A shape optimization method and system based on topological photonic crystals

Abstract

This invention relates to a method and system for shape optimization of topological photonic crystals. The method includes: opening the double degeneracy points of the band structure to form a double-bandgap band structure; calculating the current band structure based on the double-bandgap band structure, observing whether the topological phase meets the requirements, and obtaining structural parameters; if the topological phase does not meet the requirements, adjusting the structural parameters to obtain adjusted structural parameters; and modifying the adjusted structural parameters in different ways to obtain four photonic crystal unit cells with different topological phases. This invention enables shape optimization of photonic crystals based on bandgap topologies with frequency range relevance.

Description

Technical Field

[0001] This invention relates to the field of shape optimization technology for photonic crystals, and in particular to a shape optimization method and system based on topological photonic crystals. Background Technology

[0002] Recent explorations of valley degrees of freedom in photonic systems have enriched the topological phase of light and revealed robust transport of edge states around sharp bends. The two band gaps in the valley Hall system have attracted researchers' attention due to their simultaneous expansion of the operating bandwidth; however, band gaps with frequency-range-dependent topologies have not been reported, and the optimization process for photonic crystals has not been described in detail. Previously, obtaining better photonic crystal performance parameters involved extensive and tedious manual parameter modifications. In this paper, we propose using topology optimization theory to quantify the desired photonic crystal performance as an objective function. By optimizing this objective function, we obtain a topological photonic crystal with the desired properties, providing a new approach for solving similar problems in the future. Summary of the Invention

[0003] The purpose of this invention is to provide a shape optimization method and system based on topological photonic crystals, which can optimize the shape of topological photonic crystals based on band gaps with frequency range-related topology.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A shape optimization method based on topological photonic crystals includes:

[0006] By opening the double degeneracy point of the band structure, a double bandgap band structure is formed;

[0007] Based on the described dual-bandgap band structure, calculate the current band structure, observe whether the topological phase meets the requirements, and obtain the structural parameters.

[0008] If the topological phase does not meet the requirements, the structural parameters are adjusted to obtain the adjusted structural parameters;

[0009] By modifying the adjusted structural parameters in different ways, four photonic crystal units with different topological phases were obtained.

[0010] Optionally, the step of calculating the current band structure based on the dual-bandgap band structure, observing whether the topological phase meets the requirements, and obtaining the structural parameters specifically includes:

[0011] By breaking the symmetry of the internal structure of the photonic crystal, the valley Chern number and the band gap of the dual band gap band structure are combined as the merit value of the objective function, and the structure of the photonic crystal unit cell with different frequencies of dual band gap band structure that meets the requirements is simulated.

[0012] Based on the simulated structure of the photonic crystal unit cell, the structural parameters are obtained.

[0013] Optionally, adjusting the structural parameters to obtain the adjusted structural parameters specifically includes:

[0014] The structural parameters are adjusted using a genetic algorithm to obtain the adjusted structural parameters.

[0015] Optionally, the step of modifying the adjusted structural parameters to obtain four photonic crystal units with different topological phases specifically includes:

[0016] By making different modifications to the adjusted structural parameters, four photonic crystal units with different topological phases were obtained using a shape optimization reverse design method.

[0017] A shape optimization system based on topological photonic crystals includes:

[0018] A dual-bandgap band structure forming module is used to open the dual degeneracy points of the band structure and form a dual-bandgap band structure.

[0019] The structural parameter determination module is used to calculate the current band structure based on the dual-bandgap band structure, observe whether the topological phase meets the requirements, and obtain the structural parameters.

[0020] The structural parameter adjustment module is used to adjust the structural parameters when the topological phase does not meet the requirements, so as to obtain the adjusted structural parameters;

[0021] The photonic crystal unit cell determination module is used to modify the adjusted structural parameters in different ways to obtain four photonic crystal unit cells with different topological phases.

[0022] Optionally, the structural parameter determination module specifically includes:

[0023] The photonic crystal unit cell is used to break the symmetry of the internal structure of the photonic crystal, combine the valley Chern number and the band gap of the dual band gap band structure as the objective function, and automatically simulate the structure of the photonic crystal unit cell with different frequencies that meet the requirements.

[0024] The structural parameter determination unit is used to obtain structural parameters based on the simulated structure of the photonic crystal unit cell.

