A bic-based angle-independent full-polarization miniature spectrometer design method

Abstract

The application discloses a kind of angle-independent full polarization microspectrometer design methods based on BIC, it is related to optical device technical field.The application includes: etching a plurality of superlattices in germanium photonic crystal film, and each superlattice is set to four atomic square lattices, to obtain the superlattice of degenerate protection continuous domain bound state DP-BIC;A nanometer hole is engraved in each atomic square lattice;For each superlattice, the ground state radius of any one nanometer hole in the superlattice is reduced to half of the original ground state radius, the superlattice is changed from continuous domain bound state BIC to quasi-continuous domain bound state q-BIC;Ge photonic crystal film is laid on quartz substrate, and an angle-independent full polarization microspectrometer based on BIC is designed.The application significantly enhances the robustness of quasi-continuous domain bound state superlattice to the change of incident angle, and realizes polarization-independent far-field characteristics.

Description

Technical Field

[0001] This invention relates to the field of optical device technology, and in particular to a design method for an angle-independent fully polarized micro spectrometer based on BIC. Background Technology

[0002] Realizing quasi-BICs (q-BICs) typically requires breaking structural symmetries, which introduces polarization sensitivity and limits potential applications due to its dependence on the incident angle. First, the polarization sensitivity of bound states in the continuous domain (BIC) indicates that their performance can vary significantly across different polarization states. This phenomenon limits the applicability of BICs in various optical applications, especially those requiring the handling of multiple polarization states. Therefore, developing polarization-independent BIC devices is of paramount importance.

[0003] In recent years, numerous attempts have been made to realize polarization-independent BIC devices and expand their application scenarios. For example, for asymmetric nanopore arrays in silicon nitride, adjusting the size of the nanopores can effectively break the symmetry to excite q-BIC resonances while maintaining C rotational symmetry. It must be emphasized that achieving polarization-independent properties in these configurations typically requires maintaining specific rotational symmetry. Secondly, sensitivity to the incident angle is also a major challenge for BIC devices. Many existing BIC designs are only effective at specific incident angles, limiting their application potential under wide-angle illumination and multi-angle observation conditions.

[0004] Based on a metasurface with a dual-period grating structure, an equivalent dielectric constant distribution model of the dual-period grating structure is constructed, and the model is used to predict dual BIC modes. Finally, by introducing two independent BIC modes, independent manipulation of high-Q resonance is achieved, and it is proved that the two quasi-BIC modes have ultra-high Q factor values.

[0005] In this prior art, the two BIC modes are physically close together. External interference factors can affect both modes simultaneously, causing unpredictable and interconnected changes in their resonant frequency, Q value, and even field distribution. This results in unexpected coupling between the two modes, which were originally designed to be "independent," severely affecting the performance and functional reliability of the metasurface structure in practical applications and making it difficult to meet the requirements of high-performance devices based on BIC. Summary of the Invention

[0006] Therefore, it is necessary to provide a design method for an angle-independent fully polarized micro spectrometer based on BIC to address the aforementioned technical problems.

[0007] This invention provides a design method for an angle-independent fully polarized micro spectrometer based on BIC, comprising:

[0008] Multiple superlattices are etched within a germanium photonic crystal thin film, and each superlattice is set as a four-atom square lattice to induce a second fold in the first Brillouin zone and migrate the bound states of the single-atom square lattice to the high symmetry point of the superlattice, resulting in a superlattice with degeneracy-protected continuous domain bound state (DP-BIC). The superlattice in the degeneracy-protected continuous domain bound state (DP-BIC) forms a degeneracy transverse electric mode and a transverse magnetic mode at the high symmetry point, and incident light in any polarization direction excites a quasi-continuous domain bound state resonance peak of the same frequency.

[0009] A nanopore is etched in each atomic square lattice; for each superlattice, the ground state radius of any nanopore in the superlattice is reduced to half of the original ground state radius to apply an in-plane perturbation to the superlattice, transforming the superlattice from a continuous domain bound state BIC to a quasi-continuous domain bound state q-BIC; the superlattice in the quasi-continuous domain bound state q-BIC outputs an optical response of the same frequency within a set incident angle range;

[0010] An angle-independent fully polarized microspectrometer based on BIC is designed by depositing a germanium photonic crystal thin film with a superlattice containing degeneracy-protected continuous-domain bound states DP-BIC and quasi-continuous-domain bound states q-BIC on a quartz substrate.

[0011] Optionally, the original ground state radius of the nanopore is 275 nm.

[0012] Optionally, the range of in-plane perturbation is 0nm-50nm.

[0013] Optionally, the steps for forming the germanium photonic crystal thin film include:

[0014] Germanium metal is sputtered and deposited on the surface of a quartz substrate to uniformly deposit a germanium thin film on the surface of the quartz substrate;

[0015] A polymethyl methacrylate (PMMA) film is coated on the surface of a germanium thin film, and the PMMA film is patterned using electron beam lithography to obtain an initial germanium photonic crystal film.

[0016] The initial germanium photonic crystal film was patterned and developed using a mixed solution to obtain an intermediate germanium photonic crystal film;

[0017] Reactive ion etching technology was used to etch the intermediate germanium photonic crystal film to form multiple superlattices within the intermediate germanium photonic crystal film, thus obtaining the final germanium photonic crystal film.

[0018] Optionally, the mixed solution is a mixture of methyl isobutyl ketone and isophthalic acid in a 1:3 ratio.

[0019] The design method for an angle-independent fully polarized micro spectrometer based on BIC provided in this invention has the following advantages compared with the prior art:

[0020] In this invention, the superlattice composed of four atomic square lattices does not depend on the symmetry destruction along the normal axis, induces the second folding of the first Brillouin zone, and migrates the bound states of the single-atom square lattice to the high symmetry point of the superlattice, resulting in a superlattice with degeneracy-protected continuous domain bound states DP-BIC, thus realizing polarization-independent far-field characteristics.

