A reverse design method and system for three-dimensional photonic devices
By employing a reverse design method that optimizes the mesh and density variables of three-dimensional photonic devices, the incompatibility problem of three-dimensional photonic device manufacturing technologies has been solved, enabling efficient and precise design and manufacturing of photonic devices.
Patent Information
- Application Number
- CN202310170862.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-02-27
- Publication Date
- 2025-10-31
- Estimated Expiration
- 2043-02-27
AI Technical Summary
Existing reverse engineering methods for three-dimensional photonic devices are incompatible with manufacturing technologies, making it difficult to achieve precise manufacturing. Furthermore, conventional methods consume computational resources and fail to achieve ideal results.
A three-dimensional photonic device reverse design method is adopted. The physical field simulation model is meshed, and density variables are initialized, density filtering and projection calculation are performed using cylindrical voxels as units. The light field intensity and distribution are optimized by combining the approximate Heaviside projection function and the projection cost function, and the density variables are iteratively adjusted to meet the design requirements.
It effectively avoids the problem of incompatibility in manufacturing technologies, improves the performance and manufacturing precision of photonic devices, reduces optimization time, adapts to different resolution requirements, and reduces the consumption of computing resources.
Smart Images
Figure CN116300067B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of photonic device design optimization technology, and more specifically, relates to a reverse design method and system for three-dimensional photonic devices. Background Technology
[0002] As photonics expands to encompass multi-physics coupling and multi-functional applications across different disciplines, the demand for photonic devices is increasing. In recent years, reverse engineering of photonic devices has gained traction. These devices not only require excellent performance but also extremely small dimensions, making it very difficult to find the optimal design using only physical and parametric scanning methods. Such approaches not only consume significant computational resources and time but also often fail to achieve satisfactory results because the optimal design is usually not found within the traditional templates of standard photonic design libraries.
[0003] Reverse engineering has been applied to various fields of photonics, such as photonic crystal structures, metasurfaces, and nonlinear optics. Compared to traditional optical optimization algorithms, reverse engineering expands the design space of photonic devices; however, the most common full 3D volumetric optimization, which lacks explicit constraints on material distribution within the design domain, still has limitations, producing voids and depressions incompatible with 3D photonic fabrication techniques. Furthermore, existing reverse engineering methods may also introduce minute features that are difficult to fabricate. Therefore, 3D photonics requires optimization methods with specific constraints. Summary of the Invention
[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a reverse design method and system for three-dimensional photonic devices, which solves the technical problem that the existing technology is incompatible with three-dimensional photonic manufacturing technology and it is difficult to achieve precise manufacturing.
[0005] To achieve the above objectives, the present invention provides a reverse design method for three-dimensional photonic devices, comprising the following steps:
[0006] S1. Establish a physical field simulation model for the three-dimensional photonic device. Mesh the physical field simulation model using cylindrical voxels as units and initialize the density variable of each unit. The density variable of the unit is a normalized representation of the unit height.
[0007] S2. Perform density filtering and projection calculations on the density variables of each element in sequence, and set the density variables of each element to the corresponding projection results.
[0008] S3. Use a physical field simulation model to obtain the current light field intensity and distribution, and determine whether the iteration cutoff condition is met. If so, obtain the optimal height distribution of each unit based on the current density variable of each unit, and finally obtain a photonic device that meets the design requirements, and the operation ends; otherwise, update the density variable of each unit respectively, and go to step S2 for iteration; wherein, the iteration cutoff condition includes: the difference between the current light field intensity and the preset intensity threshold reaches the first preset value, and the difference between the current light field distribution and the corresponding preset distribution threshold reaches the second preset value.
[0009] More preferably, the density variable after density filtering is discretely projected using an approximate Heaviside projection function; the projection result corresponding to the i-th cell is:
[0010]
[0011] in, β is the density variable of the i-th unit after density filtering; β is the discrete control parameter; and η is the projection threshold.
[0012] More preferably, in each iteration, the projection threshold η for the current iteration is obtained by minimizing the projection cost function; the expression for the projection cost function is:
[0013]
[0014] Where, N i v is the set of indices of all elements within a radius R around the i-th element; R is a preset radius; j Let be the volume of the j-th unit.
