Joint analog-digital reverse design method and system based on edge guidance and silicon-based mode division multiplexer thereof

Abstract

The invention relates to the field of integrated silicon-based photonic devices and discloses a joint analog-digital reverse design method and system based on edge guidance and a silicon-based mode division multiplexer designed by the joint analog-digital reverse design method and system. According to the method, a simulation reverse design technology and a digital reverse design technology in photonic device design are combined, a simulation design structure is optimized by utilizing an adjoint method, and a simulation design result is converted into a digital structure with a relatively large feature size through guidance of an edge detection technology. In addition, digital design is optimized by adopting a direct binary search method, so that efficient pixelated design and higher process robustness are realized. The silicon-based mode division multiplexer designed based on the method supports multiplexing of five transverse electric modes, the size of the device is 10 [mu] m * 6 [mu] m, and the occupied area is remarkably reduced. The multiplexer has the advantages of low insertion loss, small inter-mode crosstalk and large processing tolerance, and the integration level and the performance of an optical communication system can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of integrated photonic device design, and in particular to a reverse design method of a silicon-based photonic device and its application. Background Art

[0002] With the rapid development of artificial intelligence technologies such as large language models and multimodality, data centers have increasing requirements for the communication capacity of optical interconnects. As a new type of optical multiplexing technology, mode division multiplexing can further improve the information transmission rate in a single optical fiber or waveguide based on wavelength division multiplexing technology. As a key component of the mode division multiplexing system, the design methods of the mode division multiplexer are mainly divided into intuition-first type and reverse design type.

[0003] The inverse design method can significantly reduce the size and loss of the mode division multiplexer, showing great potential for large-scale integration. However, traditional inverse design methods, whether digital or analog, face their own technical challenges, such as:

[0004] Optimization efficiency problem: Digital reverse design usually uses a brute force search algorithm to update the status of digital pixels. This method has low optimization efficiency and requires a large amount of electromagnetic simulation, which is time-consuming and consumes a lot of computing resources.

[0005] Limited design freedom: Digital reverse design has limited optimization freedom, making it difficult to fully explore the design space and potentially missing out on excellent design solutions.

[0006] High processing precision requirements: Analog reverse design usually has a small minimum feature size, and has extremely high requirements for processing precision and stability. With the current design algorithm and processing level, it is difficult to carry out high-robust processing and manufacturing, and it is not easy to achieve mass production.

[0007] Large device size: Existing design methods make it difficult to achieve extremely compact device size while ensuring performance, which limits the integration of the device.

[0008] Performance-manufacturing trade-off: When pursuing high performance, the manufacturability of the device is often sacrificed, resulting in the designed device performing well in simulation but being difficult to actually manufacture or mass-produce.

[0009] Limitations of design methods: Existing inverse design methods are often targeted at specific types of devices and lack sufficient versatility, making them difficult to apply to various complex photonic device designs.

[0010] Industrialization bottleneck: Due to the existence of the above problems, many high-performance mode division multiplexer designs are difficult to meet the actual needs of high integration and large communication capacity in fields such as data center optical interconnection, hindering the industrialization process of related technologies.

[0011] Therefore, a new design method is urgently needed that can simultaneously solve the problems of low optimization efficiency, poor processing robustness, large device size, and difficulty in balancing performance and manufacturability, and has sufficient versatility to meet the growing needs of the industry. This method should be able to improve processing robustness while ensuring high-efficiency design, achieve compact device structure and excellent performance, and be applicable to various complex photonic device designs. Summary of the invention

[0012] The purpose of the present invention is to propose a joint analog-digital reverse design method based on edge guidance and its application in the design of silicon-based mode division multiplexers, aiming to solve the technical limitations of traditional digital reverse design and analog reverse design. The present invention innovatively combines three technologies: the adjoint method optimization technology in analog reverse design of photonic devices, the direct binary search method in digital reverse design, and the edge extraction and convolution pooling technology in image processing. By using edge information to guide the transformation process of analog reverse design structure to digital reverse design structure, this method successfully integrates the high efficiency advantage of analog reverse design and the processing robustness characteristics of digital reverse design.

[0013] The present application discloses a joint analog-digital reverse design method based on edge guidance, comprising the following steps:

[0014] Initialization step: Initializing the waveguide structure of the photonic device and the initial dielectric constant distribution of the design area, generating a random dielectric constant distribution that meets the preset material refractive index range and satisfies the Gaussian distribution as the initial dielectric constant distribution of the design area;

[0015] Simulation optimization step: continuously optimizing the initial dielectric constant distribution generated in the initialization step based on the adjoint method, obtaining the gradient information of each pixel point in the design area by performing a forward and a reverse electromagnetic simulation on the design area, and updating the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution;

[0016] Edge-guided conversion step: using the optimized simulated dielectric constant distribution obtained in the analog optimization step as a simulated pattern, extracting edge information of the simulated pattern through an edge detection algorithm, and directly converting the area far from the edge into a pixel point with a larger size based on the edge information, and the dielectric constant of the area is consistent with the dielectric constant of the corresponding position in the simulated pattern, and at the same time converting the area close to and adjacent to the edge into a pixel point to be determined, and its dielectric constant needs to be further determined;

[0017] Digital optimization step: Based on the undetermined pixel points generated in the edge-guided conversion step, the final dielectric constant of the undetermined pixel points is determined by a direct binary search method, while keeping the dielectric constant of the directly converted pixel points unchanged, and after a single iterative optimization, a digital reverse design structure with a larger feature size is finally obtained.

[0018] In a preferred embodiment, the dielectric constant update rule in the simulation optimization step is:

[0019]

[0020] in,

[0021] is the dielectric constant at the pixel point x after update;

[0022] is the dielectric constant at the pixel point x before updating;

[0023] α is the update rate;

[0024] F is the objective function;

[0025] is the derivative of the objective function F with respect to the dielectric constant at the pixel point x;

[0026] x represents the spatial position coordinate within the design area;

[0027] The derivative of the objective function F with respect to the dielectric constant of the pixel point is obtained by obtaining the electric field distribution obtained by one forward transmission and one reverse transmission;

[0028] In the iterative process of analog optimization, the dielectric constant of the pixel point is gradually pushed toward the maximum and minimum boundaries through a digital filter to obtain an approximately binary dielectric constant distribution.

[0029] In a preferred embodiment, the objective function calculation formula in the simulation optimization step is:

[0030]

[0031] in is the conversion efficiency of each mode, N is the total number of modes;

[0032] F is the objective function;

[0033] N is the total number of modes;

[0034] is the conversion efficiency from the i-th TE mode to the TE0 mode;

[0035] Σ represents the sum of i from 1 to N;

[0036] The conversion efficiency Calculate by following the steps below:

[0037] (1) Perform forward electromagnetic field simulation on each input mode TEi to obtain the electric field distribution at the output end;

[0038] (2) Overlap integral of the electric field distribution at the output end and the ideal TE0 mode;

[0039] (3) Normalize the result of overlap integral to obtain conversion efficiency

[0040] In a preferred embodiment, the edge detection algorithm used in the edge-guided conversion step is a Canny edge detection algorithm, which specifically includes the following steps:

[0041] (1) Gaussian filtering: Gaussian filtering is performed on the simulated dielectric constant distribution image to reduce noise;

[0042] (2) Calculate gradient: Use the Sobel operator to calculate the gradient magnitude and direction of the image;

[0043] (3) Non-maximum suppression: non-maximum suppression of gradient amplitude along the gradient direction to refine the edge;

[0044] (4) Double threshold detection: Use high and low thresholds to perform threshold processing on the image after non-maximum suppression to obtain strong edge points and weak edge points;

[0045] (5) Edge connection: connect weak edge points to strong edge points through the hysteresis threshold method to form a complete edge;

[0046] The output of the Canny edge detection algorithm is a binary edge map, where a pixel value of 1 indicates an edge and a pixel value of 0 indicates a non-edge.

[0047] In a preferred embodiment, the image processing step after the edge detection algorithm includes:

[0048] Max pooling: Performing max pooling on the edge image obtained by the edge detection algorithm to reduce the image dimension and expand the side length of the pixel six times while keeping the overall size of the entire design area unchanged to ensure that the local features in the design area are properly preserved; and

[0049] Binarization: Binarize the image after the maximum pooling process, assign all non-zero pixel values ​​to 1, and keep the zero-value pixels as 0, so as to generate the final decision pattern;

[0050] In the final decision pattern, the pixel points with a pixel value of 1 correspond to the portion close to the edge of the original simulation pattern, and the pixel points with a pixel value of 0 correspond to the area far from the edge.

[0051] In a preferred embodiment, the specific implementation of the direct binary search method in the digital optimization step includes:

[0052] Assigning values ​​to pending pixels: For each pixel marked as pending in the edge-guided transformation step, assign the dielectric constant value of silicon and silicon dioxide respectively;

[0053] Calculate the objective function value: For each dielectric constant assignment, calculate the corresponding objective function value;

[0054] Select optimized material: compare the objective function value and select the material that can optimize the objective function as the final dielectric constant of the pixel to be determined;

[0055] Repeat optimization: repeat steps (1) to (3) for all pending pixels, and keep the dielectric constant of the pixels that have been directly converted unchanged;

[0056] Iteration completion: After completing the optimization of all pending pixels, a digital reverse design structure with a larger feature size is obtained.

