A two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization
By using a two-port matrix multiplication device based on topology optimization of accompanying electromagnetic simulation, flexible and reconfigurable matrix multiplication operations within a compact area are achieved by utilizing micro-nano structures and electrically controlled refractive index modules. This solves the problems of complex device structure and high power consumption in existing technologies and realizes efficient optical matrix calculation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-09-16
- Publication Date
- 2026-07-17
AI Technical Summary
Existing optical matrix multiplication devices are limited in terms of integration, flexibility, and power consumption, making it difficult to implement arbitrary analog matrix multiplication operations within a compact area. Furthermore, existing solutions suffer from complex structures, high power consumption, and susceptibility to failure.
A two-port matrix multiplication device based on topology optimization using adjoint electromagnetic simulation is employed. Two-dimensional matrix multiplication is realized in a limited area using micro-nano structures and an electrically controlled refractive index module. Complex matrix operations are completed through electromagnetic scattering response. The introduction of an electrically controlled refractive index module enables reconfigurability, thus avoiding the functional limitations of traditional optical computing.
It achieves compact, reconfigurable, and low-power matrix multiplication operations, solving the problems of large area and high power consumption in traditional optical computing. It has high integration and flexibility and is suitable for on-chip optical simulation computing and neural network acceleration.
Smart Images
Figure CN121326103B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of optical simulation computing and micro-nano optoelectronic technology, and particularly relates to a two-port matrix multiplication device based on topology optimization of adjoint electromagnetic simulation. Background Technology
[0002] Matrix multiplication is one of the fundamental operations in scientific computing and information processing, accounting for a major portion of computational overhead in fields such as digital signal processing and artificial intelligence algorithms (e.g., deep neural networks). Traditionally, matrix calculations are performed by electronic digital processors, whose speed and energy consumption are limited by the inherent characteristics of electronic devices. With the increasing demand for high-throughput, low-latency computing, optical computing, due to its advantages of high-speed parallelism and low power consumption, has become a potential solution to overcome the bottlenecks of electronic computing. In particular, the interference and diffraction properties of light can be used to perform analog calculations; for example, optically implemented vector-matrix multiplication has become a research hotspot. In recent years, various optical matrix multiplication devices have been proposed to accelerate large-scale matrix operations in artificial intelligence.
[0003] Currently, methods for implementing optical matrix multiplication mainly include planar light conversion (PLC), interferometer network (ILN) methods, and wavelength division multiplexing (WDM). The PLC method typically uses free-space diffraction elements (lenses, phase plates, etc.) to expand the input vector into a two-dimensional light field, and then superimposes the light fields through transmission optical elements to achieve parallel computation of matrix multiplication. This method can perform large-scale matrix operations in free space, but the system is large and sensitive to the alignment of optical elements, making it difficult to integrate. The INN method typically uses Mach-Zehnder interferometer (MZI) arrays to construct programmable optical circuits, enabling linear transformations of arbitrary matrices. For example, a two-dimensional MZI unit can perform arbitrary 2×2 unitary matrix operations, and cascading multiple MZI units can construct higher-dimensional matrix multipliers. However, such interferometer networks require a large number of phase modulators for control, the device area increases significantly with the matrix size, and phase control requires continuous power, leading to problems such as thermal drift and complex calibration. Wavelength division multiplexing (WDM) schemes utilize light of different wavelengths to carry different components of a vector, modulate the transmission of each wavelength through microring resonators to achieve matrix weighting, and then superimpose the outputs of all wavelengths to obtain the result.
[0004] Chinese patent application CN101630178A discloses a silicon-based integrated optical vector-matrix multiplier. This device utilizes silicon-on-insulator (SOI) technology and is composed of N×N nanowire microring resonators (MRRs). It achieves multiplication of an N×N matrix with an N×1 vector using thermo-optical modulation, where the matrix and vector elements are binary 0s or 1s. This scheme leverages high-refractive-index silicon waveguides for compact integration, providing a degree of reconfigurability and high-speed performance, while avoiding the problems of poor accuracy and weak programmability inherent in traditional analog optical computation. However, the weight values in this design are limited to discrete states (0 or 1), making it difficult to easily extend to arbitrary analog weight matrix operations. Furthermore, the microring resonator array requires complex fabrication processes and precise wavelength control.
