Metasurface filtering structure and design method thereof

Abstract

The invention belongs to the technical field of optical filtering, and discloses a metasurface filtering structure and a design method thereof, a unit structure with orthogonally arranged rectangular holes is constructed, length difference design is introduced, and a double-resonance mode having robustness for kx and ky wave vector component changes is realized; compared with a design thought that a traditional filtering structure depends on a single resonance mechanism or a symmetrical structure, the method enables two optical modes with different symmetry to be coupled in a target wavelength range through the precise matching of structure parameters, thereby breaking through the performance contradiction between the spectral selectivity and the angle insensitive characteristic of a traditional filtering device. According to the dual-mode resonance mechanism, a high-performance filtering function is realized under the condition that a complex multi-layer structure is not needed through collaborative design of structural periodicity, hole arrangement mode and size difference; the narrow-band filtering characteristic can be maintained, and meanwhile, the method has robustness to an incident angle.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical filtering, in particular to a metasurface filtering structure and a design method thereof. BACKGROUND

[0002] Optical filters play a crucial role in modern optical systems. According to their working principles, traditional filters are mainly divided into two categories: absorption-type and interference-type. However, both types of filters have significant technical bottlenecks in spectral selectivity and angle dependence, making it difficult to simultaneously meet the characteristics of narrow bandwidth and angle insensitivity.

[0003] Specifically, absorption-type filters utilize the absorption characteristics of materials to achieve filtering. Although the center wavelength and bandwidth are not sensitive to changes in incident angle, the effective optical thickness increases with the increase of incident angle, resulting in a decrease in peak transmittance. More importantly, such filters are limited by the absorption characteristics of the materials themselves, making it difficult to achieve high-precision narrow-band filtering, thereby limiting their use in application scenarios with high spectral accuracy requirements.

[0004] On the other hand, interference-type filters, such as structures based on Fabry-Perot cavities, achieve wavelength selection through the interference effect of multiple dielectric films, with the advantage of narrow bandwidth. However, interference-type filters have inherent angle selectivity, i.e., changes in incident angle will cause significant shifts in spectral characteristics. Specifically, as the incident angle increases, the center wavelength of the passband will experience a blue shift. This spectral shift can cause severe color distortion or signal-to-noise ratio degradation under complex incident conditions such as wide-angle imaging and laser radar, greatly limiting their performance in applications requiring wide field of view or multi-angle incidence.

[0005] Therefore, the main technical contradiction in the current field of optical filtering is that traditional filters are difficult to simultaneously meet the characteristics of narrow bandwidth and angle insensitivity. There is an urgent need in the existing technology to develop a new filter structure that can maintain narrow-band filtering characteristics while having good robustness to incident angles to adapt to more extensive application requirements.

[0006] In view of the above problems, there is an urgent need for improvement in the existing technology. SUMMARY

[0007] The present application aims to provide a metasurface filtering structure and a design method thereof, which can maintain narrow-band filtering characteristics while having robustness to incident angles.

[0008] In a first aspect, the present application provides a metasurface filter structure, comprising a plurality of unit structures arranged in an array, each of the unit structures comprising a substrate and a film layer arranged on a top surface of the substrate, four rectangular holes penetrating through the film layer are arranged on the film layer, center points of the four rectangular holes are arranged in a 2*2 matrix, and long axis directions of any two adjacent rectangular holes are perpendicular to each other, the four rectangular holes have the same width, three of the rectangular holes have the same length, and the remaining one rectangular hole has a length smaller than that of the other rectangular holes, so that circularly polarized light in a target wavelength range can excite a double resonance mode and make resonance peak frequencies of the double resonance mode coincide when the circularly polarized light is normally incident. x robust to k y robust to k x represents a wave vector component along the x-axis direction, k y represents a wave vector component along the y-axis direction, and the x-axis and the y-axis are two axes of a top surface rectangular coordinate system of the unit structure.

[0009] Preferably, the unit structure is a square unit, the center points of the four rectangular holes in the unit structure are arranged in a square, and the arrangement square of the center points of the four rectangular holes is concentrically arranged with the boundary square of the unit structure and has the same angle; any two adjacent sides of the top surface of the unit structure are parallel to the x-axis and the y-axis respectively, and the long axis direction of the rectangular hole is parallel to the x-axis or the y-axis.

[0010] Preferably, the material of the substrate is silicon dioxide, and the material of the film layer is Sb2S3.

[0011] Preferably, the length of the remaining one rectangular hole is 70 nm smaller than that of the other rectangular holes; and the target wavelength range is 1390 nm-1430 nm.

[0012] Optionally, the unit structures are integrally formed.

[0013] Optionally, the unit structures are independently arranged and spliced to form the metasurface filter structure.

[0014] In a second aspect, the present application provides a design method of the metasurface filter structure as described above, comprising the following steps:

[0015] A1. determining structural parameters of a reference unit by band analysis; the reference unit comprises a square reference substrate and a square reference film layer arranged on the reference substrate, and a rectangular hole is arranged on the reference film layer, the rectangular hole is arranged concentrically with the reference film layer and has the same angle;

[0016] A2. using the reference unit to perform period doubling in x-axis direction and y-axis direction to form a preliminary unit structure; the preliminary unit structure comprises four rectangular holes, and the long axis directions of any two adjacent rectangular holes are perpendicular to each other;

[0017] A3. adjusting the length of one of the rectangular holes in the preliminary unit structure to enable excitation of double resonance modes and make the resonance peak frequencies of the double resonance modes coincide when circularly polarized light in a target wavelength range is normally incident, thereby obtaining a final unit structure;

[0018] A4. using a plurality of the final unit structures to form the metasurface filtering structure.

