Edge-guided joint analog-digital reverse design method, system, and silicon-based mode division multiplexer

Abstract

The present invention relates to the field of integrated silicon-based photonic devices and discloses a joint analog-digital reverse design method based on edge guidance, a system and a silicon-based mode division multiplexer designed therefrom. This method combines the analog reverse design technology and the digital reverse design technology in the design of photonic devices, optimizes the analog design structure using the adjoint method, and guides the edge detection technology to convert the results of the analog design into a digital structure with a larger feature size. In addition, a direct binary search method is used to optimize the digital design to achieve efficient pixelated design and stronger process robustness. The silicon-based mode division multiplexer designed based on this method supports five transverse electric mode multiplexing, and the device size is 10μm×6μm, which significantly reduces the footprint. The multiplexer has the advantages of low insertion loss, small inter-mode crosstalk, and large processing tolerance, and can effectively improve the integration and performance of optical communication systems.

Description

Technical Field

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

[0002] With the rapid development of artificial intelligence technologies such as large language models and multimodality, data centers are increasingly demanding higher communication capacity for optical interconnects. Mode division multiplexing (MDM), a new optical multiplexing technology, can further improve the information transmission rate within a single optical fiber or waveguide based on wavelength division multiplexing (WDM). As a key component of MDM systems, the design methods for MDMs are primarily categorized into intuition-first and reverse engineering approaches.

[0003] Inverse design methods can significantly reduce the size and loss of mode division multiplexers, 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 issue: Digital reverse design usually uses a brute force search algorithm to update the status of digitized 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 machining precision requirements: Analog reverse design typically has a small minimum feature size, placing extremely high demands on machining precision and stability. Current design algorithms and machining capabilities make it difficult to achieve highly robust machining and mass production.

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

[0008] Performance-manufacturing trade-off: While 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 the design of various complex photonic devices.

[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 approach is urgently needed that can simultaneously address issues such as low optimization efficiency, poor processing robustness, large device size, and the difficulty in balancing performance and manufacturability, while also being versatile enough to meet the growing demands of the industry. This approach should be able to ensure high-efficiency design while improving processing robustness, achieving compact device structures and excellent performance, and be applicable to a variety of 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 to the design of silicon-based mode division multiplexers, aiming to overcome the technical limitations of traditional digital reverse design and analog reverse design. The present invention innovatively combines three technologies: the adjoint 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 utilizing edge information to guide the transformation process of analog reverse design structures to digital reverse design structures, this method successfully integrates the high efficiency advantages of analog reverse design and the processing robustness characteristics of digital reverse design.

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

[0014] Initialization step: 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;

[0015] Simulation optimization step: continuously optimizing the initial dielectric constant distribution generated in the initialization step based on the adjoint method, performing a forward and a reverse electromagnetic simulation on the design area, obtaining gradient information of each pixel in 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 areas away from the edge into larger pixels based on the edge information, with the dielectric constant of the area being consistent with the dielectric constant of the corresponding position in the simulated pattern. At the same time, areas close to and adjacent to the edge are converted into undetermined pixels, whose dielectric constants need 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. After a single iterative optimization, a digital inverse 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 pixel point x after update;

[0022] is the dielectric constant at 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 the electric field distribution obtained by one forward transmission and one reverse transmission;

[0028] During the iterative process of analog optimization, the dielectric constant of the pixel points 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 the following steps:

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

[0038] (2) Perform overlap integration between 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 represents an edge and a pixel value of 0 represents a non-edge.

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

[0048] Max pooling: This process applies max pooling to the edge image obtained through the edge detection algorithm, reducing the image dimension and increasing the side length of the pixels by six times, while maintaining the overall size of the design area. This ensures that local features within the design area are appropriately preserved.

[0049] Binarization: Binarize the image after the maximum pooling process, assign all non-zero pixel values ​​to 1, and keep the zero-value pixels to 0, thus generating 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] Selecting optimized materials: comparing the objective function values ​​and selecting a 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 embodiment, 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 that is discretized into several square pixels. Each pixel 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 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 multimode output waveguide is 2.3μm to 2.7μm, and is located at the edge of the rectangular design area.