[0021] Furthermore, by reducing the ground-state radius of any nanopore in each superlattice to half of its original size, this process achieves deterministic migration of the superlattice's BIC state through size modulation of a single nanopore. This enables a controllable transition of the superlattice from a continuous-domain bound state to a quasi-continuous-domain bound state. The band folding process also introduces flat bands, which significantly enhances the robustness of the quasi-continuous-domain bound state superlattice to changes in the incident angle, outputting an optical response of the same frequency within a set incident angle range. Attached Figure Description

[0022] Figure 1 This is a band degeneracy diagram in a periodic structure of a BIC-based angle-independent fully polarized microspectrometer design method provided in one embodiment. Figure 1 Image (a) is a schematic diagram of a germanium photonic crystal thin film with a periodic nanopore array. Figure 1 (b) in the diagram is a schematic diagram of the bound state supported by a single-atom square lattice. Figure 1 (c) in the diagram is a schematic diagram of the degenerate bound states supported by a four-atom superlattice. Figure 1 (d) in the diagram is a schematic diagram of Brillouin zone folding caused by a four-atom unit cell. Figure 1 (e) in the diagram is a schematic of the degenerate photonic band near the midpoint of the superlattice. Figure 1 (f) in the diagram is a schematic diagram of the Q factor of the degenerate TM q-BIC;

[0023] Figure 2 This is a device structure design diagram of an angle-independent fully polarized micro spectrometer design method based on BIC provided in one embodiment. Figure 2 (a) in the figure is a schematic diagram of a metasurface design based on a germanium photonic crystal thin film on a silicon substrate. Figure 2 (b) in the diagram is the geometric structure of the metasurface. Figure 2 (c) in the image is a SEM image of the metasurface. Figure 2 (d) in the figure is a 3D surface profile measurement diagram of the metasurface;

[0024] Figure 3 This is a reflectance diagram of a BIC-based angle-independent fully polarized micro-spectrometer design method provided in one embodiment. Figure 3(a) in the figure is a schematic diagram of the simulated reflection spectrum of the metasurface under different levels of structural perturbation. Figure 3 (b) in the diagram shows the evolution of the resonance position. Figure 3 (c) in the figure represents the dependence of the resonance wavelength and quality factor on different structural perturbation levels. Figure 3 (d) represents the inverse square dependence for different structural disturbance levels;

[0025] Figure 4 This is a schematic diagram of light incidence provided in one embodiment of a design method for an angle-independent fully polarized micro-spectrometer based on BIC. Figure 4 (a) in the diagram is a schematic diagram of 90° polarized light incident. Figure 4 (b) in the diagram shows the far-field reflection spectrum under 90° polarized light incidence. Figure 4 (c) in the figure is the near-field Ez distribution of the quasi-BIC mode under 90° polarized light incidence. Figure 4 (d) in the diagram is a schematic diagram of 45° polarized light incident. Figure 4 (e) in the figure is the far-field reflection spectrum under 45° polarized light incidence. Figure 4 (f) in the figure is the near-field Ez distribution of the quasi-BIC mode under 45° polarized light incidence. Figure 4 (g) in the diagram represents the incident light with 0° polarization. Figure 4 In the diagram, (h) represents the far-field reflection spectrum under 0° polarized light incidence. Figure 4 In the diagram, (i) shows the near-field Ez distribution of the quasi-BIC mode under 0° polarized light incidence;

[0026] Figure 5 This is a quasi-BIC resonance multi-level scattering power map of a BIC-based angle-independent fully polarized microspectrometer design method provided in one embodiment. Figure 5 (a) in the figure is the multi-level scattering power diagram of the quasi-BIC resonance at an incident angle of 0°. Figure 5 (b) in the figure is the multi-level scattering power diagram of the quasi-BIC resonance at an incident angle of 90°. Figure 5 (c) in the figure is a comparison diagram of the multi-level scattering power of the quasi-BIC resonance at an incident angle of 0°. Figure 5 (d) in the figure is a comparison of the multi-level scattering power of the quasi-BIC resonance at an incident angle of 90°;

[0027] Figure 6 This is a q-BIC resonance multi-level scattering power diagram of an angle-independent fully polarized microspectrometer design method based on BIC provided in one embodiment. Figure 6 In the figure, (a) represents the multi-level scattering power of the q-BIC resonance at an incident angle of 30°. Figure 6 (b) represents the multi-level scattering power of the q-BIC resonance at 45° incident angle. Figure 6In the figure, (c) represents the multi-level scattering power of the q-BIC resonance at an incident angle of 60°. Figure 6 (d) in the figure is a comparison diagram of the multi-level scattering power of q-BIC resonance at 30° incident angle. Figure 6 (e) in the figure is a comparison diagram of the multi-level scattering power of the q-BIC resonance at 45° incident angle. Figure 6 (f) in the figure is a comparison of the multi-level scattering power of the q-BIC resonance at 60° incident angle;

[0028] Figure 7 This is a schematic diagram of circularly polarized light incident, illustrating a design method for an angle-independent fully polarized micro-spectrometer based on BIC, provided in one embodiment. Figure 7 (a) in the diagram is a schematic diagram of left-handed circularly polarized light incident. Figure 7 (b) in the figure is a schematic diagram of the simulated far-field reflectivity and multipole scattering power under left-handed circularly polarized light excitation. Figure 7 (c) in the diagram is a schematic diagram of the quantitative decomposition of scattering contribution under left-handed circularly polarized light excitation. Figure 7 (d) in the diagram is a schematic diagram of right-handed circularly polarized light incident. Figure 7 (e) in the figure is a schematic diagram of the simulated far-field reflectivity and multipole scattering power under right-handed circularly polarized light excitation. Figure 7 (f) in the diagram is a schematic diagram of the quantitative decomposition of scattering contribution under right-handed circularly polarized light excitation;

[0029] Figure 8 This is a flowchart illustrating the fabrication process of a photonic crystal plate structure based on a BIC-based angle-independent fully polarized micro-spectrometer design method in one embodiment.

[0030] Figure 9 Here is a sample SEM image of a BIC-based angle-independent fully polarized micro-spectrometer design method provided in one embodiment. Figure 9 Image (a) is a SEM image of the 5000nm sample. Figure 9 Image (b) is a SEM image of the 1600nm sample with Δr=0nm region magnified 6250 times. Figure 9 (c) in the image is a SEM image of the 1600nm sample with a Δr=30nm region magnified 6250 times. Figure 9 (d) is the SEM image of the sample after magnification of the 1600nm Δr=50nm region by 6250 times;

[0031] Figure 10 A single sample image of a BIC-based angle-independent fully polarized microspectrometer design method provided in one embodiment;

[0032] Figure 11 This is a comparison of simulated and experimental reflectance spectra under different perturbation conditions for a BIC-based angle-independent fully polarized micro-spectrometer design method provided in one embodiment. Figure 11 (a) in the figure is a comparison of simulated and experimental reflectance spectra under different structural perturbations. Figure 11 (b) in the figure is a schematic diagram showing the simulated and experimental Q-factor as a function of the perturbation amplitude. Figure 11 (c) in the figure is a schematic diagram of the experimental reflection spectrum under various incident polarization angles;