[0015] More preferably, the discrete control parameter β gradually increases with the increase of the number of iterations; the above-mentioned iteration cutoff conditions include: the difference between the current light field intensity and the preset intensity threshold reaches a first preset value, the difference between the current light field distribution and the corresponding preset distribution threshold reaches a second preset value, and the current discrete control parameter β reaches a third preset value.
[0016] More preferably, after density filtering is performed on the density variable of each cell within a radius of R around it, smoothing is performed to obtain the density variable of each cell after density filtering.
[0017] The density variable of the i-th cell after density filtering is:
[0018]
[0019] Where, N iLet ρ be the set of indices of all elements within a radius R around the i-th element; R is a preset radius; ρ j v is the density variable of the j-th unit; j w represents the volume of the j-th unit. ij The weighting factor is determined by the distance between the i-th cell and the j-th cell surrounding it.
[0020] More preferably, the above-mentioned weighting factor w ij for:
[0021] w ij =Rd ij
[0022] Where, d ij Let be the distance between the i-th unit and its surrounding j-th units; specifically, and These are the coordinates of the i-th cell and the j-th cell surrounding it, respectively.
[0023] More preferably, the above-mentioned columnar voxels include: cylindrical voxels or prismatic voxels.
[0024] In a second aspect, the present invention provides a reverse design system for three-dimensional photonic devices, comprising: a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the reverse design method for three-dimensional photonic devices provided in the first aspect of the present invention.
[0025] Thirdly, the present invention also provides a computer-readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls the device containing the storage medium to perform the reverse design method for a three-dimensional photonic device provided in the first aspect of the present invention.
[0026] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:
[0027] 1. This invention provides a reverse design method for three-dimensional photonic devices. The physical field simulation model is meshed using cylindrical voxels as units. The refractive index of the device is characterized by the height distribution of the units. The optimal height distribution can be obtained by minimizing the difference between the light field intensity and the preset intensity threshold, as well as the difference between the current light field distribution and the corresponding preset distribution threshold. This method can effectively avoid the misalignment of holes between upper and lower layers and edge skew that are easy to occur in conventional reverse design. It is compatible with existing manufacturing technologies, makes it easier to achieve precise manufacturing, and effectively improves the performance of existing photonic components.
[0028] 2. The reverse design method for three-dimensional photonic devices provided by this invention allows the mesh to be divided as needed, and its size can be arbitrarily selected to adapt to the resolution of specific photonic device manufacturing technologies. Under compatible manufacturing conditions, it is only necessary to adjust the size of the mesh in the model to adapt to different resolution requirements. The smaller the mesh, the higher the resolution, and vice versa.
[0029] 3. The reverse design method provided by this invention uses the same mesh division in each iteration, which greatly reduces the optimization time.
[0030] 4. In traditional photonic device design, corresponding systems need to be designed for different wavelengths, otherwise noise will affect the design or greatly reduce computational efficiency. However, this invention only requires modification of parameters and mesh when establishing the physical model to realize the manufacturable design of free space and integrated photonic devices for different wavelengths.
[0031] 5. Furthermore, the reverse design method provided by the present invention sets the value with the smallest change in device volume after filtering as the projection threshold for each iteration, so as to minimize the impact of the projection algorithm on the current iteration result while realizing variable projection, thereby further improving the optimization efficiency and obtaining a better projection effect. Attached Figure Description
[0032] Figure 1 This is a flowchart of the reverse design method for a three-dimensional photonic device provided in Embodiment 1 of the present invention;
[0033] Figure 2 This is a schematic diagram of a cubic voxel unit under different density variables provided in Embodiment 1 of the present invention;
[0034] Figure 3 This is a schematic diagram of the reverse design of chiral nanostructures provided in Embodiment 1 of the present invention;
[0035] Figure 4 The density values ρ of a certain element before and after discretization by an approximate Heaviside projection function under different layer projections provided in Embodiment 1 of the present invention are shown. filt ρ ft And a schematic diagram of the relationship between β; where (a) is the density value ρ of a certain element before and after discretization by the approximate Heaviside projection function under three-layer projection. filt ρ ft (a) A schematic diagram showing the relationship between β and β; (b) The density values ρ of a certain element before and after discretization by the approximate Heaviside projection function under five-layer projection. filt ρ ft And a diagram illustrating the relationship between β and β. Detailed Implementation
[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0037] Example 1
[0038] A reverse design method for three-dimensional photonic devices, such as Figure 1 As shown, it includes the following steps:
[0039] S1. Establish a physical field simulation model for the three-dimensional photonic device. Mesh the physical field simulation model using cylindrical voxels as units and initialize the density variable of each unit. The density variable of the unit is a normalized representation of the unit height.