[0019] Preferably, step A1 comprises:

[0020] A101. setting initial structural parameters of the reference unit; the initial structural parameters comprise the side length of the top surface of the reference unit and the size of the rectangular hole;

[0021] A102. adjusting the initial structural parameters by band analysis to make the reference unit have a characteristic frequency point in the target wavelength range at the X point in the wave vector space, and the energy band along the Brillouin zone path Γ-X-M is flat; wherein Γ represents the (k x = 0, k y = 0) point in the wave vector space of the reference unit, X represents the (k x = π / a, k y = 0) point in the wave vector space of the reference unit, M represents the (k x = π / a, k y = π / a) point in the wave vector space of the reference unit, k x represents the wave vector component along the x-axis direction, k y represents the wave vector component along the y-axis direction, and a represents the lattice constant of the reference unit, the value of a is equal to the side length of the top surface of the reference unit.

[0022] Preferably, step A2 comprises:

[0023] A201. forming a composite unit by performing period doubling in the x-axis direction on the reference unit and rotating a rectangular hole obtained by period doubling in the x-axis direction by 90° around its center point;

[0024] A202. The preliminary unit structure is formed by doubling the period of the composite unit in the y-axis direction, and rotating the two rectangular holes obtained by doubling the period in the y-axis direction by 90° around the center point of the holes.

[0025] Preferably, step A3 comprises:

[0026] A301. Select one of the rectangular holes in the preliminary unit structure as a target rectangular hole;

[0027] A302. Gradually reduce the length of the target rectangular hole, and determine the conversion circularly polarized light transmission spectrum of the preliminary unit structure after each step of reduction at the target wavelength range when the circularly polarized light is normally incident, so as to determine the length of the target rectangular hole capable of exciting the double resonance mode and making the resonance peak frequencies of the double resonance mode coincide, and obtain the final unit structure.

[0028] Beneficial effects: the super surface filter structure and the design method provided by the application realize the robustness of the double resonance mode of the k x and k y wave vector component change by constructing a unit structure with orthogonally arranged rectangular holes and introducing length difference design; compared with the design idea of the traditional filter structure relying on a single resonance mechanism or a symmetric structure, the application makes two optical modes with different symmetries coupled in the target wavelength range through accurate matching of the structure parameters, thereby breaking through the performance contradiction between spectral selectivity and angle insensitivity of the traditional filter device; the double mode resonance mechanism realizes high-performance filtering function without complex multi-layer structure through the coordinated design of structure periodicity, hole arrangement mode and size difference; it can maintain the narrowband filtering characteristics while being robust to the incident angle. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 A schematic diagram of the super surface filter structure provided by the application.

[0030] Figure 2 A schematic diagram of the unit structure.

[0031] Figure 3 A top view of the unit structure.

[0032] Figure 4 A schematic diagram of the reference unit.

[0033] Figure 5 A flowchart of the design method provided by the application.

[0034] Figure 6 A LCP transmission light dispersion chart when the incident angle of the RCP incident light changes in the xz plane.

[0035] Figure 7 RCP transmitted light's retardation map for LCP incident light with varying incident angle in the yz plane.

[0036] Figure 8 RCP transmitted light's retardation map for LCP incident light with varying incident angle in the xz plane.

[0037] Figure 9 RCP transmitted light's retardation map for LCP incident light with varying incident angle in the yz plane.

[0038] Figure 10 LCP transmitted spectrum for RCP incident light with different incident angle in the xz plane.

[0039] Figure 11 LCP transmitted spectrum for RCP incident light with different incident angle in the yz plane.

[0040] Figure 12 LCP transmitted spectrum for RCP incident light with different ΔL at normal incidence.

[0041] Label description: 1, unit structure; 2, substrate; 3, film layer; 4, rectangular hole. DETAILED DESCRIPTION

[0042] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. The components of the embodiments of the present application described and shown in the accompanying drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0043] It should be noted that: similar labels and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. Meanwhile, in the description of the present application, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0044] Please refer to Figures 1-3In some embodiments of the present application, a metasurface filtering structure includes a plurality of unit structures 1 arranged in an array, each unit structure 1 including a substrate 2 and a film layer 3 disposed on the upper surface of the substrate 2, the film layer 3 having four rectangular holes 4 extending therethrough, the center points of the four rectangular holes 4 being arranged in a 2*2 matrix, and the long axis directions of any two adjacent rectangular holes 4 being perpendicular to each other, the widths (e.g. Figure 3 In some embodiments of the present application, the lengths (e.g. Figure 3 In some embodiments of the present application, the lengths (e.g. Figure 3 In some embodiments of the present application, the length (e.g. In some embodiments of the present application, the length (e.g. x In some embodiments of the present application, the length (e.g. y In some embodiments of the present application, the length (e.g. x In some embodiments of the present application, the length (e.g. y In some embodiments of the present application, the length (e.g.