[0033] Figure 12 This is a photonic band structure diagram of an angle-independent fully polarized micro-spectrometer design method based on BIC provided in one embodiment. Figure 12 (a) in the diagram is the photonic band structure of a four-atom superlattice. Figure 12 (b) in the figure shows the simulated reflectance spectra at different incident angles. Figure 12 (c) in the figure represents the reflectance spectra of the experiment at different oblique incidence angles;

[0034] Figure 13 This is a schematic diagram illustrating the relationship between the photonic crystal plate thickness and the pore radius in a design method for an angle-independent fully polarized micro-spectrometer based on BIC, provided in one embodiment. Figure 13 (a) in the figure shows the relationship between the thickness of the photonic crystal plate, the pore radius, and the q-BIC wavelength. Figure 13 (b) in the figure shows the application of environmental refractive index variation and resonant wavelength mapping to high-sensitivity detection. Figure 13 (c) in the figure shows the changes in hyperspectral detection when the thickness of the photonic crystal plate is changed. Figure 13 (d) in the figure is a mapping of the thickness of the photonic crystal plate as a function of the resonant linewidth and reflectivity. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0036] This invention provides a method for designing an angle-independent fully polarized micro-spectrometer based on BIC (Bipolar Interval Concentration-Guarded Continuous-State) superlattice, comprising: etching multiple superlattices within a germanium photonic crystal thin film, and setting each superlattice as a four-atom square lattice to induce secondary folding in the first Brillouin zone and migrate the bound states of the single-atom square lattice to the high symmetry point of the superlattice, thereby obtaining a superlattice with degeneracy-protected continuous-domain bound state (DP-BIC). The superlattice in the DP-BIC state forms degenerate transverse electric and transverse magnetic modes at the high symmetry point, and incident light in any polarization direction excites a quasi-continuous-domain bound state resonance peak of the same frequency.

[0037] A nanopore is etched within each atomic square lattice. For each superlattice, the ground-state radius of any nanopore in the superlattice is reduced to half of its original ground-state radius to apply an in-plane perturbation to the superlattice, transforming it from a continuous-domain bound state (BIC) to a quasi-continuous-domain bound state (q-BIC). The superlattice in the quasi-continuous-domain bound state (q-BIC) outputs an optical response of the same frequency within a set incident angle range.

[0038] An angle-independent fully polarized microspectrometer based on BIC is designed by depositing a germanium photonic crystal thin film with a superlattice containing degeneracy-protected continuous-domain bound states DP-BIC and quasi-continuous-domain bound states q-BIC on a quartz substrate.

[0039] The original ground state radius of the nanopore is 275 nm, and the in-plane perturbation ranges from 0 nm to 50 nm.

[0040] The formation steps of the germanium photonic crystal thin film include: sputtering and depositing germanium metal on a quartz substrate to uniformly deposit a germanium thin film on the quartz substrate surface; coating a polymethyl methacrylate (PMMA) film on the surface of the germanium thin film and patterning the PMMA film using electron beam lithography to obtain an initial germanium photonic crystal thin film; developing the pattern of the initial germanium photonic crystal thin film using a mixed solution to obtain an intermediate germanium photonic crystal thin film; and etching the intermediate germanium photonic crystal thin film using reactive ion etching to form multiple superlattices within the intermediate germanium photonic crystal thin film to obtain the final germanium photonic crystal thin film.

[0041] The mixed solution is obtained by mixing methyl isobutyl ketone and isophthalic acid in a ratio of 1:3.

[0042] A specific embodiment of the present invention is provided:

[0043] 1. Band degeneracy in periodic structures.

[0044] Although degeneracy-protected Bound States in the Continuum (DP-BIC) cannot exist in single-atom square lattices, they can be realized through carefully designed four-atom superlattice metasurfaces, where nonradiative modes are confined to the Γ point. By adjusting the radii of specific atoms within the unit cell, controllable structural perturbations can be introduced, transforming the ideal BIC into a q-BIC state with finite radiative leakage. The resulting BIC mode exhibits orthogonal polarization components in the degenerate state, allowing the q-BIC to be excited by incident light of arbitrary polarization and to be mapped to the far field. The introduction of additional atoms provides greater flexibility for customizing light-matter interactions.

[0045] To gain a deeper understanding of this transformation mechanism and verify the proposed theoretical framework, a comprehensive eigenmode analysis of a standard germanium photonic crystal slab was performed using finite element simulations. The simulation results reveal two distinct non-radiative modes at key symmetry points, demonstrating the feasibility of achieving DP-BIC through superlattice perturbations. Band folding is an important physical phenomenon in superlattices, originating from the addition or modification of lattice periodicity, leading to the redefinition of the Brillouin zone and the migration of previously non-foldable bound states. For a four-atom superlattice structure, periodic variations in the X and Y directions induce secondary folding of the first Brillouin zone, allowing bound states originally located at high symmetry points in the single-atom square lattice to migrate to the vicinity of the Γ point in the superlattice.

[0046] Specifically, the physical mechanism of band folding can be analyzed from the perspective of changes in lattice symmetry and its wave vector. In a single-atom lattice, due to the small periodicity, the Brillouin zone is large, the band distribution is relatively sparse, and the eigenvalues ​​of the bound states are not foldable. However, by combining four adjacent nanopores into a new cell, the periodicity is doubled, reducing the size of the Brillouin zone. This causes bound states originally located at a distant wave vector to shift to a high-symmetry point in the Brillouin zone after folding. Especially at the Γ point, the folded band produces a significant degeneracy effect, causing two different modes (e.g., the TE mode and the TM mode) to intersect at the same frequency, forming degenerate bound states.

[0047] Furthermore, band folding enhances the robustness of q-BIC by altering the structural symmetry. Due to the presence of degenerate states, the system's dependence on incident angle and polarization decreases, exhibiting polarization independence and angle insensitivity. Physically, this folding mechanism can be viewed as a band rearrangement caused by structural symmetry, leading to two degenerate modes near the Γ point. These modes possess very high Q-factors and can support the generation of q-BIC modes.

[0048] From a mathematical perspective, band folding is typically caused by the periodicity of lattice points. Changes in periodicity lead to a redistribution of wave vectors, with each new wave vector corresponding to a new band structure, forming a new band gap or degeneracy point. For the four-atom superlattice under discussion, by appropriately designing the cell size and the distribution of nanopores, the folding of these bands can be precisely controlled, thereby achieving a highly efficient optical response independent of incident light.