[0025] Optionally, the structural parameter adjustment module specifically includes:

[0026] The structural parameter adjustment unit is used to adjust the structural parameters using a genetic algorithm to obtain the adjusted structural parameters.

[0027] Optionally, the photonic crystal unit cell determination module specifically includes:

[0028] The photonic crystal unit is used to make different modifications to the adjusted structural parameters and to obtain four photonic crystal units with different topological phases using a shape optimization reverse design method.

[0029] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0030] This invention provides a method and system for shape optimization of topological photonic crystals. The method includes: opening the double degeneracy points of the band structure to form a double-bandgap band structure; calculating the current band structure based on the double-bandgap band structure, observing whether the topological phase meets the requirements, and obtaining structural parameters; if the topological phase does not meet the requirements, adjusting the structural parameters to obtain adjusted structural parameters; and modifying the adjusted structural parameters in different ways to obtain four photonic crystal units with different topological phases. This invention enables shape optimization of topological photonic crystals based on bandgap topologies with frequency range correlation. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of the shape optimization method based on topological photonic crystals of the present invention;

[0033] Figure 2 A schematic diagram illustrating the application of the difference function to construct the intracellular structure of a primitive cell;

[0034] Figure 3 This is a schematic diagram of the initial crystal lattice and band structure.

[0035] Figure 4 A schematic diagram showing the four optimized unit shapes and the corresponding absolute values ​​of the energy band and electric field, as well as the power flux density;

[0036] Figure 5 This is a structural diagram of the shape optimization system based on topological photonic crystals of the present invention. Detailed Implementation

[0037] 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.

[0038] The purpose of this invention is to provide a shape optimization method and system based on topological photonic crystals, which can optimize the shape of topological photonic crystals based on band gaps with frequency range-related topology.

[0039] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] Figure 1 This is a flowchart of the shape optimization method based on topological photonic crystals of the present invention. Figure 1 As shown, a shape optimization method based on topological photonic crystals includes:

[0041] Step 101: Open the double degeneracy point of the band structure to form a double bandgap band structure.

[0042] This invention utilizes a photonic crystal unit cell with two degenerate points and disrupts the symmetry of the unit cell, causing the degenerate points to separate and the energy bands above and below the degenerate points to exhibit different energy extrema, thereby achieving the effect of boundary states.

[0043] The initial photonic crystal band structure had two degenerate points. Simply put, a "degenerate point" is a state in which "several different states have the same energy." Because energy cannot be transferred between two degenerate points, the structure needs to be adjusted. The adjusted band structure not only has two band gaps, but also meets specific topological requirements (the clockwise and counterclockwise rotating energy flows in this invention) in order to transfer energy.

[0044] To establish two dual-bandgap models with different frequency ranges, a completely different approach is adopted, treating the design of the topological photonic crystal as an inverse numerical optimization problem, namely step 102.

[0045] Step 102: Based on the described dual-bandgap band structure, calculate the current band structure, observe whether the topological phase meets the requirements, and obtain the structural parameters, specifically including:

[0046] Step 1021: By breaking the symmetry of the internal structure of the photonic crystal, the valley Chern number and the band gap of the dual band gap band structure are combined as the merit value of the objective function, and the structure of the photonic crystal unit cell with different frequencies that meet the requirements is simulated automatically.

[0047] Step 1022: Obtain the structural parameters based on the simulated structure of the photonic crystal unit cell.

[0048] By breaking the symmetry of the crystal's internal structure, the valley Chern number and bandgap are combined as the figure of merit (FOM) of the objective function. This combines the bandgap width range with the corresponding valley Chern number, incorporating both into the unit cell structure within the optimization function. The program's optimization function automatically designs the structure to meet the requirements. Regarding shape construction, the smooth curve-smoothing property of the difference function is utilized to construct the desired smooth shape.

[0049] Figure 2 A schematic diagram illustrating the application of the difference function to construct the intracellular structure of the primitive cell is shown below. Figure 2 In (a), there are 12 control points, and the angle between each control point and the center line is 30 degrees. By adjusting these 12 control points, many smooth shapes can be achieved. Figure 2 (b) illustrates the main difference curve design method in this invention, namely C 3v The structure, as illustrated, can be divided into three symmetrical parts. This design method is often used when constructing photonic crystal units. Figure 2 (b) The structure has 13 control parameters: r1,...,r4,r5,...,r 12 θ, fills the unit cell with a metallic medium, and there are a total of 13 variable parameters in the entire optimization process.