[0045] In practical applications, the periodic array of the unit structures 1 can be arranged in a square, rectangular, or hexagonal lattice, and the square arrangement can match the symmetry of the structure with the distribution characteristics of the light field. The depth of the rectangular holes 4 can be adjusted according to the refractive index characteristics of the material. The material of the film layer 3 can be a dielectric material with high refractive index contrast, such as silicon nitride or sulfide glass, to enhance the interaction between light and structure. The material of the substrate 2 can be a transparent substrate such as sapphire or fused quartz, and the thickness thereof needs to meet the dual requirements of mechanical support and optical transmission.

[0046] Further, the perpendicular arrangement of the long axis direction of the rectangular holes 4 can regulate the propagation path of electromagnetic waves through grating diffraction effect, and the length difference design can achieve response adjustment of different polarization states of light field by changing the size parameters of the local resonant cavity. This structure design cooperates with the spatial symmetry breaking and size parameters to reduce the sensitivity of the resonance frequency to the change of the incident angle while maintaining the narrow bandwidth characteristics.

[0047] The core innovation of the technical solution is to construct a unit structure 1 with orthogonally arranged rectangular holes 4 and introduce a length difference design, thereby achieving the response adjustment of k x and k yThe two resonant modes are robust to wave vector component variation. Compared with the conventional filter structure which relies on a single resonant mechanism or the design idea of symmetric structure, the application breaks through the performance contradiction between spectral selectivity and angle insensitivity of the conventional filter device by accurate matching of the structure parameters, so that two optical modes with different symmetries are coupled in the target wavelength range. This dual-mode resonant mechanism realizes high-performance filtering function through the synergistic design of structure periodicity, hole arrangement and size difference without complex multi-layer structure.

[0048] The embodiment provides a specific implementation mode of a metasurface filter structure, and the core is to realize excitation and coupling of dual resonant modes through specific unit structure 1 design. The structure includes unit structures 1 arranged in a periodic array, each unit structure 1 is composed of a substrate 2 and a film layer 3 arranged on the upper surface of the substrate 2, four rectangular holes 4 are arranged through the film layer 3, the center points of the rectangular holes 4 are arranged in a 2*2 matrix, and the long axis directions of adjacent rectangular holes 4 are perpendicular to each other. Specifically, the widths of the four rectangular holes 4 are consistent, the lengths of three rectangular holes 4 are equal, and the length of the remaining rectangular hole 4 is shortened. This differential design of structure parameters enables the circularly polarized normally incident light in the target wavelength range to simultaneously excite two optical modes with different wave vector robustness, that is, the k x robust mode and the k y robust mode. By accurately regulating the geometric parameters of the rectangular holes, the resonant peak frequencies of the two modes are made to coincide in the target wavelength range, thereby forming a resonant response with strong spectral selectivity.

[0049] In the specific implementation process, the arrangement mode of the four rectangular holes 4 provides a physical basis for the generation of the dual resonant mode by breaking the symmetry of the structure: the vertical relationship of the long axis directions of adjacent rectangular holes 4 leads to differential characteristics of electromagnetic responses in the x-axis and y-axis directions, and the combination design of three equal-length rectangular holes and one short rectangular hole further introduces the breaking of local symmetry. This composite structure design enables the circularly polarized incident light to simultaneously excite two intrinsic modes with different symmetries under normal incidence conditions, and when the resonant frequencies of the two modes approach and eventually coincide in the target wavelength range, the system will exhibit a significant Fano resonance effect, thereby forming a steep transmission peak at a specific wavelength.

[0050] The technical scheme effectively solves the technical problem that the conventional optical filter structure is difficult to balance narrow bandwidth and angle insensitivity through synergistic optimization of structure parameters. Specifically, the coupling mechanism of the dual resonant mode enables the transmission spectrum to form a sharp resonant peak at the target wavelength, significantly improving the spectral selectivity; at the same time, since the two resonant modes are respectively robust to k x and k yThe system's spectral response remains stable under wide-angle incidence conditions. This technical approach, combining symmetry-breaking design with dual-mode coupling, breaks through the performance bottleneck of traditional filter structures and provides a new solution for achieving high-precision, wide-angle optical filtering.

[0051] Preferably, see Figure 2 、 Figure 3 The unit structure 1 is a square unit, and the center points of the four rectangular holes 4 in the unit structure 1 are arranged in a square. The arrangement square of the center points of the four rectangular holes 4 is concentric with the boundary square of the unit structure 1 and has the same angle; any two adjacent sides of the top surface of the unit structure 1 are parallel to the x-axis and the y-axis respectively, and the long axis direction of the rectangular hole 4 is parallel to the x-axis or the y-axis (that is, one of the length direction and the width direction of the rectangular hole 4 is parallel to the x-axis, and the other is parallel to the y-axis).

[0052] Among them, a square unit refers to a planar structural unit with four equal sides and right angles, the purpose of which is to ensure geometric symmetry in the x-axis and y-axis directions. The center points of the four rectangular holes 4 are arranged in a square, which means that the geometric figure formed by the center points of the four holes is a square. It can be achieved by equidistant distribution or by coordinate transformation, in order to ensure that the spatial distribution of the rectangular holes 4 strictly corresponds to the axis of symmetry of the unit structure 1. The arrangement square and the boundary square are concentric and arranged at the same angle, which means that the geometric centers of the two coincide and the corresponding sides are parallel to each other. The long axis direction of the rectangular hole is parallel to the x-axis or y-axis, which means that the length direction of the hole forms an angle of 0° or 90° with the x-axis.

[0053] Specifically, this technical solution builds an isotropic electromagnetic response foundation through the geometric symmetry of the square unit structure 1. The square arrangement of the four rectangular holes 4 ensures the uniformity of spatial distribution, and the concentric and angular settings eliminate the coupling interference caused by structural offset. The parallel relationship between the top surface edge of the unit structure 1 and the coordinate axis accurately corresponds the long axis direction of the rectangular hole 4 to the k x and k y Component independent control channel, where the rectangular hole along the long axis of the x-axis has 4 pairs of k y The change is robust, and the rectangular hole along the long axis of the y-axis is 4 k x The changes are robust, and this orthogonal configuration ensures the independence and stability of the dual resonance modes in the wave vector space through structural symmetry.

[0054] By the above scheme, the present application ensures the consistency of electromagnetic response in the x-axis and y-axis directions through the 1 geometric symmetry of the square unit structure, the square arrangement of the four rectangular holes 4 and the concentric and angular setting eliminate the mode coupling imbalance caused by structural deviation, and the precise correspondence between the long axis direction of the rectangular hole 4 and the coordinate axis establishes an independent wave vector component response channel. This structural design effectively maintains the stable coincidence characteristics of the double resonance mode under the change of different wave vector components, and solves the problem of resonance peak separation caused by insufficient geometric symmetry or arrangement deviation.

[0055] In some possible embodiments, the material of the substrate 2 is silicon dioxide, and the material of the film layer 3 is Sb2S3.

[0056] Specifically, the technical scheme realizes optical mode regulation through material combination. The silicon dioxide substrate provides a low-loss substrate environment by using its wide optical bandgap characteristics, and provides basic support for the localization of the electromagnetic field of the film layer structure. The Sb2S3 film layer forms polarization-dependent responses in orthogonal directions under the modulation of the rectangular hole structure based on the strong birefringence effect produced by its anisotropic crystal structure. This material combination makes the mutually perpendicular long axis directions of the four rectangular holes 4 correspond to the resonance excitation of different polarization states, respectively, and through the nonlinear refractive index characteristics of Sb2S3, the resonance peak of the double resonance mode is made to be robust to the change of k x The mode robust to the change of k y The mode robust to the change of k

[0057] Through the above scheme, the present application realizes the cooperative regulation of the double resonance mode while maintaining the narrow-band filtering characteristics. The wide optical bandgap characteristics of the silicon dioxide substrate reduce the intrinsic absorption loss of the material, and the anisotropic birefringence effect of the Sb2S3 film layer provides a physical basis for independent regulation of orthogonal polarization states, and the combination of the two effectively solves the technical contradiction that traditional filters are difficult to simultaneously consider narrow bandwidth and angle insensitivity.

[0058] In one specific embodiment, with reference to Figure 3 , the top surface side length of the unit structure 1 is 900 nm, the depth of the rectangular hole 4 is 150 nm (i.e. the thickness of the film layer 3 is 150 nm), the width of the rectangular hole 4 is 125 nm, the length of three rectangular holes 4 in the unit structure 1 is 325 nm, and the length of the remaining one rectangular hole 4 is 70 nm less than the length of the other rectangular holes 4 (i.e. ΔL=70 nm); the target wavelength range is 1390 nm-1430 nm.

[0059] Specifically, the technical scheme is designed by the geometric parameters of the sub-wavelength unit structure, so that the square unit structure with a top surface side length of 900 nm is in a sub-wavelength response interval in relation to the scale of the target wavelength range of 1390 nm-1430 nm. The Sb2S3 film layer with a thickness of 150 nm and the silicon dioxide substrate form a high refractive index contrast structure, and the interaction between light and matter is enhanced by longitudinal electromagnetic field confinement. The uniform width of the four rectangular holes 4 is designed to be 125 nm, which maintains the lateral symmetry and provides a reference size for the mode coupling of rectangular holes 4 with different lengths. The asymmetric configuration of three rectangular holes with a length of 325 nm and one rectangular hole with a length of 255 nm induces two orthogonal polarization modes through geometric size differences: the three standard length holes dominate the k x robust resonance mode, while the shortened rectangular hole excites the k y robust resonance mode through size changes. This differential design enables the double resonance modes to coincide in frequency within the 1390 nm-1430 nm wavelength band, forming a narrowband filtering response.

[0060] The chromatic dispersion of the transmission light of the above-mentioned unit structure 1 is simulated as shown in Figures 6-9 , and the transmission spectrum of the above-mentioned unit structure 1 is simulated as shown in Figure 10 and Figure 11 ; wherein, Figure 6 is the transmission light chromatic dispersion diagram when the incident angle of the RCP incident light changes in the xz plane, Figure 7 is the transmission light chromatic dispersion diagram when the incident angle of the RCP incident light changes in the yz plane, Figure 8 is the transmission light chromatic dispersion diagram when the incident angle of the LCP incident light changes in the xz plane, Figure 9 is the transmission light chromatic dispersion diagram when the incident angle of the LCP incident light changes in the yz plane, Figure 10 is the LCP transmission spectrum of the RCP incident light at different incident angles in the xz plane, Figure 11 is the LCP transmission spectrum of the RCP incident light at different incident angles in the yz plane. In the figures, angle represents the incident angle, λ represents the wavelength, Tr represents the transmittance, and Q represents the Q factor. From the figures, it can be concluded that the unit structure 1 has robust Q factors and resonance frequencies within the ±4° incident angle range in the xz and yz planes, and the polarization direction is independent. Therefore, the structure has polarization direction-independent, angle-robust, and high-Q filtering characteristics.

