Fano filter based on C4 asymmetric topology photonic crystal angular state coupling

Abstract

The invention provides a C4 asymmetric topological photonic crystal angular state coupling-based Fano filter, which is composed of a topological boundary state optical waveguide and one or more topological angular state resonant cavity structures, and Fano resonance is realized between the topological boundary state optical waveguide and the topological angular state resonant cavity structures through a coupling interface; the topological boundary state optical waveguide and the topological angular state resonant cavity are both constructed based on C4 asymmetric topological photonic crystals. Through a plurality of topological angular state resonant cavities and adjustment of the sizes of dielectric cylinders at the corners of the resonant cavities, the local field intensity can be enhanced, zero-dimensional optical localization is realized, and selective optical filtering of two or more specific frequencies is realized. The filter provided by the invention can realize an efficient single-frequency or multi-frequency-band optical filtering function, and provides a new scheme for the application of a topological photonic device in optical communication.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic technology, and more specifically, to a Fano filter based on C4 asymmetric topological photonic crystal angular state coupling. Background Technology

[0002] Optical filters are core components of modern photonic integrated circuits, and their performance directly determines the channel selection, noise suppression, and spectral efficiency of optical communication systems. Among numerous filtering mechanisms, the Fano resonance has attracted much attention due to its unique physical characteristics. The Fano resonance originates from the coherent interference between narrowband discrete states (such as local cavity modes) and broadband continuous states (such as waveguide transmission modes). Its spectrum exhibits a sharp asymmetric line shape and possesses advantages in quality factor (Q value) and strong field localization. This characteristic enables high-precision frequency selection, providing an ideal platform for dense wavelength division multiplexing and on-chip spectral analysis.

[0003] However, the practical application of traditional Fano resonant filters faces inherent limitations: First, the resonant mode is highly dependent on the geometric accuracy of the structure; nanoscale processing errors or material inhomogeneities can lead to resonant frequency drift and linear degradation. Second, high Q-value resonances are usually accompanied by narrow bandwidths, making them sensitive to environmental disturbances (such as temperature fluctuations or mechanical stress) and lacking stability. Third, most existing designs are based on symmetric photonic crystal structures, limiting their tuning flexibility and making it difficult to achieve multi-band operation or dynamic reconstruction. These factors severely restrict the reliability and integration of filters in complex environments.

[0004] In recent years, advancements in topological photonics have offered new insights into addressing these challenges. Topological photonic crystals, classified by band topological properties, support topologically protected boundary and corner states, modes of which are naturally immune to specific defects and perturbations. For example, one-dimensional topological edge states enable backscatter-free light transmission, while zero-dimensional topological corner states can form high-Q local resonances, and their frequency and field distribution can be flexibly controlled through geometric parameters. Introducing topological protection mechanisms into Fano resonance systems promises to significantly improve device robustness and design freedom while maintaining high sensitivity. Summary of the Invention

[0005] This invention proposes a Fano filter based on corner-state coupling of a C4 asymmetric topological photonic crystal. This design combines the sharp, asymmetric transmission valley of the Fano resonance with the filter's ability to filter specific frequencies of light. By optimizing the corner dielectric pillar dimensions to enhance the local field strength, efficient multi-frequency filtering is achieved. This design, while ensuring device stability and a good quality factor, broadens the application range of C4 asymmetric photonic crystals, providing a new paradigm for the practical application of topological photonic devices in on-chip systems.

