Continuous domain bound state merging method and phase change material metasurface structure

Abstract

The invention provides a continuous domain bound state merging method and a phase change material metasurface structure, and relates to the technical field of micro-nano optics. The continuous domain bound state merging method comprises the steps of obtaining an energy band structure of a phase change material metasurface structure; determining an energy band simultaneously having a symmetric protection continuous domain bound state and an accidental continuous domain bound state from the energy band structure; based on the energy band, far-field polarization of the phase-change material in the phase-change material metasurface structure in an amorphous state and a crystalline state is calculated, and a corresponding momentum space far-field polarization vector diagram is generated based on the far-field polarization; and according to the momentum space far-field polarization vector diagram, the phase change material is controlled to be converted from the amorphous state to the crystalline state, so that the symmetric protection continuous domain bound state and the accidental continuous domain bound state are combined.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the field of micro-nano optics, and more particularly, to a merging method of bound states in the continuum and a phase-change material metasurface structure. BACKGROUND

[0002] Bound states in the continuum (BICs) are completely localized states in the continuum that exist simultaneously with extended waves, without any radiation. Ideal BICs have an infinite high quality factor (Q-factor), however, in actual manufacturing, the achievable Q value is limited due to material absorption, technical defects and substrate leakage, and merging BICs becomes an effective solution to this problem. In a photonic crystal slab (PC) metasurface, in addition to the symmetry-protected BICs usually fixed at the center point (Γ point) of the Brillouin zone, there are accidental BICs located at high-symmetry points. By utilizing the topological properties of BICs, multiple BICs on the same photonic band are tuned to the same wave vector, and the resulting merged BICs can suppress out-of-plane scattering loss, reduce radiation loss, and achieve high Q value in a wider range of spatial frequencies, thereby making the metasurface more robust to defects and external disturbances.

[0003] However, the current methods of merging BICs all require changes to the geometric parameters of the structure, such as the period and thickness of the PCs, and once the metasurface structure is manufactured, it cannot be changed, which greatly limits the tunability and flexibility of merging BICs. SUMMARY

[0004] In view of this, the present disclosure provides a merging method of bound states in the continuum and a phase-change material metasurface structure.

[0005] In one aspect, the present disclosure provides a merging method of bound states in the continuum, comprising: obtaining a band structure of a phase-change material metasurface structure; determining an energy band that simultaneously has a symmetry-protected bound state in the continuum and an accidental bound state in the continuum from the band structure; based on the energy band, calculating the far-field polarization of the phase-change material in the amorphous state and the crystalline state in the phase-change material metasurface structure, generating a corresponding momentum space far-field polarization vector diagram based on the far-field polarization; and according to the momentum space far-field polarization vector diagram, merging the symmetry-protected bound state in the continuum and the accidental bound state in the continuum by controlling the phase-change material to change from the amorphous state to the crystalline state.

[0006] According to an embodiment of the present disclosure, the symmetry-protected bound state in the continuum is located at the center point of the Brillouin zone, and the accidental bound state in the continuum is located on a high-symmetry axis other than the center point of the Brillouin zone.

[0007] According to an embodiment of the present disclosure, according to the momentum space far field polarization vector diagram, the symmetrical protection continuous domain bound state and the accidental continuous domain bound state are merged by controlling the phase change material to change from the amorphous state to the crystalline state, comprising: according to the momentum space far field polarization vector diagram, the phase change material is controlled to change from the amorphous state to the crystalline state to change the refractive index of the phase change material; according to the change of the refractive index of the phase change material, the accidental continuous domain bound state is controlled to move to the center point of the Brillouin zone to merge with the symmetrical protection continuous domain bound state.

[0008] According to an embodiment of the present disclosure, further comprising: based on the energy band, calculating the quality factor of the phase change material in the amorphous state and the crystalline state in the phase change material metasurface structure; according to the quality factor, obtaining the merging direction of the symmetrical protection continuous domain bound state and the accidental continuous domain bound state when the phase change material changes from the amorphous state to the crystalline state.

[0009] According to an embodiment of the present disclosure, the quality factor of the phase change material in the amorphous state is:

[0010] ,

[0011] The quality factor of the phase change material in the crystalline state is:

[0012] ,

[0013] Wherein, Q is the quality factor, k is the wave vector, is the wave vector of the accidental continuous domain bound state.

[0014] According to an embodiment of the present disclosure, further comprising: performing multi-level decomposition on the phase change material metasurface structure to obtain components of each mode of the energy band; determining a dominant mode based on the components of each mode and merging the continuous domain bound state according to the dominant mode. According to an embodiment of the present disclosure, the multi-level decomposition of the phase change material metasurface structure to obtain the components of each mode of the energy band comprises: calculating the polarization power of the phase change material metasurface structure based on the Cartesian coordinate system; according to the polarization power, expanding the calculation of the electric dipole power, the magnetic dipole power, the electric quadrupole power, the magnetic quadrupole power and the toroidal dipole power as the components of each mode.

[0015] According to an embodiment of the present disclosure, further comprising: after the symmetrical protection continuous domain bound state and the accidental continuous domain bound state are merged according to the momentum space far field polarization vector diagram by controlling the phase change material to change from the amorphous state to the crystalline state, the phase change material metasurface structure is verified for robustness.

[0016] According to an embodiment of the present disclosure, a method for obtaining a band structure of a phase-change material metasurface structure comprises: establishing a geometric model of the phase-change material metasurface structure; setting a periodic boundary condition in a two-dimensional plane to simulate periodicity of the phase-change material metasurface structure in the two-dimensional plane; setting an electromagnetic wave incident along a vertical direction to simulate propagation of the electromagnetic wave along the vertical direction; constructing a matching layer in the vertical direction to absorb the electromagnetic wave propagating along the vertical direction; and performing numerical simulation of electromagnetic wave propagation of the phase-change material metasurface structure based on the geometric model, the periodic boundary condition and the matching layer in a numerical simulation software to obtain the band structure.

[0017] Another aspect of the present disclosure provides a phase-change material metasurface structure, comprising: a Si3N4 layer; two Sb2S3 film layers covering two sides of the Si3N4 layer, respectively, so that the phase-change material metasurface structure has a merged continuous domain bound state formed by a symmetry-protected continuous domain bound state and an accidental continuous domain bound state simultaneously when Sb2S3 in the two Sb2S3 film layers is transformed from an amorphous state to a crystalline state.

[0018] According to an embodiment of the present disclosure, by utilizing the difference in optical properties of the phase-change material before and after phase state conversion and the topological properties of BICs, the BICs are manipulated in momentum space to be close to the Γ point, thereby realizing dynamic adjustable merged BICs and high Q values in a wider spatial frequency range, and the BICs are more robust to defects and external disturbances.

[0019] According to an embodiment of the present disclosure, by introducing the phase-change material to prepare the metasurface structure, the metasurface structure is more tunable and can be integrated into various photonic devices to realize applications such as vortex beam generators, nanolaser and biosensing. BRIEF DESCRIPTION OF DRAWINGS

[0020] The above and other objects, features and advantages of the present disclosure will become more apparent from the following description of embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which:

[0021] Figure 1 A flowchart of a merging method of a continuous domain bound state according to an embodiment of the present disclosure is schematically shown;

[0022] Figure 2A A schematic diagram of a phase-change material metasurface structure according to an embodiment of the present disclosure is schematically shown;

[0023] Figure 2B A top view of a phase-change material metasurface structure according to an embodiment of the present disclosure is schematically shown;

[0024] Figure 2C A side view of a phase-change material metasurface structure according to an embodiment of the present disclosure is schematically shown;

[0025] Figure 3The band structure of a phase change material metasurface structure according to an embodiment of the present disclosure is schematically shown;

[0026] Figure 4A The quality factors of Sb2S3 in its amorphous and crystalline states according to embodiments of the present disclosure are schematically illustrated.

[0027] Figure 4B The quality factor scaling rules for Sb2S3 in amorphous and crystalline states according to embodiments of the present disclosure are illustrated schematically.

[0028] Figure 5A The momentum space far-field polarization vector diagram of the Sb2S3 amorphous state according to an embodiment of the present disclosure is schematically shown.

[0029] Figure 5B The momentum space far-field polarization vector diagram of the Sb2S3 crystalline state according to an embodiment of the present disclosure is schematically shown.

[0030] Figure 6 The diagram schematically illustrates the multipole response analysis of a phase change material metasurface structure at the resonance point according to an embodiment of the present disclosure;

[0031] Figure 7A The momentum space far-field plot of a phase change material metasurface structure according to an embodiment of the present disclosure is shown schematically for the Sb2S3 amorphous state under defects where the etched square holes are smaller than the design value.

[0032] Figure 7B The momentum space far-field plot of the Sb2S3 crystal state under etched square holes smaller than the design value is schematically shown for a phase change material metasurface structure according to an embodiment of the present disclosure.

[0033] Figure 8A The momentum space far-field plot of a phase change material metasurface structure according to an embodiment of the present disclosure is shown in the form of Sb2S3 amorphous state under the condition that the etched square hole is twisted into a parallelogram hole defect.

[0034] Figure 8B The momentum space far-field plot of the phase change material metasurface structure according to an embodiment of the present disclosure is shown schematically for the Sb2S3 crystal state under the condition that the etched square hole is twisted into a parallelogram hole defect.

[0035] Figure 9A The momentum space far-field plot of the phase change material metasurface structure according to an embodiment of the present disclosure is shown in the form of Sb2S3 amorphous state under prism hole defects with inconsistent widths above and below the etched square hole twist.

[0036] Figure 9B The momentum space far-field diagram of the Sb2S3 crystal state under the defect of etched square holes twisted into prism holes with inconsistent widths at the top and bottom is schematically shown in the embodiment of the present disclosure.

[0037] Explanation of reference numerals in the attached figures: 1. Si3N4 layer; 2. Sb2S3 thin film layer. Detailed Implementation

[0038] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0039] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0040] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0041] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0042] Figure 1 A flowchart illustrating a method for merging continuous domain bound states according to an embodiment of the present disclosure is shown schematically.

[0043] Figure 2A A schematic diagram of a phase change material metasurface structure according to an embodiment of the present disclosure is shown.

[0044] Figure 2B A top view schematically illustrates a phase change material metasurface structure according to an embodiment of the present disclosure.

[0045] Figure 2C A side view of a phase change material metasurface structure according to an embodiment of the present disclosure is shown schematically.

[0046] Figure 3The energy band structure of a phase change material metasurface structure according to an embodiment of the present disclosure is illustrated schematically.

[0047] like Figure 1 As shown, embodiments of this disclosure provide a method for merging bound states in a continuous domain, including:

[0048] Step 1: Obtain the band structure of the metasurface structure of the phase change material.

[0049] Step 2: Determine the band structure that simultaneously possesses symmetry-protected continuous bound states and accidental continuous bound states.

[0050] Step 3: Based on the energy band, calculate the far-field polarization of the phase change material in the amorphous and crystalline states in the metasurface structure of the phase change material, and generate the corresponding momentum space far-field polarization vector diagram based on the far-field polarization.

[0051] Step 4: Based on the far-field polarization vector diagram in momentum space, the phase change material is controlled to transform from an amorphous state to a crystalline state, thereby merging the symmetry-protected continuous domain bound state and the accidental continuous domain bound state.

[0052] In the embodiments of this disclosure, current methods for merging BICs require changing the geometric parameters of the structure, such as the period and thickness of the PCs, and these parameters cannot be changed once the metasurface is fabricated. This greatly limits the adjustability and flexibility of merging BICs.

[0053] Based on this, this disclosure proposes a solution for integrating phase change materials (PCMs) into metasurfaces. By determining the energy bands that simultaneously possess symmetry-protected continuous domain bound states and accidental continuous domain bound states, and generating the corresponding momentum space far-field polarization vector diagram based on far-field polarization, the optical properties of PCMs change significantly when they transition from an amorphous state to a crystalline state. This allows the merging of the symmetry-protected continuous domain bound states and accidental continuous domain bound states to achieve the merging of BICs and a higher Q value over a wider spatial frequency range.

[0054] In some possible embodiments of this disclosure, step one further includes: establishing a geometric model of the phase change material metasurface structure using numerical simulation software (COMSOL Multiphysics); setting periodic boundary conditions in the two-dimensional plane xoy to simulate the periodicity of the phase change material metasurface structure in the two-dimensional plane; setting an electromagnetic wave incident in the vertical direction to simulate the propagation of the electromagnetic wave in the vertical direction; constructing a matching layer in the vertical direction to absorb the electromagnetic wave propagating in the vertical direction; and performing numerical simulation of electromagnetic wave propagation on the phase change material metasurface structure in the numerical simulation software based on the geometric model, periodic boundary conditions, and matching layer to obtain the band structure. Figure 3 As shown, the horizontal axis represents the wave vector, and the vertical axis represents the frequency (terahertz).

[0055] In some embodiments of this disclosure, the electromagnetic wave is a transverse magnetic wave (TM).

[0056] In some embodiments of this disclosure, such as Figure 2A , 2B As shown in Figure 2C, a phase change material metasurface structure is provided, comprising: a Si3N4 layer 1; two Sb2S3 thin film layers 2, respectively covering both sides of the Si3N4 layer; for merging of the symmetry-protected continuous domain bound states and the accidental continuous domain bound states simultaneously present in the band structure when Sb2S3 changes from an amorphous state to a crystalline state; wherein, the phase change material metasurface structure is provided with periodically distributed pores penetrating the two Sb2S3 thin film layers and the Si3N4 layer.

[0057] In the embodiments of this disclosure, the merging of BICs is achieved through the phase transition of the phase change material Sb2S3, resulting in a high Q value over a wider spatial frequency range and greater robustness to defects and external disturbances. Figure 2A It can be seen that the metasurface structure of phase change materials has C 4v symmetry( ).

[0058] In some possible embodiments of this disclosure, the refractive index of Si3N4 is n Si3N4 =2.02, the refractive indices of the crystalline and amorphous Sb2S3 thin films are shown in Table 1:

[0059] Table 1

[0060]

[0061] The geometric parameters of the phase change material metasurface structure are as follows: the thickness h of the Si3N4 layer is 640 nm, the thickness t of the two Sb2S3 films is 10 nm, and a square hole with a width b of 160 nm is etched through the two Sb2S3 film layers and the Si3N4 layer on the phase change material metasurface structure with a period a of 600 nm. One of the Sb2S3 films is placed on the substrate, the refractive index of the substrate is set to 1, and the substrate can be air.

[0062] In some possible embodiments of this disclosure, step two further includes: determining an energy band TM1 from the band structure that simultaneously possesses symmetry-protected continuous-domain bound states and accidental continuous-domain bound states, wherein the symmetry-protected continuous-domain bound states are located at the center point (Γ point) of the Brillouin zone, and the accidental continuous-domain bound states are located on a higher symmetry axis other than the center point of the Brillouin zone. Furthermore, the accidental continuous-domain bound states are closer to the Γ point, facilitating subsequent tuning.

[0063] Figure 4A The quality factors of Sb2S3 in its amorphous and crystalline states are schematically illustrated according to embodiments of the present disclosure.

[0064] Figure 4B The quality factor scaling rules for Sb2S3 in amorphous and crystalline states are illustrated schematically according to embodiments of the present disclosure.

[0065] like Figure 4A As shown, in some possible embodiments of this disclosure, between step two and step three, the method further includes: calculating the quality factor of the phase change material in the amorphous and crystalline states of the phase change material metasurface structure based on the energy band TM1; and, according to the quality factor, determining the merging direction of the symmetry-protected continuous domain bound states and the accidental continuous domain bound states obtained when the phase change material transforms from the amorphous state to the crystalline state.

[0066] like Figure 4B As shown, according to embodiments of this disclosure, the quality factor of the phase change material in the amorphous state is:

[0067] ,

[0068] The quality factor of the phase change material in the crystalline state is:

[0069] ,

[0070] