A Material Design Method for Multimode Interferometers Based on Topology Optimization

Abstract

This invention discloses a material design method for multimode interferometers based on topology optimization. A geometric network model of the multimode interferometer device is constructed, including a device region and a PML layer. The device region includes an Input region, a Design region, and an Output region. The Output region contains at least one port. The Input and Output regions are filled with Si material. The material distribution of the Design region between Si and SiO2 is solved through topology optimization. By combining topology optimization, binarization processing, and the MarchingTriangle algorithm, this invention successfully realizes a complete design chain from theoretical optimization to physical implementation.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic device design and manufacturing, and in particular to a material design method for multimode interferometers based on topology optimization. Background Technology

[0002] As electronic chips and optoelectronic devices evolve towards higher performance, miniaturization, and multifunctionality, the tight coupling between manufacturing processes and design parameters becomes particularly important. However, current technologies exhibit a significant disconnect between design optimization and actual manufacturing, making it difficult to fully realize the design's potential in physical implementation. Traditional design methods typically rely on manual calculations and optimization schemes based on fixed physical models, which cannot effectively address the nonlinearity of device characteristics and the variability of manufacturing processes. In chip design, traditional methods struggle to achieve global optimization across performance, power consumption, area, and reliability; in optoelectronic device and array antenna design, existing methods often fail to accurately describe the material distribution characteristics under complex processes. Summary of the Invention

[0003] Tightly coupled chip design requires careful consideration of the synergistic optimization of manufacturing processes and device characteristics to achieve the best balance between performance, power consumption, area, and reliability. Device model optimization methods are crucial in this process, providing high-precision behavioral prediction support for circuit design by accurately modeling the physical and variability characteristics of the manufacturing process. The purpose of this invention is to design a full-chain optimization method that achieves seamless integration from theoretical optimization to manufacturing processes, and also improves the accuracy and practicality of the design by combining machine learning and optoelectronic integration technologies, thereby overcoming the current technological bottlenecks.

[0004] To achieve the above objectives, this invention adopts the basic form of a multimode interferometer (MMI) device and uses a topology optimization scheme based on sensitivity analysis to optimize the material distribution of waveguide material (Si) and cladding (SiO2) to achieve different power distributions at the output end.

[0005] This invention provides a material design method for a multimode interferometer based on topology optimization. The geometric network model of the multimode interferometer device includes a device region, which includes an Input region, a Design region, and an Output region. The Output region contains at least one port. The Input and Output regions are filled with Si material. The material distribution of the Design region between Si and SiO2 is solved by topology optimization.

[0006] Optionally, the Output area contains four ports.

[0007] Optionally, the geometric mesh model of the multimode interferometer may also include surrounding material and boundary conditions.

[0008] Optionally, the surrounding material includes a first region and a second region, wherein the first region tightly surrounds the device region and the second region tightly surrounds the first region.

[0009] Optionally, the material of the first region is SiO2, and the material of the second region is PML (perfectly matched layer).

[0010] Optionally, the boundary condition is to tightly surround a third region outside the second region, the third region being a PEC (Perfect Electrical Conductor).

[0011] Optionally, the PML is a hypothetical material used to absorb waves incident from inside the computational domain to the boundary with almost no reflection, thereby simulating an infinite space. To realize the PML in the numerical simulation, a coordinate complex stretching method is used, which can be specifically expressed as:

[0012]

[0013] in, It is a coordinate stretching function, usually taken as:

[0014]

[0015] in, It is along The absorption function of coordinates, It is angular frequency. It is the imaginary unit.

[0016] Here, we only consider the TM mode and assume that the electric field propagates in the plane, expressed by scalars as the component perpendicular to the plane. The Helmholtz equation for the two-dimensional case is:

[0017]

[0018] in, It is the wavenumber in free space. This is the source term (corresponding to the magnetic current density in Maxwell's equations). The PML's "stretched coordinates" formula corresponds to the transformation of the partial differential equation as follows:

[0019]

[0020] in, It is the depth of the coordinate point entering the PML. and The derivative corresponds to and PML layer at the edge of the directional region.

[0021] Optionally, each point in the Design region represents a design degree of freedom, which can continuously vary between SiO2 and Si, allowing design parameters to be... Discretized into a parameter space of piecewise constants Then, the dielectric constant of the material in the Design region is given by the following formula:

[0022]

[0023] in and These are the refractive indices of SiO2 and Si, respectively.

[0024] Optionally, by generating a smoothing / filtering parameter function. To normalize the problem, a minimum length scale is introduced. Smoothing is performed by solving the "damped diffusion" partial differential equation (Helmholtz filter). ,by Design variables:

[0025]

[0026] Wherein, the minimum length scale , To ensure compatibility with process conditions.