[0069] In a preferred embodiment, 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] This 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 for continuously optimizing the initial dielectric constant distribution generated by the initialization module based on the adjoint method, performing one forward and one reverse electromagnetic simulation on the design area, obtaining gradient information of each pixel point in the design area, and updating the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution;

[0073] An edge-guided conversion module, configured 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 based on this edge information, directly convert areas away from the edge into pixels of larger size, with the dielectric constant of the area being consistent with the dielectric constant of the corresponding position in the simulated pattern. At the same time, areas close to and adjacent to the edge are converted into undetermined pixels, whose dielectric constants need to be further determined;

[0074] A 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. After a single iterative optimization, a digital inverse design structure with a larger feature size is finally obtained.

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

[0076] Efficient pixelated design: This invention combines the advantages of analog and digital reverse design techniques. During the analog reverse design phase, each optimization iteration requires only two electromagnetic simulations. Furthermore, the innovative use of image processing technology for edge guidance allows the digital optimization phase to focus on only the pixels near the edge, avoiding inefficient blind searches and significantly reducing the number of electromagnetic simulations required, achieving efficient pixelated device design.

[0077] Improved process robustness: By converting analog reverse design results into digital reverse design structures, we achieved an increase in minimum feature size (120nm). Compared to analog reverse design devices, this significantly reduces process manufacturing challenges, improves processing robustness, and makes it easier to mass-produce in mainstream silicon photonics foundries.

[0078] Compact structure: The five-mode silicon-based mode division multiplexer designed based on this method is only 10μm × 6μm in length, making it the smallest silicon-based five-mode multiplexer known to date. This helps improve device integration.

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

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

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

[0082] Meeting industry needs: The devices designed using this method can meet the needs of high integration and large communication capacity in fields 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] The specification of this application records a large number of technical features, 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 lengthy. 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 such a combination of 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. Features C and D are equivalent technical means that play the same role. Technically, only one of them can be used, and it is impossible to use them at the same time. Feature E can be technically combined with feature C. Then, the solution of A+B+C+D should not be considered as having been recorded because it is technically infeasible, while the solution of A+B+C+E should be considered as having been recorded. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0086] Figure 2 It is a structural diagram of the 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 (MDM) simulation dielectric constant distribution and 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 This is a schematic plan view of the final structure 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.

[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 this application. However, those skilled in the art will understand that even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in this application can be implemented.

[0093] Description of some concepts:

[0094] Silicon-on-Insulator (SOI) Platform: The SOI platform is a semiconductor manufacturing technology primarily used in integrated circuit (IC) and photonic device manufacturing. This platform uses a thin layer of silicon dioxide as an insulating layer on a silicon substrate, with a layer of silicon deposited on top, to achieve more efficient electrical performance and better thermal management. It 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 in different modes within a single waveguide, thereby increasing the bandwidth and capacity of communication systems. Each mode (TE0, TE1, etc.) transmits different information within 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 approach that defines the required device performance and uses optimization algorithms to automatically generate a device structure that meets these performance requirements. Compared to traditional forward design, inverse design can explore a larger design space and produce more optimal designs.

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

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

[0100] Adjoint Method: A mathematical tool used for design optimization that quickly calculates the gradient of the objective function, effectively reducing the number of simulations. This method is used to improve optimization efficiency in inverse design and is particularly suitable for device design with complex structures.

[0101] Direct Binary Search (DBS): An optimization algorithm used in digital inverse design that optimizes the design by flipping the state of each pixel one by one and evaluating the performance changes.

[0102] Electromagnetic simulation: This is the numerical simulation of light wave propagation in a specific medium, used to analyze and optimize the performance of photonic devices. In this application, electromagnetic simulation is used to calculate the propagation pattern of light waves within the design area to determine the impact of the dielectric constant of each pixel on light transmission.