[0005] Another approach involves using reconfigurable media such as phase-change materials to realize programmable optical matrix operation devices. For example, some studies have combined silicon optical waveguides with germanium-antimony-tellurium phase-change materials to create reconfigurable Mach-Zehnder interferometer arrays for matrix operations and optical neural network inference. However, these approaches often require the integration of a large number of optical modulation devices, resulting in complex device structures, large sizes, and potential loss and stability issues with phase-change materials during frequent switching.
[0006] In summary, existing integrated optical matrix multiplication devices are either limited by fixed structures or discrete weights, making it difficult to balance accuracy and flexibility; or they rely on large interference networks and continuous power supply, resulting in high power consumption, large area, and complex implementation. These problems limit the development of large-scale on-chip integration and practical applications of optical matrix computing units.
[0007] Therefore, there is an urgent need for a new design method and device structure that can realize arbitrary analog matrix multiplication operations within a compact area, and possess the advantages of reconfigurability and low power consumption, in order to meet the demand for efficient matrix operation modules in the field of integrated optical computing. Summary of the Invention
[0008] This invention provides a two-port matrix multiplier device based on topology optimization of accompanying electromagnetic simulation. This two-port matrix multiplier realizes the simulation calculation function of the required two-dimensional matrix in a limited area, occupies a small area, and can achieve more flexible integration and reconfigurability.
[0009] This invention provides a two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization, including an input port, a matrix calculation region, and an output port;
[0010] The input port is used to couple external signals into the matrix calculation area;
[0011] The matrix calculation region is used to simulate a predetermined two-dimensional matrix multiplication operation mapping relationship. The matrix calculation region includes a micro-nano structure filled with materials of different refractive indices and an electrically controlled refractive index module located on the micro-nano structure. The electrically controlled refractive index module is used to change the corresponding refractive index under the action of an external control signal to reconstruct the two-dimensional matrix multiplication operation mapping relationship.
[0012] The output port is used to output the calculation results.
[0013] By employing a reverse design method based on electromagnetic field topology optimization, this invention enables flexible simulation mapping of arbitrary 2×2 unitary matrices within a given finite region. Complex matrix operations are directly performed by the electromagnetic scattering response of the device, avoiding the functional limitations imposed by structural constraints in traditional optical computing. The proposed device structure is highly compact, significantly reducing the area occupied compared to an equivalent circuit composed of multi-stage interferometers and decreasing the requirement for a large number of tunable devices. Furthermore, this invention introduces an electrically controlled refractive index module, allowing for reconfigurable adjustment of the device's dielectric distribution. This enables dynamic updates of the implemented matrix parameters as needed. Once configured, the computation process itself requires no additional energy supply, truly achieving passive high-speed computing and overcoming the drawbacks of high power consumption and susceptibility to failure in traditional reconfigurable optical computing units. In summary, this invention's device possesses outstanding advantages such as high design freedom, high integration, compact structure, reconfigurability, and passive low-power operation, making it significant for on-chip optical simulation computing and neural network acceleration.
[0014] Preferably, the method for constructing the topological shape and material distribution of micro / nano structures includes:
[0015] Based on the objective function, the topology and material distribution of the micro-nano structure are iteratively optimized using the adjoint electromagnetic topology optimization method until the objective function reaches its maximum value. The iteration is then completed to obtain the final topology and material distribution of the micro-nano structure.
[0016] The objective function is constructed based on the desired two-dimensional matrix operation result and the output two-dimensional matrix operation result. The desired two-dimensional matrix operation result is constructed based on the different refractive indices of the micro-nano structure below the electrically controlled refractive index module under the set external stimulus. The output two-dimensional matrix operation result is constructed based on the response signal of the output port corresponding to the external signal input by different input ports.
[0017] This invention uses the results of two-dimensional matrix operations corresponding to different refractive indices under the electronically controlled refractive index module as labels. By using the constructed objective function, the processed data results of the final iterated micro / nano structure are made similar to or consistent with the labels, thereby realizing the reconstruction of two-dimensional matrix operations by adjusting the refractive index of the electronically controlled refractive index module.
[0018] More preferably, the iterative optimization of the topology and material distribution of the micro / nano structure using the adjoint electromagnetic topology optimization method includes:
[0019] First, the matrix calculation region is divided into multiple pixel units. The dielectric constant of each pixel unit is initially assigned to obtain a dielectric constant matrix. The dielectric constant matrix is then mapped to a parameter matrix using the hyperbolic tangent function.
