designs primarily rely on analytical theories (such as the self-image effect) and parameter scanning of regular geometries (such as rectangular, trapezoidal, or wedge-shaped structures). However, limited by the physical laws of modal interference, traditional regular geometric designs struggle to achieve precise control of arbitrary asymmetric splitting ratios while maintaining a compact size. For example, to achieve extreme splitting ratios, traditional trapezoidal or wedge-shaped designs often require extremely long device lengths, resulting in excessively large chip footprints and difficulty in overcoming performance bottlenecks.
[0004] To overcome the limitations of traditional regular geometry, reverse design methods based on pixelated topology optimization have gradually become a research hotspot. This method discretizes the core region of the device into a subwavelength pixel array and introduces microstructural perturbations through optimization algorithms to break the regular modal interference pattern, thereby achieving performance exceeding traditional theoretical levels. However, existing pixelated topology optimization design methods still face the following challenges in practical applications:
[0005] 1. The contradiction between algorithm convergence and computational cost: It is difficult to balance exploration and development, and a fixed mutation rate is difficult to adapt to different stages of optimization. Existing topology optimization methods usually use genetic algorithms or simulated annealing algorithms with a fixed mutation rate. In the optimization of complex photonic structures, they are prone to stagnation near local optima, resulting in a significant decrease in search efficiency.
[0006] 2. Low efficiency of local search: The traditional DBS algorithm flips and tests each pixel in the entire region one by one, which will cause the search space to grow exponentially. The full-wave electromagnetic simulation is very time-consuming, resulting in extremely low optimization efficiency.
[0007] 3. Limited physical performance of devices: Purely random optimization is prone to generating non-physical isolated noise points or "island" pixels in the topology, resulting in a decrease in the overall transmission efficiency of the device.
[0008] Currently, there is a lack of an efficient reverse design method that can balance global search breadth and local trimming accuracy, while effectively reducing computational overhead, avoiding isolated pixel defects, and achieving arbitrary splitting ratios in an ultra-compact size. Summary of the Invention
[0009] The present invention aims to solve the problems of difficulty in achieving arbitrary splitting ratios in a compact size, as well as the problems of long design time and low efficiency in existing asymmetric multimode interference coupler (MMI) designs.
[0010] A hybrid reverse design method for compact asymmetric multimode interference couplers based on pixelated topology optimization, characterized by comprising:
[0011] Step 1: For the multimode interference coupler, establish a discrete model, which is equivalent to an N*M two-dimensional binary matrix;
[0012] Step 2: Global coarse optimization based on an improved genetic algorithm: A two-dimensional binary matrix is used as the individual chromosome encoding; the port transmittance obtained from three-dimensional finite difference time-domain simulation is used to construct the individual's fitness function; a sparse random strategy is used to generate the initial population during the initialization phase; during the evolutionary process, a hash-based memoized search mechanism is first used for simulation; in the selection phase, several individuals are randomly selected in each generation for local competition, and those with better fitness are selected to enter the crossover pool; in the crossover phase, a single-point crossover method is used to reorganize the topological regions of the parent individuals; in the mutation phase, some pixels in the individuals are randomly flipped; based on an elite retention strategy, some of the best individuals in each generation are directly copied to the next generation.
[0013] After each generation of evolution ends and the current global best individual is locked, a round of local search refinement is performed: a certain range of random perturbation attempts are made for the current best individual, and a limited number of search attempts are set. In each attempt, some pixels are randomly selected from the etched pixel area for state flipping, and the fitness of the new structure is quickly evaluated using three-dimensional finite difference time-domain simulation. Once it is found that the perturbed new individual has a better fitness index than the current best individual, the global best solution is immediately updated and the perturbed structure is retained; if no better solution is found, the perturbation is abandoned.
[0014] Step 3: Calculate the fitness function using the port transmittance obtained from the three-dimensional finite difference time-domain simulation.
[0015] Step 4: Export the globally optimal topology obtained in Step 2, traverse the topology, and determine the boundary pixels where the refractive index changes abruptly based on the logical value difference between a pixel and its neighboring pixels, and generate a set of boundary pixels.
[0016] Step 5: Perform boundary refinement based on the boundary pixel set.