[0103] Edge Guidance: An image processing technique used to identify critical regions (i.e., edge regions) in photonic device designs during optimization using edge detection algorithms, thereby reducing unnecessary global searches and improving design efficiency. In this paper, edge guidance technology guides the digital optimization process by processing edge information in the image.

[0104] Edge Detection Algorithm: An image processing technique used to identify the edges of objects in an image. In this invention, the Canny edge detection algorithm is used to identify material boundaries in the simulation design results.

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

[0106] Pixel: Within the design area of ​​a photonic device, each discrete unit is called a pixel. The material (e.g., silicon or silicon dioxide) and geometric dimensions of each pixel directly impact device performance. In this paper, the pixels are discretized into squares with a side length of 120 nm.

[0107] Objective Function: A function used to measure the quality of a design during the optimization process. Optimization algorithms iteratively adjust design parameters to minimize or maximize the objective function, resulting in an optimal design. In photonic device design, the objective function is related to the efficiency or loss of lightwave transmission.

[0108] Mode crosstalk: In a mode-division multiplexing device, signal coupling between multiple modes due to imperfect separation or interference can lead to signal quality degradation. This invention reduces mode crosstalk through optimized design.

[0109] Insertion Loss: This refers to the power loss of an optical signal due to reflection, scattering, or absorption when it passes through a device. It is usually expressed in dB. Lower insertion loss means higher transmission efficiency of the device.

[0110] Crosstalk: In a multi-channel system, the unwanted interference of one channel's signal on other channels. A smaller crosstalk value indicates better isolation between channels.

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

[0112] With the rapid development of artificial intelligence (AI), data center optical interconnects are increasingly demanding higher communication capacity. Mode division multiplexing (MDM), a new optical multiplexing technology, can further increase the information transmission rate within a single optical fiber or waveguide based on wavelength division multiplexing (WDM). As a core component of MDM technology, the MDM plays a key role in improving system performance.

[0113] Currently, the design methods for mode division multiplexers are mainly divided into intuition-based and reverse design methods. Among them, the reverse design method 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 engineering usually uses brute force search algorithms 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] To address the above issues, the inventors of this application have proposed an innovative solution, namely, an edge-guided joint analog-digital reverse design method. The core technical solutions 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 applying edge detection technology in image processing to photonic device design, guiding the digital conversion process by extracting edge information from analog design results.

[0119] 3) A two-stage optimization strategy: a) First, a simulation-based optimization is performed using the adjoint method 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 larger feature sizes and localized optimization is performed using a direct binary search method.

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

[0121] 5) High-efficiency digital optimization: Only the undetermined 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 overcomes 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 this application clearer, the implementation methods of this application will be further described in detail below with reference to 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 includes 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, 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.

[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 ​​within 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, enabling 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 pixel point x after update;

[0132] is the dielectric constant at 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 the electric field distribution obtained by one forward transmission and one reverse transmission;

[0137] During the iterative process of analog optimization, the dielectric constant of the pixel points 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 the following steps:

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

[0147] (2) Perform overlap integration between 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 simulation-based optimization process, which continuously optimizes the initial dielectric constant distribution based on the adjoint method. The dielectric constant determines the propagation characteristics of light in a material, so optimizing this distribution is crucial for improving the performance of photonic devices. In this step, forward and reverse electromagnetic simulations are performed to obtain gradient information for each pixel in the design area, 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 with respect to the objective function F. Through this 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, and thus calculates the gradient information of each pixel point, which greatly reduces the number of calculations required in the optimization process and improves the optimization efficiency.

[0154] During the optimization process, a digital filter is used to gradually push the dielectric constant of each pixel toward the boundary between its maximum and minimum values, bringing it closer to binary. This approach ensures that the optimized dielectric constant distribution is more suitable for subsequent digital processing and actual manufacturing.

[0155] The objective function F is calculated as follows:

[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. This conversion efficiency is determined by simulating the overlap between the input electric field and the ideal output mode, ultimately obtaining the objective function value for optimization.

