A mode analysis and mobile asymptote method for topology optimization of hollow core optical fibers

Abstract

This invention relates to the field of optical fiber communication technology and discloses a hollow-core optical fiber topology optimization method based on mode analysis and moving asymptote method. This method constructs a hollow-core optical fiber topology optimization design system, which includes a geometric modeling module, a material parameterization module, a mode analysis solution module, an adjoint sensitivity module, an MMA update module, a continuous scheduling module, and a geometric shaping and verification module. By employing a hyperbolic tangent projection function, a grayscale imaginary part penalty term, and a multi-stage continuous strategy, grayscale suppression and binarization are performed to avoid interface blurring caused by grayscale materials and significant performance degradation after shaping. Ultimately, this ensures the consistency between the design results and actual manufacturing performance. Through the collaboration and continuous scheduling of each module, stable convergence of the optimization process and automatic generation of manufacturable structures are achieved. Therefore, this invention method possesses advantages such as a wide design space, strong structural manufacturability, stable optimization process, and improved performance.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication technology, specifically to a method for optimizing the topology of hollow optical fibers using mode analysis and the moving asymptote method. Background Technology

[0002] Hollow-core optical fibers (such as anti-resonant hollow-core fibers and photonic bandgap hollow-core fibers) are a novel type of optical waveguide structure. Their design typically employs parametric geometry methods: several geometric parameters, including circular / elliptical tubes, wall thickness, tube spacing, and support ribs, are pre-defined, and optimization is performed within a finite parameter space using parameter scanning or genetic algorithms / particle swarm optimization. Evaluation metrics include confinement loss, effective refractive index, mode area, and polarization characteristics. This type of method relies on artificially assumed structural topologies (e.g., "6-tube," "8-tube," "nested tube"), and then optimizes the dimensions within these topologies.

[0003] Another approach is density-based topology optimization: a continuous design variable field (density field) is introduced within a given design domain, and the density is mapped to dielectric constant / refractive index through material interpolation. An objective function is constructed on the electromagnetic wave finite element model, and the density field is iteratively updated using adjoint sensitivity and gradient-type algorithms (such as MMA), thereby automatically generating structures in a larger design space.

[0004] However, both of the aforementioned existing technologies have significant drawbacks in practical applications. Specifically, existing technologies can be divided into two categories: one is parameterized scanning or heuristic algorithm optimization that relies on preset geometric topologies (such as the number of tubes, tube diameter, and support ribs). Its design space is severely limited, making it difficult to discover entirely new low-loss configurations beyond the preset structure. The other is density-based topology optimization, which, although capable of exploring structures in a larger space, suffers from three major drawbacks when applied to the special scenario of hollow-core optical fiber: First, the intermediate density value (grayscale) disrupts the clear air-medium interface, the foundation of light guiding, leading to a collapse in the performance of the optimized structure; second, hollow-core optical fiber, as an open-domain leakage problem, is highly sensitive to boundary conditions and associated sensitivity chains in its mode analysis, easily causing divergence or mode jumping in the optimization process; and third, the lack of effective geometric constraints (such as minimum feature size and volume fraction control) results in a large number of isolated fragments or sharp corners in the optimization results, failing to meet the engineering requirements of actual fabrication. Summary of the Invention

[0005] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a hollow fiber topology optimization method based on pattern analysis and moving asymptote method. This method has the advantages of wide design space, strong structural manufacturability, stable optimization process, and significant performance improvement. It solves the problems in existing technologies, such as design space limitation due to preset topology, non-physical grayscale material generated by traditional topology optimization, unstable solution due to open domain leakage, and fragmented optimization results that are difficult to manufacture.

[0006] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: a method for optimizing the topology of hollow optical fibers using pattern analysis and the moving asymptote method, comprising the following steps: S1. System Construction: Construct a hollow-core optical fiber topology optimization design system. The system has built-in geometric modeling module, material parameterization module, mode analysis solution module, adjoint sensitivity module, MMA update module, continuous scheduling module, and geometric shaping and verification module. S2. Establish fiber cross-section model: Based on the geometric modeling module, establish a two-dimensional fiber cross-section model, delineate the corresponding functional regions and define the integral operator; S3, Material Parametric Mapping: The material parametric module constructs a density design field, obtains a binary approximation variable through projection function processing, and then completes refractive index interpolation and grayscale penalty settings; S4. Electromagnetic mode solution modeling: The mode analysis and solution module builds an electromagnetic wave solution model, sets the guided mode characterization method and absorption boundary, and ensures the stability of open domain leakage solution. S5. Constructing a comprehensive optimization objective function: The pattern analysis and solution module combines loss limitation, volume fraction constraint and regularization penalty term to construct a comprehensive objective function that takes into account low loss, low fill rate and structural manufacturability. S6. Gradient Calculation and Variable Iterative Update: The sensitivity module and the MMA update module jointly calculate the gradient of the design variable and iteratively update the density field using the moving asymptote method. S7. Multi-stage continuous scheduling: The continuous scheduling module adjusts and optimizes parameters in stages to optimize convergence and the binarization and manufacturability of the final structure; S8. Structural Determination and Performance Verification: The geometric determination and verification module performs binarization on the optimized density field, reconstructs the geometric structure, and recalculates the performance.