[0049] For ease of analysis, an infinitely extended germanium photonic crystal thin film was modeled, which has a square array of periodic nanopores with a pore spacing of Λ / 2, as shown below. Figure 1 As shown in (a) above. To eliminate the asymmetry caused by the substrate, the metasurface is suspended in air, ensuring perfect top-to-bottom dielectric symmetry. Figure 1As shown in (b), the single-atom periodic structure supports both TE and TM modes; however, it does not support degenerate bound states. To explore modal degeneracy, four adjacent nanopores were combined into a new cell ( Figure 1 (c) Constructing a superlattice effectively doubles the periodicity. This structural modification induces secondary folding of the first Brillouin zone in both the X and Y directions. Figure 1 (d) in the text moves the non-foldable bound states in the single-atom lattice to the high-symmetry Γ point of the superlattice. Figure 1 Eigenmode analysis in (e) reveals the existence of a pair of degenerate TE (TE1 / TE2) and TM (TM1 / TM2) modes at the Γ point, verifying the existence of the degenerate protected bound state. The corresponding Q-factor spectrum of the TM mode is shown in... Figure 1 The plot in (f) shows an extremely high Q value near the Γ point. Figure 1 In (d), the Brillouin zones of the single-atom and superlattice structures are outlined in red and blue, respectively. These regions share equivalent eigenvalues ​​due to the preservation of inversion symmetry, as the Γ–X(Y) region of the single-atom lattice folds into the Γ–X′(Y′) region of the superlattice. It is noteworthy that... Figure 1 In (e), the dispersion curves of TM1 (green) and TM2 (red) intersect at the Γ point, forming eigenvalue degeneracy, which marks the formation of bound states in the continuous domain.

[0050] 2. The polarization and incident angle of the bound states in the continuous domain are independent based on degeneracy protection.

[0051] By integrating four adjacent pores into a unified module, an innovative superlattice structure was constructed. Figure 1 (c)). This novel design extends the minimum period of the periodic structure in the superlattice to twice its original value, providing a new perspective for studying degenerate modes. Notably, by adjusting the superlattice period, the first Brillouin zone in momentum space undergoes a second fold along the X and Y directions. This folding effect not only alters the arrangement in momentum space but also cleverly folds the irreducible binding modes on the individual atom hypersurface to the high-symmetry Γ point within the first Brillouin zone, thus creating favorable conditions for the occurrence of degeneracy.

[0052] 2.1 Device structure design.

[0053] Although DP-BIC cannot exist in a single-atom lattice, a four-atom superlattice structure can be designed to confine the nonradiative mode to the Γ point. Specifically, by changing the ground-state radius of specific atoms, perturbations can be introduced into the superlattice, transforming the nonradiative BIC mode into a q-BIC state. Since the designed BIC model has orthogonal polarization components in the degenerate state, it is possible to map q-BIC with arbitrary polarization in the far field. As... Figure 2 (a) and Figure 2 As shown in (b), consider a material with a high refractive index (n) g =4.0) Germanium photonic crystal thin film (thickness h) Ge A metasurface structure with a radius of r = 400 nm was constructed. This metasurface consists of circular nanopores with a radius of r = 275 nm, arranged in an infinite two-dimensional periodic lattice in the xy-plane. To enhance the mechanical stability of the device, the patterned metasurface was fabricated on a glass substrate (n...). s =1.45). Due to the orthogonality between the vertical (z-axis) refractive index distribution and the in-plane field distribution, the optical properties are not affected by the absence of the topcoat. Therefore, to simplify the fabrication process, this invention omits the spin-coating process of the PMMA capping layer, while still achieving an effectively symmetrical dielectric environment.

[0054] In the symmetric structure, all four circular holes within the unit cell have the same radius r. By reducing the radius of a single hole to r0, a structural perturbation is introduced, leading to the excitation of q-BIC. The degree of asymmetry can be quantitatively described by Δr = r - r0. These metasurfaces were precisely fabricated and characterized to validate the proposed design. Figure 2 (c) shows a high-resolution scanning electron microscope image of the top surface, revealing a periodic nanopore pattern. Figure 2 (d) in the figure shows the non-contact three-dimensional surface profile obtained by white light interferometry, which presents the surface morphology of the structure.

[0055] 2.2 Theoretical analysis and numerical calculation.

[0056] This discovery not only validates the design concept of this invention but also provides important insights into understanding the physical nature of degenerate bound states. Of particular note are the two TM mode bound states exhibiting degeneracy. Figure 1 (f) in the figure details the Q-factors of these two degenerate states under different parameters. A superlattice composed of four identical atoms can be transformed into a q-BIC state by applying an in-plane perturbation (e.g., changing the geometric parameters) to one of the atoms. This transformation is caused by the unique properties and interactions within the superlattice structure. This modification leads to a reconfiguration of the energy states within the superlattice system, transforming it from an initial nonradiative bound mode to a q-BIC state, thus exhibiting enhanced electromagnetic localization and confinement. In this q-BIC state, photons are trapped and circulate around the perturbated atom for a considerable period before escaping. Understanding how atomic-scale perturbations affect the collective behavior of superlattices provides important insights into the fundamental physical principles governing the interaction between light and matter.

[0057] The q-BIC state is characterized by high-quality resonance and extremely low radiation loss. It offers significant advantages in various photonic applications, including enhanced light trapping, improved sensing capabilities, and enhanced nonlinear optical effects. Here, a degenerate transverse magnetic mode supported by BIC is selected for further investigation. This invention calculates the far-field radiation spectrum by controlling the geometric perturbation Δr in the four-atom system. Figure 3 (a) and Figure 3 As can be seen in (b), the change in Δr transforms the non-radiative BIC into a radioactive q-BIC, with the reflection spectrum exhibiting a clear Fano linear resonance and a gradually increasing linewidth. This implies that the local photon power of the four-atom system gradually decreases.

[0058] Since the q-BIC resonance satisfies the classical Fano resonance theory, the classical Fano formula can be used to fit the Q factor of the q-BIC mode under different Δr.

[0059] (1)

[0060] in, R ( ω ) represents reflectivity. R 0 represents the background reflectance. ω 0 is the resonant frequency. τ The full width at half maximum (FWHM) of the resonance. q The Fano parameter describes the linear asymmetry of the resonance. (Finite) q This results in asymmetric spectral lines in the reflection spectrum, exhibiting classic Fano resonance characteristics.

[0061] In classic Fano resonances, the Q factor is often used to describe the sharpness or quality of the resonance. For Fano resonances in spectral analysis, the Q factor can be defined as:

[0062] (2)

[0063] Here, we focus on the degenerate TM mode supported by BIC for further investigation. Far-field reflection spectra were calculated by varying the geometric perturbation Δr in the four-atom supercell to examine the transition from BIC to q-BIC. Figure 3 (a) and Figure 3 As shown in (b), increasing Δr transforms the ideal nonradiative BIC into a radiative q-BIC, while a distinct Fano resonance profile emerges with a gradually widening linewidth. This widening reflects a gradual decrease in the system's ability to confine photons, indicating that the binding weakens with increasing structural asymmetry.

