Optical filter design method and device based on topological photonic crystal and medium

Abstract

The invention relates to a topological photonic crystal-based optical filter design method, equipment and medium, and the method comprises the steps: constructing a periodically arranged photonic crystal flat plate, and enabling a super unit to be composed of a topological non-trivial unit and a topological trivial unit, and the topological characteristic and the arrangement mode of the topological non-trivial unit are determined by calculating the two-dimensional bundling phase so as to form a topological defect state. And then, by adjusting the width of the air micropores and the defect spacing, the flatness and the coupling strength of a defect state energy band are optimized, and the stability of the resonant wavelength is ensured. Full-wave electromagnetic simulation is adopted to test transmission spectrums under different incident angles, the angle insensitivity characteristic of resonant wavelength is verified, and key structure parameters are iteratively optimized. Finally, an optical filter with efficient filtering, low energy consumption, high integration level and anti-interference capability is output, and the optical filter is widely applied to the fields of optical communication, optical sensing, high-precision spectral analysis and the like.

Description

Technical Field

[0001] The present invention relates to the field of optoelectronic technology, and particularly to a design method, device, and medium of an optical filter based on topological photonic crystals. Background Art

[0002] As a core component of modern optical systems, the performance of optical filtering devices directly affects the system efficiency in fields such as optical communication, spectral analysis, and optical sensing. Traditional photonic crystal filters mainly rely on the photonic bandgap generated by periodic structures to achieve wavelength selection functions, but there are three significant technical bottlenecks: First, their filtering characteristics are highly sensitive to the incident angle, resulting in the need to strictly control the beam incident conditions in practical applications; Second, structural defects or environmental perturbations are likely to cause frequency drift of photonic localized states, reducing the system stability; Third, to achieve a high quality factor, complex resonator designs are often required, leading to an increase in device volume and limited integration.

[0003] In recent years, the development of topological photonics has provided new ideas for breaking through the above technical bottlenecks. By introducing topological band theory, researchers have found that topological edge states have the characteristics of backward scattering suppression and defect immunity. Devices such as topological lasers and topological waveguides developed based on this principle have shown better robustness than traditional devices. However, existing topological photonic devices mostly focus on waveguide applications, and there are still key challenges in the development of filtering functions: There is an inherent contradiction between the broadband transmission characteristics of topological edge states and the narrowband selection characteristics required by filters; at the same time, there is still a lack of effective solutions for organically combining topological protection characteristics and angle-insensitive characteristics. Summary of the Invention

[0004] The present invention provides a design method, device, and medium of an optical filter based on topological photonic crystals, aiming to solve the problem of unstable spectral response of traditional optical filters when the incident angle changes.

[0005] To achieve the above object, the first aspect of the present invention provides a design method of an optical filter based on topological photonic crystals, including the following steps:

[0006] Construct a photonic crystal slab composed of periodically arranged supercells, where the supercell includes a topologically non-trivial unit and a topologically trivial unit, the topologically non-trivial unit is surrounded by the topologically trivial unit, both the topologically non-trivial unit and the topologically trivial unit include four air micropores, and the position distributions of the air micropores in the two are different;

[0007] Calculate the topological invariant of the topologically non-trivial unit based on the two-dimensional Zak phase, and determine the two-dimensional Zak phase of the topologically non-trivial unit;

[0008] Determine the specific layout position of the topological non-trivial unit within the supercell according to the two-dimensional Zak phase of the topological non-trivial unit, so that within each supercell, a topological non-trivial defect region is formed by arranging the topological non-trivial unit, and a defect state energy band structure is formed through the coupling of topological defect states in adjacent supercells;

[0009] Based on the requirement of the flatness of the energy band of the defect state energy band structure, adjust the width of the air micropores, analyze the variation relationship between the energy band frequency position and the flatness of the energy band, and screen out the width values that meet the flatness requirement of the transverse electric-like mode energy band near the band gap;

[0010] Based on the width value, adjust the number of rows or columns of the topological trivial units between adjacent topological non-trivial defects, and determine the optimal spacing parameter of the defect state coupling strength according to the change of the energy band dispersion characteristics;

[0011] Based on the optimal spacing parameter, perform full-wave electromagnetic simulation on the photonic crystal slab, and obtain the normalized transmission spectrum data through the excitation of plane waves with different incident angles in the incident plane to verify the offset of the resonance wavelength with the incident angle;

[0012] Based on the offset, iteratively optimize the width of the air micropores and the topological non-trivial defect spacing parameter to determine the structural parameters of the supercell;

[0013] Output the final design of the optical filter according to the structural parameters.

[0014] Furthermore, the length of the periodic arrangement of each supercell in the x and y directions is set to twice the lattice constant.

[0015] Furthermore, the method for determining the two-dimensional Zak phase of the topological non-trivial unit includes:

[0016] Calculate the transverse electric-like mode energy band structure of the topological non-trivial unit in the first Brillouin zone;

[0017] Obtain the eigenstate |ψ k > of the first ground state energy band in the energy band structure at each wave vector k point;

[0018] Calculate the Berry connection according to the eigenstate |ψ k >

[0019]

[0020] where A α (k) is the Berry connection, k = (k x , k y ) represents the wave vector, ψ k represents the eigenstate wave function, and |ψ k represents the eigenstate of the first ground state energy band. Denotes the partial derivative with respect to the wave vector k α , describes the infinitesimal change of the eigenstate with k, i represents the imaginary unit to ensure the Hermiticity of the Berry connection, α represents the directional component, and x and y respectively refer to the lattice directions;

[0021] Taking the trace operation and integrating the Berry connection in the first Brillouin zone to obtain the two-dimensional Zak phase, where the integration path covers the entire first Brillouin zone:

[0022]

[0023] where, θ α is the two-dimensional Zak phase, P α is the polarization intensity component, ∫ FBZ is the first Brillouin zone integral, Tr[A α (k)] is the trace of the Berry connection, Tr represents taking the trace of the matrix, and dk represents integrating over the wave vector in the first Brillouin zone;

[0024] When θ α = π, it is determined that the topological non-trivial unit has non-trivial topological properties in the α direction;

[0025] According to the combination pattern of the Zak phases θ x and θ y in the x and y directions, determine the two-dimensional Zak phase of the topological non-trivial unit, where if the phase combination pattern satisfies θ x = π and θ y = π, then it is determined that the topological non-trivial unit is in the topological non-trivial phase.