[0006] The technical solution of the present invention is as follows:

[0007] A Fano resonant filter based on C4 asymmetric topological photonic crystal angular coupling is characterized by comprising: a topological boundary state optical waveguide spliced ​​together by a first photonic crystal PC1 and a second photonic crystal PC2 with a lattice boundary as the splicing interface; and at least one topological angular resonant cavity structure located at and spliced ​​to the edge of the second photonic crystal PC2; wherein the topological angular resonant cavity structure is spliced ​​together by angular resonant cavity modules and edge modules, and the splicing interface between the two has at least one right-angle boundary; wherein:

[0008] The first photonic crystal PC1, the second photonic crystal PC2, the angular resonant cavity module, and the edge module are all asymmetric square lattice photonic crystal structures with internal dielectric pillars offset from the center of the unit cell, and the lattice constant is a;

[0009] In the first photonic crystal PC1 and the edge module, the radii r1 and r2 of the external dielectric pillars in the unit cell are both 0.125a. In the second photonic crystal PC2 and the angular resonant cavity module, the radii r1 of the external dielectric pillars are 0.1a, and the radii r2 of the internal dielectric pillars are 0.15a.

[0010] The internal dielectric pillars of the first photonic crystal PC1 are offset from the cell center by a distance of 0.125a in the direction away from the interface between the first photonic crystal PC1 and the second photonic crystal PC2, exhibiting topological nontriviality; the internal dielectric pillars of the second photonic crystal PC2 are offset from the cell center by a distance of 0.15a in the direction closer to the interface between the first photonic crystal PC1 and the second photonic crystal PC2, exhibiting topological triviality.

[0011] In the unit cell of the angular resonant cavity module and the edge module, the internal dielectric pillars are offset towards the right-angle vertex of a right-angled boundary near the interface between the first photonic crystal PC1 and the second photonic crystal PC2; the distance between the internal dielectric pillars and the center of the unit cell of the angular resonant cavity module is... a, The distance between the internal dielectric pillars in the cell of the edge module and the cell center is... a.

[0012] Furthermore, in the topological optical waveguide structure, the width of the second photonic crystal PC2 is 1 to 2 lattice constants, and the distance between the angular resonant cavity and the splicing interface of the first photonic crystal PC1 and the second photonic crystal PC2 is 2a to 3a.

[0013] Furthermore, the dielectric pillar of the square lattice photonic crystal is a circular dielectric pillar, and the lattice constant a satisfies 10 μm ≤ a ≤ 20 μm.

[0014] Furthermore, the circular dielectric pillars are made of silicon, the background material is air, and all dielectric pillars are fabricated on silicon or silicon dioxide substrates.

[0015] Furthermore, the number of the topological angular resonant cavity structures is multiple.

[0016] Furthermore, the radius of the external dielectric pillar at the right angle point of the topological angular resonant cavity structure is scaled according to a scaling factor β, 0.9 ≤ β ≤ 1.1, to improve the filtering effect and change the filtering frequency.

[0017] Furthermore, the radii of the external dielectric pillars at the right-angle points of the angular resonant cavities of multiple topological angular resonant cavities are scaled according to different scaling factors β to achieve multi-frequency filtering, where 0.9 ≤ β ≤ 1.1.

[0018] Furthermore, the filter supports a frequency range of 9.704-9.958 THz.

[0019] Furthermore, the lattice constant a satisfies 10 μm ≤ a ≤ 20 μm.

[0020] Furthermore, the lattice constant a = 15 μm.

[0021] The Fano resonance filter based on C4 asymmetric topological photonic crystal corner state coupling of this invention includes a topological boundary state optical waveguide structure and one or more topological corner state resonant cavity structures. The topological boundary state optical waveguide supports topologically protected boundary state transmission at the interface, providing a broadband continuous state for Fano resonance. Its function is to guide light and form a broadband continuous state, providing a channel for optical signal transmission. The topological boundary state optical waveguide structure and the topological corner state resonant cavity structure are coupled via near-field evanescent waves, localizing the light in a zero-dimensional corner region to form a narrowband discrete state with a good Q value. The broadband continuous state and the narrowband discrete state interfere with each other, generating a Fano resonance for optical filtering at the output end of the topological boundary state waveguide structure.