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

[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 through 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, where 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 represents an edge and a pixel value of 0 represents a non-edge.

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

[0170] Max pooling: This process applies max pooling to the edge image obtained through the edge detection algorithm, reducing the image dimension and increasing the side length of the pixels by six times, while maintaining the overall size of the design area. This ensures that local features within the design area are appropriately preserved.

[0171] Binarization: Binarize the image after the maximum pooling process, assign all non-zero pixel values ​​to 1, and keep the zero-value pixels to 0, thus generating 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, a crucial step in converting analog design results into digital structures. Specifically, an edge detection algorithm is first used to extract edge information from the optimized dielectric constant distribution. This edge information is then used to guide the subsequent digital conversion. The core of this conversion is to directly convert areas away from the edge into pixels with larger feature sizes, while areas near the edge are marked as undetermined pixels for further determination of their dielectric constant.

[0174] The Canny edge detection algorithm was used in this process, which consists of five steps: first, Gaussian filtering is performed on the image to reduce noise, then the image gradient magnitude and direction are calculated, followed by non-maximum suppression to refine the edges. Subsequently, strong and weak edge points are determined through dual-threshold detection, and finally, weak edge points are connected to strong edge points using a hysteresis threshold method to form a complete edge map. The purpose of these steps is to ensure the accuracy and completeness of edge information, providing a reliable basis for subsequent digital optimization.

[0175] After edge detection, the next step in image processing is max pooling. This process reduces the image's resolution while increasing the pixel side length by six times, preserving the local features of the design area and laying the foundation for the next step, binarization. Binarization further simplifies the image by setting all non-zero pixel values ​​to 1 and zero-valued pixels to 0, ultimately generating a simplified decision pattern that facilitates subsequent digital optimization.

[0176] Through these steps, edge-guided technology can effectively convert 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. After a single iterative optimization, a digital inverse 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 undetermined pixels: For each pixel marked as To-be-determined (TBD) in the edge-guided transformation step, assign the dielectric constant value of silicon and silicon dioxide respectively;

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

[0181] Selecting optimized materials: comparing the objective function values ​​and selecting a 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 details the digital optimization process, a key step after completing the edge-guided conversion. This step optimizes the dielectric constant of the desired pixel points through a direct binary search method to complete the final digital design. In the previous stage, the edge information of the analog design has been extracted, and the areas away from the edge have been directly assigned a specific dielectric constant. However, due to the complex edge effects of the desired pixel points near the edge, the dielectric constant still needs to be further optimized to achieve optimal performance.

[0185] First, for each candidate pixel, the method assigns two possible dielectric constant values: those of silicon and silicon dioxide. The method then evaluates the merits of each assignment by calculating an objective function. This objective function measures the pixel's contribution to the overall design performance, such as optimizing light transmission efficiency or reducing losses. By comparing the objective function values ​​for different dielectric constants, the material that maximizes the objective function is selected as the final dielectric constant for the candidate pixel.

[0186] This process isn't limited to a single pixel; it iterates across all pending pixels. For each pending pixel, the process of assigning values, calculating the objective function, and selecting the optimized material is repeated. Meanwhile, pixels that have already been directly assigned values ​​remain unchanged, ensuring the stability and efficiency of the optimization process.

[0187] After a single iterative optimization, the dielectric constants of all pending pixels were optimized, ultimately generating a digitally inverse-designed structure with a large feature size. This structure met the design performance requirements while also being robust and manufacturable. A direct binary search method avoided the inefficiency of a blind global search, significantly reducing computational complexity and accelerating optimization. This process ensured that the digital design of photonic devices was both efficient and reliable, and also highly manufacturable.

[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 that is discretized into several square pixels. Each pixel 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 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, 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, preferably 500nm; the spacing between each single-mode waveguide is equal, 800nm ​​to 950nm, preferably 875nm; the width of the multimode 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 length of the design area 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 the multiplexing and demultiplexing of multi-mode signals on a compact silicon-based platform, thereby significantly improving the information transmission capacity of the optical communication system.

