Fano resonance refractive index sensor based on topological photonic crystal angular state coupling
By using topological photonic crystal angular state coupling design, the stability problem of Fano resonance sensor was solved, realizing a high-sensitivity and high-stability optical sensor, improving the sensor's resolution and detection limit, and making it suitable for reliable detection in complex environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGSU UNIV
- Filing Date
- 2026-02-03
- Publication Date
- 2026-05-15
AI Technical Summary
Existing optical sensors based on Fano resonance suffer from stability issues in practical applications. Nanoscale processing errors and material inhomogeneities can easily disturb the optical mode, leading to resonance peak frequency drift and linear broadening, which affects the reliability and practicality of the sensor.
A topological photonic crystal-based angular coupling design is adopted. By arranging the regular hexagonal unit cells of the first and second photonic crystals and forming a mirror-symmetric triangular resonant cavity structure, a topological optical waveguide and a triangular resonant cavity are formed, realizing topologically protected boundary state and angular state coupling, thereby improving device stability and quality factor.
It achieves high-sensitivity and high-stability optical sensing, with the quality factor improved to the order of 107. The sensor is naturally immune to processing defects and structural disturbances, and provides high-precision refractive index detection.
Smart Images
Figure CN122042601A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of optoelectronic technology, and more specifically, to a Fano resonant refractive index sensor based on topological photonic crystal angular state coupling. Background Technology
[0002] Optical refractive index sensing technology is an important bridge connecting physical optics with chemical and biological detection applications. Its core lies in detecting changes in optical parameters after light waves interact with the substance being tested, thereby achieving highly sensitive, label-free detection of the composition or concentration of a substance.
[0003] Among numerous optical sensing mechanisms, Fano resonance-based sensing schemes have attracted considerable attention due to their unique physical characteristics. The Fano resonance originates from the coherent interference between a narrow-band discrete state (often called a "dark mode") and a wide-band continuous state (often called a "bright mode"), resulting in a spectrum exhibiting a typically asymmetric, steeply varying line shape. This unique line shape makes it extremely sensitive to changes in the refractive index of the surrounding medium; even minute refractive index perturbations can induce significant shifts in the resonance peak, providing an ideal platform for achieving high-precision sensing. Simultaneously, the Fano resonance is usually accompanied by a strong field enhancement effect, effectively enhancing the interaction between light and matter, further improving the intensity of the sensing signal.
[0004] Despite the significant advantages of Fano resonance in principle, its application in practical devices still faces a fundamental challenge: stability. Generating high-quality Fano resonances typically relies on precisely defined optical modes (such as photonic crystal microcavity modes and surface plasmon resonance modes). The characteristics of these optical modes are extremely sensitive to the geometry and material properties of the structure. In actual fabrication processes, nanoscale processing errors, material inhomogeneities, or even minute impurities carried by the liquid being measured in sensing applications can easily disturb these fragile optical modes, leading to frequency shifts, linear broadening, or decreased contrast in the Fano resonance peak, severely limiting the reliability and practicality of the sensor.
[0005] In recent years, topological photonics has brought new breakthrough opportunities to the field of optical sensing. The most significant advantage of topological photonic crystals (PCs) lies in their support for topologically protected optical boundary or corner states. These optical modes are naturally immune to certain types of structural perturbations and manufacturing defects, i.e., robustness. This means that optical devices designed based on topological principles will not experience significant performance degradation due to minor processing errors or material inhomogeneities, opening new avenues for achieving highly stable and reliable sensing systems. Summary of the Invention
[0006] This invention provides a Fano resonance refractive index sensor based on topological photonic crystal angular coupling. By integrating Fano resonance with topological photonic crystal structure, the stability and quality factor of the device are effectively improved while maintaining high sensitivity characteristics, providing a new path for reliable detection in complex environments.