[0022] Two topological angular resonant cavities can excite localized topological angular states at their corner points at different frequencies, and couple with topological boundary state waveguides respectively, achieving optical localization at two different frequencies. The relative positions of the waveguide and the two angular resonant cavities are designed so that the topological angular states of the two angular resonant cavities can be excited by the transmitted optical field in the waveguide and achieve strong coupling, ultimately generating two sharp and asymmetric Fano resonance transmission valleys in the waveguide's transmission spectrum. This transmission spectral pattern has two extremely low valley values ​​and a small bandwidth, which can well meet the function of dual-frequency filtering.

[0023] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art.

[0024] (1) Dual-band filtering operation: By coupling multiple topological angular resonant cavities, efficient optical filtering at multiple specific frequencies is achieved, such as dual-band filtering at 9.7242 THz and 9.7442 THz, supporting multi-channel optical communication applications.

[0025] (2) Good quality factor: The Q value of the Fano resonance is as high as 6.62×10 3 This ensures the filter's sharp frequency selectivity and low-loss characteristics. Furthermore, the transmission spectrum exhibits an asymmetric Fano line shape, with the Fano parameter q satisfying -0.2 ≤ q ≤ 0.

[0026] (3) Topological robustness: Based on topological protection of boundary states and corner states, the filter is immune to processing defects and structural disturbances, which improves its reliability in real-world environments.

[0027] (4) High design flexibility: By adjusting the size of the corner dielectric pillars or the lattice parameters, the resonant frequency of the strong resonant angle state can be flexibly controlled to enhance the coupling strength and improve the filtering effect. At the same time, different coupling frequencies can be obtained to adapt to different filtering requirements.

[0028] (5) High integration: The device has a compact structure, providing a new solution for the application of topological photonic devices in optical communication. Attached Figure Description

[0029] Figure 1 (a) is a schematic diagram of the unit cell UC1 of the first photonic crystal PC1. The lattice constant is a = 15 μm, the radius of the circular dielectric pillars is r1 = r2 = 0.125a = 1.875 μm, the internal dielectric pillars are offset upwards from the center of the unit cell by 0.125a, the dielectric constant is 11.7, and the dielectric constant of the air background is 1.00; (b) is the band structure diagram of the unit cell of the first photonic crystal PC1, which has a nontrivial band gap. The image on the right shows the electric field diagram of the unit cell at high symmetry points X and Γ.

[0030] Figure 2 (a) is a schematic diagram of the unit cell UC2 of the second photonic crystal PC2. The lattice constant is a = 15 μm, the radius of the outer circular dielectric pillar is r1 = 0.1a = 1.5 μm, the radius of the inner circular dielectric pillar is r2 = 0.15a = 2.25 μm, the inner dielectric pillar is offset from the center of the unit cell by 0.15a in the upward direction, the refractive index is 11.7, and the refractive index of the air background is 1.00. (b) is the band structure diagram of the unit cell of the second photonic crystal PC2, which has a trivial band gap. The image on the right shows the electric field diagram of the unit cell at the high symmetry points X and Γ.

[0031] Figure 3(a) is a structural diagram of the supercell SC1 of the optical waveguide, which is spliced ​​together by the first photonic crystal PC1 and the second photonic crystal PC2 with the lattice boundary as the contact surface. PC1 and PC2 are arranged vertically. (b) is the dispersion diagram of the supercell SC1. (c) is the electric field diagram at the boundary state frequency of the high symmetry point.

[0032] Figure 4 In the middle (a) and (b), respectively Figure 3 The transmission electric field diagram of the optical waveguide described in the figure at the high symmetry point frequency.