[0064] For Fano resonances, the quality factor can be understood as the ratio of the resonance center frequency to the linewidth, representing the relative sharpness of the resonance peak. A higher quality factor means a narrower, sharper resonance, with higher frequency selectivity and a longer optical coherence time. Figure 3 (c) and Figure 3 (d) in the paper investigates the relationship between the quality factor of the BIC model and the structural perturbation Δr. The dependence of the quality factor of the BIC model on Δr follows the inverse square law, which is a typical feature of the symmetry-protected BIC.

[0065] In metasurface design, an effective approach is to precisely alter the radius of the corresponding superatom in a four-atom arrangement for a specific superatom. This targeted adjustment introduces perturbations, which are crucial for promoting resonance phenomena, essential for achieving high Q-factors. These modifications allow for fine-tuning of the metasurface's optical response, resulting in q-BIC states. Furthermore, it is noteworthy that, under degeneracy conditions, when two orthogonally polarized components coexist, the bound modes exhibit a significant superposition effect between the X and Y polarization states. This phenomenon allows light of any polarization to excite q-BIC resonances, thereby enhancing the metasurface's versatility. The ability to leverage this superposition effect expands its applications, enabling the design of polarization-independent devices.

[0066] Due to the degeneracy of the TM1 and TM2 modes, the resonant frequency of the q-BIC mode is constrained by the overall degeneracy of the modes, and this q-BIC mode exhibits the same resonant peak regardless of the polarization direction of the incident light. Specifically, any polarized incident light can be considered as a linear combination of X-polarized (0° polarization angle) and Y-polarized (90° polarization angle) light. Since the x-polarized and y-polarized modes have the same resonant frequency, this linear combination of light will also excite a q-BI resonant peak of the same frequency. Figure 4 In the design, Δr=60nm is shown to display a schematic diagram of incident light with arbitrary linear polarization (polarization angle varying from 0 degrees to 90 degrees). Figure 4 (c, f, i) illustrates the near-field distributions of the electric and magnetic fields on the half-maximum plane of a germanium photonic crystal slab structure. These field distribution diagrams show that the x-polarized and y-polarized excited q-BIC modes can perfectly coincide after a 90° rotation, thus confirming their orthogonality. The arrows indicating the field currents show that the electric fields within the superlattice are equal in magnitude and opposite in direction. Importantly, at an incident light polarization angle of 45°, the electric field distribution can be decomposed into a superposition of x-polarized and y-polarized components.

[0067] To further investigate the resonance mechanism of degenerate q-BIC modes, this invention calculated the scattering power of q-BIC resonances excited by x-polarized and y-polarized incident light in Cartesian coordinates, including electric dipoles (ED), magnetic dipoles (MD), electric quadrupoles (EQ), and magnetic quadrupoles (MQ). The calculation results are plotted on [platform name missing]. Figure 5 The calculation results show that the scattering power contribution of EQ (green solid line) is significantly greater than that of other multipole components, indicating that the q-BIC resonance is mainly dominated by the quadrupole mode. Under both polarizations (x and y), the scattering power contributions of ED (purple solid line) and MD (blue solid line) are almost negligible, indicating that the dipole mode contributes little to the BIC resonance. Figure 5 The analysis results of the quasi-BIC resonance multilevel scattering power at different incident angles are shown.

[0068] Multipole resonances play a crucial role in electromagnetic scattering theory. The importance of the electric quadrupole scattering component indicates that in this q-BIC mode resonance, the main electromagnetic energy is concentrated in higher-order electric quadrupole modes. Specifically, electric quadrupole resonances originate from quadrupole-symmetric oscillating modes in the spatial distribution of charge density, leading to rapid changes in the spatial electric field and exhibiting unique directional scattering characteristics in the far field. These electric quadrupole resonances typically possess a strong electric field gradient distribution, resulting in electric dipole fields of opposite polarities in different spatial regions, consistent with previously presented electric field distributions. The significant contribution of quadrupole modes to the structure under x- and y-polarized incident conditions suggests that the physical properties of q-BIC resonances are a resonance phenomenon induced by these higher-order multipole modes.

[0069] These characteristics make the q-BIC model relatively insensitive to the polarization state of the incident light, thus achieving resonant degeneracy and symmetry. This radiation characteristic not only increases the relative independence of the q-BIC mode from the polarization of the incident light but also reduces near-field losses caused by dipole scattering, thereby enhancing the quality factor of q-BIC in the far field. This far-field radiation characteristic of the electric quadrupole also makes the q-BIC mode unique in applications requiring direction selectivity and low loss, making it ideal for efficient optical modulation and selective coupling in photonic devices. Therefore, the dominance of the electric quadrupole in the q-BIC mode not only demonstrates its contribution to the resonance under power distribution but also highlights the directionality, degeneracy, and high Q-factor of the q-BIC mode through its unique far-field radiation characteristics, providing a theoretical basis for the design of high-performance photonic devices.

[0070] Therefore, in Figure 6The calculation results of q-BIC resonance multilevel scattering power under excitation with incident light polarization angles varying from 30° to 60° are presented. Due to the change in polarization angle, the special electric and magnetic field symmetries are broken, and the formation of the loop current is suppressed, thus exhibiting a lower MQ scattering power contribution.

[0071] In many practical applications, the polarization state of incident light may not be strictly controlled, or it may vary over time or spatially within the system. Polarization-independent BIC modes can operate effectively in all linear polarization directions (e.g., horizontal, vertical, or arbitrary angles), thereby enhancing the polarization adaptability of the system. For example, in sensing applications, this mode ensures that the detected signal is unaffected by changes in input polarization, thus improving detection stability and sensitivity. However, it must be noted that in certain situations (e.g., bioimaging, optical rotation sensing, and circularly polarized emission), circularly polarized light offers more advantages. Polarization-independent BIC modes can be symmetrically coupled with left-handed and right-handed circularly polarized light, achieving insensitivity to the polarization of circularly polarized light. Because it can produce equivalent responses to left-handed and right-handed circularly polarized light, it is particularly important in chiral materials and nonlinear optics.

[0072] In circular polarization, the direction and magnitude of the electric field vector change continuously with time, causing its endpoint to trace a circle on a plane perpendicular to the propagation direction. Circular polarization can be classified into left-handed and right-handed circular polarization based on the direction of rotation of the electric field vector. Circular polarization is usually considered as a combination of two mutually perpendicular linear polarization components (typically x-polarization and y-polarization), which have equal amplitudes and a 90-degree phase difference.