[0017] Furthermore, the simulation process of the hash-based memoized search mechanism includes:
[0018] Before evaluating an individual's fitness, the hash value corresponding to its binary matrix is calculated. If the hash already exists in the cache, the historical fitness data is directly called, skipping the three-dimensional finite difference time-domain simulation calculation. If it does not exist, the simulation is executed and the results are written to the cache.
[0019] Furthermore, mutation is performed during the mutation phase using an adaptive mutation mechanism, including:
[0020] A stagnation threshold Tstag is set. If the improvement value of the optimal fitness of the population is less than the improvement threshold for consecutive Tstag generations, it is determined to enter a stag state. At this time, the mutation rate is increased to enhance the global exploration ability. When the fitness is detected to exceed the improvement threshold again, the mutation rate is restored to the mutation rate before the increase, so as to strengthen the local fine search ability again.
[0021] Furthermore, the fitness function is as follows:
[0022]
[0023] in, and These represent the forward transmittance of the fundamental mode at the two output ports, recorded by the mode extension monitor in a three-dimensional finite difference time-domain simulation. For the target spectrophotometer ratio; Theoretical total transmittance; and These are the weighting coefficients.
[0024] Furthermore, the specific process of generating the boundary pixel set includes:
[0025] Let any pixel in the two-dimensional pixel matrix be the center pixel. If the logical values of the center pixel and its four neighboring pixels (up, down, left, and right) are all the same, then the pixel is located inside the uniform material region and is not a boundary pixel. If at least one neighboring pixel has a different logical value from the center pixel, then the pixel is considered to be located in the boundary region of different materials and is defined as a boundary pixel. By applying the above judgment rules to each point of the entire pixel matrix, the set of positions of all boundary pixels can be obtained.
[0026] Furthermore, the process of boundary refinement based on the boundary pixel set includes:
[0027] The mesh precision of the simulation environment is refined, and a binary search algorithm is used to flip only the boundary pixel set. The state of the boundary pixels is flipped sequentially, and a new fitness value is calculated. If the fitness value decreases, the flip is retained; otherwise, the operation is rolled back. This process is repeated until all boundary pixels have been traversed or the fitness no longer changes.
[0028] Furthermore, during the initialization phase, when a sparse random strategy is used to generate the initial population, the random generation probability of the etched pixels is limited to the range of 0.1–0.55.
[0029] Furthermore, when entering a stagnant state, the mutation rate is dynamically increased from the normal value of 0.05 to 0.3–0.4 when increasing the mutation rate.
[0030] Furthermore, based on the elite retention strategy, in the process of directly replicating some of the best individuals to the next generation in each generation, 2% of the best individuals are directly replicated to the next generation in each generation.
[0031] Furthermore, in step two, during the global coarse optimization based on the improved genetic algorithm, the simulation uses a mesh accuracy of 0.05 μm.
[0032] Beneficial effects:
[0033] This invention proposes a cascaded global-local evolutionary strategy, combining the global exploration capability of genetic algorithms with the efficient development capability of boundary-constrained deep learning (DBS) algorithms. This effectively solves the problems of premature convergence and weak local development capability of pure genetic algorithms (GA) and the excessively large search space of pure DBS algorithms. It also effectively addresses the issues of long design time and low efficiency. Compared to genetic algorithms with a fixed mutation rate, this adaptive evolutionary strategy automatically enhances global exploration capability when the algorithm stagnates, thus effectively avoiding premature convergence and improving optimization efficiency. Since the light field distribution is mainly affected by the refractive index boundary, the flipping of non-boundary pixels has a limited contribution to device performance. Therefore, the boundary constraint strategy can significantly compress the search space while maintaining optimization capability. Compared to full-pixel scanning, the boundary constraint mechanism compresses the search space by approximately 40%-50%, significantly improving computational efficiency.
[0034] The device designed in this invention has an extremely compact size (only 56 μm). 2 This invention enables arbitrary asymmetric splitting ratios (e.g., 1:20) across a wide dynamic range, while maintaining a transmission efficiency of over 80% within the communication band. By introducing morphological filtering and boundary constraints, this invention effectively suppresses isolated "island-like" structures commonly found in pixelated designs, reduces back reflection and scattering losses, and makes the designed devices easier to manufacture and more stable in performance. Attached Figure Description
[0035] Figure 1This is a flowchart of the hybrid reverse engineering method proposed in this invention;
[0036] Figure 2 The convergence curve of Loss as algebraically changes during the optimization of the 1:2 spectrophotometer ratio is shown.
