Electromagnetic simulation method for fast reverse design of multimode interference photonic device

Abstract

The invention discloses an electromagnetic simulation method for fast reverse design of a multi-mode interference photonic device, and belongs to the field of reverse design of photonic devices.The multi-mode interference photonic device comprises silicon on insulator and a phase change layer, the phase change layer is dispersed into a pixel array composed of pixel units, each pixel unit is in a crystalline state and an amorphous state, and the phase change layer is a phase change layer. The refractive index distribution of the device is regulated and controlled by designing the distribution of the pixels, so that the interference of modes in the multimode waveguide is obviously influenced. Interference between the modes can be described through the transmission matrix, so that all pixel distribution is expressed through the transmission matrix, the electromagnetic simulation calculation process of the reverse design device can be quickly calculated through the transmission matrix, traditional electromagnetic simulation software does not need to be used for long analog simulation, the design efficiency is remarkably improved, and the design cost is reduced. The fundamental research process in the photonics field is accelerated, and a solid foundation is laid for deep development of the photon technology in the fields of communication, calculation, sensing and the like.

Description

Technical Field

[0001] The invention relates to the field of reverse design of photonic devices, and in particular to an electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices. Background Art

[0002] Since the end of the 20th century, the electronic information industry has faced a transmission bottleneck. Traditional electronic interconnection is limited in speed and bandwidth. People have begun to seek information transmission solutions with higher integration, lower power consumption and more functions, and thus photonic integrated devices have emerged. Photonic integrated circuits are a technology that integrates integrated photonic devices with different functions on a substrate to give them systematic functions. They have the advantages of small size, easy integration, low price, and large bandwidth, ultra-high speed and low energy consumption of photonic communication. They have great application potential in the fields of optical interconnection, quantum computing, optical neural network computing and biosensor chips. Application in optical interconnection can realize fast data transmission and processing, which can well solve the challenges faced in the field of electrical interconnection; at the same time, silicon-based optoelectronic integration technology is compatible with CMOS technology and can realize high-performance and large-capacity optoelectronic integrated systems at a lower cost, making it the research focus of optical interconnection technology implementation solutions.

[0003] With the rapid development of photonic integration technology, multi-mode interference (MMI) devices have become core components in the fields of optical communications, quantum computing, and sensors due to their unique wavelength selection, power distribution, and signal modulation functions. The design of traditional multi-mode interference photonic devices is highly dependent on manual experience or time-consuming full-waveguide electromagnetic simulation (such as finite element method), and structural parameters (such as waveguide width, length, gap, etc.) need to be repeatedly adjusted to achieve the target spectral response. Relying on commonly used electromagnetic simulation software such as COMSOL Multiphysics, Lumerical FDTD, etc., the full-waveguide simulation calculation is huge. Even if a high-configuration server is used for calculation, the time required for optimization calculation is still as long as dozens or even hundreds of hours, making it difficult to quickly iterate and optimize. This severely limits the research on multi-mode interference, and it is urgent to develop a new way to improve the efficiency of device optimization design.

[0004] The structure used in the present invention is the same as the structure used in invention patent CN119087579A, and a method for improving design efficiency is proposed by optimizing the design speed based on the structure used in invention patent CN119087579A. Summary of the invention

[0005] In view of this, in order to improve the design efficiency of multimode interference photonic devices, the present invention proposes an electromagnetic simulation method for rapid reverse design of multimode interference photonic devices. The present invention designs the device on a silicon-based multimode interference waveguide platform, using a reverse design method, and the structure includes: standard silicon on insulator and Sb2Se3 phase change material layer. On the basis of coupled mode theory, according to the integrity and orthogonality of the mode, any light field E in the multimode waveguide can be expressed as a superposition of its eigenmodes. By decomposing the multimode interference waveguide platform, the transmission matrix T from input to output can be calculated.

[0006] Because the input is known, it can also be decomposed into the corresponding input vector a, and the general output is the design target, which is also known, and similarly decomposed into the corresponding output vector b. When the design needs to obtain the target b, the input a, and only the transmission matrix T is required, then the entire design process can be simplified to: b = Ta, and the iterative simulation process becomes the calculation process of the transmission matrix. Using MATLAB for matrix calculation will greatly improve the design efficiency of the reverse design of multi-mode interference photonic devices, and the design speed will be qualitatively improved.