[0073] (3)

[0074] in, E 0 represents the electric field amplitude. ω It is the angular frequency. By changing the phase relationship, different polarization forms can be obtained, such as elliptic polarization and linear polarization.

[0075] like Figure 7 As shown, Figure 7A schematic diagram of circularly polarized light incident is shown. Spectral analysis and multipole scattering decomposition are performed on the q-BIC resonances excited by left-hand circularly polarized (LCP) and right-hand circularly polarized (RCP) light. Circularly polarized light can simultaneously excite degenerate modes along both the x and y polarization directions. Even after introducing symmetry-breaking perturbations to convert the ideal BIC to a q-BIC, these modes remain degenerate and possess the same resonance frequency. Therefore, in rotationally symmetric structures, the q-BIC is polarization-independent, and circularly polarized excitation can effectively induce high-Q resonances. This behavior confirms the robustness of degeneracy-protected q-BIC to polarization state changes, making it suitable for polarization-insensitive photonic applications. These results demonstrate that the designed q-BIC structure can achieve strong field enhancement under circularly polarized light excitation, thereby improving the device performance in circularly polarized-based detection and emission. This property is particularly promising for chiral optics and optical rotation measurement applications, as circularly polarized light plays a crucial role in these applications. The polarization-independent q-BIC mode provides a unified optical platform for left- and right-hand circularly polarized light, enables symmetrical interactions with chiral materials, and facilitates polarization-independent sensing and analysis.

[0076] 2.3 Device structure fabrication.

[0077] like Figure 8 As shown, a photonic crystal plate sample was prepared in a cleanroom. The preparation process of the photonic crystal plate includes several key steps. First, the quartz glass substrate was treated with acetone and ultrasonic cleaning to remove surface impurities and ensure good adhesion of materials in subsequent steps. Next, sputtering deposition was performed using a magnetron sputtering system (PD500C, Pudi Vacuum, China) with an RF power of 90W to uniformly deposit a germanium (Ge) thin film on the quartz glass substrate. The thickness of the germanium film was 400 nm. Subsequently, the crystallinity of the film was improved through a vacuum annealing process at 500°C.

[0078] Next, a spin coating operation was performed to coat a 500 nm thick polymethyl methacrylate (PMMA) film onto the germanium thin film surface as a protective layer for subsequent photolithography steps. Electron beam lithography (EBL) was used to pattern the PMMA, with a voltage set to 30 kV and an exposure dose of 250 µC / cm². Then, pattern development was performed using a PMMA developer solution (a 1:3 mixture of methyl isobutyl ketone (MIBK) and isophthalic acid (IPA)) to reveal the photonic crystal plate pattern within the PMMA layer. Subsequently, reactive ion etching (RIE) was used to form the desired superlattice structure on the germanium thin film. Finally, acetone was used to wash away any remaining PMMA, yielding the final photonic crystal plate structure. Every step in this process is precisely controlled to ensure the high quality and precise nanostructure of the final photonic crystal plate, thereby guaranteeing the achievement of the desired optical performance.

[0079] This invention prepared photonic crystal plate samples with different Δr values ​​by adjusting the radius (Δr) of one atom in a four-atom structure, and used electron microscopy to characterize the structure and size of these samples in detail. Figure 9 Image (a) shows a large-area scanning electron microscope (SEM) image, revealing the periodic nanopore array across the entire photonic crystal plate, allowing clear observation of the overall structure of the sample. Figure 9 In (b), (c), and (d), different regions were magnified to show in detail the specific size and morphological changes of the nanopores, especially the effect of the change in Δr value on the pore size.

[0080] These images reveal subtle variations in the diameter and morphology of the nanopores with different Δr values, reflecting the actual impact of atomic radius modulation on the photonic crystal plate structure. The green-marked areas indicate the size and location of specific pores, facilitating comparison of differences between various samples. These electron microscopy characterization results provide precise structural information for this invention, contributing to a deeper understanding of the physical properties of the photonic crystal plate at different Δr values, and ultimately providing experimental evidence for optimizing device design.

[0081] To facilitate subsequent spectral testing, this invention prepared samples with a single region of 0.2 mm × 0.2 mm. The SEM image of a single sample is shown below. Figure 10 As shown in the figure, the areas displayed have a regular, periodic arrangement, and the scale (0.05 mm) is marked below the image to help to more intuitively understand the scale of the structure.

[0082] This SEM image reveals that the nanopore array in the sample is uniformly distributed within a 0.2 mm × 0.2 mm area. This structure will provide a stable sample for subsequent spectral characterization tests. The image's high resolution provides crucial structural information, ensuring accurate acquisition of the photonic crystal plate's optical response data during spectral testing.

[0083] 2.4 Optical characterization of the device.

[0084] This invention fabricated a series of metasurfaces with different radius perturbations Δr, and characterized their optical response using Fourier Transform Infrared (FTIR) spectroscopy. First, the shift in resonant wavelength and the change in Q-factor were measured under different broken symmetry conditions (Δr = 30 nm and 50 nm). Experimental results show that the Q-factor exhibits a significant exponential decay trend with increasing perturbation, which is highly consistent with theoretical predictions. Specifically, when the perturbation is Δr = 30 nm and 50 nm, the decrease in Q-factor is closely related to structural defects and material losses, consistent with expectations for the metasurface performance.

[0085] Figure 11 Figure (a) shows a comparison of simulated and experimental reflectance spectra under different perturbation conditions. As can be seen from the figure, both simulated and experimental results exhibit high Q resonance, and the resonance wavelength shifts significantly with increasing perturbation. The experimental data agree very well with the simulation results, further verifying the reliability of the design. Particularly noteworthy is the narrow resonance peak observed even at Δr = 0 nm. This phenomenon can be attributed to unavoidable defects during manufacturing, which may have unintentionally disrupted the symmetry, thereby exciting the q-BIC resonance mode. Nevertheless, this effect does not significantly alter the characteristics of the q-BIC resonance, which still exhibits good resonance quality.

[0086] Next, the perturbation was fixed at 50 nm, and the polarization angle of the incident electric field was experimentally adjusted from 0° to 90° to test the robustness of the q-BIC resonance under different polarization angles. Experimental results show that the q-BIC resonance exhibits high robustness to changes in polarization angle. Within the range of 0° to 90°, the experimental reflectance spectrum remains almost unchanged, demonstrating the polarization-independent nature of the q-BIC resonance. Further experiments using left-handed and right-handed circularly polarized light also verified the polarization independence of the spectral response. This result proves that the proposed design can operate stably under different polarization conditions.