[0037] Figure 3 The simulation software outputs transmittance distribution curves for different splitting ratios (1:20, 1:5, 1:3, 1:2).
[0038] Figure 4 The simulation software outputs electric field distribution diagrams for different splitting ratios (1:20, 1:5, 1:3, 1:2). Detailed Implementation
[0039] Specific implementation method one: Combining Figure 1 This implementation method is described below.
[0040] This embodiment presents a hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization, comprising the following steps:
[0041] Step 1: Establish device model and pixelated characterization;
[0042] In this embodiment, the multimode interference (MMI) coupler is based on a silicon-on-insulator (SOI) substrate. The core region of the device is distributed on a crystalline silicon layer, with a design size of 14 μm × 4 μm.
[0043] A discrete model is established in the electromagnetic simulation software, and the core region of the MMI is equivalent to an N×M two-dimensional binary pixel matrix (in this embodiment, the pixel size is 100nm×100nm, i.e., a 140×40 matrix). The encoded value of each matrix element is either '0' or '1', where logic '0' indicates that the silicon core layer (refractive index nSi=3.46) is retained at that location, and logic '1' indicates that the location is a shallow etched hole (filled with air or cladding material) with an etching depth of 70nm.
[0044] Step 2: Perform global coarse optimization based on the improved genetic algorithm (GA);
[0045] The optimization variable is the aforementioned two-dimensional binary matrix (0 / 1 represents unetched / etched pixels), which serves as the input for individual chromosome encoding. The fitness function of an individual is constructed using the port transmittance obtained from three-dimensional finite-difference time-domain simulation. To improve global search efficiency and quickly identify potentially superior topologies, a coarse mesh with a mesh accuracy of 0.05 μm is used in the simulation phase to reduce the computational cost of a single electromagnetic solution.
[0046] In the initialization phase, a sparse random strategy is used to generate the initial population: the random generation probability of etched pixels (logic "1") is limited to the range of 0.1–0.55, which suppresses strong scattering and high-loss individuals caused by high-fill-rate structures from the statistical distribution level, thereby improving the overall quality of the population.
[0047] During the evolutionary process, a hash-based memoized search mechanism is first employed for simulation to avoid redundant simulations. Specifically, before evaluating an individual's fitness, the hash value corresponding to its binary matrix is calculated. If this hash already exists in the cache, historical fitness data is directly retrieved, skipping the three-dimensional finite-difference time-domain (FDTD) simulation calculation. If it does not exist, the simulation is performed, and the results are written to the cache. This strategy significantly reduces computational redundancy caused by repeated evaluations in topology optimization problems.
[0048] The selection operator employs tournament selection, randomly selecting several individuals in each generation for local competition, choosing those with better fitness to enter the crossover pool, thus maintaining selection pressure while avoiding premature convergence. The crossover operator uses a single-point crossover method, recombining the topological regions of parent individuals to achieve the combination and diffusion of superior gene fragments. The mutation operator randomly flips some pixels within an individual. To maintain population diversity and expand the search space, an elite preservation strategy is introduced, in which approximately 2% of the best individuals are directly copied to the next generation in each generation, ensuring that the currently obtained optimal solution does not degenerate due to random operations.
[0049] Furthermore, an adaptive mutation mechanism is introduced during the mutation phase to alleviate the local optimum problem. A stagnation threshold Tstag is set. When the optimal fitness of the population does not significantly improve for Tstag generations (which can be determined by setting an improvement threshold), the algorithm is considered to have entered a stag state. At this time, the mutation rate pmut is automatically increased dynamically from the normal value of 0.05 to 0.3–0.4 to enhance the global exploration capability. When a fitness improvement is detected again, the mutation rate is restored to 0.05 to strengthen the local fine-grained search capability again.
[0050] Specifically, to further explore potential superior structures and compensate for the shortcomings of genetic algorithms in local fine-tuning capabilities, a round of local search refinement is performed after each generation of evolution and the current globally optimal individual is locked. This process involves a small-scale (0.1%) random perturbation attempt on the current optimal individual, aiming to explore whether a better solution exists in the neighborhood. The specific process is as follows: a limited number of search attempts is set (e.g., 10 times), and in each attempt, a small number of pixels (e.g., 5 pixels) are randomly selected from the etched pixel region for state flipping. The search employs a greedy strategy: once a new individual after perturbation is found to have a better fitness index than the current best individual, the global optimum is immediately updated and the perturbation structure is retained; if no better solution is found, the perturbation is abandoned.