[0007] The Fano resonant refractive index sensor based on topological photonic crystal angular coupling provided by this invention consists of a first photonic crystal PC1 and a second photonic crystal PC2. Both the first photonic crystal PC1 and the second photonic crystal PC2 are arranged in a hexagonal cell configuration using a kakeme lattice. The dielectric pillars in the kakeme lattice are square-sectioned, with three square dielectric pillars located at the 0°, 120°, and 240° positions of the hexagonal cell, arranged in a centrally symmetrical manner. The three square dielectric pillars are distributed at the vertices of an equilateral triangle. The lattice constant of the hexagonal cell is... The distance from the center of the square dielectric pillar to the center of the unit cell in the first photonic crystal PC1 is... , It possesses topologically trivial properties; the distance from the center of the second photonic crystal PC1 dielectric pillar to the lattice center is... , It has topological nontrivial properties;
[0008] The first photonic crystal PC1 module and the second photonic crystal PC2 module are spliced together with a regular hexagonal lattice boundary as the splicing interface, and the perpendicular line between the vertex and the base of the equilateral triangle formed by the centers of the dielectric pillars in their unit cells is parallel to the splicing interface, forming a topological optical waveguide.
[0009] Two mirror-symmetrical triangular regions are set in the first photonic crystal PC1 module, with the vertices of the two triangles facing each other at the center and the bases located on both sides and parallel to each other. The two triangular regions are respectively filled with second photonic crystal PC2 modules to form two triangular resonant cavities. The cell orientation of the second photonic crystal PC2 modules in the two triangular resonant cavities is the same as that of the second photonic crystal PC2 modules constituting the topological optical waveguide, and the other is opposite to that of the second photonic crystal PC2 modules constituting the topological optical waveguide.
[0010] Furthermore, the distance between the opposite vertices of the two triangular resonant cavities is ,in is the lattice constant. .
[0011] Furthermore, the side length of the triangular resonant cavity is A lattice constant, .
[0012] Furthermore, the first photonic crystal PC1 and the second photonic crystal PC2 have the same dielectric pillars, with a side length of 1 / 2 square. , .
[0013] Furthermore, square dielectric pillars of the first photonic crystal PC1 and the second photonic crystal PC2 are fabricated on a substrate with air as the background.
[0014] Furthermore, the square dielectric pillars are made of silicon, and the substrate is made of silicon or silicon dioxide.
[0015] Furthermore, the triangular resonant cavity is shaped like an equilateral triangle, with the base of the equilateral triangle intersecting with the topological light wave.
[0016] Furthermore, the lattice constant ≤ ≤ Preferably, the lattice constant is .
[0017] Furthermore, the distance M between the triangular resonant cavity and the transmission channel of the topological optical waveguide is the distance from the PC2 lattice at the vertex of the triangular structure at the center of the mirror image to the PC2 lattice on the other side of the topological optical waveguide. .
[0018] Furthermore, the scaling factor of the dielectric pillar at the apex of the triangular resonant cavity... The range of values is .
[0019] The topological optical waveguide is formed by directly splicing a first photonic crystal PC1 with a topologically trivial lattice and a second photonic crystal PC2 with a topologically non-trivial lattice along a specific crystal orientation. This heterojunction interface supports topologically protected intrinsic boundary states, forming a channel capable of transmitting optical energy without backscattering loss.
[0020] The two triangular resonant cavities are constructed by using a second photonic crystal PC2 as the cavity region and being surrounded by a photonic crystal PC1. The triangular resonant cavities can excite highly localized topological angular states at their physical corners. When the two triangular resonant cavities are placed close to each other in space, their respective topological angular states will be strongly coupled through their decaying fields (evanescent fields), forming an energy-split parity-symmetric supermode.
[0021] In the Fano resonance refractive index sensor described in this invention, the two triangular resonant cavities are located on one side of a topological waveguide structure. The function of the topological waveguide is to transmit optical signals and provide a broadband continuous state (i.e., a "bright mode"); while the function of the two triangular resonant cavities is to support a pair of narrowband discrete states (i.e., "dark modes") with ultra-high Q values generated by topological angular state coupling. The topological waveguide structure and the two triangular resonant cavities are laterally coupled via near-field evanescent waves. The transmitted optical field in the topological waveguide can effectively excite the topological angular state supermode in the dual-cavity system, and the resonant energy of this supermode can be fed back into the transmitted light of the topological waveguide. This interaction manifests as coherent interference between the broadband transmission spectrum (bright mode) of the topological waveguide and the narrowband resonance spectrum (dark mode) of the two triangular resonant cavities, ultimately producing a sharp and asymmetric Fano resonance valley in the transmission spectrum at the output end of the waveguide. The shape and position of this Fano resonance are extremely sensitive to the refractive index changes of the analyte covering the sensor surface, thereby achieving high-precision refractive index detection.