[0050] When designing electromagnetic sensors, shape optimization can improve sensor sensitivity, reduce sensor error, and increase sensor measurement range, thereby enhancing sensor performance.

[0051] Step 103: Adjust the structural parameters to obtain the adjusted structural parameters, specifically including:

[0052] The structural parameters are adjusted using a genetic algorithm to obtain the adjusted structural parameters.

[0053] During the reverse engineering process, a genetic algorithm is used to adjust the parameters of the structure. The following describes the process of designing a primitive cell structure using a genetic algorithm:

[0054] (1) Initialization: First, a set of random data, r1,...,r4,θ1,r5,...,r8,θ2, is generated. These data can constitute the distribution of the metallic medium in the unit cell of the photonic crystal. Then, the band structure and valley Chern number obtained from this set of data are calculated. Next, the calculated data are substituted into the objective function for integration to obtain a fitness value.

[0055] (2) Selection operation: Random traversal sampling is performed on the generated data. The selection probability of this process is P. x The selected data is used as the parent generation to generate the next generation of data.

[0056] (3) Crossover: Select a pair of individuals from the chosen data and perform a crossover operation to generate two new individuals. The purpose of the crossover operation is to combine the superior characteristics of the two individuals to produce better offspring. The crossover probability in this process is P. c .

[0057] (4) Mutation: Mutation operations are performed on newly generated individuals to increase population diversity and exploration space. Mutation operations typically involve randomly changing the values ​​of one or more genes in an individual's genome. The mutation probability is P. m .

[0058] (5) Termination Decision: Optimization stops when the number of iterations exceeds the set number of iterations. When the number of iterations is less than the set number, return to step (2) and continue optimization. Alternatively, the objective function value can be observed in real-time, and optimization can be stopped manually.

[0059] Before starting shape optimization, the objective function needed for optimization must first be determined, that is, the direction in which the material distribution should move. The objective function in this invention mainly needs to adjust two directions: first, to maximize the band gap width; and second, to control the Chern number of each band, so that the Chern number of each band tends towards the desired value. The optimization equation is:

[0060] Find R = [r] i [,θ](i=1,…,12)

[0061]

[0062]

[0063] In the formula, R refers to the control variable of the metal pillars in the unit cell, and i refers to the number of variables. i ω1(k) refers to the length variable controlling the shape, and θ refers to the rotation variable controlling the shape. ω1(k) refers to the frequency of the first energy band in k-space, and ω2(k), ω3(k), ω5(k), and ω6(k) refer to the frequencies of the second, third, fifth, and sixth energy bands in k-space, respectively. C1 refers to the valley-Chen number of the first energy band, C2 refers to the valley-Chen number of the second energy band, and C5 refers to the valley-Chen number of the fifth energy band (note: different topological phases result in different starting energy bands for opening the band gap). The valley-Chen number is quantized as 1 and -1. Ω PC1 This refers to the design region inside the first type of photonic crystal, Ω. PC2This refers to the design region inside the second type of photonic crystal; the same principle applies to others. The purpose of min|C1-1|+|C5+1| is to gradually bring the valley Chern number of the first band closer to 1 and the valley Chern number of the fifth band closer to -1. R∈Ω PC1 This refers to the objective equation for the valley Chern number when designing the first type of primitive cell; the same applies to others. Regarding the calculation method for the valley Chern number, the valley-Hall dual band gap is described using the effective Hamiltonian:

[0064]

[0065] in For the photon Dirac velocity, (δk) x ,δk y ) represents the distance from point K or K′ to some point k. These are the Pauli matrices acting on the sublattice, valley space, and bandgap space, respectively, with the last term being... A bandgap with bandwidths of 2λ1 and 2λ2 is opened. This effective Hamiltonian indicates that the valley-Chern number is determined by C. vn =ζ z sgn(λ n Given n = 1, 2, λ1 and λ2 correspond to the wavelengths of the band gaps opened in the low-frequency and high-frequency components, respectively. vn The corresponding relative positions are C1 (C2) and C5. This section mainly emphasizes the design of photonic crystal structures through topology optimization; the methods for calculating the energy bands of photonic crystals are not described in detail here.