[0026] Furthermore, the method of forming the defect state energy band structure by coupling the topological defect states in adjacent supercells includes:

[0027] Based on the two-dimensional Zak phase of the topological non-trivial unit, embed the topological non-trivial unit as a defect into the supercell, and make it surrounded by topological trivial units at intervals along the x and y directions;

[0028] Set the interval between the topological non-trivial defects in adjacent supercells to n rows or n columns of topological trivial units, and control the defect state coupling strength by adjusting the n value;

[0029] When n = 1, the adjacent defect states are coupled to form a defect state energy band structure including at least one flat-like transverse electric mode energy band, and the frequency of the flat-like transverse electric mode energy band is within the photonic crystal band gap range and corresponds to a resonance wavelength insensitive to the incident angle.

[0030] Furthermore, the method of screening the width value required for the flat-like transverse electric mode energy band to be flat near the band gap includes:

[0031] Set an initial air micropore width value and construct a topological photonic crystal unit structure;

[0032] Calculate the energy band distribution of the topological photonic crystal unit structure within the first Brillouin zone and extract the energy band data within the bandgap range;

[0033] Identify the energy bands formed by topological defect states near the bandgap and extract the transverse electric-like mode energy bands;

[0034] Calculate the frequency variation of the transverse electric-like mode energy bands at different wave vector values and evaluate the flatness of the energy bands;

[0035] Adjust the air micropore width and repeat the above steps to compare the variation trends of the energy band frequencies and flatness at different micropore widths;

[0036] Select the air micropore width value that meets the energy band flatness requirement, such that the frequency dispersion of the transverse electric-like mode energy bands near the bandgap is minimized.

[0037] Furthermore, the method for adjusting the number of rows or columns of topological trivial cells between adjacent topological non-trivial defects based on the width value includes:

[0038] Construct a topological photonic crystal slab structure using the determined air micropore width value;

[0039] Set the initial number of rows or columns of topological trivial cells between topological non-trivial defects, calculate the energy band structure after supercell arrangement, and extract the energy bands formed by defect states;

[0040] Calculate the frequency variation of the transverse electric-like mode energy bands at different wave vector k values and evaluate its dispersion characteristics;

[0041] Sequentially increase the number of rows or columns of topological trivial cells and repeat the above steps, recording the frequency positions and flatness variations of the defect state energy bands at different numbers of rows or columns of topological trivial cells;

[0042] Determine the optimal number of rows or columns of topological trivial cells that can maintain the flatness of the transverse electric-like mode energy bands and optimize the defect state coupling strength by comparing the energy band characteristics at different numbers of rows or columns of topological trivial cells.

[0043] Furthermore, the method for performing full-wave electromagnetic simulation on the photonic crystal slab includes:

[0044] Construct an optical filter model based on the topological photonic crystal within the computational domain and set periodic boundary conditions;

[0045] Use the finite-difference time-domain method to discretely calculate the electromagnetic field distribution of the photonic crystal slab and define the computational grid;

[0046] Set plane wave excitation sources with different incident angles in the incident plane above the flat structure, and place a far-field energy monitor below to record the transmitted signals;

[0047] Calculate the normalized transmission spectra under different incident angle conditions, and extract the transmittance data corresponding to the resonant wavelengths of the defect states;

[0048] Calculate the offset of the transmittance with respect to the incident angle, and optimize the structural parameters of the supercell based on this offset.

[0049] Furthermore, the method for verifying the offset of the resonant wavelength with respect to the incident angle based on the normalized transmission spectrum data includes:

[0050] Set the range of change of the incident angle, and sample multiple different incident angle conditions for full-wave electromagnetic simulation;

[0051] Under each incident angle condition, calculate the normalized transmission spectrum and extract the position of the transmission valley corresponding to the resonant wavelength;

[0052] Record the resonant wavelengths under all incident angle conditions, and plot the curve of the resonant wavelength varying with the incident angle;

[0053] Calculate the maximum offset of the resonant wavelength within the incident angle range, and compare it with the set threshold for the angle-insensitive filtering characteristic;

[0054] If the maximum offset exceeds the set threshold, adjust the air micropore width or the topological non-trivial defect spacing parameter, and repeat the above steps until the angle-insensitive requirement is met.

[0055] To achieve the above object, a second aspect of the present invention provides an electronic device, including a memory and a processor, where the memory is used to store a program for supporting the processor to execute the optical filter design method based on topological photonic crystals, and the processor is configured to execute the program stored in the memory.

[0056] To achieve the above object, a third aspect of the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes the steps of the optical filter design method based on topological photonic crystals.

[0057] Advantages of the present invention:

[0058] Compared with the prior art, a method, device and medium for designing an optical filter based on topological photonic crystals provided by the present invention achieve efficient filtering of specific wavelengths and ensure the stability of the filter under different incident angle conditions by precisely designing topological defect states, optimizing the periodic arrangement of topological non-trivial units and topological trivial units, regulating the structural parameters of air micropores and the coupling strength of defect states. This method utilizes the topological protection characteristics of topological photonic crystals, enabling the defect state energy band to remain highly flat within the bandgap range, thereby ensuring that the resonance wavelength is extremely insensitive to changes in the incident angle and overcoming the problem of degradation in the filtering performance of traditional filters due to structural perturbations or angle changes. In addition, this method combines two-dimensional Zak phase calculation, full-wave electromagnetic simulation analysis and parameter optimization iteration, successfully achieving high spectral selectivity, low energy consumption and high integration of the filter, providing a brand-new and efficient optical filtering solution for optical communication, optical sensing and high-precision spectral analysis. Compared with the prior art, this method significantly improves the angle-insensitive characteristics and anti-interference ability of the filter, enabling it to operate stably in complex environments and promoting the development of efficient photonic integration systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the description of the embodiments.

[0060] Figure 1 It is a geometric structure of a photonic crystal flat panel array disclosed in an embodiment of the present invention.

[0061] Figure 2 It is a diagram showing the energy band structure of a topological photonic crystal unit and the calculation result of the Zak phase disclosed in an embodiment of the present invention.