[0057] In a preferred example, the larger pixel points are square pixel points with a side length of 80 nm to 150 nm.

[0058] The present application also discloses a silicon-based mode division multiplexer designed according to the above method, the mode division multiplexer comprising:

[0059] Five single-mode input waveguides for introducing the incident fundamental TE0 mode;

[0060] A multimode output waveguide for outputting the multiplexed optical signal after mode conversion;

[0061] The device body is a rectangular design area, which is discretized into a number of square pixels, each of which is an etched hole made of silicon or silicon dioxide;

[0062] Among them, the silicon-based mode division multiplexer can support the multiplexing and demultiplexing of five orthogonal transverse electric modes (TE modes), and can convert the TE0 mode from five separate single-mode waveguides into TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide; at the same time, due to reciprocity, the mode division multiplexer can convert the TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide into the TE0 mode in the five single-mode waveguides.

[0063] In a preferred embodiment, the material platform and specific parameters of the mode division multiplexer include:

[0064] The material platform is a silicon-on-insulator platform;

[0065] The height of the silicon waveguide is 200nm to 240nm;

[0066] The thickness of the silicon dioxide substrate is 1.5 μm to 2.5 μm;

[0067] The thickness of the silica cladding is 0.8 μm to 1.2 μm.

[0068] In a preferred example, the specific parameters of the input waveguide and output waveguide of the mode division multiplexer include: the width of the single-mode input waveguide is 450nm to 550nm; the spacing between each single-mode waveguide is equal, which is 800nm ​​to 950nm; the width of the multi-mode output waveguide is 2.3μm to 2.7μm, and is located at the edge of the rectangular design area.

[0069] In a preferred example, the design area of ​​the mode division multiplexer has a length between 8 μm and 12 μm and a width between 4 μm and 8 μm.

[0070] The present application also discloses a joint analog-digital reverse design system based on edge guidance, comprising:

[0071] An initialization module is used to initialize the waveguide structure of the photonic device and the initial dielectric constant distribution of the design area, and generate a random dielectric constant distribution that meets the preset material refractive index range and satisfies the Gaussian distribution as the initial dielectric constant distribution of the design area;

[0072] A simulation optimization module is used to continuously optimize the initial dielectric constant distribution generated by the initialization module based on the adjoint method, obtain the gradient information of each pixel point in the design area by performing a forward simulation and a reverse simulation on the design area, and update the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution;

[0073] An edge-guided conversion module is used to use the optimized simulated dielectric constant distribution obtained by the analog optimization module as a simulated pattern, extract edge information of the simulated pattern through an edge detection algorithm, and directly convert the area far from the edge into a pixel point with a larger size based on the edge information, and the dielectric constant of the area is consistent with the dielectric constant of the corresponding position in the simulated pattern, and at the same time, convert the area close to and adjacent to the edge into a pixel point to be determined, and its dielectric constant needs to be further determined;

[0074] The digital optimization module is used to determine the final dielectric constant of the undetermined pixel points generated by the edge-guided conversion module through a direct binary search method, while keeping the dielectric constant of the directly converted pixel points unchanged, and finally obtain a digital reverse design structure with a larger feature size after a single iterative optimization.

[0075] The implementation methods of this application have the following technical effects:

[0076] Efficient pixelated design: This invention combines the advantages of analog reverse design and digital reverse design technology. In the analog reverse design stage, only two electromagnetic simulations are required for each iterative optimization. At the same time, the image processing technology is innovatively introduced for edge guidance. In the digital optimization stage, only the pixel points near the edge need to be optimized, avoiding inefficient blind search, greatly reducing the number of electromagnetic simulations required, and realizing efficient pixelated device design.

[0077] Improved process manufacturing robustness: By converting analog reverse design results into digital reverse design structures, the minimum feature size has been increased (120nm). Compared with analog reverse design devices, the challenges of process manufacturing have been greatly reduced, the processing robustness has been improved, and it is easier to mass-produce through mainstream silicon photonics fabs.

[0078] Compact structure: The five-mode silicon-based mode division multiplexer designed based on this method is only 10μm×6μm in length, which is the smallest size among the currently known silicon-based five-mode multiplexers. This is conducive to improving the integration of devices.

[0079] Excellent device performance: At a wavelength of 1550nm, the insertion loss of the five modes of the designed mode division multiplexer is less than 2.0dB, and the inter-mode crosstalk is less than -19dB, realizing efficient five-mode multiplexing function.

[0080] Strong versatility: The proposed edge-guided joint analog-digital reverse design method is highly versatile and suitable for the reverse design of various photonic devices, especially for the design of devices with larger size and complex functions.

[0081] High optimization efficiency: Compared with traditional digital optimization algorithms, this method greatly reduces the number of electromagnetic simulations required and improves optimization efficiency.

[0082] Meeting industry needs: The devices designed by this method can meet the needs of high integration and large communication capacity in areas such as data center optical interconnection, and have important application prospects.

[0083] In summary, the present invention achieves the unity of high-efficiency design, high processing robustness and excellent performance by innovatively combining analog and digital inverse design methods and introducing edge-guiding technology, providing a new solution for the design and manufacture of photonic integrated devices.

[0084] A large number of technical features are recorded in the specification of this application, which are distributed in various technical solutions. If all possible combinations of technical features of this application (i.e., technical solutions) are to be listed, the specification will be too long. In order to avoid this problem, the various technical features disclosed in the above-mentioned invention content of this application, the various technical features disclosed in the various embodiments and examples below, and the various technical features disclosed in the accompanying drawings can be freely combined with each other to form various new technical solutions (these technical solutions are all deemed to have been recorded in this specification), unless the combination of such technical features is technically infeasible. For example, in one example, feature A+B+C is disclosed, and in another example, feature A+B+D+E is disclosed, and features C and D are equivalent technical means that play the same role. Technically, only one can be used, and it is impossible to use them at the same time. Feature E can be combined with feature C technically. Then, the solution of A+B+C+D should not be deemed to have been recorded because it is technically infeasible, and the solution of A+B+C+E should be deemed to have been recorded. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a flowchart of the edge-guided joint analog-digital reverse design method according to the first embodiment of the present application.

[0086] Figure 2 It is a structural schematic diagram of an edge-guided joint analog-digital reverse design system according to the second embodiment of the present application.

[0087] Figure 3 It is a schematic diagram of the overall structure of the edge-guided joint analog-digital reverse design system according to the second embodiment of the present application.

[0088] Figure 4 The invention relates to a silicon-based mode division multiplexer simulation dielectric constant distribution and an edge extraction pattern designed according to the edge-guided joint analog-digital inverse design method of the first embodiment of the present application.

[0089] Figure 5 It is a schematic plan view of the final structure of the silicon-based mode division multiplexer designed by the edge-guided joint analog-digital reverse design method according to the first embodiment of the present application.

[0090] Figure 6 This is a light field distribution diagram of a silicon-based mode division multiplexer designed according to the edge-guided joint analog-digital inverse design method of the first embodiment of the present application.

[0091] Figure 7 It is the transmission spectrum of the silicon-based mode division multiplexer designed according to the edge-guided joint analog-digital inverse design method of the first embodiment of the present application. DETAILED DESCRIPTION

[0092] In the following description, many technical details are provided to help readers better understand the present application. However, those skilled in the art can understand that the technical solution claimed in the present application can be implemented even without these technical details and various changes and modifications based on the following embodiments.

[0093] Description of some concepts:

[0094] Silicon-on-Insulator (SOI) platform: The SOI platform is a semiconductor manufacturing technology that is mainly used in the manufacture of integrated circuits (ICs) and photonic devices. This platform uses a thin layer of silicon dioxide as an insulating layer on a silicon substrate and deposits a layer of silicon on it to achieve more efficient electrical performance and better thermal control, and is widely used in the field of photonic integrated circuits.

[0095] Mode Division Multiplexer (MDM): A photonic device used to multiplex and demultiplex multiple optical signals of different modes in a single waveguide, thereby increasing the bandwidth and capacity of the communication system. Each mode (TE0, TE1, etc.) transmits different information in the same waveguide without interfering with each other.

[0096] Orthogonal Transverse Electric Mode (TE Modes): An electromagnetic wave mode in which the electric field vector is perpendicular to the propagation direction when transmitted in an optical waveguide.

[0097] Inverse Design: A photonic device design method that defines the required device performance and uses optimization algorithms to automatically generate device structures that meet these performance requirements. Compared with traditional forward design, inverse design can explore a larger design space and obtain better design solutions.

[0098] Analog Inverse Design: A form of inverse design in which each pixel of the design area can take values ​​within a continuous range of refractive indices. This approach can result in high-performance designs but may produce complex structures that are difficult to manufacture.

[0099] Digital Inverse Design: Another form of inverse design, in which each pixel of the design area can only take a discrete refractive index value. This method produces a design that is easier to manufacture, but may sacrifice performance slightly.