[0202] The multiplexer's structure consists of three main components: five single-mode input waveguides, one multimode output waveguide, and a device body. The single-mode input waveguides introduce TE0 mode optical signals, while the multimode output waveguide outputs the multiplexed optical signals after mode conversion. The device body consists of a rectangular design area within which a precisely arranged array of etched holes enables complex mode conversion. Each etched hole, composed of silicon or silicon dioxide, acts as a square pixel. The arrangement of these pixels controls the propagation and mode conversion of optical signals.

[0203] The key feature of this 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 into 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 utilizes a silicon-on-insulator (SOI) platform, the most widely used material system in 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 not only provides effective optical confinement for optical signals, but also ensures compatibility with existing silicon-based manufacturing processes, facilitating large-scale production.

[0205] In terms of waveguide parameters, each single-mode input waveguide is 500 nanometers wide, with a spacing of 875 nanometers between waveguides, ensuring separation and independent transmission of input signals. The multimode output waveguide is 2.5 microns wide to support the efficient transmission of multiple high-order modes. The multimode waveguides are strategically placed at the edges of the rectangular design area to optimize optical signal coupling efficiency and further enhance device performance.

[0206] Finally, the core design area of ​​the mode division multiplexer measures 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 increase chip integration, but also has the potential to reduce power consumption and increase device operating speed.

[0207] Overall, this silicon-based mode-division multiplexer design demonstrates the great potential of advanced photonic integration technology, provides important technical support for future high-capacity, 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 model division multiplexer designed using this method. This method combines the advantages of digital and analog reverse design, achieving both robustness and high optimization efficiency.

[0210] like Figure 2 As shown, the inverse 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 that satisfies 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 is obtained through the two electromagnetic simulations, and the dielectric constant is updated based on the gradient information.

[0213] The edge-guided analog-to-digital conversion module 103 uses the dielectric constant distribution obtained by analog inverse design as an analog pattern for edge extraction. Portions away from the edge are directly converted into larger pixels through pooling and binarization. Their dielectric constants are equal to the dielectric constant of the material at the corresponding position in the original analog pattern. Portions close to and adjacent to the edge are converted into undetermined pixels whose dielectric constants need to be further determined.

[0214] The digital reverse design module 104 determines the dielectric constant of the pixel to be determined by a direct binary search method, 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 this method.

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

[0217] Furthermore, the initialization process in step one is an important step in 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 the effective transmission of optical signals in the fundamental mode. Fundamental mode transmission refers to the lowest-order mode when light propagates in the waveguide. This mode 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 high-order modes, which helps to improve the capacity of the communication system.

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

[0219] Next, the size of the optimization region also needs to be initialized. This region is the core of the entire device design. By optimizing the dielectric constant distribution in this region, efficient conversion of optical signals between different modes can be achieved. To ensure the effectiveness of the optimization, the initial dielectric constant distribution of the design region adopts a Gaussian distribution. Gaussian distribution is a commonly used probability distribution characterized by larger values ​​in the central region and gradually decreasing values ​​away from the center. In this way, the dielectric constant distribution of the optimization region is neither too concentrated nor 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 constrained within 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 confine optical signals, while silicon dioxide has a lower dielectric constant, which facilitates optical signal propagation. 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] This initialization step provides reasonable parameter settings 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 perform simulation optimization on the dielectric constant distribution of the design area. The dielectric constant update rule expression is as follows:

[0223]

[0224] in and where α is the update rate, and F is the objective function. The derivative of the objective function F with respect to the pixel's dielectric constant can be calculated using the electric field distribution obtained from one forward and one reverse transmission. During the iterative optimization process of simulated inverse design optimization, a digital filter is used to gradually push the pixel's dielectric constant toward its maximum and minimum boundaries, resulting in 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 two, a core component of this design method, involves using the adjoint method to perform a simulation-based optimization of the dielectric constant distribution in 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 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. This filter gradually pushes the dielectric constant of each pixel toward its maximum or minimum value. The goal of this strategy is to obtain a nearly binary dielectric constant distribution, preparing for the subsequent digitization process.