[0061] In some possible implementations, the unit structures 1 are integrally formed.

[0062] Wherein, the integral forming refers to synchronously forming the plurality of unit structures 1 on a single substrate through a micro-nano processing technology, which can be realized by an electron beam lithography combined with a reactive ion etching process, or can be realized by a nano-imprinting technology for batch production. The core of the technical means is to eliminate the physical boundary between adjacent units through material continuity and structural integrity.

[0063] Specifically, the technical scheme forms a continuous medium film layer by using an integral processing method for the plurality of unit structures 1, so that the entire super surface presents uniform medium characteristics in the electromagnetic field propagation direction. At the structural level, the rectangular hole features of each unit are defined by the same photoetching mask, and are synchronously formed in the subsequent etching process, so as to ensure the consistency of the geometric parameters between the units. Such integrated design not only avoids the energy loss caused by the interface scattering in the splicing structure, but also improves the mechanical strength of the device by homogenizing the overall stress distribution. At the manufacturing level, the single forming process replaces the complex process of the traditional multiple photoetching, alignment and deposition, so as to significantly reduce the possibility of process error accumulation.

[0064] Through the above scheme, the seamless integration between the unit structures is realized, the electromagnetic field disturbance caused by the physical gap is effectively suppressed, so as to improve the stability of the transmission spectrum; at the same time, the mechanical strength of the overall structure is enhanced, so as to reduce the risk of deformation or displacement of the device in the packaging and use process; in addition, the single forming process simplifies the manufacturing process, improves the production efficiency and product yield.

[0065] In some other possible implementation manners, the unit structures 1 are independently arranged and spliced to form the super surface filtering structure.

[0066] Wherein, the independent arrangement refers to that the unit structures 1 are separated from each other in the physical space and have independent manufacturing process paths, which can realize high-precision processing at the unit level by using step-by-step electron beam lithography, nano-imprinting or micro-transfer printing technology. The splicing refers to arranging and combining a plurality of independent units according to a preset period through accurate alignment technology, which can use self-alignment assembly based on diffraction alignment marks or laser interference positioning to ensure the periodic continuation of the rectangular hole array between adjacent units. The purpose of introducing the design is to break through the size limitation of single-chip processing, and to improve the adaptation ability of the structure to the complex substrate through modular design.

[0067] Specifically, the technical scheme realizes accurate control of structural parameters at the unit level by manufacturing each unit structure independently and then assembling them. The discrete design allows each unit to be prepared separately using the optimal process, such as high-precision processing of sub-wavelength structures through electron beam lithography, while reducing the equipment requirements for large-scale nanofabrication. The precise alignment technology during the assembly process ensures the periodic continuation of the rectangular hole array between adjacent units, maintaining the robustness of the metasurface filter structure to the incident light wave vector component and breaking through the size limit of single-chip processing. The independently arranged unit structures also allow the introduction of functional transition layers, such as anti-reflection coatings or stress buffer layers, at the assembly interface, thereby improving the structural instability problem caused by differences in material thermal expansion.

[0068] Through the above scheme, the application significantly improves the process fault tolerance and scalability of the metasurface filter structure while maintaining the dual-resonance mode performance. The discrete unit design avoids the problem of scrapping the entire product due to local defects during the overall processing, and the modular design concept allows the structure to adapt to complex application scenarios such as curved substrates and irregular windows, while providing a reconfigurable foundation for subsequent local repair and performance upgrades.

[0069] Reference Figure 5 The application provides a design method of a metasurface filter structure as previously described, comprising the steps of:

[0070] A1. Determine the structural parameters of a reference unit (as shown in Figure 4 ) through band analysis; the reference unit includes a square reference substrate (a in Figure 4 ) and a square reference film layer (b in Figure 4 ) disposed on the reference substrate, and the reference film layer is provided with a rectangular hole 4, which is concentrically arranged with the reference film layer and has the same angle;

[0071] A2. Use the reference unit to double the period in the x-axis direction and the y-axis direction to form a preliminary unit structure; the preliminary unit structure contains four rectangular holes 4, and the long axis directions of any two adjacent rectangular holes 4 are perpendicular to each other;

[0072] A3. Adjust the length of one of the rectangular holes 4 in the preliminary unit structure to enable the excitation of a dual-resonance mode and the coincidence of the resonance peak frequencies of the dual-resonance mode when circularly polarized light of a target wavelength range is normally incident, to obtain a final unit structure 1;

[0073] A4. Use multiple final unit structures 1 to form a metasurface filter structure.