[0020] In each iteration, the inner product of the spatial overlap of the forward field distribution and the adjoint field distribution in the matrix calculation region obtained by the adjoint electromagnetic topology optimization method is used as the first gradient information. The second gradient information is obtained based on the objective function. The parameter matrix is updated by the first gradient information and the second gradient information. In each iteration, the β value of the hyperbolic tangent function is increased so that the parameter matrix mapping relationship approaches binary.
[0021] The iteration continues until the inner product calculation result reaches the set threshold and the objective function reaches its maximum value, and the pixel values are close to the two discrete dielectric constants. Then the iteration stops, and the final topology and material distribution of the micro / nano structure are obtained.
[0022] More preferably, the inner product calculation result of the spatial overlap of the forward field distribution and the adjoint field distribution in the matrix calculation region obtained by the adjoint electromagnetic topology optimization method is used as the first gradient information, including:
[0023] By applying a given excitation field to the input port through forward FDTD simulation, the electromagnetic field distribution and output response signal within the matrix calculation region are calculated.
[0024] The accompanying source and corresponding output port are obtained based on the electromagnetic field distribution through FDTD simulation. The accompanying source is applied at the output port, and the accompanying field distribution in the matrix region is calculated by backpropagation. The spatial overlap of the forward field distribution and the accompanying field distribution in the matrix calculation region is performed by inner product operation to obtain the first gradient information. Based on the first gradient information, the Adam adaptive moment estimation algorithm is used to iteratively adjust the parameter matrix.
[0025] This invention employs an adjoint optimization method to efficiently handle reverse design problems with a large number of design degrees of freedom (up to tens of thousands of pixel units), significantly shortening the optimization convergence time.
[0026] Further, after obtaining the parameter matrix, the parameter matrix is preprocessed by convolution with a convolution kernel of a set radius size. Then, the medium structure corresponding to the convolutional parameter matrix is optimized by introducing a penalty function, and finally a parameter matrix that meets the preset minimum feature size requirement is obtained.
[0027] Considering the actual manufacturing process, excessively small dimensions cannot be processed. Therefore, this invention introduces convolution preprocessing and a penalty function to ensure that the medium structure corresponding to the parameter matrix provided by this invention meets the manufacturing requirements.
[0028] More preferably, the input port includes a first input port and a second input port, and the output port includes a first output port and a second output port, wherein multiple sets of basis vectors, wherein the multiple sets of basis vectors are orthogonal basis vectors, are injected into the first input port and the second input port.
[0029] This invention uses the excitation signals of multiple sets of basis vectors as input, making the training process simple and efficient. After the optimization region is designed, it can be regarded as a linear system. According to the characteristics of a linear system, if each set of basis vectors achieves the optimization objective, the superimposed signal of theirs will automatically satisfy the optimization objective, and the design complexity will be reduced from N² in the general scheme to 2N (N is the voltage control number, which is 32 here).
[0030] Preferably, the materials with different refractive indices include high refractive index materials and low refractive index materials, wherein the high refractive index material is silicon and the low refractive index material is air.
[0031] More preferably, the high-refractive-index material is silicon with a relative permittivity of approximately 12.18, and the low-refractive-index material is vacuum with a relative permittivity of 1; the matrix calculation region is a square region with a side length of 5 micrometers, composed of 100×100 pixel units, each pixel unit being 50 nanometers × 50 nanometers in size; the input and output ports are optical waveguides with a width of 0.4 micrometers and a length of 1.5 micrometers, and are formed by filling silicon material. The electrically controlled refractive index module is a 0.5 micrometer × 0.5 micrometer square region, and its refractive index can be controlled by voltage to vary within the range of 1.1-2.1. The operating wavelength of the device is 1.5 micrometers.
[0032] Preferably, the input port and the output port are integrated waveguides.
[0033] More preferably, the integrated waveguides of the input and output ports are made of the same high-refractive-index material as the micro / nano structure, to ensure good mode coupling with the matrix computation region.
[0034] Preferably, by setting an appropriate penalty function, it is ensured that the amplitude and phase of the input light field are matched with the expected output light field after being processed by the unitary matrix of the two-port network simulation.