[0100] Adjoint Method: A mathematical tool for optimizing design that can effectively reduce the number of simulations by quickly calculating the gradient information of the objective function. This method is used to improve optimization efficiency in reverse design, and is particularly suitable for device design with complex structures.

[0101] Direct Binary Search (DBS): An optimization algorithm for digital reverse design that optimizes the design by flipping the state of pixels one by one and evaluating the performance changes.

[0102] Electromagnetic simulation: refers to the use of numerical methods to simulate the propagation of light waves in a specific medium, which is used to analyze and optimize the performance of photonic devices. In the present invention, electromagnetic simulation is used to calculate the propagation mode of light waves in the design area to determine the influence of the dielectric constant of each pixel on light transmission.

[0103] Edge Guidance: An image processing technique used to identify key areas (i.e., edge areas) in photonic device design through edge detection algorithms during the optimization process, thereby reducing unnecessary global searches and improving design efficiency. In the present invention, edge guidance technology guides the digital optimization process by processing edge information of the image.

[0104] Edge Detection Algorithm: An image processing technique used to identify the position of the edge of an object in an image. In the present invention, the Canny edge detection algorithm is used to identify the material boundaries in the analog design results.

[0105] Max Pooling: A downsampling operation, usually used to reduce the spatial size of an image or feature map. In the present invention, max pooling is used to increase the pixel size, thereby improving the manufacturability of the design.

[0106] Pixel: In the design area of ​​photonic devices, each discrete basic unit is called a pixel. The material (such as silicon or silicon dioxide) and geometric size of each pixel directly affect the performance of the device. In the present invention, the pixel is discretized into a square with a side length of 120nm.

[0107] Objective Function: A function used to measure the quality of a design during the optimization process. The optimization algorithm iteratively adjusts the design parameters to minimize or maximize the objective function value to obtain the best design. In photonic device design, the objective function is related to the efficiency or loss of light wave transmission.

[0108] Mode Crosstalk: In a mode division multiplexing device, signal coupling between multiple modes due to imperfect separation or interference may cause signal quality degradation. The present invention reduces the mode crosstalk through optimized design.

[0109] Insertion Loss: refers to the power loss caused by reflection, scattering or absorption when the optical signal passes through the device, usually expressed in dB. Smaller insertion loss means higher transmission efficiency of the device.

[0110] Crosstalk: In a multi-channel system, the unwanted interference of the signal of one channel on other channels. Smaller crosstalk values ​​indicate better isolation between channels.

[0111] The following is a brief description of some of the innovative features of this application:

[0112] With the rapid development of artificial intelligence technology, the requirements for communication capacity of data center optical interconnection are increasing. As a new type of optical multiplexing technology, mode division multiplexing technology can further improve the information transmission rate in a single optical fiber or waveguide based on wavelength division multiplexing technology. As the core component of mode division multiplexing technology, mode division multiplexer plays a key role in improving system performance.

[0113] At present, the design methods of mode division multiplexers are mainly divided into intuition-first type and reverse design type. Among them, the method based on reverse design can significantly reduce the size and loss of mode division multiplexers, showing the potential for large-scale integration. However, traditional reverse design methods, whether digital or analog, face their own challenges:

[0114] Digital reverse design usually uses a brute force search algorithm to update the status of digital pixels, resulting in low optimization efficiency and limited optimization freedom.

[0115] Although analog reverse design has high optimization efficiency, the minimum feature size it usually produces is small, and the requirements for processing accuracy and stability are too high, making it difficult to achieve high-robustness mass manufacturing.

[0116] In view of the above problems, the inventors of this application proposed an innovative solution, namely, an edge-guided joint analog-digital reverse design method. The core technical solution and key technical concepts of this method include:

[0117] 1) Combining the advantages of analog and digital reverse design: Utilizing the high efficiency of analog design and the processing robustness of digital design, a balance is achieved between optimization efficiency and manufacturing feasibility.

[0118] 2) Introducing edge-guided technology: Innovatively apply edge detection technology in image processing to photonic device design, and guide the digital conversion process by extracting edge information from analog design results.

[0119] 3) Two-stage optimization strategy: a) First, the adjoint method is used for simulation-based optimization to quickly obtain a high-performance continuous dielectric constant distribution. b) Then, based on edge information, the simulation results are converted into a digital structure with a larger feature size, and a direct binary search method is used for local optimization.

[0120] 4) Feature size enlargement: Through edge guidance and maximum pooling processing, the minimum feature size is increased from 20nm to 120nm, which significantly improves the processing robustness of the device.

[0121] 5) High-efficiency digital optimization: Only the pending pixels near the edge are optimized, avoiding the global blind search in traditional methods and significantly reducing the number of electromagnetic simulations required.

[0122] This innovative approach not only solves the limitations of traditional inverse design methods, but also achieves the unity of high efficiency, high performance and high manufacturability, opening up new avenues for the design of complex photonic devices such as mode division multiplexers.

[0123] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below in conjunction with the accompanying drawings.

[0124] The first embodiment of the present application relates to a joint analog-digital reverse design method based on edge guidance, the process of which is as follows: Figure 1 As shown, the method comprises the following steps:

[0125] Step 100: Initialization step: Initialize the waveguide structure of the photonic device and the initial dielectric constant distribution of the design area, generate a random dielectric constant distribution that meets the preset material refractive index range and satisfies the Gaussian distribution, and use it as the initial dielectric constant distribution of the design area.

[0126] Specifically, step 100 describes the initialization process of the photonic device design, which specifically includes setting the initial dielectric constant distribution of the waveguide structure and the design area. Technically, the core of this step is to generate a random dielectric constant distribution that conforms to the preset material refractive index range. The refractive index is a key parameter for the performance of photonic devices, which determines the propagation characteristics of light in different materials. In order to ensure the accuracy of the design and the effectiveness of the optimization, Gaussian distribution is used to randomly generate these dielectric constants during initialization to ensure that the values ​​in the design area are statistically reasonable while avoiding overly uniform or unreasonable distributions. In addition, such a Gaussian distribution can also ensure that subsequent optimization steps have higher degrees of freedom and flexibility, allowing the algorithm to find the optimal solution in a wider design space, thereby improving the performance of the device.

[0127] Step 200: Simulation optimization step: The initial dielectric constant distribution generated in the initialization step is continuously optimized based on the adjoint method, and the gradient information of each pixel point in the design area is obtained by performing a forward and a reverse electromagnetic simulation on the design area respectively, and the dielectric constant distribution is updated based on the gradient information to obtain an optimized simulated dielectric constant distribution.

[0128] Optionally, the dielectric constant update rule in the simulation optimization step is:

[0129]

[0130] in,

[0131] is the dielectric constant at the pixel point x after update;

[0132] is the dielectric constant at the pixel point x before updating;

[0133] α is the update rate;

[0134] F is the objective function;

[0135] is the derivative of the objective function F with respect to the dielectric constant at the pixel point x;

[0136] The derivative of the objective function F with respect to the dielectric constant of the pixel point is obtained by obtaining the electric field distribution obtained by one forward transmission and one reverse transmission;

[0137] In the iterative process of analog optimization, the dielectric constant of the pixel point is gradually pushed toward the maximum and minimum boundaries through a digital filter to obtain an approximately binary dielectric constant distribution.

[0138] Optionally, the objective function calculation formula in the simulation optimization step is:

[0139]

[0140] in,

[0141] F is the objective function;

[0142] N is the total number of modes;

[0143] is the conversion efficiency from the i-th TE mode to the TE0 mode;

[0144] Σ represents the sum of i from 1 to N;

[0145] The conversion efficiency Calculate by following the steps below:

[0146] (1) Perform forward electromagnetic field simulation on each input mode TEi to obtain the electric field distribution at the output end;

[0147] (2) Overlap integral of the electric field distribution at the output end and the ideal TE0 mode;

[0148] (3) Normalize the result of overlap integral to obtain conversion efficiency

[0149] Specifically, step 200 describes the process of simulation-based optimization, which continuously optimizes the initial dielectric constant distribution based on the adjoint method. The dielectric constant determines the propagation characteristics of light in the material, so optimizing this distribution is crucial to improving the performance of photonic devices. In this step, the gradient information of each pixel in the design area is obtained through forward and reverse electromagnetic simulations, and the dielectric constant distribution is updated based on this gradient information.

[0150] Specifically, the dielectric constant update rule for each pixel is calculated based on the derivative of the objective function FFF with respect to the pixel. The update formula is:

[0151]

[0152] in, is the updated dielectric constant, is the dielectric constant before updating, α is the updating rate, is the derivative of the dielectric constant of the pixel point by the objective function F. Through such an iterative process, the dielectric constant distribution in the design area is gradually optimized, and finally the optimized distribution is obtained.

[0153] The adjoint method is used in this process. It is an effective optimization method that obtains the electric field distribution through one forward and one reverse transmission, thereby calculating the gradient information of each pixel point, greatly reducing the number of calculations required in the optimization process and improving the optimization efficiency.

[0154] During the optimization process, the dielectric constant of the pixel point is gradually pushed to the boundary of the maximum and minimum values ​​through the digital filter, making it close to binary. This method can ensure that the optimized dielectric constant distribution is more suitable for subsequent digital processing and actual manufacturing.