[0066] The initial two-dimensional valley-shaped unit cells of the photonic crystal were made of air and a metal (dielectric constants of 1 and 1, respectively). Figure 3 This is a schematic diagram of the initial lattice and band structure, as shown below. Figure 3 As shown in (a), the lattice constant of the unit cell, i.e., the side length a0 of the valley, is 50 mm. The dark gray region represents metal, and the light gray region represents air. The center of the circular metal element coincides with the centroid of the equilateral triangles that make up the rhombus. Periodic boundary conditions are applied to the upper and lower boundaries and the left and right boundaries of the rhombus, respectively, and the band structure is calculated. The calculated band diagram is shown below. Figure 3 As shown in (b), by observing its band structure, it can be seen that there are two degeneracy points at point K in the reciprocal lattice space, located near 8 GHz and 11.7 GHz respectively. To achieve the effect of a wavelength division multiplexer, these two degeneracy points should first be opened to form a unit cell structure with opposite valley Chern numbers in the upper and lower bands. In this invention, only the transverse magnetic field mode (TM) is considered, where the magnetic field is confined to the xy plane and the electric field is perpendicular to the xy plane.

[0067] Genetic algorithms (GALs) are optimization algorithms based on the principles of biological evolution. They find optimal solutions to problems by simulating the process of biological evolution. In the electromagnetic field, GALs are frequently used for solving electromagnetic field calculations and antenna design. GALs can solve complex electromagnetic field distribution problems, such as the propagation of electromagnetic waves in complex media and the distribution of electromagnetic fields in complex structures. In the design of electromagnetic devices, GALs can be used to optimize device design, such as optimizing the size, structure, and radiation characteristics of electromagnetic components. Simulation calculations based on other algorithms, such as particle swarm optimization, direct bisection, and adjoint methods, can also be used for prediction and assessment.

[0068] Step 104: Modify the adjusted structural parameters to obtain four photonic crystal units with different topological phases, specifically including:

[0069] By making different modifications to the adjusted structural parameters, four photonic crystal units with different topological phases were obtained using a shape optimization reverse design method.

[0070] By varying the structural parameters controlling the unit cell of the photonic crystal, all four topological phases of the dual-bandgap design were discovered. Frequency-range-dependent edge states were exhibited at the domain walls between valley photonic crystals with frequency-range-dependent topologies. Broadband photonic detours of three joint valley photonic crystals were demonstrated by switching the operating frequency. This work may have potential applications in multi-band photonic devices, such as wavelength division multiplexers.

[0071] In designing topological photonic crystals, a key factor is to interchange the symmetry of the photonic band around the photonic bandgap. This operation induces a topological transition, thereby generating edge states.

[0072] In the initial case, the circular metal pillar within the unit cell exhibits two degeneracy points at point K in the reciprocal lattice space, located near 8 GHz and 11.5 GHz, respectively, by observing its band structure. Optimizing the shape of the circular metal pillar to break its spatial symmetry within the lattice clearly reveals the opening of these two degeneracy points.

[0073] To realize the function of wavelength division multiplexer, four different topological photonic crystals were designed. Figure 4 The diagram shows the four optimized unit cell shapes and their corresponding absolute values ​​of energy bands, electric fields, and power flux densities. The four optimized topological photonic crystal shapes are shown below. Figure 4 As shown in (a), the light gray area represents air with a dielectric constant of 1, and the dark gray area represents a metallic material with a dielectric constant of 1. The individual shapes are C. 3vThe symmetry of the band structure significantly opens up the corresponding band degeneracy point, with the band gaps of the two bands of PC1 ranging from 8.01 GHz to 8.64 GHz and from 11.34 GHz to 11.73 GHz, respectively. At point K in the second band, its |E z As shown on the right side of 4(b), the power flow density is defined as q, where the power flow is distributed counterclockwise in the unit cell. + A clockwise distribution is defined as p - Because the degeneracy points of the energy bands are opened, the energy extrema at point K exhibit completely opposite states. Therefore, bands two and three, and bands five and six, show completely opposite power flow distributions, and the corresponding valley-Chern numbers are also completely opposite. Calculating the valley-Chern numbers for each energy band is also within the scope of the optimization formula. Figure 4 (b) shows the valley Chern numbers of the PC1 bands. The valley Chern numbers of the second and fifth bands are both 1, while the valley Chern numbers of the third and sixth bands are both -1. This provides a basis for the realization of topological photonic crystal wavelength division multiplexers. Figure 4 The case shown in (c) is completely opposite to that in 3(b), except that the frequency range of the band gap is the same. Figure 4 In (c), the valley Chern numbers of the second and fifth bands are -1, and the valley Chern numbers of the third and sixth bands are 1; the rotation direction of the power flow at point K in the second and fifth bands is clockwise, denoted as p. - The power flow of the third and sixth bands at point K rotates counterclockwise, denoted as q. + ,and Figure 4 (b) The situation is exactly the opposite. Combining the unit cell shown in (b) with the unit cell shown in (c), the generation of boundary states will be observed, and these boundary states will be generated simultaneously in both the low-frequency range (approximately 8.2 GHz) and the high-frequency range (approximately 11.4 GHz).