[0087] Figure 11 Figure (b) further illustrates the relationship between the Q-factor extracted from simulation and experimental results and the perturbation Δr. Based on the experimental data and simulation results, it can be seen that the Q-factor decreases exponentially with increasing perturbation Δr, and the experimental Q-factor is slightly lower than the simulation result. This difference mainly stems from the influence of material loss and structural defects. However, despite the decrease in the experimental Q-factor, the prepared structure still achieved high Q-factors of 945 (Δr=30nm) and 427 (Δr=50nm), demonstrating the robustness and reliability of the proposed method.

[0088] The superlattice design employs a square lattice with each unit cell containing four pores. With this design, the degenerate BIC modes correspond to orthogonal x and y polarized electric fields. To achieve q-BIC resonance, the degeneracy is eliminated by selectively reducing the radius of one of the pores, allowing radiation to couple to the far field and form a stable quasi-BIC mode. This process precisely controls the symmetry in the structure, thereby modulating the light propagation characteristics. Figure 11 As shown in (c), the reflection spectral response under different polarization states was experimentally investigated, including linear polarization angles from 0° to 90°, and circularly polarized light from LCP and RCP. The results show that the reflection spectra of the q-BIC resonance are almost identical at different polarization angles, indicating its polarization independence. This further confirms the polarization robustness of the q-BIC resonance, and its performance at 10... 3 Even at Q-factors of this magnitude, the photon confinement effect remains very strong. Detailed experiments and analysis further confirm that the designed quasi-BIC metasurface exhibits excellent polarization independence, providing strong support for its potential in various optical applications.

[0089] like Figure 12As shown in (a), the design of the photonic band structure is based on the band folding mechanism in a four-atom superlattice metasurface, utilizing two key functions of this mechanism: first, the formation of a degenerate nonradiative state, and second, the introduction of a secondary band folding process. Secondary band folding effectively reduces the size of the Brillouin zone and produces a pronounced flat band characteristic in the process. Physically, the flatness of the photonic band implies a group velocity close to zero, which significantly extends the photon lifetime and enhances the interaction between light and matter. This property is crucial for achieving high Qq-BIC resonances because it effectively reduces radiation losses while significantly enhancing angular stability. This stability not only ensures the reliability of the resonance mode under various conditions but also provides a solid theoretical foundation for applications in photonic crystals and metasurface technologies.

[0090] To further enhance the application prospects of this design, this invention focuses specifically on the angular stability of the q-BIC resonance. Maintaining spectral stability over a wide range of incident angles is crucial for achieving devices with consistent optical performance, especially for polarization-independent devices and broadband photonic sensors, which require high precision and wide-angle response. Angular stability is verified through a combination of experiments and simulations. Figure 12 (b) and Figure 12 As shown in (c), the structure with a fixed radius perturbation Δr = 50 nm exhibits excellent angular stability in its reflection spectra at different incident angles (from 0° to 15°). This result demonstrates that the quasi-BIC mode can stably maintain its resonance characteristics even in the presence of structural perturbations.

[0091] Specifically, this invention compares simulated and experimental reflectance spectra at various incident angles. By introducing a structural perturbation (Δr = 50 nm) into the simulation, controlled symmetry violation was successfully induced, which not only excited q-BIC but also maintained a high Q factor. Figure 12 The high consistency between the experimental data and simulation results in (b) not only verifies the accuracy of the design model but also demonstrates the effectiveness of the design strategy. It is worth noting that even at Δr=0nm, the spectrum still shows a narrow resonance peak due to unavoidable defects in the manufacturing process. This indicates that the designed metasurface has a high tolerance for manufacturing defects and can maintain good optical performance in practical applications.

[0092] Figure 12Figure (c) shows the experimental reflectance spectra at different incident angles (from 0° to 15°). It can be observed that the q-BIC resonance remains almost unchanged at various oblique incident angles, demonstrating its angle-insensitive behavior. This experimental result not only confirms the robustness of the q-BIC resonance to the incident angle but also demonstrates the potential of this design in practical applications. The q-BIC resonance maintains a high Q-factor and strong photon confinement effect regardless of whether the incident angle is perpendicular or oblique, giving it a unique advantage in optical devices requiring wide-angle responses.

[0093] The four-atom superlattice structure achieves highly stable q-BIC resonances through band folding mechanisms, providing a solid foundation for practical applications in optical sensing, nonlinear optics, and polarization-independent photonic devices. Experimental results and simulation data demonstrate that this q-BIC resonance exhibits excellent angular and polarization robustness, effectively resisting the effects of manufacturing defects and maintaining stable optical performance over a wide range of incident angles. This characteristic makes this design suitable not only for high-sensitivity optical sensors but also for a wide range of applications, including high-performance filters, broadband photonic sensing platforms, and nonlinear metasurface platforms, opening up new research directions for the future development of photonics.

[0094] 3. Research on applications based on degeneracy-protected bound states in continuous domains.

[0095] The metasurface platform presented in this invention exhibits polarization-independent and angle-independent q-BIC resonance, showing great potential in a wide range of photonic applications. To gain a deeper understanding of the influence of metasurface structure parameters on q-BIC properties, the study explored the variation of the quasi-BIC resonant wavelength by manipulating two key parameters: the photonic crystal plate thickness (hGe) and the pore radius (r).

[0096] Specifically, as hGe gradually increases, a significant linear redshift trend is observed at the q-BIC resonant wavelength. Figure 13 This is a schematic diagram showing the relationship between the thickness of the photonic crystal plate and the radius of the pores. Figure 13The red dashed line in (a) clearly depicts this trend. Conversely, a linear blue shift is observed in the q-BIC resonant wavelength as r gradually increases, visually represented by the blue dashed line in the figure. These phenomena can be attributed to the change in the equivalent dielectric constant within the photonic crystal plate. The equivalent dielectric constant is a key parameter describing electrical properties and directly affects the resonant wavelength. An increase in the equivalent dielectric constant leads to a shift in the resonant wavelength to longer wavelengths. Conversely, a decrease leads to a shift to shorter wavelengths. Therefore, the q-BIC resonant wavelength can be effectively controlled by precisely adjusting the thickness of the photonic crystal plate and the aperture radius, providing a substantial reference for designing optical devices with specific functions. Polarization-independent high Q-factor q-BIC resonances have significant advantages in the field of high-sensitivity sensing. The research focuses on examining the change in the refractive index of the upper surface environment and its impact on spectral characteristics. Specifically, the metasurface design is optimized to exhibit enhanced sensitivity to changes in the refractive index of the upper surface environment. The main objective of this design is to explore the intrinsic relationship between refractive index changes and spectral shifts. Figure 13 (b) shows the calculation results, indicating that a refractive index change of 0.4 results in a significant linear shift in the spectrum, ranging from 173 nm. Furthermore, this invention calculates a refractive index sensitivity of 433 nm / RIU. This exceptional level of sensitivity highlights the superior performance of this metasurface design in detecting minute changes in refractive index, thus holding significant importance for advancing high-sensitivity sensing.