[0233] By combining the adjoint method, objective function optimization, and digital filtering, step two efficiently searches for the optimal solution in continuous space, laying a solid foundation for subsequent edge-guided transformation and digital optimization. This step fully demonstrates the advantages of analog optimization: high efficiency and a high degree of optimization freedom, creating the conditions for achieving 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 as follows Figure 4 As shown in (a), extremely small cracks and etched holes are clearly visible. 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 2. Figure 4 (b) 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 dimensionality 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 final judgment pattern is then obtained by binarization, assigning all non-zero pixels a value of 1 and leaving zero-valued pixels unchanged. Figure 4 (c) In this decision pattern, pixels with a value of 1 correspond to the portion of the original simulated pattern close to the edge, while pixels with a value of 0 correspond to areas away from the edge. Next, dielectric constant mapping is performed based on the decision pattern. The dielectric constants of all pixels with a value of 0 are directly mapped, while pixels with a value of 1 are marked as TBD (To-be-determined).

[0235] Furthermore, step three is a key step in the entire design method. Its primary purpose is to transform the results obtained through simulation optimization into a digital structure more suitable for actual manufacturing. In this step, edge information is cleverly used to guide the transformation process, achieving a balance between performance optimization and manufacturability.

[0236] Initial simulations resulted in an array of square pixels with a side length of 20 nanometers, whose dielectric constant varied continuously within the range of silicon and silicon dioxide. While this design had excellent theoretical performance, it was 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 address this manufacturing challenge, the analog pattern had to be converted into a digital pattern with larger feature sizes. The resulting structure consisted of square pixels with sides of 120 nanometers, with each pixel material limited to either silicon or silicon dioxide. This adjustment significantly increased the minimum feature size, making the design more amenable to 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 an edge pixel and 0 represents a non-edge pixel. This process extracts key geometric information from the original design.

[0239] Next, the edge map undergoes a max-pooling process, which reduces the pattern's resolution while increasing the pixel side length from 20 nanometers to 120 nanometers. This operation maintains the overall size of the design area, ensuring consistency in the physical dimensions of the design before and after conversion.

[0240] Then, the final decision pattern is obtained through binarization processing, such as Figure 4 (c) shows the pattern. Pixels with a value of 1 correspond to the critical edge regions of the original design, while pixels with a value of 0 correspond to areas further away from the edge. This process effectively distinguishes critical structures from non-critical areas in the design.

[0241] Finally, the dielectric constant is mapped based on the decision pattern. Pixels with a value of 0 in the decision pattern are directly mapped to silicon dioxide, while pixels with a value of 1 are marked as "To be determined" (TBD), allowing flexibility for subsequent optimization.

[0242] Through this edge-guided conversion approach, Step 3 successfully transforms the high-performance but difficult-to-manufacture analog design into a digital structure suitable for practical processes. This approach not only preserves 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 a direct binary search method to determine the dielectric constant of the TBD pixel. For each pixel marked as TBD, assign the dielectric constant of silicon and silicon dioxide respectively, and calculate the value of the objective function for each. The dielectric constant of the material with the larger objective function value is selected as the final pixel dielectric constant. After performing this operation for each TBD pixel, exit the optimization and end the reverse design.

[0244] Furthermore, step 4 is the last key step of this design method, which aims to determine the final material properties of the pixels marked as to be determined (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 one of two possible materials: silicon or silicon dioxide. These two materials are commonly used in photonic device manufacturing, meet practical process requirements, and simplify the complexity of material selection. This binary selection method allows the system to quickly determine which material is most suitable for optimizing device performance.

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

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

[0248] Once the material selection for all TBD pixels is complete, 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 lies in combining the high-performance characteristics of analog optimization with a concise digital optimization process. By focusing on optimizing key areas near the edge, it ensures computational efficiency while enabling fine-tuning of the local structure, guaranteeing the overall performance of the design.