[0007] The technical solution adopted by the present invention is:

[0008] Preferably, according to the coupled mode theory, any optical field E in a multimode waveguide can be expressed as a superposition of its eigenmodes according to the integrity and orthogonality of the modes, that is:

[0009] Among them, ξ i is the waveguide eigenmode, k i is the coefficient of the corresponding eigenmode. Within the scope of the invention, ξ i is the transverse electric mode (TE) of the multimode waveguide, and only the guided mode is considered.

[0010] Preferably, the input is decomposed into corresponding input vectors a: a=[a1,a2,…,a N-1 ,a N ] T (2)

[0011] Preferably, the output is decomposed into corresponding output vectors b: b=[b1,b2,…,b N-1 ,b N ] T (3)

[0012] Among them, a i , b i are the coefficients of the corresponding eigenmodes.

[0013] Preferably, the entire design process can be simplified as follows: b=Ta, and the corresponding matrix form is:

[0014] Among them, a j is the jth eigenmode coefficient of the input field, b i is the i-th eigenmode coefficient of the output field, T i,j is a matrix element representing the coupling coefficient between the jth modal component of the input field and the ith modal component of the output field.

[0015] Furthermore, given an input field and setting a target output field, the reverse design process of a multi-mode interference photonic device using electromagnetic simulation software such as COMSOL Multiphysics can be decomposed into the calculation process of formula (4), that is, the input field is decomposed into the mode field input vector a corresponding to the eigenmode as the basis vector, as shown in formula (2), and the output field is decomposed into the mode field output vector b corresponding to the eigenmode as the basis vector, as shown in formula (3). The simulation calculation process of the reverse design can be replaced by the transfer matrix calculation. The speed of using MATLAB to calculate the matrix is ​​much faster than the simulation speed of electromagnetic simulation software.

[0016] Furthermore, the reverse design uses a binary search algorithm (DBS), and the specific algorithm design process is explained in the following specific implementation section and will not be repeated here.

[0017] Furthermore, the silicon-based multimode interference waveguide platform is composed of a standard silicon-on-insulator (SOI) and a Sb2Se3 phase change material layer. The specific silicon-on-insulator substrate includes a silicon dioxide layer (SiO2) and a silicon layer (Si) located thereon. The SiO2 layer is 3um thick, the Si layer is 220nm thick, the Sb2Se3 layer is 23nm thick, the width is 6μm, and the length is 33μm. It is discretized into 8×44 square units with a side length of 750nm. The crystalline and amorphous states of each unit are determined by an algorithm based on a quality factor (FOM). Here we call these units "pixels" and the area composed of these pixels is called the "design area".

[0018] Furthermore, there are 8 pixels in a column in the design area. If "0" represents the crystalline state and "1" represents the amorphous state, there are 256 possible combinations of pixels in this column. Through formula (4), under specific input and output conditions, the transfer matrix T corresponding to all possible combinations can be obtained, which serves as the basis of the designed fast inverse design method.

[0019] Furthermore, each column of crystalline and amorphous combinations has a corresponding transfer matrix T, and the iterative simulation process of the optimization algorithm can be equivalently replaced by matrix operations, and the calculation speed is extremely fast.

[0020] The beneficial effects brought by the technical solution provided by the present invention are: The electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices proposed in the present invention can greatly improve the speed of reverse design of multi-mode interference photonic devices. For example, the time required to complete the optimization design of a mode converter using COMSOL Multiphysics is about 10 hours, but it takes about 5 minutes to complete the same design using MATLAB through the transmission matrix, which greatly improves the design speed. At the same time, since the transmission loss of the Sb2Se3 phase change material used in the design area is extremely low, the phase change state can be reversibly switched by laser excitation, so a variety of different functions can be realized on the same multi-mode interference device. Rapid design can be achieved in a short time, which is of great significance to the multifunctionality of the device and its wide application. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a schematic flow chart of an electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices proposed in the present invention.

[0022] Figure 2 Flowchart of the DBS optimization algorithm used in the reverse design of the present invention.

[0023] Figure 3 This is a schematic diagram of the structure of a multi-mode interference photonic device designed in an electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices proposed by the present invention.

[0024] Figure 4 This is a schematic side view of the structure of a multi-mode interference photonic device designed in the method proposed in the present invention.