[0062] Figure 3 It is an energy band structure diagram of a photonic crystal flat panel in the x direction disclosed in an embodiment of the present invention.

[0063] Figure 4 It is a full-wave electromagnetic simulation diagram based on the finite-difference time-domain method disclosed in an embodiment of the present invention.

[0064] Figure 5 It is a diagram showing the transmittance and reflectance of a photonic crystal flat panel under different incident angle conditions disclosed in an embodiment of the present invention.

[0065] Figure 6 It is a diagram showing the influence of the width of air micropores on the energy band structure of defect states disclosed in an embodiment of the present invention.

[0066] Figure 7 It is a diagram showing the influence of the distance between adjacent topological non-trivial defects on the energy band structure disclosed in an embodiment of the present invention.

[0067] Figure 8It is a diagram showing the influence of the size of the topologically non-trivial defect region on the energy band structure disclosed in the embodiments of the present invention. Detailed implementation manners

[0068] The following will describe in detail the specific implementation manners of the present invention in conjunction with the accompanying drawings. The optical filter design method based on topological photonic crystals provided in this embodiment realizes the filtering function insensitive to the incident angle by constructing a photonic crystal supercell array with topological defect states and utilizing the flatness of the energy bands of the topological defect states. The following implementation steps will specifically elaborate on how to achieve this goal through key links such as the combination design of topologically non-trivial units and trivial units, Zak phase calculation, energy band regulation, and parameter optimization, and will illustrate the technical details and implementation manners of each step in conjunction with the accompanying drawings.

[0069] According to the embodiments of the present invention, it should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the following manufacturing method, in some cases, the steps shown or described can be executed in a different order than here.

[0070] The present invention provides an optical filter design method based on topological photonic crystals, including the following steps:

[0071] Step S1, construct a photonic crystal slab composed of periodically arranged supercells, where the supercell includes a topologically non-trivial unit and a topologically trivial unit, the topologically non-trivial unit is surrounded by the topologically trivial unit, and both the topologically non-trivial unit and the topologically trivial unit include four air micropores, and the position distributions of the air micropores of the two are different;

[0072] First, construct a photonic crystal slab composed of periodically arranged supercells. This slab structure is the core part of the entire optical filter. The supercell consists of a topologically non-trivial unit and a topologically trivial unit, where the topologically non-trivial unit is surrounded by the topologically trivial unit to form local topological defect states, thereby achieving specific optical responses.

[0073] As Figure 1 (a) shows, the photonic crystal slab is composed of a plurality of periodically arranged photonic crystal supercells. The structure of each supercell is as Figure 1 (b) shows, and it is composed of a topologically non-trivial unit ( Figure 1 (c) left side) and the surrounding topologically trivial units ( Figure 1 (c) right side) together. The characteristic of this structure is that both the topologically non-trivial unit and the topologically trivial unit include four air micropores, but their micropore position distributions are different.

[0074] Specifically, the lattice constant a of each unit is set to 1 μm, the width w of the micropores is set to 0.34 μm, and the period of the supercell in the x and y directions is twice the lattice constant, i.e., p = 2 μm. The thickness of the photonic crystal slab is set to 0.5 μm, and the dielectric constant is 11.7 and does not vary with wavelength, i.e., it is a non-dispersive material.

[0075] In addition, the arrangement of the supercells is crucial for the overall characteristics of the filter. Figure 7 (b) shows the initially set arrangement of the supercells, where each topologically non-trivial unit is surrounded by half the area of eight topologically trivial units. This structure ensures that topological defects in the supercell can effectively form topological defect states, and the defect states can form a stable energy band structure through periodic coupling of adjacent supercells.

[0076] Step S2: Calculate the topological invariant of the topologically non-trivial unit based on the two-dimensional Zak phase to determine the two-dimensional Zak phase of the topologically non-trivial unit.

[0077] After constructing the periodically arranged photonic crystal slab, it is necessary to clarify the topological properties of the topologically non-trivial units. Topological properties are usually characterized by topological invariants, and in the photonic crystal system, the two-dimensional Zak phase is an effective topological invariant that can be used to distinguish topologically non-trivial and topologically trivial units.

[0078] As shown in the formula, the two-dimensional Zak phase is calculated by integrating the Berry connection within the first Brillouin zone (FBZ):

[0079]

[0080] Where:

[0081] P = (P x , P y ) represents the two-dimensional polarization intensity;

[0082] k = (k x , k y ) represents the wave vector;

[0083] represents the Berry connection;

[0084] It should be noted that A α (k) is the Berry connection, k = (k x , k y ) represents the wave vector, ψ k represents the eigenstate wave function, |ψ k > represents the eigenstate of the first ground state energy band, represents the wave vector k αThe partial derivative, describing the infinitesimal change of the eigenstate with k, where i represents the imaginary unit to ensure the Hermiticity of the Berry connection, α represents the directional component, x and y respectively refer to the lattice directions, and θ α is the two-dimensional Zak phase, and P α is the polarization intensity component, and ∫ FBZ is the integral over the first Brillouin zone, and Tr[A α (k)] is the trace of the Berry connection, where Tr represents taking the trace of a matrix, and dk represents integrating over the wave vectors in the first Brillouin zone.

[0085] Before calculating the two-dimensional Zak phase, it is first necessary to analyze the band structure of the photonic crystal unit. By solving the eigenmodes of the photonic crystal, the electromagnetic field distributions at different k points can be obtained, thereby calculating the Berry connection and finally obtaining the Zak phase.

[0086] According to the calculation results of the Zak phase, topological non-trivial units and topological trivial units can be distinguished:

[0087] When the Zak phase is (0, 0), the unit is in the topological trivial phase;

[0088] When the Zak phase is (π, π), the unit is in the topological non-trivial phase.

[0089] As Figure 2 shown, by performing band calculations on the photonic crystal unit, it can be found that the band structures of the two types of units are significantly different. In the frequency range from 94.6 THz to 112.7 THz (corresponding to 2.66 μm to 3.17 μm), there is an obvious band gap, and the calculated value of the Zak phase of the topological non-trivial unit is (π, π), proving its topological non-trivial characteristics, while the calculated value of the Zak phase of the topological trivial unit is (0, 0).