[0007] Preferably, in S1: the geometric modeling module is used to establish a geometric model of the cross-section of the hollow fiber, define the central hollow region, the cladding design domain and the outer boundary absorption layer, and set the integration operators intop1, intop2 and intopD; The material parameterization module is used to define the design variable field θ(x,y) and obtain the projected density field through projection and filtering. Constructing complex refractive index based on refractive index interpolation This enables the material transition from air to silicon dioxide. The mode analysis solution module is used to solve the propagation constant and electromagnetic field distribution of the guided mode based on electromagnetic wave frequency domain mode analysis, and uses PML absorbing boundary to simulate open domain leakage. The adjoint sensitivity module is used to calculate the gradient of the objective function with respect to the design variables using the discrete adjoint method, thus avoiding variable-wise perturbation. The MMA update module is used to update the design variable field θ using the moving asymptote method, and sets a moving limit to control the maximum change of the variable in each iteration. The continuous scheduling module is used to execute a multi-stage continuous strategy, gradually adjusting the projection slope β and the grayscale penalty coefficient. and volume fraction target ; The geometry shaping and verification module is used to threshold the final density field, reconstruct the binary geometric structure, and use high-precision grid recalculation to limit the loss.

[0008] Preferably, in S2: the geometric modeling module is responsible for optical fiber geometric modeling, region division and boundary setting, and establishes two-dimensional or 2.5D hollow fiber cross-sectional geometry. The overall model is divided into a central hollow region, a cladding design domain and an outer boundary absorption layer. The central hollow region is fixed as air, the cladding design domain is a variable material region, and the outer boundary preferably adopts a PML absorption layer to simulate an open-domain electromagnetic wave leakage scenario.

[0009] Preferably, in S2, the geometric modeling module simultaneously defines three types of integral operators, clarifying the area of ​​action and function of each operator: (1) intop1: Acts on the central hollow core or core measurement region, used to calculate the electromagnetic field distribution and energy concentration parameters related to the core region in the objective function; (2) intop2: applies to the entire domain or a specified normalized region, and is used to calculate the global electromagnetic energy and total power flow; (3) intopD: Acts on the cladding design domain and is used to calculate the material volume fraction and perimeter penalty value.

[0010] Preferably, in step S3: the material parameterization module is responsible for design variable construction, material refractive index mapping, and grayscale suppression processing, as follows: (1) Construct the design variable field, and denote the density field as θ(x,y)∈[0,1], which is the core control variable for topology optimization, with initial values ​​of Take 0.5; (2) The hyperbolic tangent projection function is used to map the smooth density field into a variable that is closer to a binary distribution. The projection formula is: ; In the formula, β represents the projection slope; the larger the slope, the stronger the binarization effect. denoted by hyperbolic tangent projection operator, Ƞ represents the projection threshold, and θ represents the density field control variable, with a value range of [0,1]. (3) Perform real part interpolation of the refractive index. Within the cladding design domain, the effective real part of the refractive index changes linearly with the projection variable, specifically satisfying: ,in, The effective real part of the refractive index within the cladding design domain, and the air refractive index. Refractive index of silicon dioxide , These are binary approaching variables after projection processing; (4) Add a grayscale imaginary part penalty term, introduce artificial damping to suppress intermediate grayscale materials, and ensure a clear interface between air and silica. The formula for calculating the imaginary part is: ,in, This represents the imaginary part of the effective refractive index within the cladding design domain. The penalty coefficient is... This is the lower bound for numerical stability. (5) An optional inverse interpolation of the dielectric constant can be used to further enhance the two-phase contrast of the material. The formula is as follows: , Effective refractive index ,in, Indicates the inverse interpolation dielectric constant. Represents the effective dielectric constant, air dielectric constant The dielectric constant of silicon dioxide .

[0011] Preferably, in S4: the mode analysis and solution module is responsible for electromagnetic field solution, mode analysis, and boundary condition configuration, and adopts electromagnetic wave frequency domain and full-field three-component vector mode analysis, through out-of-plane wavenumber... Characterize the fiber guiding mode, where α is the propagation constant; the outer boundary is preferably selected as the PML absorption layer to simulate the open domain electromagnetic wave leakage scenario. When the use of scattering boundary or transition boundary causes the analytical derivative chain to be unclosed and the solution to fail, immediately switch to the PML absorption layer.