[0074] Figure 4 The PC3 case shown in (d) differs slightly from the previous two. First, its basic structure consists of two irregular triangles. Second, it has a wider bandgap, ranging from 6.67 GHz to 9.19 GHz in the low-frequency range and from 11.0 GHz to 12.16 GHz in the high-frequency range. Its valley-Cell number in the low-frequency part is the opposite of that in the PC1 case, which means that when PC1 and PC3 are combined, boundary states will be generated in the low-frequency part; its valley-Cell number in the high-frequency part is the same as that in the PC1 case, so no boundary states will be generated.

[0075] Figure 4(e) shows that PC4 is the complete opposite of PC3, with the valley Chern number and power flux density of the corresponding bands being completely opposite. The valley Chern number in the high-frequency range is opposite to that of PC1, which means that when PC4 and PC1 are combined, boundary states will be generated in the high-frequency range; its valley Chern number in the low-frequency range is the same as that of PC1, so no boundary states will be generated. This kind of completely opposite property of different unit cells after special symmetry treatment is also one of the characteristics of topological photonic crystallography, making it easier for designers to obtain another unit cell with opposite properties.

[0076] This invention is based on the theory that combining two photonic crystals with different topological phases will form boundary states. By optimizing the shape of a circular metal pillar as the initial structure and using the band gap and the corresponding valley Chern number as optimization constraints, four photonic crystal unit cells with dual band gaps and different valley Chern numbers were designed. These four designed photonic crystal unit cells with dual band gaps and different valley Chern numbers provide a foundation for the subsequent design of wavelength division multiplexers and also provide guidance for designing the frequency range-dependent characteristics of topological structures.

[0077] Figure 5 This is a structural diagram of the shape optimization system based on topological photonic crystals of the present invention. Figure 5 As shown, a shape optimization system based on topological photonic crystals includes:

[0078] The dual-bandgap band structure forming module 201 is used to open the dual degeneracy point of the band structure to form a dual-bandgap band structure.

[0079] The structural parameter determination module 202 is used to calculate the current band structure based on the dual bandgap band structure, observe whether the topological phase meets the requirements, and obtain the structural parameters.

[0080] The structural parameter adjustment module 203 is used to adjust the structural parameters when the topological phase does not meet the requirements, so as to obtain the adjusted structural parameters.

[0081] The photonic crystal unit cell determination module 204 is used to make different modifications to the adjusted structural parameters to obtain four photonic crystal unit cells with different topological phases.

[0082] The structural parameter determination module 202 specifically includes:

[0083] The photonic crystal unit cell is used to break the symmetry of the internal structure of the photonic crystal, combine the valley Chern number and the band gap of the dual band gap band structure as the objective function, and automatically simulate the structure of the photonic crystal unit cell with different frequencies that meet the requirements.

[0084] The structural parameter determination unit is used to obtain structural parameters based on the simulated structure of the photonic crystal unit cell.

[0085] The structural parameter adjustment module 203 specifically includes:

[0086] The structural parameter adjustment unit is used to adjust the structural parameters using a genetic algorithm to obtain the adjusted structural parameters.