[0040] Specifically, methods such as the Optimality Criteria Method (OC) and Mathematical Programming (MP) can be used to establish physical field simulation models for three-dimensional photonic devices. After obtaining the physical field simulation model of the three-dimensional photonic device, the design region in the physical field simulation model is meshed.
[0041] This invention uses cylindrical voxels as the unit for meshing the physics simulation model, effectively avoiding issues such as misalignment of holes between layers and edge distortion that easily occur in conventional reverse engineering. This facilitates subsequent etching and other processing methods and is compatible with existing manufacturing technologies. The cylindrical voxels can be cylindrical, prismatic, or other columnar voxels; the prismatic voxels can be cubic, cuboid, hexagonal, octagonal, etc. Specifically, as... Figure 2 The diagram shows a cubic voxel unit under different density variables; black represents solids, and white represents the medium in contact with the solids. In the calculations, the height is represented by the proportion of the solid portion (i.e., the density variable), thus the refractive index of each unit is characterized by the solid height. Changes in the voxel's solid height alter the refractive index of each unit; the higher the height, the closer the refractive index is to that of an optically denser medium; the lower the height, the closer the refractive index is to that of an optically less dense medium. Therefore, the height distribution is crucial for the light field intensity and distribution of three-dimensional photonic devices. Furthermore, the mesh can be divided as needed, with its length and width arbitrarily chosen to adapt to the resolution of specific photonic device manufacturing technologies. Taking chiral nanostructures as an example, the meshing of chiral nanostructures is as follows: Figure 3The diagram illustrates the design results obtained by reverse designing a chiral nanostructure with left-circularly polarized (LCP) and right-circularly polarized (RCP) light selectivity using the reverse design method provided by this invention. This design can maximize the transmission of LCP light through the zero-order diffraction order and redirect the transmission of RCP light to the first-order diffraction order or into reflection. The magnified part is a schematic diagram of a unit structure. This invention uses a wavelength of 520 nm as an example; therefore, the design region of a unit is a square with a side length of 500 nm. Each voxel has a length and width of 100 nm and a height of 340 nm. Below the optimization layer is a 300 nm thick titanium dioxide waveguide layer, and the substrate is silicon dioxide. The LCP and RCP light sources are emitted from the top of this structure. The parameters of the unit structure schematic diagram are h: 340 nm, w: 100 nm, t: 300 nm, p: 500 nm, where t is the thickness of the titanium dioxide waveguide layer, h is the optimizable height of the voxel, w is the side length of the square grid, and p is the total side length of a unit structure.
[0042] The refractive index of each unit is calculated by introducing a density variable. The formula used for refractive index calculation is:
[0043]
[0044] Where, n i Let be the refractive index of the i-th unit, e1 be the refractive index of the optically less dense medium, e2 be the refractive index of the optically denser medium, and ρ be the refractive index of the i-th unit. i is the density variable of the i-th cell, used to represent the normalized result of the cell height. It is a variable introduced for ease of calculation, and its value ranges between 0 and 1. The initial value of the cell density can be assigned any real number between 0 and 1; different initial values will not affect the final optimization result.
[0045] S2. Perform density filtering and projection calculations on the density variables of each element in sequence, and set the density variables of each element to the corresponding projection results.
[0046] In this embodiment, the density variable of each cell is filtered within a radius of R around it and then smoothed to obtain the density result of each cell after density filtering.