[0012] Preferably, in step S5: the pattern analysis and solution module superimposes volume fraction constraints and perimeter smoothing penalties to construct a complete optimization objective system, as follows: (1) The core objective is to minimize the limiting loss, in dB / m, which serves as the main guideline for topology optimization; (2) Add the normalized field energy ratio as an auxiliary target to enhance the energy concentration in the core region and suppress leakage. The formula is: ; In the formula, Obj represents the normalized field energy ratio, intop1 represents the measurement region acting on the central hollow core or core, and intop2 represents the measurement region acting on the entire domain or a specified normalized region. The electric field strength of the electromagnetic field; (3) Calculate the material volume fraction and apply a penalty, design the domain area. Material volume Volume fraction The volume penalty term is ; (4) Add a perimeter smoothing penalty and define the gradient squared term as: θ(x,y) represents the original design variable field, and x and y represent the cross-sectional coordinates. The spatial derivatives of the design variables in two directions are given, and the perimeter / smoothing penalty term is further defined. for: grad2 represents the squared gradient; (5) Construct a comprehensive objective function, unifying it into a minimization form: , Represents the overall objective function. Represents the main objective function. Indicates the perimeter / smoothing penalty weight. Indicates the volume penalty weight. This indicates a volume penalty.

[0013] Preferably, in step S6: the sensitivity module and the MMA update module are executed collaboratively. The sensitivity module uses the discrete adjoint method to calculate the gradient of the objective function. Through one forward modeling and one adjoint modeling, the gradient values ​​of all design variables are obtained. The MMA update module uses the moving asymptote method to iteratively update the design variable field θ, sets reasonable moving limits, and controls the maximum change of the design variables in each iteration.

[0014] Preferably, in step S7: the continuous scheduling module adopts a multi-stage continuous iteration strategy: (1) Gradually increase the projection slope β. In the early stage, a small slope ensures the stability of gradient calculation, and in the later stage, a large slope strengthens the binarization of the structure. (2) Gradually reduce the gray level penalty coefficient The grayscale is suppressed by a high coefficient in the early stage, and the coefficient is reduced after the structure is formed; (3) Gradually reduce the target value of volume fraction. First, ensure the structure is formed, and then gradually fit the engineering requirements of low fill rate and low leakage of hollow optical fiber. (4) Controlling the filter radius And the grid size, ensuring the ratio of the filter radius to the grid size. It remains at 3-6.

[0015] Preferably, in step S8: the geometry shaping and verification module is responsible for the binary reconstruction of the structure and the final performance verification, and outputs a manufacturable qualified optical fiber structure; a threshold of 0.5 is selected to perform threshold segmentation on the final optimized projection density field, reconstruct the air-silica binary geometry, and obtain a regular structure that can be industrially manufactured; a high-precision grid is used to perform pattern analysis on the shaped geometry and generate the final hollow fiber design report.

[0016] Compared with existing technologies, this invention provides a method for optimizing the topology of hollow optical fibers using pattern analysis and the moving asymptote method, which has the following advantages: 1. This invention introduces a continuous density field that does not require a preset number of tubes / rib topology as a design variable, and adopts adjoint sensitivity and MMA iterative updates to achieve the technical effect of automatically generating complex cladding structures such as multi-layer rings, connecting ribs, and double rings in a larger design space. This breaks through the design space limitations of traditional parametric methods and provides the possibility for exploring the globally optimal structure.

[0017] 2. This invention employs a hyperbolic tangent projection function, a grayscale imaginary part penalty term, and a multi-stage continuousization strategy (such as gradually increasing the projection slope β) to effectively suppress intermediate density values ​​(grayscale) that occur during the optimization process. This makes the final output structure closer to a pure air / silica binary distribution, thereby effectively avoiding interface blurring and significant performance degradation after shaping caused by grayscale materials, and ultimately ensuring the consistency between the design results and actual manufacturing performance.

[0018] 3. By introducing a volume fraction penalty term and filtering radius control, and combining the movement constraint strategy of the moving asymptote method, this invention achieves the technical effects of precisely controlling the material ratio, forcibly realizing a low filling rate, and ensuring that the minimum feature size meets manufacturing requirements. It can effectively solve the problem of unmanufacturability caused by fragmentation, disconnection, or too many sharp corners in the topology optimization results in traditional technologies, and greatly improve the engineering feasibility of existing optimization schemes.