[0074] The core innovation of the embodiment is that the orthogonal arrangement rectangular hole structure formed by doubling the period is combined with the length difference design, so as to realize the robustness to the change of the incident angle while maintaining the narrowband filtering characteristics. Specifically, the band analysis is used to optimize the reference unit parameters to enhance the wave vector adaptability, the four-hole structure with broken symmetry is constructed by doubling the period in the x-axis / y-axis directions, and the single-hole length adjustment is used to trigger the coupling of the double resonance modes, so that the k x and k y The two optical modes with complementary response to the wave vector component change are fused at the target wavelength, and finally the angle stability of the overall structure is expanded through the periodic arrangement. This technical solution based on mode coupling and symmetry design breaks through the contradiction between spectral selectivity and angle insensitivity characteristics of the traditional filtering structure.

[0075] Specifically, step A1 includes:

[0076] A101. Setting initial structure parameters of the reference unit; the initial structure parameters include the side length of the top surface of the reference unit and the size of the rectangular hole;

[0077] A102. Adjusting the initial structure parameters through band analysis, so that the reference unit has a characteristic frequency point in the target wavelength range at the X point in the wave vector space, and the band along the Brillouin zone path Γ-X-M is flat; wherein Γ represents the (k x =0, k y =0) point of the wave vector space of the reference unit, X represents the (k x =π / a, k y =0) point of the wave vector space of the reference unit, M represents the (k x =π / a, k y =π / a) point of the wave vector space of the reference unit, k x represents the wave vector component along the x-axis direction, k y represents the wave vector component along the y-axis direction, and a represents the lattice constant of the reference unit, and the value of a is equal to the side length of the top surface of the reference unit.

[0078] The side length of the top surface of the reference unit refers to the side length of the square unit constituting the reference unit, and the size of the rectangular hole 4 includes three dimensional parameters of length, width and depth. The band analysis refers to a technical means for calculating and analyzing the photonic band structure by finite element simulation or plane wave expansion method, and the purpose is to establish the mapping relationship between the structure parameters and the electromagnetic response characteristics. The band flatness of the Brillouin zone path Γ-X-M refers to that the absolute value of the slope of the band curve along a specific path in the momentum space does not exceed a preset threshold (for example, 0.05 (2π / a) -1 ), which can effectively suppress the frequency drift caused by the change of the wave vector, thereby improving the robustness of the optical mode to the change of the incident angle.

[0079] In the reference unit, at the X point in the wave vector space, there is a characteristic frequency point in the target wavelength range, which means that the frequency corresponding to the energy band passing through the X point (i.e., the characteristic frequency point) is in the target wavelength range.

[0080] Specifically, the scheme establishes a parameter optimization mechanism driven by band analysis, first sets the initial structure parameters to provide an iterative physical model basis for subsequent band analysis. In the band analysis process, the characteristic frequency point in the target wavelength range is bound with the band characteristics of the X point, ensuring that when the circularly polarized light is normally incident, the flat band characteristics of the structure at the X point can effectively suppress the frequency drift caused by the change of wave vector. At the same time, the flat band design along the Γ-X-M path essentially constructs a photonic state with low group velocity in the momentum space, which provides the basis for mode coupling for the excitation of double-resonance mode in the subsequent period doubling step. The equivalent setting of the lattice constant a and the top side length makes the band analysis results can be directly mapped to the actual structure parameters, avoiding the parameter mismatch between the theoretical model and the physical implementation.

[0081] The initial structure parameters can be determined based on expert experience or according to the material of the substrate 1 and the film layer 2.

[0082] Through the above scheme, the present application realizes the closed-loop design from physical principle to engineering parameter. This design method not only improves the physical accuracy of parameter optimization, but also provides necessary band condition support for the excitation of double-resonance mode in the subsequent period doubling step. By constraining the flatness of the band along the Γ-X-M path, a photonic state distribution with direction independence is essentially constructed in the momentum space, which provides a new design dimension for solving the angle sensitivity problem of traditional filtering structure.

[0083] Further, step A2 comprises:

[0084] A201. Form a composite unit by doubling the period of the reference unit in the x-axis direction and rotating the rectangular hole obtained by doubling the period in the x-axis direction by 90° around its center point;

[0085] A202. Form a preliminary unit structure by doubling the period of the composite unit in the y-axis direction and rotating the two rectangular holes obtained by doubling the period in the y-axis direction by 90° around their center points.

[0086] The period doubling refers to copying the structural features of the original structure (the reference unit in step A201 and the composite unit in step A202) and arranging them periodically in a specified direction (the arrangement result is that the boundaries of the original structure and the newly added structure coincide, for example, the top surface of the reference unit has a side length of A, and the composite unit obtained after period doubling along the x-axis direction has a top surface x-direction side length of 2A), which can be achieved by mirror copying or translation copying and other geometric operation methods; rotating 90° around the center point of the rectangle hole refers to rotating the long axis direction of the rectangle hole by a quarter of the circumference angle with respect to the original direction with the geometric center of the rectangle hole as the rotation axis. The purpose of introducing these features is to accurately control the spatial orientation and arrangement relationship of the rectangle hole through the step-by-step construction strategy.