[0033] Figure 5 In diagram (a), the right-hand topological angular resonant cavity structure of this invention is shown, consisting of a third photonic crystal PC3 surrounded by an external fourth photonic crystal PC4. The internal dielectric pillars of PC3 are offset from the center of the unit cell towards the upper left corner. At point a, the internal media column of PC4 deviates from the center of the unit cell towards the upper left corner. a. (b) is the electric field diagram at the angular frequency of 9.855 THz corresponding to the first topological angular resonant cavity structure; (c) is the second topological angular resonant cavity structure on the left side of this invention, which is surrounded by the fifth photonic crystal PC5 by the external sixth photonic crystal PC6. The internal dielectric pillars of PC5 are offset from the cell center towards the upper right corner of the cell. a. The internal media columns of PC6 are offset from the cell center towards the upper right corner of the cell. a. (d) is the electric field diagram at the angular frequency of 9.855 THz corresponding to the second topological angular resonant cavity structure.

[0034] Figure 6 This is a schematic diagram of a Fano resonant filter structure based on an asymmetric C4 photonic crystal according to the present invention. The topological waveguide structure is located on the upper side, light enters from the left side and exits from the right side, and two angular resonant cavities are distributed on the left and right sides, with a distance of 2a from the waveguide structure.

[0035] Figure 7 (a) is a graph showing the variation of the electric field intensity with the scaling factor β of the corner dielectric pillar of the topological corner resonant cavity structure in this invention. The lower right figure shows the scaling method. The solid line is the original radius of the corner dielectric pillar, and the dashed line is the scaled radius of the corner dielectric pillar. The scaling is achieved by multiplying the original radius r1 by β. β satisfies 0.9 ≤ β ≤ 1.1; (b) is the transmission spectrum in the waveguide of the Fano resonant filter in this invention, which satisfies two transmission valleys with frequencies of 9.7242 THz and 9.7442 THz, respectively; (c) and (d) are the transmission electric field diagrams at the frequencies of the transmission valleys in this invention.

[0036] Figure 8The diagram shows the electric field of the angular resonant cavity when the scaling value β is 0.97, 0.99, 1.02, and 1.03, with corresponding angular frequency frequencies of 9.9325 THz, 9.8825 THz, 9.8111 THz, and 9.7885 THz, respectively. Detailed Implementation

[0037] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0038] The unit cell of a square lattice photonic crystal structure comprises five dielectric pillars, four of which are located at the four vertices in the positive direction and are denoted as the outer dielectric pillars, and one is located at the center of the square and is denoted as the inner dielectric pillar. The Fano filter described in this invention is designed based on the asymmetric structure of a square lattice photonic crystal. In the following embodiments of this invention, the unit cell of the photonic crystal comprises five circular dielectric pillars made of silicon, with air as the background. The radius of the outer dielectric pillar is denoted as r1, the radius of the inner dielectric pillar is denoted as r1, and the lattice constant is set as a = 15 μm. In the embodiments, "upper," "lower," "left," and "right" refer to the accompanying drawings.

[0039] Example 1:

[0040] Figure 1 Figure (a) shows the structure of the first photonic crystal PC1. The radius of the circular dielectric pillar is r1 = r2 = 0.125a = 1.875 μm. The inner dielectric pillar is offset from the center of the unit cell by 0.125a in the direction directly upward, that is, the distance from the center of the unit cell is 1.875 μm.

[0041] Figure 2 Figure (a) shows the structure of the second photonic crystal PC2. The radius of the outer dielectric pillar is r1 = 0.1a = 1.5μm, and the radius of the inner dielectric pillar is r2 = 0.15a = 2.25μm. The inner dielectric pillar is offset from the center of the unit cell by 0.15a in the direction directly upward, that is, the distance from the center of the unit cell is 2.25μm.

[0042] Figure 1 (b) and Figure 2Figure (b) shows the band gaps of the first photonic crystal PC1 and the second photonic crystal PC2, respectively. The right side shows the electric field diagrams at the boundary state frequencies of the high-symmetry points X and Γ, which can be used to determine the topological properties of the first photonic crystal PC1 and the second photonic crystal PC2. Specifically, the first photonic crystal PC1 and the second photonic crystal PC2 possess topological nontriviality and topological triviality, respectively.