[0019] 4. This invention optimizes the PML absorbing boundary and uses the discrete adjoint method for gradient calculation, combined with... The lower bound damping term effectively avoids the problem of open domain leakage, which can lead to non-closed analytical derivative chains, solution failures, or drastic fluctuations in the objective function. This improves the numerical stability, convergence reliability, and repeatability of the optimization process. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the cross-section and design domain of the hollow fiber of the present invention; Figure 3 This is a schematic diagram illustrating the geometric parameters and integration region definition of the model of the present invention; Figure 4 When the method of this invention is applied to an example, the generated geometric results and modulus field diagram are optimized; in( Figure 2 ), 1. Hollow area; 2. Design domain; 3. Fixed material area; 4. External PML layer. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please see Figures 1-4 A method for optimizing the topology of hollow-core optical fibers using pattern analysis and the moving asymptote method, comprising the following steps: S1. System Construction: Construct a hollow fiber topology optimization design system for topology optimization in reverse design of hollow fiber. The system has built-in geometric modeling module, material parameterization module, mode analysis solution module, adjoint sensitivity module, MMA update module, continuous scheduling module, and geometric shaping and verification module. S2. Establish fiber cross-section model: Based on the geometric modeling module, establish a two-dimensional fiber cross-section model, delineate the corresponding functional regions and define the integral operator; S3, Material Parametric Mapping: The material parametric module constructs a density design field, obtains a binary approximation variable through projection function processing, and then completes refractive index interpolation and grayscale penalty settings; S4. Electromagnetic mode solution modeling: The mode analysis and solution module builds an electromagnetic wave solution model, sets the guided mode characterization method and absorption boundary, and ensures the stability of open domain leakage solution. S5. Constructing a comprehensive optimization objective function: The pattern analysis and solution module combines loss limitation, volume fraction constraint and regularization penalty term to construct a comprehensive objective function that takes into account low loss, low fill rate and structural manufacturability. S6. Gradient Calculation and Variable Iterative Update: The sensitivity module and the MMA update module jointly calculate the gradient of the design variable and iteratively update the density field using the moving asymptote method. S7. Multi-stage continuous scheduling: The continuous scheduling module adjusts and optimizes parameters in stages, taking into account both optimization convergence and the binarization and manufacturability of the final structure. S8. Structural Determination and Performance Verification: The geometric determination and verification module performs binarization on the optimized density field, reconstructs the geometric structure, and recalculates the performance.

[0023] Specifically, the geometric modeling module in S1 is used to establish the geometric model of the hollow fiber cross section, define the central hollow region, the cladding design domain and the outer boundary absorption layer, and set the integration operators intop1, intop2 and intopD; The material parameterization module is used to define the design variable field θ(x,y) and obtain the projected density field through projection and filtering. Constructing complex refractive index based on refractive index interpolation This enables the material transition from air to silicon dioxide. The mode analysis solution module is used to solve the propagation constant and electromagnetic field distribution of the guided mode based on electromagnetic wave frequency domain mode analysis, and uses PML absorbing boundary to simulate open domain leakage. The adjoint sensitivity module is used to calculate the gradient of the objective function with respect to the design variables using the discrete adjoint method, avoiding variable-wise perturbations. The MMA update module is used to update the design variable field θ using the moving asymptote method, and sets a moving limit to control the maximum change of the variable in each iteration. The continuous scheduling module is used to execute a multi-stage continuous strategy, gradually adjusting the projection slope β and the grayscale penalty coefficient. and volume fraction target ; The geometry shaping and verification module is used to threshold the final density field, reconstruct the binary geometric structure, and use high-precision grid recalculation to limit the loss.

[0024] Specifically, the geometry modeling module in S2 is responsible for fiber geometry modeling, region division, and boundary setting, providing a basic computational domain for subsequent optimization; it establishes the geometry of a two-dimensional or 2.5D hollow fiber cross-section, and the overall model is divided into a central hollow region, a cladding design domain, and an outer boundary absorption layer. The central hollow region is fixed as air, the cladding design domain is a variable material region, and the outer boundary preferably adopts a PML absorption layer to simulate open-domain electromagnetic wave leakage scenarios.

[0025] The advantages are: by accurately dividing functional areas, fixing hollow media, and selecting appropriate absorption layers, a solid foundation for optimized calculation is established, which fits the actual working scenario of hollow optical fiber and accurately simulates open domain leakage conditions, providing a standardized and stable computational domain for subsequent electromagnetic solutions and topology iterations.

[0026] Specifically, the geometric modeling module in S2 synchronously defines three types of integral operators, clarifying the scope and function of each operator: (1) intop1: Acts on the central hollow or core measurement area to calculate the electromagnetic field distribution, energy concentration and other parameters related to the core area in the objective function, and to evaluate the energy gathering effect of the light guide area; (2) intop2: operates on the entire domain or a specified normalized region, used to calculate the global electromagnetic energy and total power flow, and works with intop1 to achieve energy parameter normalization. (3) intopD: operates on the cladding design domain and is specifically used to calculate the material volume fraction and perimeter penalty value, control the optimized structural morphology, and avoid the occurrence of fragmented and unmanufacturable structures.

[0027] The advantages are: by having three types of integral operators work together, the energy parameters can be accurately calculated and the structural morphology can be effectively controlled, ensuring the quantification of the objective function. At the same time, the structural fragmentation and deformity can be avoided from the source, taking into account both the accuracy of performance evaluation and the regularity of the structure.

[0028] Specifically, the material parameterization module in S3 is executed. This module is responsible for design variable construction, material refractive index mapping, and grayscale suppression processing to ensure that the material distribution conforms to the characteristics of the air-silica two-phase system. (1) Construct the design variable field, and denote the density field as θ(x,y)∈[0,1], which is the core control variable for topology optimization, with initial values ​​of Take 0.5; (2) The hyperbolic tangent projection function is used to map the smooth density field into a variable that is closer to a binary distribution. The projection formula is: ; In the formula, β represents the projection slope; the larger the slope, the stronger the binarization effect. Ƞ represents the hyperbolic tangent projection operator, which is used to squeeze the continuous density field toward the binary ends of 0 and 1, weakening the intermediate gray values; Ƞ represents the projection threshold, which is used to divide the boundary between air and medium; θ represents the density field control variable in step (1), with a value range of [0,1]. (3) Perform real part interpolation of the refractive index. Within the cladding design domain, the effective real part of the refractive index changes linearly with the projection variable, specifically satisfying: ,in, The effective real part of the refractive index within the cladding design domain, and the air refractive index. Refractive index of silicon dioxide , The binary approaching variable after projection processing in step (2); (4) Add a grayscale imaginary part penalty term, introduce artificial damping to suppress intermediate grayscale materials, and ensure a clear interface between air and silica. The formula for calculating the imaginary part is: ,in, This represents the imaginary part of the effective refractive index within the cladding design domain, used for grayscale suppression and numerical stabilization. The penalty coefficient is... To establish a lower limit for numerical stability and avoid computational ill-conditioning caused by approximate losslessness; (5) An optional inverse interpolation of the dielectric constant can be used to further enhance the two-phase contrast of the material. The formula is as follows: , Effective refractive index ,in, Indicates the inverse interpolation dielectric constant. Represents the effective dielectric constant, air dielectric constant The dielectric constant of silicon dioxide .

[0029] The advantages are: by constructing a design variable field, hyperbolic tangent projection, and refractive index interpolation combined with grayscale imaginary part penalty, the material distribution can be precisely controlled, effectively suppressing intermediate grayscale materials, avoiding non-physical mixing states, ensuring a clear air-silica interface, conforming to the actual material properties of hollow optical fibers, and improving the stability of numerical calculations.

[0030] Specifically, in S4, the mode analysis and solution module is executed. This module is responsible for electromagnetic field solving, mode analysis, and boundary condition configuration, ensuring the accuracy of electromagnetic parameter calculations during the optimization process. It employs electromagnetic wave frequency domain and full-field three-component vector mode analysis, using out-of-plane wavenumbers... The fiber guiding mode is characterized, where α is the propagation constant; the outer boundary is preferably selected as the PML absorption layer to accurately simulate the open domain electromagnetic wave leakage scenario. When the use of scattering boundary or transition boundary causes the analytical derivative chain to be unclosed and the accompanying solution to fail, the PML absorption layer is immediately switched to improve the stability of the accompanying solution.

[0031] The advantages are: by selecting vector mode analysis and adapting to PML absorbing boundaries, the open domain leakage field can be solved accurately, while avoiding the problems of derivative chain breakage and associated solution failure. This allows the electromagnetic parameter calculation to fit the actual working conditions, and ultimately ensures that the entire optimization iteration process proceeds smoothly and does not diverge.