[0087] Specifically, this scheme accurately controls the spatial arrangement and orientation of the rectangle hole through a step-by-step construction method. In A201, when the reference unit is period doubled along the x-axis direction, the newly added rectangle hole realizes the conversion of the long axis direction from the x-axis to the y-axis by rotating 90°. This mirror symmetry operation not only maintains the periodicity in the x-axis direction but also introduces a direction change, laying the foundation for the anisotropic features of the subsequent composite unit. When entering A202, during the period doubling of the composite unit along the y-axis direction, the newly added two rectangle holes are again rotated 90° around the center point. At this time, the rotation direction is orthogonally related to the previous step, so that the final four rectangle holes present a 2x2 matrix arrangement and the long axis directions of adjacent holes are strictly perpendicular. This step-by-step rotation and superposition construction strategy realizes the accurate reproduction of complex geometric features through mathematical symmetry operations, effectively solving the direction deviation or arrangement misplacement problems that may occur in traditional methods, and providing a structural basis for subsequent adjustment of single hole length to excite a double resonance mode.

[0088] Through the above scheme, when constructing the preliminary unit structure, the step-by-step period doubling and rotation operation is applied in cooperation, which significantly improves the structural accuracy and orientation control ability of the rectangle hole arrangement. This method not only ensures the geometric requirement that the long axis directions of adjacent rectangle holes are strictly perpendicular, but also maintains the periodic symmetry of the overall structure, providing a reliable structural basis for subsequent adjustment of single hole length to realize frequency coincidence of the double resonance mode. This construction method effectively solves the technical difficulty that complex geometric features are difficult to be stably reproduced by traditional processing methods, and realizes the reproducible manufacturing of the metasurface filtering structure.

[0089] In some embodiments, step A3 comprises:

[0090] A301. Select one of the rectangle holes in the preliminary unit structure as a target rectangle hole;

[0091] A302. gradually reduce the length of the target rectangular hole, and determine the conversion circularly polarized light transmission spectrum of the preliminary unit structure after each step of reduction under the normal incidence of circularly polarized light in the target wavelength range (wherein the conversion circularly polarized light refers to the circularly polarized light with the opposite rotation direction to the incident circularly polarized light, for example, when the incident light is right-handed circularly polarized light, the conversion circularly polarized light is left-handed circularly polarized light), so as to determine the length of the target rectangular hole capable of exciting the double resonance mode and making the resonance peak frequencies of the double resonance mode coincide, and obtain the final unit structure.

[0092] wherein the target rectangular hole refers to a specific rectangular hole in the unit structure that needs to be differentiated and adjusted, and the selection is determined according to the symmetry characteristics of the unit structure, and specifically can be any one of the four rectangular holes 4. Gradual reduction refers to adjusting the length of the target rectangular hole in a decreasing manner with a preset step, and the step can adopt an arithmetic sequence or an adaptive adjustment strategy, and the purpose is to establish a mapping relationship between the structure parameters and the optical response. The simulation determines the transmission spectrum, which specifically can adopt the finite difference time domain method (FDTD) or the finite element method (FEM) for numerical calculation.

[0093] Specifically, the scheme solves the double resonance mode matching problem through a simulation-driven iterative optimization method. First, the target rectangular hole is selected as the parameter adjustment object, the length thereof is gradually reduced, and the transmission spectrum change is monitored in real time, so as to dynamically capture the influence law of the structure parameter change on the optical response. The application of simulation technology makes the electromagnetic field distribution characteristics under the nanoscale visible, and provides a theoretical basis for the accurate regulation of the resonance peak position. This parameter adjustment strategy breaks through the limitations of the traditional trial-and-error method, systematically establishes the mapping relationship between the structure parameters and the optical response, realizes the accurate control of the double resonance mode excitation condition, and finally achieves the technical goal of coinciding the resonance peak frequencies.

[0094] Through the above scheme, the present application realizes the accurate control of the double resonance mode excitation condition. The method solves the technical bottleneck that the excitation efficiency and the frequency matching accuracy are difficult to be considered in the traditional parameter adjustment method through the iterative optimization strategy combining simulation and experiment, significantly improves the spectral selectivity and angle robustness of the metasurface filtering structure, and provides a reliable technical path for the narrow bandwidth and angle-insensitive optical filtering application.

[0095] For example, in one embodiment, through steps A1 and A2, the top surface side length of the preliminary unit structure obtained is 900 nm, the depth of the rectangular hole 4 is 150 nm, the width of the rectangular hole 4 is 125 nm, and the length of the rectangular hole 4 is 325 nm; the target wavelength range is 1390 nm-1430 nm. The length of one of the rectangular holes 4 is gradually reduced, and the LCP transmission spectrum of the preliminary unit structure after each step of reduction under the normal incidence of RCP incident light in the target wavelength range is determined through simulation, as shown in FIG. 4.Figure 12 As shown in the figure, ① and ② represent the resonance peaks of two modes of the excited double resonance mode, Q1 and Q2 represent the Q factors of the two modes (in the figure, if only Q is given without Q1 and Q2, it means Q1 = Q2 = Q), and ΔL represents the reduction amount of the length of the target rectangular hole; it can be seen from the figure that when ΔL = 70 nm, the resonance peaks of the two modes coincide under normal incidence, thereby determining the length of the target rectangular hole as 325 nm-70 nm = 255 nm.