[0043] By splicing the first photonic crystal PC1 and the second photonic crystal PC2 with the lattice boundary as the contact surface, a topologically protected boundary state can be formed at the splicing point of the first photonic crystal PC1 and the second photonic crystal PC2. Figure 3 Image (a) shows a supercell SC1 composed of a first photonic crystal PC1 and a second photonic crystal PC2 arranged vertically and spliced ​​together with lattice boundaries as contact surfaces. Multiple supercells are arranged to form a waveguide structure. The periodic wave vector kx is scanned, the eigenvalues ​​are solved, and the wave frequency is calculated to obtain... Figure 3 The dispersion curve shown in (b) has two dispersion curves within the band gap, with frequency ranges of 9.749 THz to 10.437 THz and 10.815 to 11.313 THz. The optical signal can only propagate along the splicing interface of the first photonic crystal PC1 and the second photonic crystal PC2 within these two frequency bands, which meets the broadband continuous state requirement of Fano resonance. Figure 3 In diagram (c), the electric field diagrams at the frequencies of high-symmetry points A and B in these two frequency ranges show that energy is concentrated at the splicing interface rather than dispersed at other locations in the supercell.

[0044] Figure 4 In the middle (a) and (b), respectively Figure 3 The diagram shows the transmission electric field of the optical waveguide described above at a high symmetry point frequency. As can be seen from the diagram, energy is confined at the interface and can only be transmitted along the interface.

[0045] Figure 5 Figures (a) and (c) show schematic diagrams of two square topological angular resonant cavity structures. Figure 5 In diagram (a), the first topological angular resonant cavity structure is located at the lower right corner of the filter, consisting of a square third photonic crystal PC3 surrounded by a fourth photonic crystal PC4. Within the cell of the third photonic crystal PC3, the radius of the outer dielectric pillar is 0.1a, and the radius of the inner dielectric pillar is 0.15a; the inner dielectric pillar deviates from the center of the cell towards the upper left corner. a. The radii of both the internal and external dielectric pillars of the fourth photonic crystal PC4 are 0.25a, ​​i.e., r1 = r2 = 0.25a; the internal dielectric pillars are offset from the center of the unit cell towards the upper left corner. a.

[0046] The inner square third photonic crystal PC3 has a side length of n = 6 lattice elements, i.e., a side length of 6a. This structure enables energy-localized topological corner states at the corners of the square third photonic crystal PC3. When the inner dielectric pillar, the third photonic crystal PC3 at the upper left corner, and the fourth photonic crystal PC4 form a box-like structure, the corner of the square third photonic crystal PC3 at the upper left corner is excited, and the electric field diagram at this time is as follows. Figure 4 As shown in (b), the frequency of this angular state is 9.855 THz.

[0047] Figure 5 In section (c), the second topological angular resonant cavity structure is located at the lower left corner of the filter, surrounded by the fifth photonic crystal PC5 by the sixth photonic crystal PC6. The outer dielectric pillar of the fifth photonic crystal PC5 has a radius of 0.1a, and the inner dielectric pillar has a radius of 0.15a; its inner dielectric pillar is offset from the cell center towards the upper right corner of the cell. a. The internal and external dielectric pillars of the sixth photonic crystal PC6 both have a radius of 0.25a, ​​i.e., r1 = r2 = 0.25a; the internal dielectric pillars are offset from the cell center towards the upper right corner of the cell. a. The internal square fifth photonic crystal PC5 is also composed of n = 6 lattices. When the fifth photonic crystal PC and the sixth photonic crystal PC65, with the internal dielectric pillar at the upper right corner, form a box-like structure, the corner point at the upper right corner of the square fifth photonic crystal PC is excited, and the electric field diagram at this time is as follows. Figure 4 As shown in (d), the frequency of this angular state is 9.855 THz. All of these angular state frequencies meet the narrowband discrete state requirements of the Fano resonance.