[0250] In summary, step 4 successfully transforms the analog design into a digital design that offers good performance and is suitable for manufacturing through an efficient binary selection strategy. This step concludes the entire design process, effectively integrating the advantages of all previous steps to ultimately provide a practical and efficient solution for photonic device design.

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

[0252] in other words, Figure 5 This demonstrates the superiority of the method of the present invention. The complex structure in the design area 302 is optimized by an edge-guided joint analog-digital inverse design method, which effectively realizes multi-mode conversion and multiplexing. 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 equal intervals 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 improves the chip's integration density, but also reduces insertion loss and improves thermal stability. Figure 5The demonstrated structure strikes a good balance between high performance, manufacturability, and integration, fully demonstrating the broad potential of the inventive method in practical applications.

[0253] Figure 6 The optical field distribution of the silicon-based mode division multiplexer designed using 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 conversion 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) reflects 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 device's outstanding performance in achieving multi-mode multiplexing capabilities.

[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 the TE0 to TE4 modes in the multimode output waveguide when the TE0 mode is input from the first to fifth single-mode waveguides, respectively. The horizontal axis represents the wavelength range (1530nm to 1570nm), and the vertical axis represents the mode conversion efficiency (in dB). From these spectra, the following key performance indicators can be summarized: At the center wavelength of 1550nm, the insertion loss of all five modes is less than 2.0dB, demonstrating the device's efficient mode conversion capability. The crosstalk between each mode is less than -19dB, demonstrating excellent mode isolation performance. Over the 40nm wavelength range (1530nm-1570nm), the device exhibits excellent broadband characteristics, with stable conversion efficiency and crosstalk levels. 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 line), further verifying the high mode selectivity.

[0261] These performance indicators fully demonstrate that this silicon-based mode division multiplexer not only successfully achieves efficient multiplexing of five modes, but also exhibits superior characteristics such as low loss, low crosstalk, and broadband. The realization of such complex functionality within a compact size of only 10μm × 6μm highlights the great potential of this method 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 high-capacity, high-density optical communication systems.

[0262] It should be noted that this example combines analog reverse design and digital reverse design techniques. In analog reverse design, each iterative optimization requires only 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 the tedious and inefficient blind search optimization. Compared with traditional digital optimization algorithms, this example greatly reduces the number of required electromagnetic simulations and achieves efficient pixelated device design. By converting analog reverse-designed devices into digital reverse-designed devices, this example achieves an increase in the minimum feature size (120nm). Compared with analog reverse-designed devices, this greatly reduces the process manufacturing challenges and can be processed and manufactured by mainstream silicon photonic fabs. In addition, the five-mode silicon-based mode division multiplexer designed in this example is only 10μm long, the smallest size among current silicon-based five-mode multiplexers. Finally, the edge-guided combined analog and digital reverse design method proposed in this example is extremely versatile and can be applied to the reverse design of various photonic devices, especially those 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 presented in this example demonstrate significant advantages. This example can play a significant role in data center optical interconnects, improving integration and communication capacity to meet growing data transmission demands.

[0264] In general, the above example has the following technical effects:

[0265] Efficient pixelated device design: This example combines analog and digital reverse design techniques. In the analog reverse design, each iterative optimization requires only two electromagnetic simulations. Furthermore, this example introduces image processing technology into the reverse design of photonic devices for the first time. Guided by edge information, the digital optimization process only requires iterative optimization of pixels near the edge, avoiding tedious and inefficient blind search optimization. Compared to traditional digital optimization algorithms, this significantly reduces the number of required electromagnetic simulations and enables efficient pixelated device design.

[0266] Process robustness: The above example achieves an increase in minimum feature size (120nm) by converting analog reverse-design devices to digital reverse-design devices. This significantly reduces process manufacturing challenges compared to analog reverse-design devices and allows for fabrication in mainstream silicon photonics fabs.