[0035] Preferably, the electrically controlled refractive index module includes a set of microelectrodes, and an external control signal stimulates the microelectrodes to change the refractive index of the micro / nano structure located below.
[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0037] This invention directly utilizes the electromagnetic scattering response of micro / nano structures to perform complex matrix operations, avoiding the functional limitations imposed by structural constraints in traditional optical calculations. The proposed device structure is highly compact, significantly reducing the area occupied compared to an equivalent circuit composed of multi-stage interferometers, and also reducing the requirement for a greater number of tunable devices.
[0038] This invention introduces an electrically controlled refractive index module within the matrix calculation region. By changing the refractive index of the electrically controlled refractive index module, it is possible to perform operations on different unitary matrices, thus achieving flexible integrated and reconfigurable capabilities. Attached Figure Description
[0039] Figure 1 This is a two-dimensional planar schematic diagram of the dielectric constant distribution of a two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization, provided for a specific embodiment of the present invention.
[0040] Figure 2 This is a schematic diagram illustrating the analog computational performance of the matrix multiplication device described in this invention.
[0041] Figure 3 This is a comparison curve of the simulation results for multiple control voltages under the single-port input condition of the matrix multiplication device described in this invention. Detailed Implementation
[0042] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Other equivalent implementations obtained by those skilled in the art based on the design concept of the present invention without making inventive contributions should also be considered within the scope of protection of the present invention.
[0043] In existing technologies, each change to a two-dimensional matrix multiplication operation requires the use of an adjoint electromagnetic topology optimization method to rearrange the topology and materials in the micro / nano structure, which is complex and consumes a lot of power. The specific embodiment of this invention simply sets an electrically controlled refractive index module in the matrix calculation area. By adjusting the refractive index of the electrically controlled refractive index module, the two-dimensional matrix multiplication operation of the 2×2 unitary matrix can be flexibly reconstructed, which is simple, flexible and consumes less power.
[0044] A specific embodiment of the present invention provides a two-port matrix multiplication device based on topology optimization of accompanying electromagnetic simulation, including an input port 1, an output port 2, a matrix calculation region 3 and an output port 4, wherein the input port 1 includes a first input port 11 and a second input port 12, the output port 2 includes a first output port 21 and a second output port 22, and the matrix calculation region 3 includes a micro / nano structure 31 and an electrically controlled refractive index module 32 located on the micro / nano structure.
[0045] The input port 1 provided in the specific embodiment of the present invention is an integrated waveguide, which is connected to the matrix calculation region 3 and is used to couple external signals into the matrix calculation region 3.
[0046] The matrix calculation region 3 provided in the specific embodiment of the present invention is located on the substrate and is used to simulate the predetermined two-dimensional matrix multiplication operation mapping relationship. That is, the matrix calculation region 3 can realize the simulation calculation of the required 2×2 unitary matrix and can also realize the ability of flexible integration and reconstruction.
[0047] The micro / nano structure 31 provided in the specific embodiment of the present invention is composed of materials with different refractive indices. In one embodiment, the materials with different refractive indices include high refractive index materials and low refractive index materials, wherein the high refractive index material is silicon and the low refractive index material is air.
[0048] The electrically controlled refractive index module 32 provided in this specific embodiment includes a set of microelectrodes disposed above the matrix calculation region 3, which can apply a local electric field to the dielectric material there, allowing the dielectric constant distribution of region 32 to be reconfigured as needed. The introduction of the electrically controlled refractive index module 32 endows the device with reconfigurability: the user can dynamically modify the arrangement of high and low refractive index materials in region 4 of the electrically controlled module according to the desired matrix operation, realizing different matrix multiplication functions. For example, under initial voltage control, when the input light field passes through the matrix calculation region, its output light field vector is equal to the input light field vector multiplied by a unitary matrix A; according to the voltage-refractive index mapping relationship, modifying the control voltage can make the output light field vector equal to the input light field vector multiplied by a certain unitary matrix B.
[0049] In one specific embodiment, the matrix calculation region 3 provided in this embodiment is a square planar design region on a substrate with a side length of 5µm, and the region is divided into a regular pixel grid (such as 100×100 pixel units). Each pixel unit is approximately 50nm×50nm in size, and the filling material is either high-refractive-index silicon pixels or an air background. Through such an arrangement of high and low refractive index dielectric microstructures, the matrix calculation region 3 produces a specific modulation effect on the input light field under a given voltage.