[0090] After clarifying the Zak phase of the topological non-trivial unit, the topological invariant can be further used to guide the subsequent design of optical devices. For example, distributing the topological non-trivial units reasonably in the supercell to ensure that topological defect states can be formed, and finally achieving high stability and high selectivity of the filter.

[0091] Step S3, determine the specific arrangement position of the topological non-trivial unit within the supercell according to the two-dimensional Zak phase of the topological non-trivial unit, so that in each supercell, a topological non-trivial defect region is formed by arranging the topological non-trivial unit, and a defect state band structure is formed through the coupling of topological defect states in adjacent supercells;

[0092] After determining the topological invariant of the topologically non-trivial unit, rationally design its layout within the supercell to form a stable topologically non-trivial defect region. The existence of the topologically non-trivial defect is the key to the operating principle of the filter, as it determines the generation of defect states and their propagation characteristics in the photonic crystal slab.

[0093] As Figure 1 (b) shows, the basic structure of the supercell consists of a topologically non-trivial unit surrounded by half-regions of multiple topologically trivial units. Since the Zak phase of the topologically non-trivial unit is (π, π), while the Zak phase of the topologically trivial unit is (0, 0), topological defect states will be generated at their adjacent interfaces. This topological defect state optically manifests as a localized resonance mode, which can support the propagation of light at specific frequencies and couple with each other between supercells to form a new defect state energy band structure.

[0094] To optimize the formation of the defect state energy band, it is necessary to consider the layout of the topologically non-trivial units in the supercell and the arrangement relationship between adjacent units. In the initial design, each supercell contains a topologically non-trivial unit and is surrounded by topologically trivial units. This structure ensures the localization of topological defects and at the same time ensures the effective coupling of defect states between different supercells to form a stable energy band structure. As Figure 3 shown, at k x = 0, among the four defect state energy bands, energy bands 3 and 4 are located within the bandgap, while the frequencies of energy bands 1 and 2 are slightly lower than the bandgap edge, indicating that their energies are mainly affected by the coupling of adjacent defect states.

[0095] The coupling strength of the defect state energy band is affected by the periodic arrangement of the supercells. To optimize the characteristics of the defect state energy band, the number of rows (columns) of topologically trivial units between adjacent topologically non-trivial units can be adjusted, as Figure 7 (a) and 7(b) show. When the interval of topologically trivial units between adjacent supercells increases to 2 or 3, the energy band structure changes significantly. Specifically:

[0096] When the number of rows (columns) is 2, energy bands 1 and 3 of the transverse electric-like mode exhibit strong frequency dispersion characteristics, while energy bands 2 and 4 are relatively flat;

[0097] When the number of rows (columns) is 3, energy bands 2 and 3 of the transverse electric-like mode exhibit strong dispersion characteristics, while energy bands 1 and 4 are relatively flat, but the flat region of energy band 1 is smaller.

[0098] After comprehensive consideration, the best choice is to set the number of rows (columns) of adjacent topologically non-trivial units to 1 to ensure sufficient coupling of defect states and at the same time maintain the flatness of the energy band in the bandgap, so that the filter can maintain a stable optical response at different incident angles.

[0099] In addition, if the spacing between adjacent fixed units remains unchanged, the band characteristics can also be optimized by adjusting the area of the topologically non-trivial defect region. As Figure 8 (a) and Figure 8 (b) show, when the topologically non-trivial defect region expands to 2×2 or 3×3, the frequency dispersion characteristics of the defect state bands change, and their band structures are respectively as Figure 8 (c) and Figure 8 (d) show. Specifically:

[0100] In the 2×2 defect region, bands 1 and 4 show strong dispersion, while bands 2 and 3 are relatively flat;

[0101] In the 3×3 defect region, bands 1, 2, and 3 show strong dispersion, while only band 4 remains flat.

[0102] Taking into account the requirements of the locality of the topological defect state and the flatness of the band, a 1×1 topologically non-trivial defect region is finally selected as the optimized design scheme. This structure can not only effectively form stable topological defect states, but also ensure that the defect state bands remain stable when the incident angle changes, achieving an efficient angle-insensitive optical filtering effect.

[0103] Through the design of this step, the reasonable layout of the topologically non-trivial units within the supercell is ensured, the formation of the topological defect state is optimized, and stable defect state bands with optical characteristics are formed through the periodic coupling between supercells.

[0104] Step S4. Based on the requirement of the flatness of the defect state band structure, adjust the width of the air microholes, analyze the relationship between the change of the band frequency position and the flatness of the band, and screen out the width value that makes the TE-like mode band present a flat requirement near the bandgap;

[0105] After completing the arrangement of the topologically non-trivial units, in order to optimize the performance of the optical filter, it is necessary to further adjust the width w of the air microholes in the photonic crystal to control the frequency position and flatness of the defect state bands. The geometric parameters of the air microholes directly affect the effective refractive index distribution of the photonic crystal, thus determining the characteristics of the band structure.

[0106] The flatness of the band is an important indicator to measure the stability of the defect state. A flat band means that the resonance frequency of the defect state changes less with the wave vector k x and thus maintains a stable optical response under excitation at different incident angles. Therefore, the goal of this step is to find the optimal parameter setting that can form a flat band near the bandgap by precisely adjusting the width w of the air microholes.

[0107] As Figure 6As shown, with different widths \(w\) of air micro - pores, the frequency distribution of the defect - state energy bands changes significantly. When \(w = 0.2\ \mu m\) (see Figure 6 (a)), the frequencies of the four defect - state energy bands are relatively low and have strong dispersion characteristics, that is, the energy bands are relatively steep, indicating that they are sensitive to the change of the incident angle and are not conducive to the stability of the optical filter. As \(w\) increases to \(0.3\ \mu m\) (see Figure 6 (b)- Figure 6 (c)), the overall frequency of the defect - state energy bands increases. At the same time, the energy bands 1, 3, and 4 of the transverse - electric - like (TE - like) mode gradually become flatter, indicating that the sensitivity of the topological defect states to the change of the incident angle is reduced at this time, which is conducive to the filter to achieve the angle - insensitive characteristic.