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

[0268] Versatility: The edge-guided joint analog-digital reverse design method proposed in the above example is highly versatile and can be applied to the reverse design of various photonic devices, especially those 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 (MDM) presented in this example demonstrate significant advantages. This example can play a significant role in data center optical interconnects, improving integration and communication capacity to meet growing data transmission demands.

[0270] The second embodiment of the present application relates to a joint analog-digital reverse design system based on edge guidance, the structure of which 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 for continuously optimizing the initial dielectric constant distribution generated by the initialization module based on the adjoint method, performing one forward and one reverse electromagnetic simulation on the design area, obtaining gradient information of each pixel point in the design area, and updating the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution;

[0273] An edge-guided conversion module, configured 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 based on this edge information, directly convert areas away from the edge into pixels of larger size, with the dielectric constant of the area being consistent with the dielectric constant of the corresponding position in the simulated pattern. At the same time, areas close to and adjacent to the edge are converted into undetermined pixels, whose dielectric constants need to be further determined;

[0274] A 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. After a single iterative optimization, a digital inverse design structure with a larger feature size is finally obtained.

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

[0276] It should be understood that the division of the various steps described in the embodiments of the present invention is mainly for the purpose of clearly illustrating the technical solutions 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 embodiment of the above-mentioned edge-guided joint analog-digital reverse design system can be understood with reference to the relevant description of the aforementioned edge-guided joint analog-digital reverse design method. The functions of each module shown in the embodiment 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, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the method described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a magnetic 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 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 circuits (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 drive, etc. The steps of the method disclosed in each embodiment of the present invention can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

[0280] All documents mentioned in this application are considered to be included in their entirety in the disclosure of this application so that they can be used as a 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 may 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: 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; Simulation optimization step: continuously optimizing the initial dielectric constant distribution generated in the initialization step based on the adjoint method, performing a forward and a reverse electromagnetic simulation on the design area, obtaining gradient information of each pixel in 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 areas away from the edge into larger pixels based on the edge information, with the dielectric constant of the area being consistent with the dielectric constant of the corresponding position in the simulated pattern. At the same time, areas close to and adjacent to the edge are converted into undetermined pixels, whose dielectric constants need 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. After a single iterative optimization, a digital inverse 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 pixel point x after update; is the dielectric constant at 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 the electric field distribution obtained by one forward transmission and one reverse transmission; During the iterative process of analog optimization, the dielectric constant of the pixel points 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 the following steps: (1) Perform forward electromagnetic field simulation on each input mode TEi to obtain the electric field distribution at the output end; (2) Perform overlap integration between 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, wherein 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 represents an edge and a pixel value of 0 represents 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: This process applies max pooling to the edge image obtained through the edge detection algorithm, reducing the image dimension and increasing the side length of the pixels by six times, while maintaining the overall size of the design area. This ensures that local features within the design area are appropriately preserved. Binarization: Binarize the image after the maximum pooling process, assign all non-zero pixel values ​​to 1, and keep the zero-value pixels to 0, thus generating 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; Selecting optimized materials: comparing the objective function values ​​and selecting a 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 that is discretized into several square pixels. Each pixel 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 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, wherein: 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, ranging from 800nm ​​to 950nm; the width of the multimode 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, wherein: 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 for continuously optimizing the initial dielectric constant distribution generated by the initialization module based on the adjoint method, performing one forward and one reverse electromagnetic simulation on the design area, obtaining gradient information of each pixel point in the design area, and updating the dielectric constant distribution based on the gradient information to obtain an optimized simulated dielectric constant distribution; An edge-guided conversion module, configured 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 based on this edge information, directly convert areas away from the edge into pixels of larger size, with the dielectric constant of the area being consistent with the dielectric constant of the corresponding position in the simulated pattern. At the same time, areas close to and adjacent to the edge are converted into undetermined pixels, whose dielectric constants need to be further determined; A 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. After a single iterative optimization, a digital inverse design structure with a larger feature size is finally obtained.

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