[0050] In this embodiment, the working mechanism of the matrix multiplication device is as follows: the input vector signal to be calculated is encoded into an optical signal and then injected into the device from the input waveguide 1. For example, for 2×2 matrix multiplication, the two input values can be modulated onto two orthogonal polarization states or two parallel channels and simultaneously sent into the input waveguide 1; for higher-dimensional matrix operations, time-division multiplexing, multi-mode multiplexing, or wavelength-division multiplexing can also be used to load multi-dimensional information into a single input port.
[0051] The functionality of the above structure was verified using finite-difference time-domain electromagnetic simulation. Figure 2 The transient electric field intensity distribution within the matrix calculation region 32 under the influence of six sets of test input signals in the device of this embodiment is shown. It can be seen that the light introduced from different input ports 1 forms a complex interference pattern within the design region, and the high-refractive-index and low-refractive-index pixel layout at different locations guides the light field to the expected distribution. Ultimately, the light field mainly converges and couples to a designated location, and is output from the output port 2.
[0052] Figure 3 The simulation results for multiple control voltages under single-port input conditions are presented, along with a comparison curve of the simulation results. The horizontal axis represents the refractive index of the electronically controlled refractive index module, and the vertical axis represents the normalized light intensity measured at the output port of this device.
[0053] Depend on Figure 3 As can be seen, most test points of the device of this invention are close to ideal straight lines, indicating that the device has achieved the set matrix multiplication mapping relationship, and the output results are in good agreement with the theoretical values. Even considering the actual conditions of processing errors and material losses, a very small number of points still show some deviation, but the overall error is still within an acceptable range, indicating that the matrix multiplication device of this invention has good robustness and accuracy.
[0054] In one specific embodiment, this embodiment provides a method for constructing the topological shape and material distribution of micro / nano structures, including:
[0055] Based on the objective function, the topology and material distribution of the micro-nano structure are iteratively optimized using the adjoint electromagnetic topology optimization method until the objective function reaches its maximum value. The iteration is then completed to obtain the final topology and material distribution of the micro-nano structure.
[0056] The objective function is constructed based on the desired two-dimensional matrix operation result and the output two-dimensional matrix operation result. The desired two-dimensional matrix operation result is constructed based on the different refractive indices of the micro-nano structure below the electrically controlled refractive index module under the set external stimulus. The output two-dimensional matrix operation result is constructed based on the response signal of the output port corresponding to the external signal input by different input ports.
[0057] Furthermore, the objective function L is:
[0058]
[0059]
[0060] in, N Given a number of external control signals, in one embodiment, the external control signal is a voltage. i For a given external control signal index, n iTo determine the refractive index of the micro / nano structure beneath the electrically controlled refractive index module when the i-th external control signal is applied, The unit amplitude of the electric field at the first output port when light is input from the first input port; The unit amplitude of the electric field at the second output port when light is input from the first input port; The unit amplitude of the electric field at the first output port when light is input from the second input port; The electric field amplitude at the second output port is the unit amplitude when light is input from the second input port.
[0061] When the objective function L When optimized to the maximum value:
[0062] And in the opposite direction.
[0063] And in the same direction.
[0064] Therefore, after the objective function has achieved maximum optimization, the design region representation matrix is as follows:
[0065]
[0066] In one embodiment, n i The refractive index is adjustable from 1.1 to 2.1, thus allowing for the realization of any corresponding unitary matrix. The electrically controlled refractive index module consists of photoelectric materials and microelectrodes. The voltage applied to the microelectrodes changes the refractive index of the photoelectric materials, which can be adjusted according to the voltage range n = 1.1-2.1. The module is a 0.5µm * 0.5µm rectangle located at the center of the design area.
[0067] In a specific embodiment of the present invention, different refractive indices under the electronically controlled refractive index module are used to construct the desired two-dimensional matrix operation result. The constructed objective function is used to make the final iterated micro-nano structure processing data result similar to or consistent with the label, thereby realizing the reconstruction of two-dimensional matrix operation by adjusting the refractive index of the electronically controlled refractive index module.