[0047] Specifically, the density result of the density variable of the i-th unit after density filtering is:
[0048]
[0049] Where, N i Let ρ be the set of indices of all elements within a radius R around the i-th element; R is a preset radius; ρ j v is the density variable of the j-th unit;j Let v be the volume of the j-th element. Since the mesh of the model remains unchanged during the iteration process, v j It is a constant; w ij The weighting factor is determined by the distance between the i-th unit and its surrounding j-th units, specifically: w ij =Rd ij ; where d ij Let be the distance between the i-th cell and the j-th cell surrounding it.
[0050] Furthermore, approximate Heaviside projection functions, Sigmoid functions, etc., can be used to perform projection calculations on the density variables after density filtering. In this embodiment, the approximate Heaviside projection function is used to perform projection calculations (discretization) on the density variables after density filtering, and the projection result corresponding to the i-th cell is as follows:
[0051]
[0052] in, It is the density projection value of the i-th cell obtained by approximating the Heaviside projection function; β represents the density variable of the i-th unit after density filtering; β is the discretization control parameter used to control the sharpness of the discretization process. The larger the value of β, the higher the degree of dispersion of the variable. In this embodiment, the discretization control parameter β gradually increases with the number of iterations. Figure 4 As shown, under different layer projections, the density values ρ of a certain element before and after discretization by the approximate Heaviside projection function are... filt ρ ft And a schematic diagram of the relationship between β; wherein, Figure (a) shows the density values ρ of a certain element before and after discretization by the approximate Heaviside projection function under three-layer projection. filt ρ ft And a schematic diagram of the relationship between β; Figure (b) shows the density values ρ of a certain element before and after discretization by the approximate Heaviside projection function under five-layer projection. filt ρ ft The diagram illustrates the relationship between β and density variable. As can be seen from the diagram, after discrete projection using the approximate Heaviside projection function, the density variable becomes more discrete as the value of β increases. In this embodiment, the discrete control parameter β gradually increases with the number of iterations.
[0053] Furthermore, η is the projection threshold, which can be preset; however, in this embodiment, in order to minimize the impact of the projection algorithm on the current iteration result while realizing variable projection, the value that minimizes the change in device volume after filtering is set as the projection threshold for each iteration, so as to improve optimization efficiency and obtain better projection effect; specifically, in each iteration, the projection threshold η under the current iteration is obtained by minimizing the projection cost function; the expression of the projection cost function is:
[0054]
[0055] Where, N i v is the set of indices of all elements within a radius R around the i-th element; R is a preset radius; j Let be the volume of the j-th unit.
[0056] S3. Obtain the current light field intensity and distribution using a physical field simulation model, and determine whether the iteration cutoff condition is met. If so, obtain the optimal normalized height of each unit based on the current density variable of each unit, and then obtain the optimal height distribution of each unit, ultimately obtaining a photonic device that meets the design requirements, and the operation ends; otherwise, update the density variable of each unit separately, and proceed to step S2 for iteration. The iteration cutoff condition includes: the difference between the current light field intensity and the preset intensity threshold reaches a first preset value, and the difference between the current light field distribution and the corresponding preset distribution threshold reaches a second preset value. The first and second preset values are both small values close to 0; in this embodiment, the first preset value is 0.005, and the second preset value is 0.5.
[0057] It should be noted that this invention is equivalent to solving the objective function problem, that is, determining the optimal value of the density variable for each unit by simultaneously minimizing the difference between the light field intensity and a preset intensity threshold, and the difference between the light field distribution and the corresponding preset distribution threshold. Specifically, gradient descent, Global Convergence Moving Asymptote Method (GCMMA) can be used to optimize the variables, while Moving Asymptote Method (MMA), OC, and other methods can be used to solve the problem of minimizing the performance cost function.
[0058] Taking iterative descent as an example, the chain gradient method is used to obtain the objective function with respect to the density variable ρ. j The gradient is obtained using the following formula:
[0059]
[0060] in, For ρ j The expression for the derivative is:
[0061]
[0062] f is the objective function. In the design of this chiral nanostructure, the objective function to be minimized is:
[0063]
[0064] The objective function maximizes the difference in transmission between LCP and RCP light to the 0th order diffraction order, meaning the LCP light diffracts to the zeroth order and the RCP light diffracts to the first order {(1,0), (0,1), (-1,0), and (0,-1)} or is reflected. If the input is LCP light, the objective function requires maximizing the light field intensity at the zeroth order; if the input is RCP light, the objective function requires maximizing the light field intensity at the first order.