[0155] The objective function F calculation formula is:

[0156]

[0157] Where N is the total number of modes, From TE0 mode to TE i The conversion efficiency of each mode is summed to measure the overall optimization effect. The conversion efficiency is determined by simulating the overlap between the input electric field and the ideal output mode, and finally the objective function value for optimization is obtained.

[0158] In summary, step 200 gradually optimizes the dielectric constant distribution of the design region of the photonic device by using the adjoint method and the dielectric constant update rule, laying a foundation for the subsequent digital structure conversion. This process improves the device performance while ensuring the feasibility of manufacturing.

[0159] Step 300: Edge-guided conversion step: The optimized simulated dielectric constant distribution obtained in the analog optimization step is used as a simulated pattern, and the edge information of the simulated pattern is extracted by an edge detection algorithm. Based on the edge information, the area far away from the edge is directly converted into a pixel point with a larger size, and the dielectric constant of the area is consistent with the dielectric constant of the corresponding position in the simulated pattern. At the same time, the area close to and adjacent to the edge is converted into a pixel point to be determined, and its dielectric constant needs to be further determined.

[0160] Optionally, the area close to and adjacent to the edge refers to an area whose distance from the edge line obtained by edge detection is within a preset threshold range, wherein the preset threshold range is a distance of 1-3 pixels, preferably a distance of 2 pixels.

[0161] Optionally, the larger pixel is a square pixel with a side length of 80 nm to 150 nm, preferably a square pixel with a side length of 100 nm to 130 nm, and more preferably a square pixel with a side length of 120 nm.

[0162] Optionally, the edge detection algorithm used in the edge-guided conversion step is a Canny edge detection algorithm, which specifically includes the following steps:

[0163] (1) Gaussian filtering: Gaussian filtering is performed on the simulated dielectric constant distribution image to reduce noise;

[0164] (2) Calculate gradient: Use the Sobel operator to calculate the gradient magnitude and direction of the image;

[0165] (3) Non-maximum suppression: non-maximum suppression of gradient amplitude along the gradient direction to refine the edge;

[0166] (4) Double threshold detection: Use high and low thresholds to perform threshold processing on the image after non-maximum suppression to obtain strong edge points and weak edge points;

[0167] (5) Edge connection: connect weak edge points to strong edge points through the hysteresis threshold method to form a complete edge;

[0168] The output of the Canny edge detection algorithm is a binary edge map, where a pixel value of 1 indicates an edge and a pixel value of 0 indicates a non-edge.

[0169] Optionally, the image processing step after the edge detection algorithm includes:

[0170] Max pooling: Performing max pooling on the edge image obtained by the edge detection algorithm to reduce the image dimension and expand the side length of the pixel six times while keeping the overall size of the entire design area unchanged to ensure that the local features in the design area are properly preserved; and

[0171] Binarization: Binarize the image after the maximum pooling process, assign all non-zero pixel values ​​to 1, and keep the zero-value pixels as 0, so as to generate the final decision pattern;

[0172] In the final decision pattern, the pixel points with a pixel value of 1 correspond to the portion close to the edge of the original simulation pattern, and the pixel points with a pixel value of 0 correspond to the area far from the edge.

[0173] Specifically, step 300 describes the edge-guided conversion step, which is an important process for converting analog design results into digital structures. Specifically, an edge detection algorithm is first used to extract edge information of the dielectric constant distribution after simulation optimization, and the edge information is used to guide the subsequent digital conversion. The core of this conversion is to directly convert the area far from the edge into a pixel with a larger characteristic size, while the area near the edge is marked as a pixel to be determined, and its dielectric constant is further determined.

[0174] In this process, the Canny edge detection algorithm is used, which includes five steps: first, the image is Gaussian filtered to reduce noise, then the gradient amplitude and direction of the image are calculated, and then non-maximum suppression is performed to refine the edge. Subsequently, the strong and weak edge points are determined by double threshold detection, and finally the weak edge points are connected to the strong edge points by the hysteresis threshold method to form a complete edge map. The purpose of these steps is to ensure the accuracy and completeness of the edge information in order to provide a reliable basis for subsequent digital optimization.

[0175] After edge detection, the next step of image processing is maximum pooling. This process reduces the resolution of the image and increases the side length of the pixel to six times the original, ensuring that the local features of the design area are preserved and laying the foundation for the next step of binarization. Binarization further simplifies the image, setting all non-zero pixel values ​​to 1 and zero-value pixels to 0, ultimately generating a simplified decision pattern to facilitate subsequent digital optimization processing.

[0176] Through these steps, edge-guided technology can effectively transform analog design results into digital structures with larger feature sizes, significantly improving the processing robustness of photonic device design, while reducing the computational complexity of global search and optimizing design efficiency.

[0177] Step 400: Digital optimization step: Based on the undetermined pixel points generated in the edge-guided conversion step, the final dielectric constant of the undetermined pixel points is determined by a direct binary search method, while keeping the dielectric constant of the directly converted pixel points unchanged, and after a single iterative optimization, a digital reverse design structure with a larger feature size is finally obtained.

[0178] Optionally, a specific implementation of the direct binary search method in the digital optimization step includes:

[0179] Assigning values ​​to pixels to be determined: For each pixel marked as To-be-determined (TBD) in the edge-guided transformation step, assign the dielectric constant values ​​of silicon and silicon dioxide respectively;

[0180] Calculate the objective function value: For each dielectric constant assignment, calculate the corresponding objective function value;

[0181] Select optimized material: compare the objective function value and select the material that can optimize the objective function as the final dielectric constant of the pixel to be determined;

[0182] Repeat optimization: repeat steps (1) to (3) for all pending pixels, and keep the dielectric constant of the pixels that have been directly converted unchanged;

[0183] Iteration completion: After completing the optimization of all pending pixels, a digital reverse design structure with a larger feature size is obtained.

[0184] Specifically, step 400 describes in detail the digital optimization process, which is a key step after completing the edge-guided conversion. This step optimizes the dielectric constant of the pixel to be determined by direct binary search to complete the final digital design. In the previous stage, the edge information of the analog design has been extracted, and the area far away from the edge has been directly assigned a certain dielectric constant. However, due to the complex edge effect, the dielectric constant of the pixel to be determined near the edge still needs to be further optimized to achieve the best performance.

[0185] First, for each pixel to be determined, the method assigns two possible dielectric constant values, namely the dielectric constant of silicon and silicon dioxide. Then, the pros and cons of each assignment are evaluated by calculating the objective function value. The objective function measures the contribution of the pixel to the overall design performance, such as optimizing light wave transmission efficiency or reducing losses. By comparing the objective function values ​​under different dielectric constants, the material that maximizes the objective function is selected as the final dielectric constant of the pixel to be determined.

[0186] This process is not limited to a single pixel, but iterates for all pending pixels. For each pending pixel, the process of assigning values, calculating the objective function, and selecting the optimized material is repeated. At the same time, the pixels that have been directly assigned values ​​remain unchanged, which ensures the stability and efficiency of the optimization process.

[0187] After a single iteration optimization, the dielectric constants of all pending pixels were optimized, and finally a digital reverse design structure with a large feature size was generated. This structure not only meets the design performance requirements, but also has both robustness and feasibility in processing. The direct binary search method avoids the inefficiency of blind global search, significantly reduces the computational complexity, and improves the optimization speed. This process ensures that the digital design of photonic devices is not only efficient and reliable, but also has high manufacturing adaptability.

[0188] The silicon-based mode division multiplexer designed according to the above method is further explained below.

[0189] The silicon-based mode division multiplexer designed according to the above method includes:

[0190] Five single-mode input waveguides for introducing the incident fundamental TE0 mode;

[0191] A multimode output waveguide for outputting the multiplexed optical signal after mode conversion;

[0192] The device body is a rectangular design area, which is discretized into a number of square pixels, each of which is an etched hole made of silicon or silicon dioxide;

[0193] Among them, the silicon-based mode division multiplexer can support the multiplexing and demultiplexing of five orthogonal transverse electric modes (TE modes), and can convert the TE0 mode from five separate single-mode waveguides into TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide; at the same time, due to reciprocity, the mode division multiplexer can convert the TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide into the TE0 mode in the five single-mode waveguides.

[0194] Optionally, the material platform and specific parameters of the mode division multiplexer include:

[0195] The material platform is a silicon-on-insulator (SOI) platform;

[0196] The height of the silicon waveguide is 200 nm to 240 nm, preferably 220 nm;

[0197] The thickness of the silicon dioxide substrate is 1.5 μm to 2.5 μm, preferably 2 μm;

[0198] The thickness of the silica cladding layer is 0.8 μm to 1.2 μm, preferably 1 μm.

[0199] Optionally, specific parameters of the input waveguide and output waveguide of the mode division multiplexer include: the width of the single-mode input waveguide is 450nm to 550nm, preferably 500nm; the spacing between each single-mode waveguide is equal, 800nm ​​to 950nm, preferably 875nm; the width of the multi-mode output waveguide is 2.3μm to 2.7μm, preferably 2.5μm, and is located at the edge of the rectangular design area.