[0108] Further optimization analysis shows that when \(w\) is set to \(0.34\ \mu m\), the flatness of the defect - state energy bands reaches the best state. Under this setting, energy band 1 shows extremely small dispersion near the lower edge of the band gap, indicating that its resonant wavelength has a very small response to the change of the incident angle, thus achieving a stable filtering effect in a relatively large incident - angle range.

[0109] Physically, the width of the air micro - pores affects the local electromagnetic - field distribution, thus changing the equivalent refractive index of the photonic crystal, and then adjusting the energy - band structure. Increasing \(w\) will cause the overall energy band to shift to the high - frequency direction, and at the same time affect the locality of the defect states and the dispersion degree of the energy bands. Therefore, choosing an appropriate \(w\) should not only ensure that the defect - state energy bands are in an appropriate band - gap position but also ensure their flatness, so as to optimize the stability and selectivity of the optical filter.

[0110] In this step, by adjusting the width \(w\) of the air micro - pores, the frequency position and the flatness of the defect - state energy bands are optimized, so that the filter has stable transmission characteristics at different incident angles.

[0111] Step S5: Based on the width value, adjust the number of rows or columns of the topological - trivial units between adjacent topological non - trivial defects, and determine the optimal spacing parameter of the defect - state coupling strength according to the change of the energy - band dispersion characteristics;

[0112] After determining the optimal width \(w\) of the air micro - pores, it is also necessary to optimize the spacing between adjacent topological non - trivial defects to adjust the coupling strength of the topological defect states. The coupling degree of the topological defect states directly affects the dispersion characteristics of the defect - state energy bands, thus determining the angle - insensitive performance of the filter. Therefore, the goal of this step is to optimize the optimal spacing parameter between topological non - trivial defects on the premise of ensuring sufficient band - gap stability.

[0113] The coupling strength of topological defect states depends on the number of rows (columns) of topologically trivial cells between adjacent topologically non-trivial cells. When the interval between adjacent topologically non-trivial cells is small, the interaction between defect states is enhanced, leading to increased band dispersion, thereby increasing the sensitivity of the resonance frequency to the change in the incident angle. On the contrary, if the interval is too large, the coupling effect between defect states is weakened, which may lead to an increase in the localization degree of the defect state band, thus affecting the working efficiency of the filter.

[0114] As Figure 7 (a) and 7(b) show, different configurations of the number of rows (columns) of topologically trivial cells affect the morphology of the defect state band:

[0115] When the number of rows (columns) of topologically trivial cells between adjacent topologically non-trivial defects increases to 2 ( Figure 7 (c)), the dispersion characteristics of the quasi-transverse electric mode bands 1 and 3 are enhanced, while bands 2 and 4 are relatively flat. This indicates that the interaction between defect states is strong, resulting in bands 1 and 3 being more sensitive to the change in the incident angle, while bands 2 and 4 have better stability.

[0116] When the number of rows (columns) increases to 3 ( Figure 7 (d)), the quasi-transverse electric mode bands 2 and 3 exhibit stronger dispersion characteristics, while bands 1 and 4 become relatively flat, but the flat region of band 1 shrinks. This shows that after further increasing the interval, the stability of band 1 decreases, affecting the overall performance of the filter.

[0117] Based on the above analysis, by comparing at different numbers of rows (columns) of topologically trivial cells, it is found that when the interval between adjacent topologically non-trivial defects is 1 row (column) of topologically trivial cells, the best balance between band flatness and defect state localization degree is achieved. Therefore, this configuration is finally selected as the optimal spacing parameter, enabling the filter to maintain good angle-insensitive performance at different incident angles while ensuring efficient coupling of the defect state band.

[0118] Through the optimization of this step, the flatness of the topological defect state band is ensured, making the resonance wavelength of the filter change minimally under different incident angle conditions, thereby improving the stability and robustness of the optical filter.

[0119] Step S6: Perform full-wave electromagnetic simulation on the photonic crystal slab based on the optimal spacing parameter, and obtain the normalized transmission spectrum data by exciting plane waves with different incident angles in the incident plane to verify the offset of the resonance wavelength with the incident angle;

[0120] After completing the layout optimization of the topologically non-trivial unit and adjusting the coupling strength of the topological defect states, the next step is to perform full-wave electromagnetic simulation to verify the actual optical performance of the photonic crystal slab. The core objective of this simulation process is to test the resonance wavelength stability of the filter under different incident angles and quantify its angle-insensitive characteristics.

[0121] To achieve this goal, the finite-difference time-domain method (FDTD) is used for full-wave simulation to analyze the propagation characteristics of incident light in the photonic crystal slab. As Figure 4 shown, during the simulation process:

[0122] A p-polarized plane wave (the electric field component is in the plane of incidence) is introduced above the photonic crystal slab, and different incident angles θ are set for excitation; an energy monitor is placed below the photonic crystal slab to record the spectral response of the transmitted light to calculate the normalized transmission spectrum.

[0123] The simulation results show that when the incident angle θ = 0°, an obvious transmission valley (i.e., the transmittance is close to 0%) appears at a wavelength of 3.24 μm, which is exactly the optical resonance characteristic of the defect state. This phenomenon indicates that a strong local mode is formed in the defect state energy band at this wavelength, making it difficult for light of this wavelength to transmit, thus playing an optical filtering role.

[0124] When the incident angle θ changes from 0° to 30°, it is found that the change in the resonance wavelength is extremely small, only slightly shifting from 3.24 μm to 3.234 μm, indicating that this optical filter can maintain a stable spectral response within a wide range of incident angles. This characteristic benefits from the pre-optimized coupling of topological defect states, resulting in a relatively high energy band flatness, thus weakening the influence of the incident angle change on the resonance wavelength.

[0125] Further analyzing the normalized transmission spectrum (as Figure 5 shown), it can be observed that near a wavelength of 3.24 μm, as the incident angle increases from -30° to 30°: the transmittance is always lower than 10%, indicating that the filter can effectively suppress the transmission of this wavelength; the reflectance remains above 90%, further verifying that this structure has strong selectivity and high reflectivity for light of this specific wavelength.