[0022] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art.
[0023] 1. High Quality Factor: A high-quality resonant cavity is obtained through a topological corner coupling mechanism, which increases the Fano resonance Q value to 10. 7 This significantly improves the sensor's resolution and detection limit by a factor of two.
[0024] 2. High sensitivity and high figure of merit (FOM): Numerical data proves that its sensitivity can reach [value missing]. The quality factor (FOM) is as high as It has excellent overall sensing performance.
[0025] 3. Inherent robustness: Based on topologically protected boundary states and corner states, the sensor has natural immunity to processing defects and structural disturbances, ensuring high stability and reliability in practical applications.
[0026] 4. Flexible and controllable design: By adjusting the dual-cavity spacing parameter m, the coupling strength and Fano resonance profile can be precisely controlled, which provides convenience for optimizing sensor performance. Attached Figure Description
[0027] Figure 1 (a) is a schematic diagram of a 5×4 photonic crystal structure of the first photonic crystal module PC1, which consists of expanded square silicon dielectric pillars; wherein the distance from the center of the dielectric pillar to the center of the lattice is... , It is the lattice constant, and the side length of the square dielectric pillar is... Three dielectric pillars are located at the 0°, 120°, and 240° positions of a regular hexagonal unit cell, arranged in a centrally symmetrical manner. The three pillars are distributed at the vertices of an equilateral triangle, with the top vertex labeled 1 and the bottom vertex labeled 2. The refractive index of the dielectric pillars is... The refractive index of the air background is ;
[0028] (b) is a schematic diagram of the 5×4 photonic crystal structure of the second photonic crystal module PC2, which is composed of contracted square silicon dielectric pillars; wherein, the distance from the center of the dielectric pillar to the center of the lattice is... ;
[0029] (c) is the band diagram of the expanded photonic crystal PC1, which has a mediocre band gap. The inset in the middle is a schematic diagram of the first Brillouin zone.
[0030] (d) is the band diagram of the contracted photonic crystal PC2, which has a nontrivial band gap;
[0031] (e) is the electric field phase distribution of the unit cell of the photonic crystal PC1 at point K in the first and second energy bands;
[0032] (f) is the electric field phase distribution of the unit cell of photonic crystal PC2 at point K in the first and second energy bands.
[0033] Figure 2 (a) is a schematic diagram of the supercell of the photonic crystal composite structure consisting of the first photonic crystal module PC1 and the second photonic crystal module PC2, and the two boundary states in the wave vector. and The diagram shows the electric field distribution; the two photonic crystals have the same lattice orientation.
[0034] (b) shows the dispersion curve of the photonic crystal combination structure composed of PC1 and PC2. In the dispersion curve diagram, the band gap ranges from 124.75 THz to 183.60 THz. The two curved curves in the band gap represent the boundary states, with frequencies ranging from 129.57 THz to 137.95 THz and from 153.53 THz to 156.70 THz.
[0035] Figure 3 (a) is a schematic diagram of the triangular resonant cavity composed of the first photonic crystal module PC1 and the second photonic crystal module PC2. PC1 surrounds PC2, and the two photonic crystal lattices are oriented in the same direction.
[0036] (b) is a schematic diagram of the eigenmodes of the triangular resonant cavity composed of PC1 and PC2, where the circular markings represent the angular modes of the structure;
[0037] (c) is a schematic diagram of the electric field distribution of the triangular resonant cavity composed of PC1 and PC2 at frequencies of 155.47131THz, 155.4715THz and 155.47303THz. The electric field energy is concentrated at the three corners of the triangle formed by PC2. (d) is a schematic diagram of the electric field distribution of the triangular resonant cavity composed of PC1 and PC2 at a frequency of 155.4715 THz. The electric field energy is concentrated in the lower left corner of the triangle formed by PC2. (e) is a schematic diagram of the electric field distribution of the triangular resonant cavity composed of PC1 and PC2 at a frequency of 155.47303 THz. The electric field energy is concentrated at the top corner of the triangle formed by PC2.
[0038] Figure 4 Image (a) is a schematic diagram of a mirror-symmetric double-triangular resonant cavity composed of the first photonic crystal module PC1 and the second photonic crystal module PC2. The dielectric pillars at the four corners are magnified as follows. PC1 surrounds PC2 to form two triangular structures, with the vertices of the two triangular structures located in the middle and the bases located on both sides, and are placed in a mirror symmetrical manner.
[0039] (b) is a schematic diagram of the eigenmodes of the mirror-symmetric double-triangular resonant cavity composed of PC1 and PC2, where the circular markings represent the angular modes of the structure.
[0040] Figure 5 This is a schematic diagram of the Fano resonant refractive index sensor structure, composed of the first photonic crystal module PC1 and the second photonic crystal module PC2. The topological waveguide structure is located on the left. Light enters along the upper "light input" arrow and exits from the lower "light output" arrow. The distance from the center of the two triangular resonant cavities to the waveguide structure is... .
[0041] Figure 6 In (a), the Fano resonant refractive index sensor is in the background refractive index. The electric field intensity distribution at a frequency of 154.463792 THz when Fano resonance occurs shows that the energy is concentrated at the center of two mirror-symmetric triangular structures.
[0042] (b) is the background refractive index of the Fano resonant refractive index sensor. The transmittance spectrum distribution at a frequency of 154.463792 THz when Fano resonance is generated, where the circles represent transmittance data and the curves are the Fano fitting curves.
[0043] (c) is the background refractive index of the Fano resonant refractive index sensor. The electric field intensity distribution diagram when Fano resonance occurs at a frequency of 156.562983 THz shows that the energy is concentrated at the center of the two mirror-symmetric triangular structures.
[0044] (d) is the background refractive index of the Fano resonant refractive index sensor. The transmittance spectrum distribution at a frequency of 156.562983 THz when Fano resonance is generated is shown, where the circles represent transmittance data and the curves are the Fano fitting curves.
[0045] Figure 7 The transmission spectra of the angularly coupled Fano resonant refractive index sensor at different refractive indices are shown. When the refractive index of the air background varies from 1.00000 to 1.00010, the ranges of the two resonance peaks are 154.46377 THz-154.46397 THz and 156.55915 THz-156.56298 THz.
[0046] Figure 8 It is the refractive index change of the refractive index detector. and resonance position change The graph of the function between. Detailed Implementation
[0047] 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.
[0048] This invention enables the realization of two crystal structures for an angularly coupled Fano resonance refractive index sensor: a first photonic crystal PC1 with topological triviality and a second photonic crystal PC2 with topological nontriviality. Both the first photonic crystal PC1 and the second photonic crystal PC2 are arranged in a hexagonal lattice structure with an air background and square silicon dielectric pillars. The dielectric pillars in the lattice are square in cross-section, with three square pillars located at 0°, 120°, and 240° of the hexagonal cell, arranged in a centrally symmetrical manner. The three square pillars are distributed at the vertices of an equilateral triangle, and the lattice constant of the hexagonal cell is given. .
[0049] In the first unit cell UC1 of the first photonic crystal PC1, the three square silicon dielectric pillars are located close to the lattice center, and the distance from the center of the dielectric pillar to the lattice center is... satisfy In the second unit cell UC2 of the second photonic crystal PC2, three dielectric pillars are located near the lattice edge, and the distance from the center of the dielectric pillar to the center of the lattice is... satisfy .
[0050] The electromagnetic waves studied in this invention are in the TM mode. In this embodiment, the lattice constant is... The value is This represents the distance between different hexagonal lattices; the side length of the square dielectric pillar. The dielectric pillar material is silicon, with a refractive index of The background material is air, with a refractive index of .
[0051] Figure 1 The first unit cell UC1 shown in (a) (a) exhibits topologically trivial properties; (b) demonstrates the second unit cell UC2. It has topological nontrivial properties. Figure 1 In the diagram, (c) and (d) represent the band gaps of the first photonic crystal PC1 and the second photonic crystal PC2, respectively. The frequencies of the topologically trivial and topologically nontrivial photonic band gaps are approximately the same, ranging from 126.44 THz to 182.32 THz.
[0052] The topological optical waveguide is formed by directly splicing a topologically trivial lattice photonic crystal PC1 and a topologically non-trivial lattice photonic crystal PC2 along a specific crystal orientation. This heterojunction interface supports topologically protected intrinsic boundary states, forming a channel capable of transmitting optical energy without backscattering loss.
[0053] A topological waveguide is formed by splicing the first photonic crystal module PC1 and the second photonic crystal module PC2 together with a regular hexagonal lattice boundary as the splicing interface, and aligning the perpendicular line between vertex 1 and base 2 of the equilateral triangle formed by the centers of the dielectric pillars in their unit cells with the splicing interface (i.e., the optical wave transmission channel). The first photonic crystal PC1 and the second photonic crystal PC2 form an optical waveguide, and topologically protected boundary states can be formed at the splicing point. For periodic wave vectors... The system performs a scan, solves for eigenvalues, calculates the frequency of the wave, and obtains the dispersion curve of the topological waveguide structure. Figure 2 Figure (a) shows a schematic diagram of a supercell with a minimum period, composed of a first photonic crystal PC1 and a second photonic crystal PC2, and the two boundary state wave vectors located at... and A schematic diagram of the electric field distribution. Figure 2Figure (b) shows the dispersion curves of this optical waveguide structure. There are two dispersion curves within the band gap, with frequencies ranging from 153.53 THz to 156.7 THz and from 129.57 THz to 137.95 THz. Only optical signals within this frequency range can propagate along the interface, which is considered as the broadband continuous state (bright mode) of the Fano resonance.
[0054] Figure 3 (a) is a schematic diagram of the triangular resonant cavity composed of the first photonic crystal module PC1 and the second photonic crystal module PC2. PC1 surrounds PC2, and the lattices of the two photonic crystals are oriented in the same direction. (b) is a schematic diagram of the eigenmodes of the triangular resonant cavity composed of PC1 and PC2, where the circles mark the angular modes of the structure. (c) is a schematic diagram of the electric field distribution of the triangular resonant cavity composed of PC1 and PC2 at frequencies of 155.47131 THz, 155.4715 THz, and 155.47303 THz. The electric field energy is concentrated at the three corners of the triangle formed by PC2.
[0055] Both resonant cavity structures of this invention are composed of a triangular second photonic crystal PC2 surrounded by a first photonic crystal PC1. The two triangular resonant cavities are placed in mirror symmetry, and the distance between the lattice vertices of the two triangular structures is the coupling distance between the two resonant cavities. . Figure 4 As shown in (a), the side length of the triangle formed by the second photonic crystal PC2 modules is... A lattice constant, i.e., a side length of 7a, and a distance between the two triangles. To reduce the influence of the angular states at the four corners of the two base sides of the two triangular resonant cavities, we chose to enlarge the dielectric pillars at the four corners to... This structure can excite localized topological angle states at its corners. When the cavities of two resonant cavities are brought close together, their topological angle states couple, forming an even-odd symmetric supermode with an extremely high quality factor Q. The calculated distribution of its eigenmodes is as follows: Figure 3 As shown in (b), the red circles mark the angular states, and the two marks are located in the large band gap, representing two supermodes with frequencies of 154.4611 THz and 156.5636 THz. These two supermodes are considered as narrowband discrete states (dark modes) of the Fano resonance.
[0056] The Fano resonant refractive index sensor based on topological photonic crystal angular coupling described in this invention consists of a topological optical waveguide and two triangular resonant cavities located in the first photonic crystal PC1 module, as follows: Figure 4As shown, two triangular resonant cavities are located on one side of the topological waveguide structure. The function of the topological waveguide is to transmit optical signals and provide a broadband continuous state (i.e., the "bright mode"); while the function of the double triangular resonant cavities is to support a pair of narrowband discrete states (i.e., the "dark mode") with ultra-high Q values generated by the coupling of the topological angular states. The entire structured light is input from the upper port and output from the lower port along the direction of the arrow. The frequencies of the discrete state supermode are 154.4611 THz and 156.5636 THz, while the range of the continuous state boundary state waveguide is 153.53 THz-156.7 THz and 129.57 THz-137.95 THz. The supermode is located within the frequency band of the boundary state. Therefore, the two can couple, and the transmittance spectrum produces a valley.
[0057] The topological waveguide structure is laterally coupled to the two triangular resonant cavities via near-field evanescent waves. The transmitted optical field in the topological waveguide can effectively excite the topological angular supermode in the dual-cavity system, and the resonant energy of this supermode can be fed back into the transmitted light of the topological waveguide. This interaction manifests as coherent interference between the broadband transmission spectrum (bright mode) of the topological waveguide and the narrowband resonant spectrum (dark mode) of the two triangular resonant cavities. The optical field in the waveguide excites the topological angular supermode in the two resonant cavities through near-field evanescent coupling. After the bright mode and dark mode interfere, a sharp Fano resonance valley is generated in the waveguide transmission spectrum. Figure 6 (a) shows the electric field intensity at the resonant frequency of 156.562983 THz, with energy concentrated in the vertex region of the double triangular cavity. (b) shows the corresponding transmittance spectrum, and the transmittance data fits the Fano curve well. Figure 6 Figures (b) and (c) show the electric field intensity diagram and transmittance spectrum corresponding to the resonant frequency at 156.562983 THz.
[0058] Because the Fano resonance is very sensitive to changes in the background refractive index, the location of the resonance will also change when the background refractive index changes. Figure 7 and Figure 8 This shows the transmittance spectrum and refractive index variation as the background refractive index changes. The change value of the position of the resonance wavelength The functional relationship is shown. When the refractive index changes by Δn = 0.00010, the position of the Fano resonance valley undergoes a significant wavelength shift. Calculations show that the transmittance valley exhibits an extremely high quality factor Q, reaching as high as... and The sensitivity of the sensor at its two resonant positions. and Quality Factor and It demonstrated excellent sensing performance.
[0059] 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 refractive index sensor based on topological photonic crystal angular state coupling, characterized in that, It consists of a first photonic crystal PC1 and a second photonic crystal PC2. Both the first photonic crystal PC1 and the second photonic crystal PC2 are arranged in a kakeme lattice according to a regular hexagonal unit cell arrangement. The dielectric pillars in the kakeme lattice are square dielectric pillars, located at the 0°, 120°, and 240° positions of the regular hexagonal unit cell, and arranged in a centrally symmetrical manner. The three square dielectric pillars are distributed at the vertices of an equilateral triangle. The lattice constant of the regular hexagonal unit cell is... The distance from the center of the square dielectric pillar to the center of the unit cell in the first photonic crystal PC1 is... , It possesses topologically trivial properties; the distance from the center of the second photonic crystal PC1 dielectric pillar to the lattice center is... , It has topological nontrivial properties; The first photonic crystal PC1 module and the second photonic crystal PC2 module are spliced together with a regular hexagonal lattice boundary as the splicing interface, and the perpendicular line between the vertex and the base of the equilateral triangle formed by the centers of the dielectric pillars in their unit cells is parallel to the splicing interface, forming a topological optical waveguide. Two mirror-symmetrical triangular regions are set in the first photonic crystal PC1 module. The vertices of the two triangles are opposite each other and located at the center, and the bases are located on both sides and are parallel to each other. The two triangular regions are respectively filled with second photonic crystal PC2 modules to form two triangular resonant cavities. The unit cell orientation of the second photonic crystal PC2 modules in the two triangular resonant cavities is the same as that of the second photonic crystal PC2 modules constituting the topological optical waveguide, and the other is opposite to that of the second photonic crystal PC2 modules constituting the topological optical waveguide.
2. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The distance between the opposite vertices of the two triangular resonant cavities is Where a is the lattice constant, .
3. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The side length of the triangular resonant cavity is A lattice constant, .
4. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The first photonic crystal PC1 and the second photonic crystal PC2 have the same dielectric pillars, with a side length of 1. , .
5. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, Square dielectric pillars of the first photonic crystal PC1 and the second photonic crystal PC2 are fabricated on a substrate with air as the background.
6. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The square dielectric pillars are made of silicon, and the substrate is made of silicon or silicon dioxide.
7. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The two triangular resonant cavities are equilateral triangles, with the mirror center of the equilateral triangle located on the inside and the base on the outside. The line connecting the two opposite vertices of the two equilateral triangles to the mirror center is perpendicular to the two bases.
8. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, Lattice constant ≤ ≤ Preferably, the lattice constant is .
9. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The distance M between the triangular resonant cavity and the transmission channel of the topological optical waveguide is the distance from the PC2 lattice at the vertex of the triangular structure at the center of the mirror image to the PC2 lattice on the other side of the topological optical waveguide. .
10. The Fano resonant refractive index sensor based on topological photonic crystal angular coupling according to claim 1, characterized in that, The scaling factor of the dielectric pillar at the apex of the triangular resonant cavity The range of values is .