[0032] Specifically, in S5, the pattern analysis and solution module takes loss limitation as the core objective, superimposed with volume fraction constraints and perimeter smoothing penalties to construct a complete optimization objective system: (1) The core objective is to minimize the limiting loss, in dB / m, which serves as the main guideline for topology optimization; (2) Add the normalized field energy ratio as an auxiliary target to enhance the energy concentration in the core region and suppress leakage. The formula is: ; In the formula, Obj represents the normalized field energy ratio, which measures the degree of energy concentration in the fiber core. A higher value indicates a higher energy concentration and lower leakage loss in the core. intop1 indicates the measurement area applied to the central hollow core or core region, while intop2 indicates the measurement area applied to the entire region or a specified normalized region. The electric field strength of the electromagnetic field; (3) Calculate the material volume fraction and apply a penalty, design the domain area. Material volume Volume fraction The volume penalty term is ; (4) Add a perimeter smoothing penalty to avoid sharp corners and fragmented shapes in the optimized structure. Define the gradient squared term as: θ(x,y) represents the original design variable field, and x and y represent the cross-sectional coordinates. The spatial derivatives of the design variables in two directions are given, and the perimeter / smoothing penalty term is further defined. for: grad2 represents the squared gradient; (5) Construct a comprehensive objective function, unifying it into a minimization form: , Represents the overall objective function. This represents the main objective function. When the main objective uses the normalized field energy ratio, since it is in a maximization form, it needs to be converted to a minimization form, i.e. , Indicates the perimeter / smoothing penalty weight. This represents the volume penalty weight, ensuring a unified objective and consistent optimization direction. This indicates a volume penalty.

[0033] The advantages are: by constructing a comprehensive objective function that combines a core objective with multiple regularized penalties, it takes into account low confinement loss, low material fill rate and structural regularity, which can ensure excellent optical fiber guiding performance, avoid structural deformities, and meet the requirements of hollow fiber engineering applications.

[0034] Specifically, in S6, the sensitivity module and the MMA update module work together. The adjoint sensitivity module is responsible for gradient calculation, while the MMA update module is responsible for iterative updating of design variables to ensure optimization convergence and stability. The discrete adjoint method is used to calculate the gradient of the objective function. By performing one forward modeling and one adjoint modeling, the gradient values ​​of all design variables are obtained without having to perturb each individual variable, thus improving computational efficiency. The moving asymptote method (MMA) is used to iteratively update the design variable field θ. Reasonable movement constraints are set to control the maximum change of design variables in each iteration, avoiding structural abrupt changes that could lead to non-convergence of the forward modeling and adjoint modeling, while also preventing fragmentation of the optimization structure.

[0035] The advantages are: the discrete adjoint method significantly improves the efficiency of gradient calculation, and the MMA algorithm strictly controls the iteration range of variables. It can not only balance optimization speed and convergence stability, but also eliminate structural mutation, solution collapse and structural fragmentation problems, so as to make the topology iteration smooth and orderly.

[0036] Specifically, in S7, the continuous scheduling module is executed. This module is responsible for the segmented adjustment of optimization parameters to achieve a balance between convergence and structural performance, and adopts a multi-stage continuous iteration strategy: (1) Gradually increase the projection slope β. In the early stage, a small slope ensures the stability of gradient calculation, and in the later stage, a large slope strengthens the binarization of the structure. (2) Gradually reduce the gray level penalty coefficient In the early stages, a high coefficient is used to suppress grayscale and ensure numerical stability. After the structure is formed, the coefficient is reduced to approximate the characteristics of real, non-destructive materials (this can correct the direction of parameter changes, similar to S3). (Maintain consistency between definitions and engineering logic) (3) Gradually reduce the target value of volume fraction. First, ensure the structure is formed, and then gradually fit the engineering requirements of low fill rate and low leakage of hollow optical fiber. (4) Controlling the filter radius And the grid size, ensuring the ratio of the filter radius to the grid size. Maintaining a value between 3 and 6 avoids structural fragmentation caused by the grid while preserving fine structures such as double-ring structures.

[0037] The advantages are: by adjusting and optimizing parameters in multiple stages, the optimization convergence and structural binarization effect are balanced, the structural precision and manufacturability are taken into account, and the actual engineering needs are gradually met, avoiding optimization failure due to aggressive parameters.

[0038] Specifically, in S8, the geometry shaping and verification module is executed. This module is responsible for the binarization reconstruction of the structure and the final performance verification, and outputs a manufacturable qualified optical fiber structure. A threshold of 0.5 is selected to perform threshold segmentation on the final optimized projection density field, reconstruct the air-silica binary geometry, remove the intermediate grayscale region, and obtain a regular structure that can be industrially manufactured. A high-precision grid is used to perform pattern analysis on the shaped geometry, recalculate key performance indicators such as limiting loss, verify the optimization effect, and generate the final hollow-core optical fiber design report.

[0039] The advantages are: by eliminating invalid grayscale areas through threshold binarization, a regular optical fiber structure that can be actually manufactured is restored, and then high-precision grid recalculation and verification are performed to ensure that the performance of the final output optical fiber structure meets the standards and has the feasibility of industrial mass production.

[0040] In summary, the method of this invention abandons the limitations of traditional preset topologies and automatically generates high-quality hollow fiber cladding structures within a large design space. Through the full-process control of material parameterization, grayscale suppression, stable electromagnetic solution, gradient iteration, multi-stage scheduling, and structural verification, it completely solves the pain points of traditional hollow fiber design, such as narrow design space, grayscale interference performance, unstable solution, and unmanufacturable structure. The final result is a hollow fiber structure with low confinement loss, low fill factor, and regular manufacturability, which balances optimization stability, light guiding performance, and engineering practicality, and is therefore applicable to the reverse topology optimization design of various hollow fibers.

[0041] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the topology of hollow-core optical fibers using pattern analysis and the moving asymptote method, characterized in that, Includes the following steps: S1. System Construction: Construct a hollow-core optical fiber topology optimization design system. The system has built-in geometric modeling module, material parameterization module, mode analysis solution module, adjoint sensitivity module, MMA update module, continuous scheduling module, and geometric shaping and verification module. S2. Establish fiber cross-section model: Based on the geometric modeling module, establish a two-dimensional fiber cross-section model, delineate the corresponding functional regions and define the integral operator; S3, Material Parametric Mapping: The material parametric module constructs a density design field, obtains a binary approximation variable through projection function processing, and then completes refractive index interpolation and grayscale penalty settings; S4. Electromagnetic mode solution modeling: The mode analysis and solution module builds an electromagnetic wave solution model, sets the guided mode characterization method and absorption boundary, and ensures the stability of open domain leakage solution. S5. Constructing a comprehensive optimization objective function: The pattern analysis and solution module combines loss limitation, volume fraction constraint and regularization penalty term to construct a comprehensive objective function that takes into account low loss, low fill rate and structural manufacturability. S6. Gradient Calculation and Variable Iterative Update: The sensitivity module and the MMA update module jointly calculate the gradient of the design variable and iteratively update the density field using the moving asymptote method. S7. Multi-stage continuous scheduling: The continuous scheduling module adjusts and optimizes parameters in stages to optimize convergence and the binarization and manufacturability of the final structure; S8. Structural Determination and Performance Verification: The geometric determination and verification module performs binarization on the optimized density field, reconstructs the geometric structure, and recalculates the performance.

2. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S1: the geometric modeling module is used to establish the geometric model of the hollow fiber cross section, define the central hollow region, the cladding design domain and the outer boundary absorption layer, and set the integration operators intop1, intop2 and intopD; The material parameterization module is used to define the design variable field θ(x,y) and obtain the projected density field through projection and filtering. Constructing complex refractive index based on refractive index interpolation This enables the material transition from air to silicon dioxide. The mode analysis solution module is used to solve the propagation constant and electromagnetic field distribution of the guided mode based on electromagnetic wave frequency domain mode analysis, and uses PML absorbing boundary to simulate open domain leakage. The adjoint sensitivity module is used to calculate the gradient of the objective function with respect to the design variables using the discrete adjoint method, thus avoiding variable-wise perturbation. The MMA update module is used to update the design variable field θ using the moving asymptote method, and sets a moving limit to control the maximum change of the variable in each iteration. The continuous scheduling module is used to execute a multi-stage continuous strategy, gradually adjusting the projection slope β and the grayscale penalty coefficient. and volume fraction target ; The geometry shaping and verification module is used to threshold the final density field, reconstruct the binary geometric structure, and use high-precision grid recalculation to limit the loss.

3. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S2: the geometric modeling module is responsible for optical fiber geometric modeling, region division and boundary setting, and establishes the cross-sectional geometry of two-dimensional or 2.5D hollow optical fiber. The overall model is divided into a central hollow region, a cladding design domain and an outer boundary absorption layer. The central hollow region is fixed to air, the cladding design domain is a variable material region, and the outer boundary preferably adopts a PML absorption layer to simulate the open domain electromagnetic wave leakage scenario.

4. The method for optimizing the topology of hollow-core optical fiber using pattern analysis and moving asymptote method according to claim 3, characterized in that, In S2, the geometric modeling module simultaneously defines three types of integral operators, clarifying the scope and function of each operator: (1) intop1: Acts on the central hollow core or core measurement region, used to calculate the electromagnetic field distribution and energy concentration parameters related to the core region in the objective function; (2) intop2: applies to the entire domain or a specified normalized region, and is used to calculate the global electromagnetic energy and total power flow; (3) intopD: Acts on the cladding design domain and is used to calculate the material volume fraction and perimeter penalty value.

5. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S3: the material parameterization module is responsible for design variable construction, material refractive index mapping, and grayscale suppression processing, as detailed below: (1) Construct the design variable field, and denote the density field as θ(x,y)∈[0,1], which is the core control variable for topology optimization, with initial values ​​of Take 0.5; (2) The hyperbolic tangent projection function is used to map the smooth density field into a variable that is closer to a binary distribution. The projection formula is: ; In the formula, β represents the projection slope; the larger the slope, the stronger the binarization effect. denoted by hyperbolic tangent projection operator, Ƞ represents the projection threshold, and θ represents the density field control variable, with a value range of [0,1]. (3) Perform real part interpolation of the refractive index. Within the cladding design domain, the effective real part of the refractive index changes linearly with the projection variable, specifically satisfying: ,in, The effective real part of the refractive index within the cladding design domain, and the air refractive index. Refractive index of silicon dioxide , These are binary approaching variables after projection processing; (4) Add a grayscale imaginary part penalty term, introduce artificial damping to suppress intermediate grayscale materials, and ensure a clear interface between air and silica. The formula for calculating the imaginary part is: ,in, This represents the imaginary part of the effective refractive index within the cladding design domain. The penalty coefficient is... This is the lower bound for numerical stability. (5) An optional inverse interpolation of the dielectric constant can be used to further enhance the two-phase contrast of the material. The formula is as follows: , Effective refractive index ,in, Indicates the inverse interpolation dielectric constant. Represents the effective dielectric constant, air dielectric constant The dielectric constant of silicon dioxide .

6. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S4: the mode analysis and solution module is responsible for electromagnetic field solution, mode analysis, and boundary condition configuration, and adopts electromagnetic wave frequency domain and full-field three-component vector mode analysis, through out-of-plane wavenumber... Characterize the fiber guiding mode, where α is the propagation constant; the outer boundary is preferably selected as the PML absorption layer to simulate the open domain electromagnetic wave leakage scenario. When the use of scattering boundary or transition boundary causes the analytical derivative chain to be unclosed and the solution to fail, immediately switch to the PML absorption layer.

7. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S5: the pattern analysis and solution module superimposes volume fraction constraints and perimeter smoothing penalties to construct a complete optimization objective system, as detailed below: (1) The core objective is to minimize the limiting loss, in dB / m, which serves as the main guideline for topology optimization; (2) Add the normalized field energy ratio as an auxiliary target to enhance the energy concentration in the core region and suppress leakage. The formula is: ; In the formula, Obj represents the normalized field energy ratio, intop1 represents the measurement region acting on the central hollow core or core, and intop2 represents the measurement region acting on the entire domain or a specified normalized region. The electric field strength of the electromagnetic field; (3) Calculate the material volume fraction and apply a penalty, design the domain area. Material volume Volume fraction The volume penalty term is ; (4) Add a perimeter smoothing penalty and define the gradient squared term as: θ(x,y) represents the original design variable field, and x and y represent the cross-sectional coordinates. The spatial derivatives of the design variables in two directions are given, and the perimeter / smoothing penalty term is further defined. for: grad2 represents the squared gradient; (5) Construct a comprehensive objective function, unifying it into a minimization form: , Represents the overall objective function. Represents the main objective function. Indicates the perimeter / smoothing penalty weight. Indicates the volume penalty weight. This indicates a volume penalty.

8. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S6: the sensitivity module and the MMA update module are executed in concert. The sensitivity module uses the discrete adjoint method to calculate the gradient of the objective function. Through one forward modeling and one adjoint modeling, the gradient values ​​of all design variables are obtained. The MMA update module uses the moving asymptote method to iteratively update the design variable field θ, sets reasonable moving limits, and controls the maximum change of the design variables in each iteration.

9. The method for optimizing the topology of hollow optical fibers using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S7: the continuous scheduling module adopts a multi-stage continuous iteration strategy. (1) Gradually increase the projection slope β. In the early stage, a small slope ensures the stability of gradient calculation, and in the later stage, a large slope strengthens the binarization of the structure. (2) Gradually reduce the gray level penalty coefficient The grayscale is suppressed by a high coefficient in the early stage, and the coefficient is reduced after the structure is formed; (3) Gradually reduce the target value of volume fraction. First, ensure the structure is formed, and then gradually fit the engineering requirements of low fill rate and low leakage of hollow optical fiber. (4) Controlling the filter radius And the grid size, ensuring the ratio of the filter radius to the grid size. It remains at 3-6.

10. The method for optimizing hollow fiber topology using pattern analysis and moving asymptote method according to claim 1, characterized in that, In S8: the geometry shaping and verification module is responsible for the binary reconstruction of the structure and the final performance verification, and outputs a manufacturable qualified optical fiber structure; a threshold of 0.5 is selected to perform threshold segmentation on the final optimized projection density field, reconstruct the air-silica binary geometry, and obtain a regular structure that can be industrially manufactured; a high-precision grid is used to perform pattern analysis on the shaped geometry and generate the final hollow fiber design report.

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