[0097] q-BIC resonances with extremely narrow linewidths are considered a crucial pathway to miniaturizing spectrometers. However, the resonant characteristics of traditional metasurfaces are greatly affected by the incident angle and polarization state of the light source. This limitation hinders the widespread application and development of metasurfaces. To overcome this problem, this invention proposes an innovative polarization-independent q-BIC resonance design. Figure 13 (c) and Figure 13 As shown in (d), this design exhibits insensitivity to the polarization state of incident light while maintaining an extremely narrow linewidth resonance. This means that the resonance characteristics remain unaffected regardless of changes in the polarization of the incident light. Furthermore, thanks to its flat-band characteristics, the design also demonstrates excellent angular robustness, effectively overcoming the strict limitations on the incident angle in traditional designs. This polarization-independent, angular-robust q-BIC resonant design will greatly promote the rapid development of miniature spectrometers based on metasurface narrowband filtering technology, opening a new path for technological innovation and widespread application in this field.

[0098] 4. Summary.

[0099] This invention proposes an innovative metasurface design method that achieves high-Q, polarization- and angle-insensitive q-BIC resonances through secondary Brillouin zone folding. By precisely controlling the radius of individual nanopores in a four-atom supercell, the nonradiative DP-BIC is successfully transformed into a radiative q-BIC, while simultaneously inducing a flat photonic band that enhances angular stability. Importantly, this method does not rely on symmetry breaking along the normal axis, thus significantly enhancing its compatibility with conventional manufacturing platforms and equipment.

[0100] This invention begins with band degeneracy in periodic structures, introducing the concept of degeneracy-protected quasi-BIC (q-BIC) resonance, and analyzes in detail the flat-band characteristics induced by second degeneracy. A structural design scheme for the device is proposed through numerical simulation, and a detailed analysis from the perspective of electromagnetic multipole decomposition is provided. These theoretical analyses provide a solid foundation for understanding the physical mechanism of q-BIC resonance. To verify the correctness of the theory, corresponding samples were prepared and optical tests were conducted. The experimental results are highly consistent with theoretical expectations, further verifying the feasibility of the design scheme. Based on these experimental results, this invention proposes several applicable directions, including polarization-independent sensors, compact micro-spectroscopy, and angle-insensitive photonic filters. These applications demonstrate the broad potential of this metasurface design, particularly its advantages in optical sensing and information processing. Experimental results show that the design can achieve sharp and high-Q resonances over a wide range of polarization and incident angles, with a potential refractive index sensitivity exceeding 433 nm / RIU. These findings not only deepen the understanding of the quasi-BIC physical mechanism in structured media but also provide practical solutions for developing polarization-independent optical sensors, compact micro-spectroscopy, and angle-insensitive photonic filters.

[0101] In summary, the four-atom superlattice structure achieves highly stable q-BIC resonances through band folding mechanisms, providing a solid foundation for practical applications in optical sensing, nonlinear optics, and polarization-independent photonic devices. Experimental results and simulation data demonstrate that this q-BIC resonance exhibits excellent angular and polarization stability, effectively resisting the effects of manufacturing defects and maintaining good optical performance in practical applications. This characteristic makes the proposed design suitable not only for high-sensitivity optical sensors but also for a wide range of applications, including high-performance filters, broadband photonic sensing platforms, and nonlinear metasurface platforms. It opens up new research directions for the future development of photonics, and the design's flexibility and robustness make this metasurface platform a strong candidate for integration into next-generation on-chip optical systems.

[0102] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A design method for an angle-independent fully polarized micro-spectrometer based on BIC, characterized in that, include: Multiple superlattices are etched within a germanium photonic crystal thin film, and each superlattice is configured as a four-atom square lattice to induce a second fold in the first Brillouin zone and migrate the bound states of the single-atom square lattice to the high symmetry point of the superlattice, resulting in a superlattice with degeneracy-protected continuous-domain bound state (DP-BIC). The superlattice in the DP-BIC state forms a degeneracy transverse electric mode and a transverse magnetic mode at the high symmetry point, and incident light of any polarization direction excites a quasi-continuous-domain bound state resonance peak of the same frequency. A nanopore is etched within each of the atomic square lattices; for each superlattice, the ground state radius of any nanopore in the superlattice is reduced to half of the original ground state radius to apply an in-plane perturbation to the superlattice, transforming the superlattice from a continuous domain bound state BIC to a quasi-continuous domain bound state q-BIC; the superlattice in the quasi-continuous domain bound state q-BIC outputs an optical response of the same frequency within a set incident angle range; An angle-independent fully polarized microspectrometer based on BIC is designed by depositing a germanium photonic crystal thin film with a superlattice containing degeneracy-protected continuous-domain bound states DP-BIC and quasi-continuous-domain bound states q-BIC on a quartz substrate.

2. The design method for an angle-independent fully polarized micro spectrometer based on BIC as described in claim 1, characterized in that, The original ground state radius of the nanopore is 275 nm.

3. The design method for an angle-independent fully polarized micro spectrometer based on BIC as described in claim 1, characterized in that, The range of the in-plane perturbation is 0nm-50nm.

4. The design method of an angle-independent fully polarized micro spectrometer based on BIC as described in claim 1, characterized in that, The steps for forming the germanium photonic crystal thin film include: Germanium metal is sputtered and deposited on the surface of a quartz substrate to uniformly deposit a germanium thin film on the surface of the quartz substrate; A polymethyl methacrylate (PMMA) film is coated on the surface of a germanium thin film, and the PMMA film is patterned using electron beam lithography to obtain an initial germanium photonic crystal film. The initial germanium photonic crystal film was patterned and developed using a mixed solution to obtain an intermediate germanium photonic crystal film; Reactive ion etching technology was used to etch the intermediate germanium photonic crystal film to form multiple superlattices within the intermediate germanium photonic crystal film, thus obtaining the final germanium photonic crystal film.

5. The design method of an angle-independent fully polarized micro spectrometer based on BIC as described in claim 4, characterized in that, The mixed solution is a mixture of methyl isobutyl ketone and isophthalic acid in a 1:3 ratio.

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