[0126] To quantitatively measure the angle-insensitive performance of this filter, calculate the average transmittance at different incident angles <t>, and its calculation formula is as follows:

[0127]

[0128] Where: T(θ i ) is the transmittance at the incident angle θ i , N is the total number of statistically incident angles; θ i is the i-th incident angle, and the incident angle range covers -30° to 30°.

[0129] The calculation results show that the <t>The value is 3.75%, further proving its ability to maintain a low transmittance at different incident angles, that is, having good angle-insensitive filtering characteristics.

[0130] This step verifies the actual performance of the filter through full-wave electromagnetic simulation, demonstrating its ability to maintain stable resonance wavelengths and low transmittance within a wide range of incident angles. This experimental verification provides data support for subsequent optimization and actual manufacturing, and proves the feasibility of the filter design based on topological photonic crystals in applications such as optical communication and sensing.

[0131] Step S7: Based on the offset, iteratively optimize the air micropore width and the topological non-trivial defect spacing parameters to determine the structural parameters of the supercell;

[0132] After completing the full-wave electromagnetic simulation and verifying the angle-insensitive characteristics of the filter, it is necessary to further optimize the key structural parameters to ensure that the filter maintains stable optical performance under a wider range of working conditions. Specifically, this step iteratively optimizes the air micropore width w and the spacing p of the topological non-trivial defects based on the offset of the resonance wavelength to improve the flatness and stability of the defect state energy band.

[0133] First, optimize the air micropore width w. As Figure 6 shown, different w values will significantly affect the position and dispersion characteristics of the defect state energy band:

[0134] When w is too small (such as 0.2 μm), the frequency of the energy band is low and the dispersion is large, resulting in the resonance wavelength being easily affected by the change of the incident angle;

[0135] When w is too large (such as 0.4 μm), although the frequency of the energy band increases, the locality of the defect state weakens, affecting the selectivity of the filter.

[0136] Therefore, by simulating and testing the normalized transmittance spectra corresponding to different w values and calculating the resonance wavelength offset at different incident angles, finally w = 0.34 μm is selected because the energy band flatness is the best at this value, making the resonance wavelength offset of the filter within the incident angle range of -30° to 30° the smallest, only 0.006 μm, ensuring the angle-insensitive filtering characteristics.

[0137] Secondly, optimize the topological non-trivial defect spacing p. As Figure 7 shown, adjusting the number of rows (columns) of topological trivial cells between adjacent topological non-trivial defects will affect the dispersion characteristics of the defect state energy band:

[0138] When the number of rows (columns) of topological trivial cells is 2, energy bands 1 and 3 have strong dispersion, indicating that the coupling effect between defect states is too strong, making the resonance wavelength easily affected by the incident angle;

[0139] When the number of rows (columns) of topologically trivial units is 3, energy bands 2 and 3 become more dispersive, indicating that the coupling of topological defect states is too weak at this time, resulting in a decline in the filter performance.

[0140] After optimization analysis, the number of rows (columns) of topologically trivial units is finally selected as 1, that is, the spacing between adjacent topologically non-trivial defects is set to p = 2 μm, ensuring that the energy bands of defect states remain flat at the resonance wavelength of 3.24 μm, while reducing the sensitivity of the energy bands to the change of the incident angle.

[0141] In this step, by iteratively optimizing the parameters of the air micropore width and the topological defect spacing, the optimal structural parameters of the supercell are finally determined, enabling the filter to maintain a low transmittance (<10%) and a stable resonance wavelength (offset <0.006 μm) under different incident angle conditions. This optimization process ensures the high efficiency, stability, and applicability of the filter.

[0142] Step S8: Output the final design of the optical filter according to the structural parameters.

[0143] After optimizing the key parameters (the air micropore width w and the spacing p of topologically non-trivial defects), the determined structural parameters of the supercell are used to output the complete optical filter design to ensure its characteristics of high stability, low transmittance, and angle insensitivity.

[0144] First, combining the foregoing optimization results, the core structural parameters of the final optical filter are as follows:

[0145] Air micropore width: w = 0.34 μm, to ensure the flatness of the energy bands of defect states and minimize the sensitivity of the resonance wavelength to the change of the incident angle;

[0146] Spacing of topologically non-trivial defects: p = 2 μm, with only 1 row (column) of topologically trivial units spaced between adjacent topologically non-trivial defects, to maintain an appropriate coupling strength of defect states and optimize the energy band structure;

[0147] Thickness of the photonic crystal slab: h = 0.5 μm, dielectric constant ε = 11.7 (non-dispersive), to ensure the stability of the material within the target wavelength range.

[0148] Based on these parameters, a structural model of the final optical filter is generated using a three-dimensional electromagnetic simulation modeling tool, and further optimization verification is carried out:

[0149] Calculate the bandgap range and the energy bands of defect states to ensure that the filter has stable optical resonance characteristics near 3.24 μm;

[0150] Perform a normalized transmittance test (such as Figure 5 As shown, within the range of incident angles from -30° to 30°, the transmittance is always lower than 10%, and the reflectance is higher than 90%, proving the efficient optical properties of the filter.

[0151] Perform the optical resonance wavelength shift test to ensure that the resonance wavelength change is less than 0.006 μm, meeting the design requirements of the angle-insensitive filter.

[0152] Finally, based on the comprehensive optimization and simulation verification of this step, an integrated design scheme of the angle-insensitive optical filter based on topological photonic crystals is output, providing theoretical support for the physical manufacturing and experimental testing of the device. This filter can be widely applied in the fields of optical communication, optical sensing, high-precision spectral analysis, etc.

[0153] In this embodiment, as described in step S1 above, the length of each supercell arranged periodically in the x and y directions is set to twice the lattice constant.

[0154] In this embodiment, as described in step S3 above, the method of forming the defect state energy band structure by coupling the topological defect states in adjacent supercells includes:

[0155] Step S31: Based on the two-dimensional Zak phase of the topological non-trivial unit, embed the topological non-trivial unit as a defect into the supercell, so that it is surrounded by topological trivial units at intervals along the x and y directions;

[0156] Step S32: Set the interval between topological non-trivial defects in adjacent supercells to n rows or n columns of topological trivial units, and control the defect state coupling strength by adjusting the n value;

[0157] Step S33: When n = 1, the adjacent defect states couple to form a defect state energy band structure containing at least one flat-like transverse electric mode energy band. The frequency of the flat-like transverse electric mode energy band is within the photonic crystal band gap range and corresponds to the resonance wavelength insensitive to the incident angle.