[0200] Optionally, the design area length of the mode division multiplexer is between 8 μm and 12 μm, preferably 10 μm; and the width is between 4 μm and 8 μm, preferably 6 μm.

[0201] More specifically, the silicon-based mode division multiplexer is based on advanced photonic integration technology and can realize multiplexing and demultiplexing of multi-mode signals on a compact silicon-based platform, thereby greatly improving the information transmission capacity of optical communication systems.

[0202] The structure of the multiplexer mainly consists of three parts: five single-mode input waveguides, one multi-mode output waveguide and a device body. The single-mode input waveguide is responsible for introducing the optical signal of the TE0 mode, while the multi-mode output waveguide is responsible for exporting the multiplexed optical signal after mode conversion. The device body is a rectangular design area, in which a complex mode conversion function is realized through a precisely arranged array of etched holes. Each etched hole is a square pixel point, composed of silicon or silicon dioxide, and the propagation and mode conversion of the optical signal are regulated by the combination and arrangement of these pixels.

[0203] The key feature of the mode division multiplexer is that it supports the multiplexing and demultiplexing of five orthogonal transverse electrical modes (TE0 to TE4). Specifically, it can convert the TE0 mode signal from five single-mode waveguides into the TE0, TE1, TE2, TE3 and TE4 modes in the multimode waveguide. This design significantly improves the information transmission capacity in the optical fiber. In addition, due to the principle of optical reciprocity, the multiplexer can also perform the reverse process, separating the TE0 to TE4 modes in the multimode waveguide and converting them back to the TE0 mode in the single-mode waveguide. This bidirectional working capability makes the device have great application prospects in complex optical communication networks.

[0204] In terms of material selection and structural design, the multiplexer uses a silicon-on-insulator (SOI) platform, which is the most widely used material system in current photonic integrated circuits. Specifically, the device's silicon waveguide height is 220 nanometers, the silicon dioxide substrate thickness is 2 microns, and the cladding thickness is 1 micron. This structure can not only provide effective optical confinement for optical signals, but also ensure the compatibility of the device with existing silicon-based manufacturing processes, facilitating large-scale production.

[0205] In terms of waveguide parameters, the width of each single-mode input waveguide is 500 nanometers, and the spacing between waveguides is 875 nanometers, ensuring the separation and independent transmission of input signals. The width of the multimode output waveguide is 2.5 microns to support the effective transmission of multiple high-order modes. The multimode waveguides are cleverly arranged at the edge of the rectangular design area to optimize the coupling efficiency of the optical signal and further improve the performance of the device.

[0206] Finally, the core design area of ​​the mode division multiplexer is only 10 microns by 6 microns. This compact design demonstrates the potential of photonic devices in integration and miniaturization. Smaller size not only helps to improve the integration of chips, but also may reduce power consumption and increase the operating speed of devices.

[0207] In general, this silicon-based mode division multiplexer design demonstrates the great potential of advanced photonic integration technology, provides important technical support for future high-capacity and high-efficiency optical communication systems, and demonstrates its advantages in achieving highly integrated and high-efficiency devices.

[0208] In order to better understand the technical solution of the present application, a specific example is provided below for illustration. The details listed in the example are mainly for ease of understanding and are not intended to limit the scope of protection of the present application.

[0209] This example proposes a joint analog-digital reverse design method based on edge guidance and a mode division multiplexer designed using this method. This method combines the advantages of digital reverse design and analog reverse design, and has both processing robustness and high optimization efficiency.

[0210] like Figure 2 As shown, the reverse design method includes an initialization module 101, an analog optimization module 102, an edge-guided analog-to-digital conversion module 103, and a digital optimization module 104; wherein:

[0211] The initialization module 101 initializes the input and output waveguide structures and the dielectric constant distribution of the design area, and generates a random distribution satisfying the Gaussian distribution according to the set material refractive index range as the initialization dielectric constant distribution of the device design area;

[0212] The simulation optimization module 102 continuously optimizes the dielectric constant distribution of the design area based on the adjoint method. In each iterative optimization, a forward and a reverse electromagnetic simulation are performed on the design area. The gradient information of each pixel point in the device design area can be obtained through two electromagnetic simulations, and the dielectric constant is updated based on the gradient information.

[0213] The edge-guided analog-to-digital module 103 uses the dielectric constant distribution obtained by analog reverse design as the analog pattern for edge extraction, and directly converts the part far from the edge into a pixel with a larger size through pooling and binarization operations, whose dielectric constant is equal to the dielectric constant of the material at the corresponding position in the original analog pattern, and converts the part close to and adjacent to the edge into a pixel to be determined, whose dielectric constant value needs to be further determined;

[0214] The digital reverse design module 104 determines the dielectric constant of the pixel to be determined by direct binary search, while the dielectric constant of the directly converted pixel remains unchanged, and finally obtains a digital reverse design structure with a larger feature size after a single iteration.

[0215] The following further describes the edge-guided joint analog-digital reverse design method and the specific steps of designing an analog-to-digital multiplexer using the method.

[0216] Step 1: Initialize the device structure to be optimized, including the input and output waveguide dimensions, the optimized region dimensions, and the initial dielectric constant distribution of the optimized region. The input waveguide should be able to support fundamental mode transmission, the output waveguide should be able to support multimode transmission, and the relationship between the waveguide dimensions and the number of allowed modes should be obtained through finite element simulation. The dielectric constant distribution of the design region satisfies the Gaussian distribution, the maximum value should be less than or equal to the dielectric constant of silicon, and the minimum value should be greater than or equal to the dielectric constant of silicon dioxide.

[0217] Furthermore, the initialization process in step one is an important part of the design of photonic devices, which aims to lay the foundation for subsequent optimization steps. First, the dimensions of the input and output waveguides need to be set. The input waveguide is responsible for introducing the fundamental mode TE0 mode, which means that its size needs to meet the requirements for effective transmission of optical signals in the fundamental mode. Fundamental mode transmission refers to the lowest order mode when light propagates in the waveguide, which has the characteristics of stability and low loss. On the other hand, the output waveguide needs to be able to support multimode transmission, that is, it must be of sufficient size to accommodate the propagation of multiple higher-order modes, which helps to increase the capacity of the communication system.

[0218] To determine the exact dimensions of the waveguide, finite element simulation tools are usually used. This is a numerical analysis method that can accurately calculate the relationship between the waveguide dimensions and the number of modes it supports, ensuring that the input and output waveguides can operate in the specified modes.

[0219] Next, the size of the optimization area also needs to be initialized. This area is the core part of the entire device design. By optimizing the dielectric constant distribution in this area, efficient conversion of optical signals between different modes can be achieved. In order to ensure the optimization effect, the initial dielectric constant distribution of the design area adopts Gaussian distribution. Gaussian distribution is a commonly used probability distribution, which is characterized by larger values ​​in the central area and gradually decreasing values ​​away from the center. In this way, the dielectric constant distribution of the optimization area will not be too concentrated or too dispersed in the initial stage, providing sufficient flexibility for subsequent optimization.

[0220] Finally, the maximum and minimum values ​​of the dielectric constant need to be limited to the dielectric constant range of silicon and silicon dioxide, respectively. Silicon and silicon dioxide are commonly used materials in photonic devices. Silicon has a higher dielectric constant, which helps to confine optical signals, while silicon dioxide has a lower dielectric constant, which helps the propagation of optical signals. Therefore, ensuring that the dielectric constant is distributed between these two values ​​helps maintain the manufacturability of the material and the functional stability of the photonic device.

[0221] Through this initialization step, reasonable parameter settings are provided for the subsequent optimization process, ensuring that the design of photonic devices can be carried out efficiently and accurately.

[0222] Step 2: Use the adjoint method to simulate and optimize the dielectric constant distribution in the design area. The dielectric constant update rule expression is as follows:

[0223]

[0224] in and are the dielectric constants at the pixel point x before and after the update, α is the update rate, and F is the objective function. The derivative of the objective function F with respect to the dielectric constant of the pixel point can be obtained through the electric field distribution obtained by one forward and one reverse transmission. In the iterative optimization process of the simulated inverse design optimization, the dielectric constant of the pixel point is gradually pushed to the maximum and minimum boundaries through the digital filter to obtain an approximately binary dielectric constant distribution.

[0225] Furthermore, the objective function calculation formula is:

[0226]

[0227] in is the conversion efficiency of each mode, and N is the total number of modes.

[0228] Furthermore, step 2 is one of the core links of this design method, which involves using the adjoint method to perform analog optimization on the dielectric constant distribution of the design area. The goal of this step is to find the optimal dielectric constant distribution in the continuous solution space, laying the foundation for the subsequent digitalization process.

[0229] In this step, an iterative update strategy is adopted, the core of which is the dielectric constant update rule. This rule can be expressed as a mathematical formula: In this formula, and represent the dielectric constants at the pixel point x before and after the update, α is the update rate, and F is the objective function to be optimized.

[0230] The selection of the objective function F is crucial to the entire optimization process. In this method, F is defined as the average value of the conversion efficiency of each mode, that is, in represents the conversion efficiency of each mode, and N is the total number of modes. This definition ensures that the optimization goal is to improve the overall mode conversion performance.