[0068] In one specific embodiment, this embodiment utilizes the adjoint electromagnetic topology optimization method to iteratively optimize the topological shape and material distribution of the micro / nano structure, including:
[0069] First, the matrix calculation region is divided into multiple pixel units. The dielectric constant of each pixel unit is initially assigned a continuous parameter representation to obtain the dielectric constant matrix. The dielectric constant matrix is then mapped to the parameter matrix through the hyperbolic tangent function (tanh) to transform the discrete optimization of the dielectric constant into the continuous optimization of the parameters.
[0070] In each iteration, the inner product of the spatial overlap of the forward field distribution and the adjoint field distribution in the matrix calculation region obtained by the adjoint electromagnetic topology optimization method is used as the first gradient information. The second gradient information is obtained based on the objective function. The parameter matrix is updated by using the first and second gradient information. In each iteration, the β value of the hyperbolic tangent function is increased so that the parameter matrix mapping relationship approaches binary.
[0071] This embodiment continues to iterate until the inner product calculation result reaches the set threshold and the objective function reaches the maximum value, and the pixel values are close to the two discrete dielectric constants, then the iteration stops, and the final micro / nano structure topology and material distribution are obtained.
[0072] In one specific embodiment, this embodiment uses the inner product calculation result of the spatial overlap of the forward field distribution and the adjoint field distribution in the matrix calculation region obtained by the adjoint electromagnetic topology optimization method as the first gradient information, including:
[0073] By applying a given excitation field to the input port through forward FDTD simulation, the electromagnetic field distribution and output response signal within the matrix calculation region are calculated.
[0074] The accompanying source and corresponding output port are obtained based on the electromagnetic field distribution through adjoint FDTD simulation. The accompanying source is applied at the output port, and the accompanying field distribution within the matrix region is calculated via backpropagation. The spatial overlap of the forward field distribution and the accompanying field distribution within the matrix calculation region is then performed to obtain the first gradient information. Based on this first gradient information, the Adam adaptive moment estimation algorithm is used to iteratively adjust the parameter matrix. This invention, by employing the adjoint optimization method, can efficiently handle reverse design problems with a large number of design degrees of freedom (up to tens of thousands of pixel units), significantly shortening the optimization convergence time.
[0075] In order to meet the actual process requirements, the parameter matrix is optimized in this embodiment. The specific steps are as follows: after obtaining the parameter matrix, the parameter matrix is preprocessed by convolution with a convolution kernel of a set radius size R. Then, the medium structure corresponding to the convolution parameter matrix is optimized by introducing a penalty function, and finally the parameter matrix that meets the preset minimum feature size requirement is obtained.
[0076] In a specific embodiment of the present invention, excitation signals for multiple sets of orthogonal basis vectors are injected into the first and second input ports. Using the excitation signals of multiple sets of basis vectors as inputs simplifies and simplifies the training process.
[0077] In one specific embodiment, the high refractive index material provided in this embodiment is silicon with a relative permittivity of approximately 12.18, and the low refractive index material is vacuum with a relative permittivity of 1. The matrix calculation region is a square region with a side length of 5 micrometers, composed of 100×100 pixel units, each pixel unit being 50 nanometers × 50 nanometers in size. The input port and output port are optical waveguides with a width of 0.4 micrometers and a length of 1.5 micrometers, and are formed by filling silicon material. The electrically controlled refractive index module is a 0.5 micrometer × 0.5 micrometer square region, and its refractive index can be controlled by voltage to vary within the range of 1.1-2.1. The operating wavelength of the device is at 1.5 micrometers.
[0078] In a specific embodiment of the present invention, by setting an appropriate penalty function, the amplitude and phase of the input light field after being processed by the unitary matrix simulated by the two-port network are matched with the expected output light field.
[0079] It should be noted that the specific structural dimensions and parameters (such as pixel size, operating band, etc.) mentioned in the above embodiments are merely examples and can be adjusted according to actual application requirements during optimization design. For example, for higher frequency terahertz band computing chips, the pixel size and device size can be appropriately enlarged; for operations requiring larger-scale matrices, functionality can be expanded by cascading multiple matrix computing regions or adding input / output ports, and these improvements are all within the scope of the design concept of this invention. Through the description of the above embodiments, those skilled in the art can clearly understand that the matrix multiplication device of this invention can achieve highly integrated optical matrix operations with a novel topology optimization design method, accelerating the development of analog computing.