[0051] Step 3: Construct the multi-objective fitness function (Loss Function);
[0052] A fitness function (LossFunction) is constructed based on the port transmittance obtained from three-dimensional finite-difference time-domain simulation, aiming to minimize the splitting ratio deviation and maximize the transmission efficiency. The fitness function is as follows:
[0053]
[0054] in, and These represent the forward transmittance of the fundamental mode at the two output ports, recorded by the mode extension monitor in a three-dimensional finite difference time-domain simulation. Set the target splitting ratio (e.g., set it to 0.8, corresponding to a 1:4 splitting ratio). The theoretical total transmittance is set to 1.0; and These are the weighting coefficients, which are set to 1 and 2 respectively in this embodiment.
[0055] Step 4: Perform topology preprocessing and boundary constraints;
[0056] The globally optimal topology obtained in step two is exported. This topology is traversed, and boundary pixels where refractive index changes abruptly are identified based on the logical value differences between a pixel and its neighboring pixels, generating a set of boundary pixels. Specifically, let any pixel in the two-dimensional pixel matrix be the center pixel. If the center pixel has the same logical value as all four of its four neighboring pixels (up, down, left, and right), then this pixel is located within a homogeneous material region and is not a boundary pixel. If at least one of these five neighboring pixels has a different logical value from the center pixel, then this pixel is considered to be located at the boundary between different materials, and this pixel is defined as a boundary pixel. By applying the above determination rule point by point to the entire pixel matrix, the set of all boundary pixel locations can be obtained. Figure 1 As shown in the schematic diagram, only pixels located at the "silicon / etched via" boundary are marked as optimizable regions. Since the electromagnetic field distribution in photonic devices is mainly affected by the refractive index abrupt boundary, the flipping of pixels within a uniform region contributes little to the device performance. Therefore, the boundary constraint strategy described above can significantly reduce the search space for subsequent optimization while maintaining the ability to optimize key structural regions.
[0057] Step 5: Perform local refinement using the boundary-based direct binary search (DBS) algorithm;
[0058] The mesh precision of the simulation environment is refined, and the DBS algorithm is used to perform flipping operations only on the boundary pixel set determined in step four ('0' becomes '1' or '1' becomes '0').
[0059] The specific process is as follows: The states of the boundary pixels are flipped sequentially, and the new fitness values are calculated. If... If the performance is improved, the flip is retained; otherwise, the operation is rolled back. This process is repeated until all boundary pixels have been traversed or the fitness no longer changes.
[0060] Step Six: Simulation Verification and Result Analysis;
[0061] Based on the above process, the following simulation verification is performed:
[0062] (1) Run the 3D FDTD software on a computer with an NVIDIA RTX 3060 GPU installed.
[0063] (2) Set the target splitting ratio Rtarget to be 1:20, 1:5, 1:3 and 1:2 respectively.
[0064] (3) Design using the hybrid optimization strategy described in this embodiment. For example... Figure 2 As shown, the optimization process exhibits stepwise convergence, typically converging within 40 generations.
[0065] (4) After optimization, the device performance is as follows: Figure 3 and Figure 4 As shown in the figure. The results indicate that all designs achieved the preset splitting ratio within a wide wavelength range of 1500-1600 nm, with a stable overall transmission efficiency above 0.80. In particular, for the extreme asymmetric case of 1:20, the splitting ratio deviation was less than 1%.