[0231] The derivative of the objective function with respect to the dielectric constant (dF / dεx) is obtained through one forward and one reverse electromagnetic simulation. The application of this adjoint method greatly improves the optimization efficiency because it only requires two simulations to obtain the gradient information of all pixels.

[0232] During the optimization process, a digital filter is also introduced. The function of this filter is to gradually push the dielectric constant of the pixel point to the maximum or minimum boundary. The purpose of this strategy is to obtain an approximately binary dielectric constant distribution to prepare for the subsequent digitization process.

[0233] Through this method that combines the adjoint method, objective function optimization, and digital filtering, step 2 can efficiently search for the optimal solution in the continuous space, laying a solid foundation for subsequent edge-guided conversion and digital optimization. This step fully demonstrates the advantages of analog optimization, namely high efficiency and a high degree of optimization freedom, creating conditions for obtaining a high-performance final design.

[0234] Step 3: Use edge information to achieve the conversion from analog pattern to digital pattern. In the analog reverse design process, the final analog pattern obtained contains an array of square pixels with a side length of 20nm. Each pixel can adjust the dielectric constant and continuously take values ​​between the dielectric constants of silicon and silicon dioxide, which is not conducive to robust process manufacturing. The dielectric constant distribution of the mode division multiplexer obtained by analog reverse design is shown in the figure below. Figure 4 As shown in (a), the narrow cracks and etching holes with extremely small widths are clearly visible. In order to solve this problem, the analog pattern needs to be converted into a digital pattern with a larger feature size, where the smallest unit is a square pixel with a side length of 120nm, and the dielectric constant of each pixel is fixed to the standard value of silicon or silicon dioxide. First, the edge analysis of the analog pattern is performed using the Canny edge detection algorithm to generate an edge map, as shown in Figure 1. Figure 4 (b) shows. The pixel values ​​of the edge map are set to 0 or 1, where 0 represents non-edge pixels and 1 indicates edge pixels. The maximum pooling process is then performed, which reduces the dimension of the pattern and increases the side length of the pixel to six times the original, while ensuring that the overall size of the design area remains unchanged. The binary process is then performed to assign all non-zero pixels a value of 1, while zero-value pixels remain unchanged, thereby obtaining the final judgment pattern, as shown in Figure 4 (c) In this decision pattern, the pixel with a value of 1 corresponds to the part close to the edge of the original simulation pattern, while the pixel with a value of 0 corresponds to the area far from the edge. Next, dielectric constant mapping is performed based on the decision pattern, directly mapping the dielectric constants of all 0-valued pixels, and 1-valued pixels are marked as TBD (To-be-determined).

[0235] Furthermore, step three is the key link in the entire design method, and its main purpose is to convert the results obtained through simulation optimization into a digital structure that is more suitable for actual manufacturing. In this step, edge information is cleverly used to guide the conversion process, achieving a balance between performance optimization and manufacturing feasibility.

[0236] Initial simulations resulted in an array of square pixels with a side length of 20 nanometers, with a dielectric constant that varies continuously within the range of silicon and silicon dioxide. Although this design has excellent performance in theory, it is difficult to reliably manufacture in practice due to the small feature size and complex material distribution. Figure 4 (a) shows the simulation results, showing the tiny etched holes and slits.

[0237] To solve this manufacturing challenge, the analog pattern must be converted into a digital pattern with a larger feature size. The converted structure consists of square pixels with a side length of 120 nanometers, and the material of each pixel is limited to silicon or silicon dioxide. This adjustment significantly increases the minimum feature size, making the design more compatible with manufacturing requirements.

[0238] The first step of the conversion is to apply the Canny edge detection algorithm to analyze the simulated pattern and extract edge information to generate Figure 4 (b) shows the edge map. The pixel values ​​in the edge map are set to 0 or 1, where 1 represents edge pixels and 0 represents non-edge pixels. This process extracts key geometric information from the original design.

[0239] Next, the edge map is processed by max pooling to reduce the resolution of the pattern while increasing the side length of the pixel from 20 nanometers to 120 nanometers. This operation keeps the overall size of the design area unchanged, ensuring the consistency of the physical size of the design before and after the conversion.

[0240] Then, the final decision pattern is obtained through binarization processing, such as Figure 4 (c) shows that in the pattern, the pixel value of 1 corresponds to the key edge area in the original design, and the pixel value of 0 corresponds to the part far from the edge. This process effectively distinguishes the key structure and non-key area in the design.

[0241] Finally, the dielectric constant is mapped based on the decision pattern. For the pixel points with a value of 0 in the decision pattern, their dielectric constant is directly mapped to silicon dioxide, while the pixel points with a value of 1 are marked as to be determined (TBD), leaving flexibility for subsequent optimization.

[0242] Through this edge-guided conversion method, step three successfully transforms the high-performance but difficult-to-manufacture analog design into a digital structure suitable for actual processes. This method not only retains the core performance of the design, but also greatly improves the manufacturability of the device, laying a solid foundation for subsequent digital optimization.

[0243] Step 4: Use the direct binary search method to determine the dielectric constant of the TBD pixel. For each pixel marked as TBD, assign the dielectric constants of silicon and silicon dioxide respectively, and calculate the value of the objective function respectively, and select the dielectric constant of the material with a larger objective function value as the final pixel dielectric constant. After performing this operation for each TBD pixel, exit the optimization directly and end this reverse design.

[0244] Furthermore, step 4 is the last key step of the design method, which aims to determine the final material properties of the pixels marked as TBD in step 3. This step adopts the direct binary search method, which is an efficient and targeted optimization strategy.

[0245] In this step, each TBD pixel is assigned two possible materials: silicon or silicon dioxide. These two materials are commonly used in the manufacture of photonic devices, meet actual process requirements, and simplify the complexity of material selection. Through this binary selection method, the system can quickly determine which material is more suitable for optimizing the performance of the device.

[0246] Whenever a material is assigned to a pixel, the system calculates the corresponding objective function value. The objective function reflects the performance of the device, such as mode conversion efficiency or insertion loss. By comparing the objective function values ​​of silicon and silicon dioxide, the system selects the material that can make the objective function value larger as the final dielectric constant of the pixel.

[0247] This process is only performed once for each TBD pixel, that is, once a material is selected for a pixel, it will not be re-evaluated. This one-time decision greatly improves the efficiency of optimization, avoids complex iterative processes, and ensures quick and effective results.

[0248] When the material selection for all TBD pixels is completed, the entire optimization process ends and no further iterations are performed. This strategy simplifies the optimization process while retaining the optimization advantages obtained in the previous simulation design.

[0249] The innovation of step 4 is that it combines the high-performance characteristics of analog optimization in a concise digital optimization process. By focusing on optimizing key areas near the edge, it ensures both computational efficiency and fine-tuning of local structures, thus ensuring the overall performance of the design.

[0250] In summary, step 4 successfully transforms the analog design into a digital design solution with good performance and suitable for manufacturing through an efficient binary selection strategy. This step is the final link of the entire design process, which effectively integrates the advantages of all previous steps and ultimately provides a practical and efficient solution for the design of photonic devices.

[0251] Figure 5 A planar schematic diagram of a silicon-based mode division multiplexer is shown, and the multiplexer is designed using the edge-guided joint analog-digital inverse design method described in the first aspect above. The mode division multiplexer can convert the TE0 mode from five separate single-mode waveguides into the TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide; at the same time, due to reciprocity, the mode division multiplexer can convert the TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide into the TE0 mode in the five single-mode waveguides. The material platform of the silicon-based mode division multiplexer is an SOI platform, the silicon waveguide height is 220nm, the silicon dioxide substrate thickness is 2μm, and the silicon dioxide cladding thickness is 1μm. The mode division multiplexer consists of three parts: a single-mode input waveguide array 301, a design area 302, and a multimode output waveguide 303. The single-mode input waveguide array 301 is composed of five single-mode input waveguides with a width of 500nm, which are used to introduce the incident fundamental mode TE0 mode, and the spacing between each single-mode waveguide is equal, which is 875nm; the design area 302 is the main part of the device, which is a rectangular design area with a size of 10μm×6μm, and the area is discretized into a number of pixel points, each pixel point is a square etched hole with a side length of 120nm, and the material of each pixel point is silicon or silicon dioxide; the multi-mode output waveguide 303 is a multi-mode output waveguide with a width of 2.5μm, which is used to export the multiplexed light after mode conversion.

[0252] in other words, Figure 5 The superiority of the method of the present invention is reflected. The complex structure in the design area 302 is optimized by an edge-guided joint analog-digital inverse design method, which effectively realizes the conversion and multiplexing of multiple modes. Although the structure in the design area seems complex, the material properties of each pixel are clearly defined as silicon or silicon dioxide, which not only simplifies the manufacturing process but also greatly improves the manufacturability of the device. At the same time, the minimum feature size of 120 nanometers ensures good compatibility with existing lithography processes. The design of the single-mode input waveguide array 301 and the multi-mode output waveguide 303 has been carefully optimized to ensure efficient optical coupling. The five input waveguides are arranged at an equal spacing of 875 nanometers. This design not only reduces crosstalk, but also facilitates docking with standard optical fiber arrays. The 2.5-micron-wide multi-mode output waveguide provides sufficient space to support the transmission of 5 different TE modes while maintaining compatibility with standard silicon photonic single-mode waveguides. The compact size of the entire device (10 microns × 6 microns design area) demonstrates the outstanding advantages of this design method in achieving high integration. This miniaturized design not only increases the chip's integration density, but also reduces insertion loss and improves thermal stability. Figure 5The demonstrated structure is a good balance of high performance, manufacturability and integration, fully demonstrating the broad potential of the method in practical applications.