[0027] Optionally, after smoothing, the intermediate variables... Apply a smooth threshold projection to obtain a “binarized” density parameter that tends to be 0 or 1 almost everywhere. :

[0028]

[0029] Among them, gradually increasing slowly Differentiability optimization can be achieved in the above manner. In the interpolation formula, Replaced with filtering and thresholding :

[0030]

[0031] The above equation is the one that will be used in the Helmholtz partial differential equation. coefficient.

[0032] Alternatively, the weak form of the PML Helmholtz partial differential equation is:

[0033]

[0034] Optionally, the gradient operator can be treated as a variable, here They are two vectors and The element-wise "product" of the above weak form is used to solve for the magnetic field component in the direction of propagation. The electric field is obtained from the magnetic field by the following formula:

[0035]

[0036] Optionally, the field intensity at the four output waveguides is maximized and optimized, ensuring that the relative proportions of each field intensity meet design requirements. The field strength at the center point is In two-dimensional form, the optimization objective can be simplified to:

[0037]

[0038] in It is a magnetic field vector, and

[0039]

[0040] in, and It is a finite element basis function, the Dirac function. It can be approximated as a Gaussian function, and the final optimization objective is:

[0041]

[0042] in, This is an adjustable parameter used to balance the weights between the two optimization objectives. , is the output port The proportion of output power to total output power. The target output power coefficient is obtained in reinforcement learning.

[0043] Optional, in In the middle, only Depending on the design parameters, this can be obtained through the adjoint method. Compared to The derivative:

[0044]

[0045] in From the adjoint solution It is possible to obtain relative to the chain rule. Final derivative:

[0046]

[0047] Optionally, the material distribution pattern obtained after topology optimization can be fixed by binarization to generate a clear material layout scheme.

[0048] Optionally, the MarchingTriangle algorithm with a custom meshing scheme can be used to adapt to the finite element mesh data and solution results, and quickly generate a standardized GDS (Graphic Data System) file.

[0049] The beneficial effects of this invention are as follows: by combining topology optimization, binarization processing, and the MarchingTriangle algorithm, a complete design chain from theoretical optimization to physical realization has been successfully achieved. This technology not only improves the efficiency and accuracy of device design, but also explores a completely new path for the design and manufacturing of complex optoelectronic devices, laying an important foundation for the automated design and manufacturing of future optoelectronic devices, and has broad application prospects and promotional value. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. Wherein:

[0051] Figure 1 For the geometric and mesh model of the multimode interferometer;

[0052] Figure 2 The material surrounding the multimode interferometer and the PML layer;

[0053] Figure 3 The results are for solving the magnetic field components in the transmission direction of the multimode interferometer in TM mode.

[0054] Figure 4 The images show the effects of Helmholtz smoothing filtering. The left side shows the effect before smoothing, and the right side shows the effect after smoothing.

[0055] Figure 5 for The binarization result is shown below;

[0056] Figure 6 The simulated magnetic field strength of the multimode interferometer obtained after topology optimization;

[0057] Figure 7 The topology optimization results are fully exported to a GDS file for chip fabrication. Detailed Implementation

[0058] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the examples in the specification.

[0059] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0060] This invention provides a material design method for multimode interferometers based on topology optimization. It adopts the basic device form of a multimode interferometer (MMI) and uses a topology optimization scheme based on sensitivity analysis to optimize the material distribution of waveguide material (Si) and cladding (SiO2) to achieve different power distributions at the output end.

[0061] First, write a script file to generate the basic geometry and mesh model of MMI. Figure 1 In the design, the waveguide regions identified by Input and Output are filled with Si, while the material distribution in the Design region is solved by topology optimization between Si and SiO2. Ideally, the TE mode light source is injected from the waveguide identified by Input, undergoes multimode interference in the Design region, and is recoupled to the four Output ports (1-4), completing the power redistribution.

[0062] Solving Maxwell's equations using the finite element method requires adding surrounding materials and appropriate boundary conditions to the geometric mesh model of the MMI in order to simulate open regions with limited computational power. For example... Figure 2 As shown, the yellow area represents SiO2, and the green area represents a perfectly matched layer (PML). PEC (Perfect Conductor) boundary conditions are applied around the perimeter. PML is a hypothetical material widely used as an absorbing boundary in numerical simulations to absorb waves incident from the computational domain onto the boundary with almost no reflection, thus simulating infinite space. To implement PML in the numerical simulation, a coordinate complex stretching method is employed, which can be specifically expressed as...

[0063]

[0064] in, It is a coordinate stretching function, usually taken as:

[0065]

[0066] in, It is along The absorption function of coordinates, It is angular frequency. It is the imaginary unit.

[0067] Since we only consider the TM mode here and assume that the electric field propagates in the plane, expressed as a scalar component perpendicular to the plane, the Helmholtz equations for the two-dimensional case are:

[0068]

[0069] in, It is the wavenumber in free space. This is the source term (corresponding to the magnetic current density in Maxwell's equations). The PML's "stretched coordinates" formula corresponds to the transformation of the partial differential equation as follows:

[0070]

[0071] in, It is the depth of the coordinate point entering the PML. and The derivative corresponds to and The PML layer at the edge of the directional region. The results obtained by solving the above partial differential equation at a wavelength of 1550 nm are as follows... Figure 3 As shown in the figure. The horizontal and vertical axes are in units of length (μm), and the color bars on the right represent the magnetic field strength.

[0072] Density-based topology optimization techniques are used to maximize the electric field strength at the center. Each point in the Design region represents a degree of design freedom, which can continuously vary between SiO2 and Si, allowing for adjustments to the design parameters. Discretized into a parameter space of piecewise constants Then, the dielectric constant of the material in the Design region is given by the following formula:

[0073]

[0074] in and These are the refractive indices of SiO2 and Si, respectively.

[0075] In practice, to avoid obtaining overly detailed features as spatial resolution increases, it is necessary to generate a smoothing / filtering parameter function. To normalize the problem, a minimum length scale is introduced. Smoothing is performed by solving the "damped diffusion" partial differential equation (Helmholtz filter). ,by Design variables:

[0076]

[0077] This invention selects the minimum length scale ,in To ensure compatibility with process conditions. Its smoothing effect is as follows: Figure 4 As shown.

[0078] After smoothing, the intermediate variables Apply a smooth threshold projection to obtain a “binarized” density parameter that tends to be 0 or 1 almost everywhere. :

[0079]

[0080] Its function graph is as follows Figure 5 As shown. When The binarization process transforms into a step function, which makes the optimization problem non-differentiable. Therefore, this invention employs a gradually and slowly increasing... This is how differentiability is achieved, and finally, in the above... In the interpolation formula, Replaced with filtering and thresholding :

[0081]

[0082] The above equation is the one that will be used in the Helmholtz partial differential equation. coefficient.

[0083] In summary, the weak form of the PML Helmholtz partial differential equation is:

[0084]

[0085] If we consider the gradient operator as a variable, then here... They are two vectors and The element-wise "product" of the above weak form is used to solve for the magnetic field component in the direction of propagation. The electric field can be obtained from the magnetic field using the following formula:

[0086]

[0087] The optimization objective of this invention consists of two parts: maximizing the field intensity at the four output waveguides and ensuring that the relative proportions of each field intensity meet certain design requirements. Assuming... The field strength at the center point is In two-dimensional form, the optimization objective can be simplified to:

[0088]

[0089] in It is a magnetic field vector, and

[0090]

[0091] Here and It is a finite element basis function; in practical applications, the Dirac function... It can be approximated as a Gaussian function, and the final optimization objective is:

[0092]

[0093] in, This is an adjustable parameter used to balance the weights between the two optimization objectives. , is the output port The proportion of output power to total output power. The target output power coefficient is obtained in reinforcement learning.

[0094] exist In the middle, only Depending on the design parameters, this can be obtained through the adjoint method. Compared to The derivative:

[0095]

[0096] in From the adjoint solution It is possible to obtain relative to the chain rule. Final derivative:

[0097]

[0098] The final device shape obtained through topology optimization is as follows: Figure 6 As shown, inverse design was performed here, targeting the optimized power distributions from four different stages of reinforcement learning. The four power ratios are... , , and .exist Figure 6 middle, This represents the error between the target power distribution ratio and the design result; the smaller the value, the better. It can be seen that several different power distributions can be achieved with high precision through the constructed topology optimization scheme.

[0099] Finally, the material distribution pattern obtained after topology optimization is fixed through binarization to generate a clear material layout scheme. For example... Figure 7As shown, the black areas in the binarized image represent Si (silicon) material, and the white areas represent SiO2 (silicon dioxide) material. This process not only transforms the optimization results from a continuous distribution to a specific physical material distribution, but also lays the foundation for subsequent design stages. Based on this, a MarchingTriangle algorithm for custom mesh generation schemes was further developed. This algorithm can efficiently adapt to finite element mesh data and solution results, quickly generating standardized GDS (Graphic Data System) files. GDS files are an industry-standard file format in the integrated circuit manufacturing field, used to describe the geometric layout and material distribution of devices. Using the MarchingTriangle algorithm, the study achieved a direct conversion from topology optimization results to tape-out design files. This method effectively reduces the tedious manual operations required from optimization to tape-out in the traditional design process, significantly improving design efficiency and accuracy.

[0100] Specifically, the MarchingTriangle algorithm takes a finite element mesh generation scheme as input and can accurately reconstruct the boundary contour based on the material properties in the mesh, automatically generating a high-precision GDS graphic file suitable for chip fabrication processes. The key to this algorithm is that it can both preserve the fine structure after topology optimization and meet the strict requirements of integrated circuit manufacturing processes for geometry, thereby achieving seamless integration between optimized design and process implementation.

[0101] This innovative approach not only ensures the physical feasibility of material distribution but also provides a direct path for verifying topology optimization schemes. The generated GDS file allows the optimized structure to be implemented in the actual manufacturing process, further validating the consistency between design and actual performance. This automated design-to-manufacturing conversion path significantly shortens the time from theoretical research to actual device development, providing strong support for the practical application of topology optimization in engineering.

Claims

1. A multi-mode interferometer material design method based on topology optimization, characterized in that: a geometric network model of a multi-mode interferometer device is constructed, including a device region, the device region including an Input region, a Design region and an Output region, the Output region containing at least one port, the region materials of the Input region and the Output region being filled with Si, and the material of the Design region being solved by topology optimization between Si and SiO2; the geometric network model of the multi-mode interferometer further includes surrounding materials and boundary conditions; the surrounding materials include a first region and a second region, the first region closely surrounding the device region, and the second region closely surrounding the first region; the material of the first region is SiO2, and the material of the second region is PML; the PML is a kind of imaginary material used to absorb waves incident on the boundary from the inside of the calculation domain, almost no reflection, thereby simulating an infinite space, in order to realize the PML in numerical simulation, a coordinate complex stretching method is adopted, which is specifically represented as: ， wherein is a coordinate stretch function, taken as: ， wherein is the absorption function along the coordinate, is the angular frequency, is the imaginary unit; Only TM mode is considered here and the electric field is assumed to propagate in the plane, represented by a scalar as the component in the vertical plane direction, the Helmholtz equation in two dimensions is: ， wherein is the wave number in free space, is the source term in Maxwell's equations corresponding to the magnetic current density, the formula for the coordinate complex stretching method of PML corresponds to the transformation of the partial differential equation to: ， wherein, is the depth of the coordinate point into the PML, and the derivative corresponds to and the PML layer of the directional region edge.

2. The topography-optimized multi-mode interferometer material design method of claim 1, wherein: The Output region contains four ports.

3. The topological optimization based multi-mode interferometer material design method of claim 1, wherein: The boundary condition is to set a third region closely outside the second region, and the third region is PEC.

4. The topography-optimized multi-mode interferometer material design method of claim 1, wherein: Each point of the Design region is a design degree of freedom, continuously varying between SiO2and Si, which will determine the design parameter Discretization of the parameter space into piecewise constant Afterwards, the dielectric constant of the material of the Design region is given by ， wherein and are the refractive indices of SiO2and Si, respectively.

5. The topologically optimized multi-mode interferometer material design method of claim 4, wherein: By generating a smooth / filtered parameter function to normalize the problem to introduce a minimum length scale , the smoothing is performed by solving a damped diffusion partial differential equation to design variables: ， wherein the minimum length scale , in order to be compatible with process conditions.

6. The topologically optimized multi-mode interferometer material design method of claim 5, wherein: After smoothing, the parameter function Apply a smoothing threshold projection to obtain a binarized density parameter that tends to be 0 or 1 almost everywhere : ， Wherein, the gradually slow increase way is used to realize the differentiable optimization, and the in the above-mentioned Design area of the material dielectric constant formula will Replace the filtered and threshold processed : ， The above formula is to be used in the Helmholtz partial differential equation coefficients.

7. The topologically optimized multi-mode interferometer material design method of claim 6, wherein: The weak form of the PML Helmholtz partial differential equation is: ， where the gradient operator is considered as a variable, here is the element-wise product of two vectors and The above weak form is used to solve for the magnetic field components in the direction of propagation, the electric field being obtained from the magnetic field by ， The field intensity at the four output waveguides is maximized and optimized, and the relative proportion of each field intensity meets the design requirements, so that The field intensity at the center point is |E( )| 2 In a two-dimensional form, the optimization target is simplified as: ， wherein is the magnetic field vector, and ， where and are finite element basis functions, the Dirac function is approximated by a Gaussian function, and the final optimization objective is: ， wherein, is a tunable parameter term to balance the weights between the two optimization objectives, is an output port is the proportion of the output power in the total output power, is the target output power coefficient to be solved in reinforcement learning.

8. The topologically optimized multi-mode interferometer material design method of claim 7, wherein: In only depending on the design parameters, by the accompanying method it is possible to obtain derivative with respect to the derivative with respect to ， wherein from the adjoint solution The final derivative with respect to is obtained by the chain rule: ， The material distribution pattern obtained after topology optimization is fixed by binary processing to generate a clear material layout scheme.

9. The topologically optimized multi-mode interferometer material design method of claim 8, wherein: The MarchingTriangle algorithm with a self-defined mesh division scheme is used to adapt the finite element mesh data and the solution result, and a standardized GDS file is quickly generated.

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