Claims
1. A two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization, characterized in that, Includes input ports, matrix calculation area, and output ports; The input port is used to couple external signals into the matrix calculation area; The matrix calculation region is used to simulate a predetermined two-dimensional matrix multiplication operation mapping relationship. The matrix calculation region includes a micro-nano structure filled with materials of different refractive indices and an electrically controlled refractive index module located on the micro-nano structure. The electrically controlled refractive index module is used to change the corresponding refractive index under the action of an external control signal to reconstruct the two-dimensional matrix multiplication operation mapping relationship. The output port is used to output the calculation results; Methods for constructing the topological shape and material distribution of micro / nano structures include: Based on the objective function, the topology and material distribution of the micro-nano structure are iteratively optimized using the adjoint electromagnetic topology optimization method until the objective function reaches its maximum value. The iteration is then completed to obtain the final topology and material distribution of the micro-nano structure. The objective function is constructed based on the desired two-dimensional matrix operation result and the output two-dimensional matrix operation result. The desired two-dimensional matrix operation result is constructed based on the different refractive indices of the micro-nano structure below the electrically controlled refractive index module under the set external stimulus. The output two-dimensional matrix operation result is constructed based on the response signal of the output port corresponding to the external signal input by different input ports. The iterative optimization of the topology and material distribution of the micro / nano structure using the adjoint electromagnetic topology optimization method includes: First, the matrix calculation region is divided into multiple pixel units. The dielectric constant of each pixel unit is initially assigned to obtain a dielectric constant matrix. The dielectric constant matrix is then mapped to a parameter matrix using the hyperbolic tangent function. In each iteration, the inner product of the spatial overlap of the forward field distribution and the adjoint field distribution in the matrix calculation region obtained by the adjoint electromagnetic topology optimization method is used as the first gradient information. The second gradient information is obtained based on the objective function. The parameter matrix is updated by the first gradient information and the second gradient information. In each iteration, the β value of the hyperbolic tangent function is increased so that the parameter matrix mapping relationship approaches binary. The iteration continues until the inner product calculation result reaches the set threshold and the objective function reaches its maximum value, and the pixel values are close to the two discrete dielectric constants. Then the iteration stops, and the final topology and material distribution of the micro / nano structure are obtained.
2. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 1, characterized in that, The inner product of the spatial overlap of the forward field distribution and the adjoint field distribution in the matrix computation region, obtained through the adjoint electromagnetic topology optimization method, is used as the first gradient information, including: By applying a given excitation field to the input port through forward FDTD simulation, the electromagnetic field distribution and output response signal within the matrix calculation region are calculated. The accompanying source and corresponding output port are obtained based on the electromagnetic field distribution through FDTD simulation. The accompanying source is applied at the output port, and the accompanying field distribution in the matrix region is calculated by backpropagation. The spatial overlap of the forward field distribution and the accompanying field distribution in the matrix calculation region is performed by inner product operation to obtain the first gradient information. Based on the first gradient information, the Adam adaptive moment estimation algorithm is used to iteratively adjust the parameter matrix.
3. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 1, characterized in that, After obtaining the parameter matrix, the parameter matrix is preprocessed by convolution with a convolution kernel of a set radius size. Then, the medium structure corresponding to the convolutional parameter matrix is optimized by introducing a penalty function, and finally a parameter matrix that meets the preset minimum feature size requirement is obtained.
4. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 1, characterized in that, The input port includes a first input port and a second input port, and the output port includes a first output port and a second output port. Excitation signals of multiple sets of basis vectors are injected into the first input port and the second input port.
5. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 1, characterized in that, The different refractive index materials include high refractive index materials and low refractive index materials, wherein the high refractive index material is silicon and the low refractive index material is air.
6. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 1, characterized in that, The input and output ports are integrated waveguides.
7. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 6, characterized in that, The integrated waveguides for the input and output ports are the same as those for high-refractive-index materials in micro / nano structures.
8. The two-port matrix multiplication device based on adjoint electromagnetic simulation topology optimization according to claim 1, characterized in that, The electrically controlled refractive index module includes a set of microelectrodes. When an external control signal is applied to stimulate the microelectrodes, the refractive index of the micro / nano structure located below changes.