[0065] Preferably, in each iteration, the sensitivity of the density variable is calculated using the adjoint sensitivity method to guide the update direction of the density variable in each iteration.
[0066] During the optimization process, the density variable ρ i The value must be between 0 and 1. To avoid discretization errors, the continuity and differentiability of variables are maintained during the optimization process. The objective function is minimized by the algorithm under constraints. In this embodiment, β gradually increases during the iteration process. Therefore, when both the objective function and the design variables converge, and β increases to the discretization requirement (β reaches the third preset value, which is 2 in this embodiment), the algorithm will continue to optimize the process. 9 When the value reaches 0, the optimization is considered complete.
[0067] Example 2
[0068] A reverse design system for a three-dimensional photonic device includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the reverse design method for a three-dimensional photonic device provided in Embodiment 1 of the present invention.
[0069] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.
[0070] Example 3
[0071] A computer-readable storage medium includes a stored computer program, wherein when the computer program is run by a processor, it controls the device where the storage medium is located to execute the reverse design method for a three-dimensional photonic device provided in Embodiment 1 of the present invention.
[0072] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.
[0073] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A reverse design method for a three-dimensional photonic device, characterized in that, Includes the following steps: S1. Establish a physical field simulation model for the three-dimensional photonic device. Divide the physical field simulation model into a mesh using cylindrical voxels as units, and initialize the density variable of each unit. The density variable of the unit is a normalized representation of the unit height. S2. Perform density filtering and projection calculations on the density variables of each element in sequence, and set the density variables of each element to the corresponding projection results. The density variables after density filtering are discretely projected using an approximate Heaviside projection function; the projection result corresponding to the i-th cell is: in, β is the density variable of the i-th unit after density filtering; β is the discrete control parameter; η is the projection threshold. S3. Using the physical field simulation model, obtain the current light field intensity and distribution, and determine whether the iteration cutoff condition is met. If yes, obtain the optimal height distribution of each unit based on the current density variable of each unit, and the operation ends; otherwise, update the density variable of each unit respectively, and go to step S2 for iteration; wherein, the iteration cutoff condition includes: the difference between the current light field intensity and the preset intensity threshold reaches a first preset value, and the difference between the current light field distribution and the corresponding preset distribution threshold reaches a second preset value; In each iteration, the projection threshold η is obtained by minimizing the projection cost function for the current iteration; The expression for the projection cost function is: Where, N i v is the set of indices of all elements within a radius R around the i-th element; R is a preset radius; j Let be the volume of the j-th unit.
2. The reverse engineering method according to claim 1, characterized in that, The discrete control parameter β gradually increases with the increase of the number of iterations; The iteration cutoff conditions include: the difference between the current light field intensity and the preset intensity threshold reaches a first preset value, the difference between the current light field distribution and the corresponding preset distribution threshold reaches a second preset value, and the current discrete control parameter β reaches a third preset value.
3. The reverse engineering method according to claim 1, characterized in that, After density filtering of the density variable of each cell within a radius of R, smoothing is performed to obtain the density variable of each cell after density filtering. The density variable of the i-th cell after density filtering is: Where, N i Let ρ be the set of indices of all elements within a radius R around the i-th element; R is a preset radius; ρ j v is the density variable of the j-th unit; j w is the volume of the j-th unit; ij The weighting factor is determined by the distance between the i-th cell and the j-th cell surrounding it.
4. The reverse engineering method according to claim 3, characterized in that, Weighting factor w ij for: w ij =R-d ij Where, d ij Let be the distance between the i-th cell and the j-th cell surrounding it.
5. The reverse engineering method according to any one of claims 1-4, characterized in that, The columnar voxels include: cylindrical voxels or prismatic voxels.
6. A reverse design system for a three-dimensional photonic device, characterized in that, include: A memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the reverse engineering method according to any one of claims 1-5.
7. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein when the computer program is run by a processor, it controls the device containing the storage medium to perform the reverse engineering method according to any one of claims 1-5.