[0066] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. A compact asymmetric multi-mode interference coupler hybrid inverse design method based on pixelated topology optimization, characterized in that, include: Step 1: For the multimode interference coupler, establish a discrete model, which is equivalent to an N*M two-dimensional binary matrix; Step 2: Perform global coarse optimization based on the improved genetic algorithm: use the two-dimensional binary matrix as the input for individual chromosome encoding; The fitness function of an individual is constructed using the port transmittance obtained from three-dimensional finite difference time-domain simulation; a sparse random strategy is used to generate the initial population during the initialization phase. In the evolution process, a hash-based memoized search mechanism is first used for simulation; During the selection phase, several individuals are randomly selected from each generation to compete locally, and those with better fitness are selected to enter the crossover pool. During the crossover phase, a single-point crossover method is used to reorganize the topological regions of the parent individuals; during the mutation phase, some pixels in the individuals are randomly flipped; based on the elite preservation strategy, some of the best individuals in each generation are directly copied to the next generation. After each generation of evolution ends and the current global best individual is locked, a round of local search refinement is performed: a certain range of random perturbation attempts are made for the current best individual, and a limited number of search attempts are set. In each attempt, some pixels are randomly selected from the etched pixel area for state flipping, and the fitness of the new structure is quickly evaluated using three-dimensional finite difference time-domain simulation. Once it is found that the perturbed new individual has a better fitness index than the current best individual, the global best solution is immediately updated and the perturbed structure is retained; if no better solution is found, the perturbation is abandoned. Step 3: Calculate the fitness function using the port transmittance obtained from the three-dimensional finite difference time-domain simulation. Step 4: Export the globally optimal topology obtained in Step 2, traverse the topology, and determine the boundary pixels where the refractive index changes abruptly based on the logical value difference between a pixel and its neighboring pixels, and generate a set of boundary pixels. Step 5: Perform boundary refinement based on the boundary pixel set.
2. The compact asymmetric multi-mode interference coupler hybrid inverse design method based on pixelated topology optimization of claim 1, wherein, The simulation process of the hash-based memoized search mechanism includes: Before evaluating an individual's fitness, the hash value corresponding to its binary matrix is calculated. If the hash already exists in the cache, the historical fitness data is directly called, skipping the three-dimensional finite difference time-domain simulation calculation. If it does not exist, the simulation is executed and the results are written to the cache.
3. The compact asymmetric multi-mode interference coupler hybrid inverse design method based on pixelated topology optimization of claim 1, wherein, Mutation is performed during the mutation phase using an adaptive mutation mechanism, including: A stagnation threshold Tstag is set. If the improvement value of the optimal fitness of the population is less than the improvement threshold for consecutive Tstag generations, it is determined to enter a stag state. At this time, the mutation rate is increased to enhance the global exploration ability. When the fitness is detected to exceed the improvement threshold again, the mutation rate is restored to the mutation rate before the increase, so as to strengthen the local fine search ability again.
4. The hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to claim 1, characterized in that, The fitness function is as follows: in, and These represent the forward transmittance of the fundamental mode at the two output ports, recorded by the mode extension monitor in a three-dimensional finite difference time-domain simulation. For the target spectrophotometer ratio; Theoretical total transmittance; and These are the weighting coefficients.
5. The hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to claim 1, characterized in that, The specific process of generating the boundary pixel set includes: Let any pixel in the two-dimensional pixel matrix be the center pixel. If the logical values of the center pixel and its four neighboring pixels (up, down, left, and right) are all the same, then the pixel is located inside the uniform material region and is not a boundary pixel. If at least one neighboring pixel has a different logical value from the center pixel, then the pixel is considered to be located in the boundary region of different materials and is defined as a boundary pixel. By applying the above judgment rules to each point of the entire pixel matrix, the set of positions of all boundary pixels can be obtained.
6. The hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to claim 1, characterized in that, The process of boundary refinement based on the boundary pixel set includes: The mesh precision of the simulation environment is refined, and a binary search algorithm is used to flip only the boundary pixel set. The state of the boundary pixels is flipped sequentially, and a new fitness value is calculated. If the fitness value decreases, the flip is retained; otherwise, the operation is rolled back. This process is repeated until all boundary pixels have been traversed or the fitness no longer changes.
7. A hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to any one of claims 1 to 6, characterized in that, During the initialization phase, a sparse random strategy is used to generate the initial population, and the random generation probability of etched pixels is limited to the range of 0.1–0.
55.
8. A hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to any one of claims 1 to 6, characterized in that, When entering a stagnant state, the mutation rate is dynamically increased from the normal value of 0.05 to 0.3–0.4 when increasing the mutation rate.
9. A hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to any one of claims 1 to 6, characterized in that, Based on the elite retention strategy, in the process of directly replicating some of the best individuals to the next generation in each generation, 2% of the best individuals are directly replicated to the next generation in each generation.
10. A hybrid reverse design method for a compact asymmetric multimode interference coupler based on pixelated topology optimization according to any one of claims 1 to 6, characterized in that, In step two, during the global coarse optimization based on the improved genetic algorithm, the simulation used a mesh accuracy of 0.05 μm.