[0096] In summary, the super surface filter structure and the design method thereof provided by the present application have at least the following advantages:

[0097] 1. Angle insensitivity: It presents an angular dispersion flat band in the xz and yz planes within ±4° incident angle range, that is, the resonance frequency is constant under different incident angles;

[0098] 2. Polarization direction independence: The super surface has consistent response to RCP / LCP incident light, and presents an angular dispersion flat band within ±4° incident angle range;

[0099] 3. Q factor is robust to wave vector: The Q factor does not decrease significantly with the change of wave vector k.

[0100] The above only describes the embodiments of the present application and is not used to limit the protection scope of the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A metasurface filtering structure, characterized in that: The invention comprises a plurality of unit structures arranged in an array, each of the unit structures comprising a substrate and a film layer arranged on the upper surface of the substrate, the film layer being provided with four rectangular holes penetrating the film layer, the center points of the four rectangular holes being arranged in a 2*2 matrix, and the long axis directions of any two adjacent rectangular holes being perpendicular to each other, the four rectangular holes having the same width, three of which having the same length, and the remaining one having a length smaller than that of the other rectangular holes, so that when circularly polarized light in a target wavelength range is incident normally, a double resonance mode can be excited and the resonance peak frequency of the double resonance mode can be overlapped; wherein, the two modes of the double resonance mode are respectively for k x Robust to changes and k y Optical modes that are robust to variations, k x represents the wave vector component along the x-axis, k y represents the wave vector component along the y-axis direction, and the x-axis and y-axis are two axes of the rectangular coordinate system on the top surface of the unit structure.

2. The supersurface filtering structure according to claim 1, characterized in that The unit structure is a square unit, and the center points of the four rectangular holes in the unit structure are arranged in a square. The arrangement square of the center points of the four rectangular holes is concentric with the boundary square of the unit structure and has the same angle; any two adjacent sides of the top surface of the unit structure are parallel to the x-axis and the y-axis respectively, and the long axis direction of the rectangular hole is parallel to the x-axis or the y-axis.

3. The supersurface filtering structure according to claim 2, characterized in that: The material of the substrate is silicon dioxide, and the material of the film layer is Sb2S3.

4. The supersurface filtering structure according to claim 3, characterized in that: The top surface side length of the unit structure is 900nm, the depth of the rectangular hole is 150nm, the width of the rectangular hole is 125nm, the length of three of the rectangular holes in the unit structure is 325nm, and the length of the remaining rectangular hole is 70nm smaller than that of the other rectangular holes; the target wavelength range is 1390nm-1430nm.

5. The metasurface filtering structure according to any one of claims 1 to 4, characterized in that: The unit structures are integrally formed with each other.

6. The metasurface filtering structure according to any one of claims 1 to 4, characterized in that: The unit structures are independently arranged and spliced ​​to form the metasurface filtering structure.

7. A method for designing a metasurface filtering structure according to claim 5 or 6, characterized in that: Including steps: A1. Determine the structural parameters of a reference unit through energy band analysis; the reference unit includes a square reference substrate and a square reference film layer disposed on the reference substrate, with a rectangular hole disposed concentrically with the reference film layer and at the same angle. A2. Using the reference unit, the period in the x-axis and y-axis directions is doubled to form a preliminary unit structure; the preliminary unit structure comprises four rectangular holes, and the long axes of any two adjacent rectangular holes are perpendicular to each other; A3. Adjusting the length of one of the rectangular holes in the preliminary unit structure so that when circularly polarized light of the target wavelength range is incident normally, a double resonance mode can be excited and the resonance peak frequencies of the double resonance modes coincide to obtain the final unit structure; A4. Utilize multiple of the final unit structures to form the metasurface filtering structure.

8. The design method according to claim 7, characterized in that: Step A1 includes: A101. Set the initial structural parameters of the reference unit; the initial structural parameters include the top side length of the reference unit and the size of the rectangular hole; A102. Adjust the initial structural parameters through energy band analysis so that the reference unit has a characteristic frequency point within the target wavelength range at point X in the wave vector space, and the energy band along the Brillouin zone path Γ-XM is flat; where Γ represents the wave vector space of the reference unit (k x =0,k y =0) point, X represents the (k x =π / a,k y =0) point, M represents the (k x =π / a,k y =π / a) point, k x represents the wave vector component along the x-axis, k y represents the wave vector component along the y-axis direction, a represents the lattice constant of the reference unit, and the value of a is equal to the side length of the top surface of the reference unit.

9. The design method according to claim 7, characterized in that: Step A2 includes: A201. A composite unit is formed by doubling the period of the reference unit in the x-axis direction and rotating a rectangular hole obtained by doubling the period along the x-axis direction by 90° around its center point; A202. The preliminary unit structure is formed by doubling the period of the composite unit in the y-axis direction and rotating the two rectangular holes obtained by doubling the period along the y-axis direction by 90° around their own center points.

10. The design method according to claim 7, characterized in that: Step A3 includes: A301. Select one of the rectangular holes in the preliminary unit structure as the target rectangular hole; A302. Gradually reduce the length of the target rectangular hole, and determine through simulation the converted circularly polarized light transmission spectrum of the preliminary unit structure after each step of reduction when circularly polarized light in the target wavelength range is normally incident, thereby determining the length of the target rectangular hole that can excite the double resonance mode and make the resonance peak frequency of the double resonance mode coincide, and obtaining the final unit structure.

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