[0253] Figure 6 The optical field distribution of the silicon-based mode division multiplexer designed by the method of the present invention under TE0 mode incidence is demonstrated. Figure 6 (a)-(e) show the optical field evolution process when the TE0 mode is input from the 1st to the 5th single-mode waveguide:

[0254] (a) Shows the transformation of TE0 mode into TE0 mode in a multimode waveguide.

[0255] (b) shows the process of TE0 mode conversion to TE1 mode, and an obvious mode node can be seen in the figure.

[0256] (c) shows the transition from TE0 to TE2 mode, and two clear mode nodes are observed.

[0257] (d) shows the transition from TE0 to TE3 mode, with three mode nodes appearing in the figure.

[0258] (e) shows the transition from TE0 to TE4 mode, with four obvious mode nodes.

[0259] These optical field distribution diagrams intuitively demonstrate that the mode division multiplexer can efficiently convert a single TE0 mode into TE modes of different orders, verifying the excellent performance of the device in realizing multi-mode multiplexing functions.

[0260] Figure 7 The transmission spectrum characteristics of the silicon-based mode division multiplexer are demonstrated. Figure 7 (a)-(e) correspond to the spectral responses of TE0 to TE4 modes in the multimode output waveguide when the TE0 mode is input from the 1st to the 5th single-mode waveguide. The horizontal axis represents the wavelength range (1530nm to 1570nm) and the vertical axis represents the mode conversion efficiency (unit: dB). From these spectra, the following key performance indicators can be summarized: At the central wavelength of 1550nm, the insertion loss of all five modes is less than 2.0dB, indicating that the device has efficient mode conversion capability. The crosstalk between each mode is less than -19dB, demonstrating excellent mode isolation performance. Within the wavelength range of 40nm (1530nm-1570nm), the device exhibits good broadband characteristics, and the conversion efficiency and crosstalk levels remain stable. The conversion efficiency of each input mode to the target output mode (solid line) is significantly higher than that of other non-target modes (dashed lines), further verifying the efficient mode selectivity.

[0261] These performance indicators fully prove that the silicon-based mode division multiplexer not only successfully achieves efficient multiplexing of five modes, but also has excellent characteristics such as low loss, low crosstalk and broadband. In particular, such complex functions are achieved in a compact size of only 10μm×6μm, highlighting the great potential of the method of the present invention in the design of highly integrated photonic devices. This combination of high performance and miniaturization provides a solid device foundation for the development of future large-capacity and high-density optical communication systems.

[0262] It should be pointed out that this example combines analog reverse design and digital reverse design technology. In analog reverse design, each iterative optimization only requires two electromagnetic simulations. At the same time, this example introduces image processing technology into the reverse design of photonic devices for the first time. With the guidance of edge information, only the pixels near the edge need to be flipped and iteratively optimized during the digital optimization process, avoiding cumbersome and inefficient blind search optimization. Compared with traditional digital optimization algorithms, the number of required electromagnetic simulations is greatly reduced, and efficient pixelated device design is achieved. This example achieves an increase in the minimum feature size (120nm) by converting analog reverse design devices into digital reverse design devices. Compared with analog reverse design devices, the challenges in process manufacturing are greatly reduced, and it can be processed and manufactured by mainstream silicon photonic wafer factories. In addition, the five-mode silicon-based mode division multiplexer designed in this example is only 10μm long, which is the smallest size among the current silicon-based five-mode multiplexers. Finally, the edge-guided combined analog-digital reverse design method proposed in this example is extremely versatile and can be suitable for the reverse design of various photonic devices, especially for the design of devices with larger size and more complex functions.

[0263] In summary, the edge-guided joint analog-digital reverse design method and silicon-based mode division multiplexer provided in this example have obvious advantages. This example can play an important role in the field of data center optical interconnection, improve integration and communication capacity, and meet the growing data transmission needs.

[0264] In general, the above examples have the following technical effects:

[0265] Efficient pixelated device design: The above example combines analog reverse design and digital reverse design technology. In analog reverse design, each iterative optimization only requires two electromagnetic simulations. At the same time, the above example introduces image processing technology into the reverse design of photonic devices for the first time. With the guidance of edge information, only the pixel points near the edge need to be flipped and iteratively optimized during the digital optimization process, avoiding tedious and inefficient blind search optimization. Compared with traditional digital optimization algorithms, the number of electromagnetic simulations required is greatly reduced, achieving efficient pixelated device design.

[0266] Process manufacturing robustness: The above example achieves an increase in the minimum feature size (120nm) by converting analog reverse design devices into digital reverse design devices. Compared with analog reverse design devices, the challenges in process manufacturing are greatly reduced and can be processed and manufactured by mainstream silicon photonics foundries.

[0267] Compact structure: The five-mode silicon-based mode division multiplexer designed in the above example is only 10μm long, which is the smallest size among the current silicon-based five-mode multiplexers;

[0268] Versatility: The edge-guided joint analog-digital reverse design method proposed in the above example is highly versatile and can be suitable for the reverse design of various photonic devices, especially for the design of devices with larger size and more complex functions.

[0269] In summary, the edge-guided joint analog-digital reverse design method and silicon-based mode division multiplexer provided in the above examples have obvious advantages. The above examples can play an important role in the field of data center optical interconnection, improve integration and communication capacity, and meet the growing data transmission needs.

[0270] The second embodiment of the present application relates to a joint analog-digital reverse design system based on edge guidance, and its structure is as follows: Figure 2 and Figure 3 As shown, the edge-guided joint analog-digital reverse design system includes:

[0271] An initialization module is used to initialize the waveguide structure of the photonic device and the initial dielectric constant distribution of the design area, and generate a random dielectric constant distribution that meets the preset material refractive index range and satisfies the Gaussian distribution as the initial dielectric constant distribution of the design area;

[0272] A simulation optimization module is used to continuously optimize the initial dielectric constant distribution generated by the initialization module based on the adjoint method, obtain the gradient information of each pixel point in the design area by performing a forward simulation and a reverse simulation on the design area, and update the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution;

[0273] An edge-guided conversion module is used to use the optimized simulated dielectric constant distribution obtained by the analog optimization module as a simulated pattern, extract edge information of the simulated pattern through an edge detection algorithm, and directly convert the area far from the edge into a pixel point with a larger size based on the edge information, and the dielectric constant of the area is consistent with the dielectric constant of the corresponding position in the simulated pattern, and at the same time, convert the area close to and adjacent to the edge into a pixel point to be determined, and its dielectric constant needs to be further determined;

[0274] The digital optimization module is used to determine the final dielectric constant of the undetermined pixel points generated by the edge-guided conversion module through a direct binary search method, while keeping the dielectric constant of the directly converted pixel points unchanged, and finally obtain a digital reverse design structure with a larger feature size after a single iterative optimization.

[0275] The first implementation manner is a method implementation manner corresponding to the present implementation manner. The technical details in the first implementation manner can be applied to the present implementation manner, and the technical details in the present implementation manner can also be applied to the first implementation manner.

[0276] It should be understood that the division of the various steps described in the embodiments of the present invention is mainly to clearly illustrate the technical solution of the present invention. In practical applications, these steps can be flexibly adjusted according to specific needs and technical conditions. For example, multiple steps can be combined into one step for execution, or a certain step can be subdivided into multiple sub-steps for implementation. In addition, the execution order of each step may also vary according to actual conditions. As long as these changed, adjusted or rearranged technical solutions still contain the core technical ideas and basic logical relationships of the present invention, they should be deemed to fall within the scope of protection of the present invention. The scope of protection of the present invention should not be limited to the specific step sequence described, but should cover various equivalent changes and modifications that can achieve the same technical effects.

[0277] It should be noted that those skilled in the art should understand that the implementation functions of each module shown in the implementation of the above-mentioned edge-guided joint analog digital reverse design system can be understood by referring to the relevant description of the aforementioned edge-guided joint analog digital reverse design method. The functions of each module shown in the implementation of the above-mentioned edge-guided joint analog digital reverse design system can be implemented by a program (executable instruction) running on a processor, or by a specific logic circuit. If the above-mentioned edge-guided joint analog digital reverse design system in the embodiment of the present application is implemented in the form of a software function module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present application can be essentially or partly reflected in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM, Read Only Memory), a disk or an optical disk. Thus, embodiments of the present application are not limited to any specific combination of hardware and software.

[0278] Accordingly, an embodiment of the present application further provides a computer storage medium, in which computer executable instructions are stored. When the computer executable instructions are executed by a processor, the various method embodiments of the present application are implemented.

[0279] In addition, the embodiment of the present application also provides a joint analog-digital reverse design system based on edge guidance, which includes a memory for storing computer executable instructions, and a processor; the processor is used to implement the steps in the above-mentioned method implementation methods when executing the computer executable instructions in the memory. Among them, the processor can be a central processing unit (Central Processing Unit, referred to as "CPU"), or other general-purpose processors, digital signal processors (Digital Signal Processor, referred to as "DSP"), Application Specific Integrated Circuit (Application Specific Integrated Circuit, referred to as "ASIC"), etc. The aforementioned memory can be a read-only memory (read-only memory, referred to as "ROM"), a random access memory (random access memory, referred to as "RAM"), a flash memory (Flash), a hard disk or a solid-state hard disk, etc. The steps of the method disclosed in each embodiment of the present invention can be directly embodied as a hardware processor execution, or a combination of hardware and software modules in the processor.

[0280] All documents mentioned in this application are considered to be included in the disclosure of this application as a whole, so that they can be used as the basis for modification when necessary. In addition, it should be understood that after reading the above disclosure of this application, those skilled in the art can make various changes or modifications to this application, and these equivalent forms also fall within the scope of protection claimed in this application.

Claims

1. A joint analog-digital reverse design method based on edge guidance, characterized in that: The following steps are involved: Initialization step: Initializing the waveguide structure of the photonic device and the initial dielectric constant distribution of the design area, generating a random dielectric constant distribution that meets the preset material refractive index range and satisfies the Gaussian distribution as the initial dielectric constant distribution of the design area; Simulation optimization step: continuously optimizing the initial dielectric constant distribution generated in the initialization step based on the adjoint method, obtaining the gradient information of each pixel point in the design area by performing a forward and a reverse electromagnetic simulation on the design area, and updating the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution; Edge-guided conversion step: using the optimized simulated dielectric constant distribution obtained in the analog optimization step as a simulated pattern, extracting edge information of the simulated pattern through an edge detection algorithm, and directly converting the area far from the edge into a pixel point with a larger size based on the edge information, and the dielectric constant of the area is consistent with the dielectric constant of the corresponding position in the simulated pattern, and at the same time converting the area close to and adjacent to the edge into a pixel point to be determined, and its dielectric constant needs to be further determined; Digital optimization step: Based on the undetermined pixel points generated in the edge-guided conversion step, the final dielectric constant of the undetermined pixel points is determined by a direct binary search method, while keeping the dielectric constant of the directly converted pixel points unchanged, and after a single iterative optimization, a digital reverse design structure with a larger feature size is finally obtained.

2. The method according to claim 1, characterized in that The dielectric constant update rule in the simulation optimization step is: in, is the dielectric constant at the pixel point x after update; is the dielectric constant at the pixel point x before updating; α is the update rate; F is the objective function; is the derivative of the objective function F with respect to the dielectric constant at the pixel point x; x represents the spatial position coordinate within the design area; The derivative of the objective function F with respect to the dielectric constant of the pixel point is obtained by obtaining the electric field distribution obtained by one forward transmission and one reverse transmission; In the iterative process of analog optimization, the dielectric constant of the pixel point is gradually pushed toward the maximum and minimum boundaries through a digital filter to obtain an approximately binary dielectric constant distribution.

3. The method according to claim 1, characterized in that The objective function calculation formula in the simulation optimization step is: in is the conversion efficiency of each mode, N is the total number of modes; F is the objective function; N is the total number of modes; is the conversion efficiency from the i-th TE mode to the TE0 mode; Σ represents the sum of i from 1 to N; The conversion efficiency Calculate by following the steps below: (1) Perform forward electromagnetic field simulation on each input mode TEi to obtain the electric field distribution at the output end; (2) Overlap integration of the electric field distribution at the output end and the ideal TE0 mode; (3) Normalize the result of overlap integral to obtain conversion efficiency 4. The method according to claim 1, characterized in that: The edge detection algorithm used in the edge-guided conversion step is the Canny edge detection algorithm, which specifically includes the following steps: (1) Gaussian filtering: Gaussian filtering is performed on the simulated dielectric constant distribution image to reduce noise; (2) Calculate gradient: Use the Sobel operator to calculate the gradient magnitude and direction of the image; (3) Non-maximum suppression: non-maximum suppression of gradient amplitude along the gradient direction to refine the edge; (4) Double threshold detection: Use high and low thresholds to perform threshold processing on the image after non-maximum suppression to obtain strong edge points and weak edge points; (5) Edge connection: connect weak edge points to strong edge points through the hysteresis threshold method to form a complete edge; The output of the Canny edge detection algorithm is a binary edge map, where a pixel value of 1 indicates an edge and a pixel value of 0 indicates a non-edge.

5. The method according to claim 4, characterized in that The image processing steps after the edge detection algorithm include: Max pooling: Performing max pooling on the edge image obtained by the edge detection algorithm to reduce the image dimension and expand the side length of the pixel six times while keeping the overall size of the entire design area unchanged to ensure that the local features in the design area are properly preserved; and Binarization: Binarize the image after the maximum pooling process, assign all non-zero pixel values ​​to 1, and keep the zero-value pixels as 0, so as to generate the final decision pattern; In the final decision pattern, the pixel points with a pixel value of 1 correspond to the portion close to the edge of the original simulation pattern, and the pixel points with a pixel value of 0 correspond to the area far from the edge.

6. The method according to claim 1, characterized in that The specific implementation of the direct binary search method in the digital optimization step includes: Assign values ​​to pending pixels: For each pixel marked as pending in the edge-guided transformation step, Dielectric constant values ​​assigned to silicon and silicon dioxide, respectively; Calculate the objective function value: For each dielectric constant assignment, calculate the corresponding objective function value; Select optimized material: compare the objective function value and select the material that can optimize the objective function as the final dielectric constant of the pixel to be determined; Repeat optimization: repeat steps (1) to (3) for all pending pixels, and keep the dielectric constant of the pixels that have been directly converted unchanged; Iteration completion: After completing the optimization of all pending pixels, a digital reverse design structure with a larger feature size is obtained.

7. The method according to claim 1, characterized in that The larger pixel points are square pixel points with a side length of 80nm to 150nm.

8. A silicon-based mode division multiplexer designed according to the method of any one of claims 1 to 7, characterized in that: The mode division multiplexer includes: Five single-mode input waveguides for introducing the incident fundamental TE0 mode; A multimode output waveguide for outputting the multiplexed optical signal after mode conversion; The device body is a rectangular design area, which is discretized into a number of square pixels, each of which is an etched hole made of silicon or silicon dioxide; Among them, the silicon-based mode division multiplexer can support the multiplexing and demultiplexing of five orthogonal transverse electric modes (TE modes), and can convert the TE0 mode from five separate single-mode waveguides into TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide; at the same time, due to reciprocity, the mode division multiplexer can convert the TE0, TE1, TE2, TE3 and TE4 modes in the bus multimode waveguide into the TE0 mode in the five single-mode waveguides.

9. The silicon-based mode division multiplexer according to claim 8, characterized in that: The material platform and specific parameters of the mode division multiplexer include: The material platform is a silicon-on-insulator platform; The height of the silicon waveguide is 200nm to 240nm; The thickness of the silicon dioxide substrate is 1.5 μm to 2.5 μm; The thickness of the silica cladding is 0.8 μm to 1.2 μm.

10. The silicon-based mode division multiplexer according to claim 8, characterized in that: The specific parameters of the input waveguide and output waveguide of the mode division multiplexer include: the width of the single-mode input waveguide is 450nm to 550nm; the spacing between each single-mode waveguide is equal, which is 800nm ​​to 950nm; the width of the multi-mode output waveguide is 2.3μm to 2.7μm and is located at the edge of the rectangular design area.

11. The silicon-based mode division multiplexer according to claim 8, characterized in that: The design area length of the mode division multiplexer is between 8 μm and 12 μm, and the width is between 4 μm and 8 μm.

12. A joint analog-digital reverse design system based on edge guidance, characterized in that: include: An initialization module is used to initialize the waveguide structure of the photonic device and the initial dielectric constant distribution of the design area, and generate a random dielectric constant distribution that meets the preset material refractive index range and satisfies the Gaussian distribution as the initial dielectric constant distribution of the design area; A simulation optimization module is used to continuously optimize the initial dielectric constant distribution generated by the initialization module based on the adjoint method, obtain the gradient information of each pixel point in the design area by performing a forward simulation and a reverse simulation on the design area, and update the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution; An edge-guided conversion module is used to use the optimized simulated dielectric constant distribution obtained by the analog optimization module as a simulated pattern, extract edge information of the simulated pattern through an edge detection algorithm, and directly convert the area far from the edge into a pixel point with a larger size based on the edge information, and the dielectric constant of the area is consistent with the dielectric constant of the corresponding position in the simulated pattern, and at the same time, convert the area close to and adjacent to the edge into a pixel point to be determined, and its dielectric constant needs to be further determined; The digital optimization module is used to determine the final dielectric constant of the undetermined pixel points generated by the edge-guided conversion module through a direct binary search method, while keeping the dielectric constant of the directly converted pixel points unchanged, and finally obtain a digital reverse design structure with a larger feature size after a single iterative optimization.

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