[0048] The Fano filter structure described in this invention is as follows: Figure 6 As shown, a topological boundary state optical waveguide is formed by splicing a first photonic crystal structure PC1 and a second photonic crystal PC2 with the lattice boundary as the contact surface. A first topological angular resonant cavity structure and a second topological angular resonant cavity structure are located at the edge of the second photonic crystal PC2 and spliced ​​thereto. The first topological angular resonant cavity structure is located on the right side, and the second topological angular resonant cavity structure is located on the left side, arranged side-by-side. The topological waveguide structure is located on the upper side, with light entering from the left and exiting from the right. The two topological angular resonant cavities are located on the lower side and are distributed side-by-side. The width of the second photonic crystal PC2 is one lattice constant, and the distance between the resonant cavity and the optical transmission interface is 2a.

[0049] A topological boundary state optical waveguide couples with topological angular states in two topological angular resonant cavities, achieving frequency overlap between a broadband continuous state and a narrowband discrete state, generating two sharp Fano resonance line shapes in the waveguide's transmission spectrum. The optical field in the waveguide excites supermodes of the topological angular states in the two cavities through near-field evanescent coupling. After interference between the bright and dark modes, a sharp Fano resonance valley is generated in the waveguide's transmission spectrum, such as... Figure 6 As shown.

[0050] If adopted Figure 5 The first topological angle resonator structure and the second topological angle resonator structure shown are as follows: Figure 3 The Fano filter can be constructed using the optical waveguide structure shown, thus achieving the filtering function of 9.855THz light waves.

[0051] Example 2:

[0052] To achieve dual-frequency filtering, the optical waveguide structure in the filter can be coupled to each of the two topological angular resonant cavity structures separately by differentiating their angular frequencies. Specifically, the radius of the dielectric pillar at the corner of the angular resonant cavity is adjusted and scaled between 0.9 and 1.1, resulting in a curve showing the relationship between the scaling factor and the electric field intensity, as shown below. Figure 7 As shown in (a). A higher electric field strength means a stronger coupling between the angular resonant cavity and the waveguide, and a stronger Fano resonance effect. In this embodiment, the scaling values ​​of 1.05 and 1.06, corresponding to the first high electric field strength of 34.525 and the second high electric field strength of 34.401, are selected as the scaling values ​​of the corner dielectric pillars of the two angular resonant cavities. Specifically, the scaling value of the corner dielectric pillar of the second topological angular resonant cavity structure on the left is 1.06, and the scaling value of the corner dielectric pillar of the first topological angular resonant cavity structure on the right is 1.05. After coupling, the transmittance is as follows: Figure 7 As shown in (b), the two asymmetric Fano resonant profiles exhibit two extremely low transmission valleys. When the frequencies are 9.7242 THz and 9.7442 THz, the transmittance in the waveguide is below 0.05, meaning that light at these frequencies is localized in the angular resonant cavity and effectively filtered out of the waveguide, achieving filtering at both 9.7242 THz and 9.7442 THz. The two transmission valleys also exhibit a high quality factor of 6.62 × 10⁻⁶. 3 . Figure 7Figures (c) and (d) show the electric field diagrams at the two transmission valley frequencies. The light is well localized in the two angular resonant cavities, demonstrating excellent filtering performance. When the scaling values ​​of the corner dielectric pillars are 1.03, 1.02, 0.99, and 0.97, the angular resonant cavities can localize light at frequencies of 9.7885 THz, 9.8111 THz, 9.8825 THz, and 9.9325 THz, respectively, thus providing suitable filtering for the corresponding frequencies. The results are as follows... Figure 8 As shown, each scaling value exhibits excellent filtering performance.

[0053] As an extension of this embodiment, by setting multiple corner dielectric pillars with different scaling values ​​in the topological angular resonant cavity structure, filtering at multiple frequencies can be achieved. The filter design scheme described in this invention supports a filtering range of 9.704-9.958 THz.