[0158] In this embodiment, as described in step S4 above, the method of screening the width value required for the transverse electric mode energy band to be flat near the band gap includes:

[0159] Step S41: Set the initial air micropore width value and construct the topological photonic crystal unit structure;

[0160] Step S42: Calculate the energy band distribution of the topological photonic crystal unit structure in the first Brillouin zone and extract the energy band data within the band gap range;

[0161] Step S43: Identify the energy bands formed by topological defect states near the band gap and extract the transverse electric mode energy bands;

[0162] Step S44: Calculate the frequency variation of the quasi-transverse-electric (TE) mode energy band at different wave vector values, and evaluate the flatness of the energy band;

[0163] Step S45: Adjust the width of the air micro-holes, and repeat the above steps to compare the variation trends of the energy band frequencies and flatness at different micro-hole widths;

[0164] Step S46: Select the value of the air micro-hole width that meets the requirements of the energy band flatness, so that the frequency dispersion of the quasi-TE mode energy band near the band gap is minimized.

[0165] In this embodiment, as described in step S5 above, the method for adjusting the number of rows or columns of the topologically trivial cells between adjacent topologically non-trivial defects based on the width value includes:

[0166] Step S51: Construct a topologically photonic crystal slab structure with the determined air micro-hole width value;

[0167] Step S52: Set the number of rows or columns of the topologically trivial cells between the initial topologically non-trivial defects, calculate the energy band structure after the supercell arrangement, and extract the energy band formed by the defect states;

[0168] Step S53: Calculate the frequency variation of the quasi-TE mode energy band at different wave vector k values, and evaluate its dispersion characteristics;

[0169] Step S54: Sequentially increase the number of rows or columns of the topologically trivial cells, repeat the above steps, and record the frequency positions and flatness variations of the defect state energy bands at different numbers of rows or columns of the topologically trivial cells;

[0170] Step S55: Determine the optimal number of rows or columns of the topologically trivial cells that can maintain the flatness of the quasi-TE mode energy band and optimize the defect state coupling strength by comparing the energy band characteristics at different numbers of rows or columns of the topologically trivial cells.

[0171] In this embodiment, as described in step S6 above, the method for performing full-wave electromagnetic simulation on the photonic crystal slab includes:

[0172] Step S61a: Construct an optical filter model based on the topologically photonic crystal in the computational domain, and set the periodic boundary conditions;

[0173] Step S62a: Discretely calculate the electromagnetic field distribution of the photonic crystal slab using the finite-difference time-domain method, and define the computational grid;

[0174] Step S63a: Set plane wave excitation sources with different incident angles in the incident plane above the slab structure, and place a far-field energy monitor below to record the transmitted signals;

[0175] Step S64a: Calculate the normalized transmission spectra under different incident angle conditions, and extract the transmittance data corresponding to the resonant wavelengths of the defect states;

[0176] Step S65a: Calculate the offset of the transmittance with respect to the change in the incident angle, and optimize the structural parameters of the supercell based on this offset.

[0177] In this embodiment, as described in step S6 above, the method for verifying the offset of the resonant wavelength with respect to the incident angle based on the normalized transmission spectrum data includes:

[0178] Step S61b: Set the range of change of the incident angle, and perform full-wave electromagnetic simulation by sampling multiple different incident angle conditions;

[0179] Step S62b: Under each incident angle condition, calculate the normalized transmission spectrum and extract the position of the transmission valley corresponding to the resonant wavelength;

[0180] Step S63b: Record the resonant wavelengths under all incident angle conditions, and plot the curve of the resonant wavelength changing with the incident angle;

[0181] Step S64b: Calculate the maximum offset of the resonant wavelength within the range of the incident angle, and compare it with the set threshold for the angle-insensitive filtering characteristic;

[0182] Step S65b: If the maximum offset exceeds the set threshold, adjust the air micropore width or the topological non-trivial defect spacing parameter, and repeat the above steps until the angle-insensitive requirement is met.

[0183] According to another aspect of the embodiments of the present application, an electronic device is further provided, including a processor and a memory. When the processor executes the computer program stored in the memory, the steps of the method are implemented.

[0184] In the above embodiments of the present invention, the descriptions of the respective embodiments have their own emphases. For the parts not detailed in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

[0185] In several embodiments provided by the present application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are merely illustrative. For example, the division of the units can be a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces. The indirect couplings or communication connections of the units or modules can be in an electrical or other form.

[0186] In addition, in each embodiment of the present invention, the functional units can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

[0187] If the above-mentioned integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in each embodiment of the present invention. The foregoing storage medium includes: various media such as USB flash drives, read-only memories (ROMs), random access memories (RAMs), mobile hard disks, magnetic disks, or optical discs that can store program codes.

[0188] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.< / t> < / t>

Claims

1. A method for designing an optical filter based on topological photonic crystals, characterized in that: The steps include: Constructing a photonic crystal slab composed of periodically arranged super units, wherein the super unit comprises a topological non-trivial unit and a topological trivial unit, wherein the topological non-trivial unit is surrounded by a topological trivial unit, and the topological non-trivial unit and the topological trivial unit both comprise four air micropores, and the positions of the air micropores of the two are distributed differently; Calculate the topological invariant of the topological non-trivial unit based on the two-dimensional Zach phase, and determine the two-dimensional Zach phase of the topological non-trivial unit; According to the two-dimensional Zach phase of the topological non-trivial unit, the specific arrangement position of the topological non-trivial unit in the super unit is determined, so that in each super unit, a topological non-trivial defect region is formed by arranging the topological non-trivial unit, and a defect state band structure is formed by coupling the topological defect states in adjacent super units; Based on the band flatness requirement of the defect state band structure, the width of the air micropore is adjusted, the relationship between the band frequency position and the band flatness is analyzed, and the width value that makes the transverse electric mode-like band present the flatness requirement near the band gap is screened out; Adjusting the number of topological trivial unit rows or columns between adjacent topological non-trivial defects based on the width value, and determining the optimal spacing parameter of the defect state coupling strength according to the change of the energy band dispersion characteristics; Based on the optimal spacing parameters, full-wave electromagnetic simulation is performed on the photonic crystal slab, and normalized transmission spectrum data is obtained by plane wave excitation at different incident angles in the incident plane to verify the offset of the resonance wavelength with the incident angle; Iteratively optimizing the air micropore width and topological non-trivial defect spacing parameters based on the offset to determine the structural parameters of the super unit; The final design of the optical filter is output according to the structural parameters.

2. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: The length of each supercell periodically arranged in the x and y directions is set to twice the lattice constant.

3. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: The method for determining the two-dimensional Zach phase of the topological non-trivial unit comprises: Calculate the transverse electric mode-like band structure of the topological non-trivial unit in the first Brillouin zone; Obtain the eigenstate |ψ of the first ground state energy band in the energy band structure at each wave vector k point k > According to the eigenstate |ψ k > Calculate Bailey connection: Among them, A α (k) is Bailey connection, k = (k x ,k y ) represents the wave vector, ψ k represents the eigenstate wave function, |ψ k represents the eigenstate of the first ground-state band, Denotes the wave vector k α The partial derivative of describes the small changes of the eigenstate with k, i represents the imaginary unit to ensure the Hermitian property of the Berry connection, α represents the directional component, and x and y refer to the lattice directions respectively; The Bailey connection is traced and integrated in the first Brillouin zone to obtain the two-dimensional Zach phase, where the integration path covers the entire first Brillouin zone: Among them, θ α is the two-dimensional Zach phase, P α is the polarization intensity component, ∫ FBZ is the first Brillouin zone integral, Tr[A α (k)] is the trace of the Bailey connection, Tr represents the trace of the matrix, and dk represents the integration of the wave vector in the first Brillouin zone; When θ α =π, it is determined that the topological non-trivial unit has a non-trivial topological characteristic in the α direction; According to the Zack phase θ in the x and y directions x and θ y The combination mode of θ determines the two-dimensional Zach phase of the topological non-trivial unit, where if the phase combination mode satisfies θ x =π and θ y =π, it is determined that the topologically non-trivial unit is in a topologically non-trivial phase.

4. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: Methods for forming defect state band structures by coupling topological defect states in adjacent supercells include: Based on the two-dimensional Zach phase of the topological non-trivial unit, the topological non-trivial unit is embedded as a defect in a super unit so that the topological non-trivial unit is surrounded by topological trivial units in the x and y directions; The spacing between topological non-trivial defects in adjacent supercells is set to n rows or n columns of topological trivial cells, and the coupling strength of defect states is controlled by adjusting the value of n; When n=1, adjacent defect states couple to form a defect state band structure including at least one flat quasi-transverse electric mode energy band, the frequency of which is within the photonic crystal band gap and corresponds to a resonant wavelength that is insensitive to the incident angle.

5. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: Methods for screening out the required width value for making the transverse electric mode-like energy band flat near the band gap include: Setting the initial air micropore width value and constructing a topological photonic crystal unit structure; Calculating the energy band distribution of the topological photonic crystal unit structure in the first Brillouin zone, and extracting energy band data within the band gap range; Identify the energy bands formed by topological defect states near the band gap and extract the transverse electric mode-like energy bands; Calculate the frequency variation of the quasi-TE mode energy band under different wave vector values ​​and evaluate the flatness of the energy band; Adjust the width of the air micropores and repeat the above steps to compare the band frequency and flatness change trends under different micropore widths; The width of the air micropore is selected to meet the requirements of band flatness, so that the frequency dispersion of the transverse electric mode-like energy band near the band gap is minimized.

6. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: The method for adjusting the number of topological trivial unit rows or columns between adjacent topological non-trivial defects based on the width value comprises: Using a certain value of air micropore width, a topological photonic crystal slab structure is constructed; Set the number of topological trivial unit rows or columns between the initial topological non-trivial defects, calculate the band structure after superunit arrangement, and extract the energy band formed by the defect state; Calculate the frequency variation of the quasi-TE mode energy band under different wave vector k values ​​and evaluate its dispersion characteristics; The number of rows or columns of topological trivial units is increased successively, and the above steps are repeated to record the frequency position and flatness changes of the defect state energy band under different numbers of rows or columns of topological trivial units; By comparing the band characteristics under different numbers of rows or columns of topological trivial units, the optimal number of rows or columns of topological trivial units that can maintain the flatness of the transverse electric mode band and optimize the defect state coupling strength is determined.

7. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: The method for performing full-wave electromagnetic simulation on the photonic crystal slab comprises: Construct an optical filter model based on topological photonic crystals in the computational domain and set periodic boundary conditions; Using a finite-difference time-domain method to perform discrete calculations on the electromagnetic field distribution of the photonic crystal slab, and defining a calculation grid; A plane wave excitation source with different incident angles in the incident plane is set above the flat plate structure, and a far-field energy monitor is placed below to record the transmission signal; Calculate the normalized transmission spectra under different incident angles and extract the transmittance data corresponding to the defect state resonance wavelength; The offset of the transmittance variation with the incident angle is calculated, and the structural parameters of the supercell are optimized based on the offset.

8. The optical filter design method based on topological photonic crystal according to claim 1, characterized in that: Methods for verifying the shift of the resonant wavelength with the incident angle based on the normalized transmission spectrum data include: Set the range of the incident angle and sample multiple different incident angle conditions for full-wave electromagnetic simulation; Under each incident angle condition, the normalized transmission spectrum is calculated and the transmission valley position corresponding to the resonance wavelength is extracted; Record the resonant wavelength under all incident angle conditions and draw a curve of the resonant wavelength changing with the incident angle; Calculate the maximum offset of the resonant wavelength within the incident angle range and compare it with the set threshold of the target angle-insensitive filter characteristic; If the maximum offset exceeds the set threshold, the air micropore width or topological non-trivial defect spacing parameter is adjusted, and the above steps are repeated until the angle insensitivity requirement is met.

9. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the optical filter design method based on topological photonic crystals as described in any one of claims 1 to 8, and the processor is configured to execute the program stored in the memory.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the optical filter design method based on topological photonic crystals in any one of claims 1 to 8 are executed.

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