[0087] The photonic crystal unit cell determination module 204 specifically includes:

[0088] The photonic crystal unit is used to make different modifications to the adjusted structural parameters and to obtain four photonic crystal units with different topological phases using a shape optimization reverse design method.

[0089] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0090] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A shape optimization method based on topological photonic crystals, characterized in that, include: By opening the double degeneracy point of the band structure, a double bandgap band structure is formed; Based on the described dual-bandgap band structure, calculate the current band structure, observe whether the topological phase meets the requirements, and obtain the structural parameters. If the topological phase does not meet the requirements, the structural parameters are adjusted to obtain the adjusted structural parameters; By modifying the adjusted structural parameters in different ways, four photonic crystal unit cells with different topological phases were obtained; The process of calculating the current band structure based on the dual-bandgap band structure, observing whether the topological phase meets the requirements, and obtaining the structural parameters specifically includes: By breaking the symmetry of the internal structure of the photonic crystal, the valley Chern number and the band gap of the dual-bandgap band structure are combined as the merit value of the objective function to simulate the structure of a photonic crystal unit cell with different frequencies that meets the requirements. The objective function adjusts in two directions: first, by expanding the band gap width, and second, by controlling the valley Chern number of each band. The optimization equation is as follows: In the formula, It refers to the control variable of the metal pillars in the unit cell. This refers to the number of variables. This refers to controlling the length variable of the shape. It refers to the rotational variable that controls the shape. It refers to the frequency point of the first energy band in k-space. , , These refer to the frequency points of the third, fifth, and sixth energy bands in k-space, respectively. This refers to the valley number of the first energy band. This refers to the valley-Chern number of the second energy band. This refers to the valley number of the fifth energy band. This refers to the design region inside the first type of photonic crystal. This refers to the design region inside the second type of photonic crystal; Based on the simulated structure of the photonic crystal unit cell, the structural parameters are obtained; The adjustment of the structural parameters to obtain the adjusted structural parameters specifically includes: The structural parameters are adjusted using a genetic algorithm to obtain the adjusted structural parameters; The process of modifying the adjusted structural parameters to obtain four photonic crystal unit cells with different topological phases specifically includes: By making different modifications to the adjusted structural parameters, four photonic crystal units with different topological phases were obtained using a shape optimization reverse design method.

2. A topology photonic crystal based shape optimization system, comprising: include: A dual-bandgap band structure forming module is used to open the dual degeneracy points of the band structure and form a dual-bandgap band structure. The structural parameter determination module is used to calculate the current band structure based on the dual-bandgap band structure, observe whether the topological phase meets the requirements, and obtain the structural parameters. The structural parameter adjustment module is used to adjust the structural parameters when the topological phase does not meet the requirements, so as to obtain the adjusted structural parameters; The photonic crystal unit cell determination module is used to modify the adjusted structural parameters in different ways to obtain four photonic crystal unit cells with different topological phases. The structural parameter determination module specifically includes: The photonic crystal unit cell structure determination unit is used to break the symmetry of the internal structure of the photonic crystal, combining the valley Chern number and the band gap of the dual-bandgap band structure as the best value of the objective function, to simulate the structure of photonic crystal unit cells with different frequencies that meet the requirements; the objective function adjusts in two directions: first, to expand the band gap width, and second, to control the valley Chern number of each band. The optimization equation is: In the formula, It refers to the control variable of the metal pillars in the unit cell. This refers to the number of variables. This refers to controlling the length variable of the shape. It refers to the rotational variable that controls the shape. It refers to the frequency point of the first energy band in k-space. , , These refer to the frequency points of the third, fifth, and sixth energy bands in k-space, respectively. This refers to the valley number of the first energy band. This refers to the valley-Chern number of the second energy band. This refers to the valley number of the fifth energy band. This refers to the design region inside the first type of photonic crystal. This refers to the design region inside the second type of photonic crystal; The structural parameter determination unit is used to obtain structural parameters based on the simulated structure of the photonic crystal unit cell; The structural parameter adjustment module specifically includes: The structural parameter adjustment unit is used to adjust the structural parameters using a genetic algorithm to obtain the adjusted structural parameters; The photonic crystal unit cell determination module specifically includes: The photonic crystal unit is used to make different modifications to the adjusted structural parameters and to obtain four photonic crystal units with different topological phases using a shape optimization reverse design method.

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