[0054] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A Fano resonant filter based on angular state coupling of a C4 asymmetric topological photonic crystal, characterized in that, It includes: a topological boundary state optical waveguide spliced ​​together by a first photonic crystal PC1 and a second photonic crystal PC2 with a lattice boundary as the splicing interface; and at least one topological corner resonant cavity structure located at and spliced ​​to the edge of the second photonic crystal PC2; the topological corner resonant cavity structure is spliced ​​together by corner resonant cavity modules and edge modules, and the splicing interface between the two has at least one right-angle boundary; wherein: The first photonic crystal PC1, the second photonic crystal PC2, the angular resonant cavity module, and the edge module are all asymmetric square lattice photonic crystal structures with internal dielectric pillars offset from the center of the unit cell, and the lattice constant is a; In the first photonic crystal PC1 and the edge module, the radii r1 and r2 of the external dielectric pillars in the unit cell are both 0.125a. In the second photonic crystal PC2 and the angular resonant cavity module, the radii r1 of the external dielectric pillars are 0.1a, and the radii r2 of the internal dielectric pillars are 0.15a. The internal dielectric pillars of the first photonic crystal PC1 are offset from the cell center by a distance of 0.125a in the direction away from the interface between the first photonic crystal PC1 and the second photonic crystal PC2, exhibiting topological nontriviality; the internal dielectric pillars of the second photonic crystal PC2 are offset from the cell center by a distance of 0.15a in the direction closer to the interface between the first photonic crystal PC1 and the second photonic crystal PC2, exhibiting topological triviality. In the unit cell of the angular resonant cavity module and the edge module, the internal dielectric pillars are offset towards the right-angle vertex of a right-angled boundary near the interface between the first photonic crystal PC1 and the second photonic crystal PC2; the distance between the internal dielectric pillars and the center of the unit cell of the angular resonant cavity module is... a, The distance between the internal dielectric pillars in the cell of the edge module and the cell center is... a.

2. The Fano resonant filter according to claim 1, characterized in that, In the topological waveguide structure, the width of the second photonic crystal PC2 is 1 to 2 lattice constants, and the distance between the angular resonant cavity and the splicing interface of the first photonic crystal PC1 and the second photonic crystal PC2 is 2a to 3a.

3. The Fano resonant filter according to claim 1, characterized in that, The dielectric pillar of the square lattice photonic crystal is a circular dielectric pillar, and the lattice constant a satisfies 10 μm ≤ a ≤ 20 μm.

4. The Fano resonant filter according to claim 1, characterized in that, The circular dielectric pillars are made of silicon, and the background material is air. All dielectric pillars are fabricated on silicon or silicon dioxide substrates.

5. The Fano resonant filter according to claim 1, characterized in that, The number of the topological angular resonant cavity structures is multiple.

6. The Fano resonant filter according to any one of claims 1-5, characterized in that, The radius of the external dielectric pillar at the right angle point of the angular resonant cavity of the topological angular resonant cavity structure is scaled according to the scaling factor β, 0.9 ≤ β ≤ 1.1, to improve the filtering effect and change the filtering frequency.

7. The Fano resonant filter according to claim 5, characterized in that, The radii of the external dielectric pillars at the right-angle points of the angular resonant cavities of multiple topological angular resonant cavities are scaled according to different scaling factors β to achieve multi-frequency filtering, where 0.9 ≤ β ≤ 1.

1.

8. The Fano resonant filter according to claim 1, characterized in that, The filter supports a frequency range of 9.704-9.958 THz.

9. The Fano resonant filter according to any one of claims 1-8, characterized in that, The lattice constant a satisfies 10 μm ≤ a ≤ 20 μm.

10. The Fano resonant filter according to any one of claims 1-8, characterized in that, The lattice constant a = 15 μm.

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