[0025] Figure 5 Comparison of the output electric field amplitude at the device output position between the finite element simulation software and matrix calculation results for the same multi-mode interference structure.

[0026] Figure 6 A phase shaper is designed to utilize the electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices proposed by the present invention. DETAILED DESCRIPTION

[0027] In order to make the technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Among them, the accompanying drawings are only used for exemplary descriptions, and only schematic diagrams are shown, not physical diagrams, and cannot be understood as limiting the present invention.

[0028] See also Figure 1 , 2 and Figure 4 The electromagnetic simulation method for fast reverse design of multi-mode interference photonic devices proposed in this invention needs to calculate the possible transmission matrix of the multi-mode interference device in advance, and then use the operations between the transmission matrix to replace the simulation process of the device by the mainstream electromagnetic simulation software. In this way, the speed of matrix calculation will be much faster than the speed of electromagnetic simulation software simulation, and a fast reverse design method will be constructed. The following needs to analyze how to obtain the transmission matrix that can equivalently replace the electromagnetic simulation simulation.

[0029] According to the integrity and orthogonality of the modes, any optical field E in a multimode waveguide can be represented as a superposition of its eigenmodes, namely:

[0030] Among them, ξ i is the waveguide eigenmode, k i is the coefficient of the corresponding eigenmode. Within the scope of the invention, ξ i is the transverse electric mode (TE) of the multimode waveguide, and only the guided mode is considered.

[0031] The input is decomposed into the corresponding input vector a: a=[a1,a2,…,a N-1 ,a N ] T

[0032] The output is decomposed into the corresponding output vector b: b=[b1,b2,…,b N-1 ,b N ] T

[0033] Among them, a i , b i are the coefficients of the corresponding eigenmodes.

[0034] The entire design process can be simplified as follows: b = Ta, and its corresponding matrix form is:

[0035] Among them, a j is the jth eigenmode coefficient of the input field, b i is the i-th eigenmode coefficient of the output field, T i,j is a matrix element representing the coupling coefficient between the jth modal component of the input field and the ith modal component of the output field.

[0036] In reverse design, both input and output are known parameters in advance, that is, the elements of input vector a and output vector b are known. According to the formula, b1 = a1T 1,1 +a2T 1,2 +…+aN-1 T 1,N-1 +a N T 1,N , when only a1 and b1 are not zero, T can be calculated 1,1 The values ​​of other matrix elements are obtained in a similar way.

[0037] See also Figure 3 The design area 20 of the multi-mode interference photonic device designed in this embodiment has a size of 6 μm in width and 33 μm in length, and is discretized into 8×44 square units with a side length of 750 nm. Each column has 8 units, and there are 256 possible combinations of crystalline and amorphous states. This is true for each subsequent column. Therefore, as long as the transmission matrix corresponding to these 256 arrangements is obtained, the transmission matrix can be used for reverse design.

[0038] The width of the multi-mode interference photonic device design area 20 designed in this embodiment is 6 μm, and the number of effective guided modes accommodated is 26 guided modes, so the dimension of the transmission matrix is ​​a 26-order complex square matrix. All transmission matrices are obtained by the method described above.

[0039] On this basis, see Figure 1 and 2 The specific implementation steps of using DBS algorithm to quickly reverse design multi-mode interference devices are as follows:

[0040] Operation S11 calculates the transfer matrix T corresponding to all combinations of pixels in a single column. For example, when all pixels are in a crystalline state, the pixel code is 00000000, corresponding to T1. In this way, the corresponding transfer matrices of all 256 combinations are calculated. The algorithm can find the unique corresponding transfer matrix according to the arrangement of the pixels in the column to perform operations.

[0041] In operation S12, the crystalline and amorphous pixel patterns of the design area 20 are initialized as the optimized starting patterns, and the current FOM value is calculated through the transfer matrix.

[0042] Operation S13 changes the phase change state of a pixel in the design area 20, such as from a crystalline state to an amorphous state, or vice versa, and calculates the FOM through the transfer matrix corresponding to the pixel encoding index. If there is an improvement, the changed phase change state is retained and the FOM is updated. If not, the original state is restored.

[0043] Operation S14, repeatedly executing operation S13, randomly changing the state of a certain pixel in a column, switching from left to right, column by column, until all cells in the design area 20 are traversed, completing one iteration.

[0044] Operation S15, operations S13-S14 are repeatedly performed until changing the state of the pixel can no longer further improve the FOM, and the optimization stops.

[0045] The above method can be used to achieve rapid reverse design of multi-mode interference devices, and the device performance designed by this method is almost consistent with the performance of the device optimized by using the common electromagnetic simulation software COMSOL Multiphysics. Figure 5 As shown, on the same multi-mode interference waveguide structure, the output amplitude function curve (solid line) obtained by COMSOL simulation and the output amplitude function curve (dashed line) obtained by calculating the transmission matrix of the structure using MATLAB are almost completely overlapped, indicating that the method proposed in the present invention is effective and feasible.

[0046] On this basis, a phase shaper is designed using the method proposed in the present invention, such as Figure 6 As shown, by adjusting the state of the phase change material on the multimode interference waveguide to control the phase of the light field, the mode in the multimode waveguide can be focused on a specified position point.

[0047] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical method and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. An electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices, characterized in that: The operation between transmission matrices can be used to replace the simulation process of some electromagnetic simulation software. The structure of the multi-mode interference photonic device includes: a silicon substrate on an insulator and a phase change layer (2).

2. A silicon-on-insulator substrate comprises a silicon dioxide layer (11) and a silicon layer (12) thereon, the silicon-on-insulator comprises an input waveguide region (10), a design region (20) formed by a phase change layer (2), and an output waveguide region (30), wherein the design region (20) is discretized into a pixel array consisting of a plurality of pixel units, each pixel unit being made of a phase change material having a crystalline state and an amorphous state.

3. The structure of the multimode interference photonic device according to claim 1, characterized in that: The silicon-on-insulator substrate includes a silicon dioxide layer (SiO2) and a silicon layer (Si) located thereon, the SiO2 layer is 3um thick, the Si layer is 220nm thick, and the width is 3um.

4. The phase change layer (2) according to claim 1, characterized in that: The phase change material is Sb2Se3, with a layer thickness of 23nm, a width of 6μm, and a length of 33μm. It is discretized into 8×44 square units with a side length of 750nm. The crystalline and amorphous states of each unit are determined by the algorithm based on the quality factor (FOM). Here we call these units "pixels" and the area composed of these pixels is called the "design area", that is, the design area (20).

5. According to claim 1, the design area (20) has 8 pixels in a column. If "0" represents the crystalline state and "1" represents the amorphous state, there are 256 possible combinations of the pixels in this column. Through formula (4), under specific input and output conditions, the transfer matrix T corresponding to all possible combinations can be obtained, which serves as the basis of the designed fast inverse design method.

6. The reverse design optimization algorithm used in the electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices according to claim 1 is a binary search algorithm (DBS), and the specific implementation process is shown in Figure 2.

7. An electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices according to any one of claims 1 to 6, characterized in that: The operation between transmission matrices can be used to replace the simulation process of some electromagnetic simulation software. The steps of implementing the method include: S11, calculating the transmission matrix T corresponding to all combinations of pixels in a single column. For example, when all pixels are in a crystalline state, the pixel code is 00000000, corresponding to T1, and the corresponding transmission matrix is ​​calculated for all 256 combinations; S12, initializing the crystalline and amorphous pixel patterns of the design area (20); S13, changing the phase change state of a pixel in the design area (20), calculating the FOM through the transfer matrix corresponding to the pixel encoding index, if there is an improvement, retaining the changed phase change state and updating the FOM, if not, restoring the original state; S14, repeatedly executing operation S13, randomly changing the state of a certain pixel in a column, until all cells in the design area (20) are traversed; S15, repeating operations S13-S14 until changing the state of the pixel can no longer further improve the FOM, and the optimization stops.

8. The electromagnetic simulation method for rapid reverse design of multi-mode interference photonic devices according to claim 7, characterized in that: The operation S13 includes: The figure of merit FOM can have different calculation expressions depending on the required device functions and is determined according to the design goals; The value of FOM is no longer calculated by simulation using common electromagnetic simulation software, but is obtained by calculation between transfer matrices under the DBS algorithm architecture. That is, each column of pixels has a corresponding transfer matrix T. By multiplying these matrices with the input vector a through formula (4), the corresponding output b′ can be calculated and compared with the target b. Iterative optimization is performed until the calculated output is close to the target b, thereby achieving rapid reverse design.

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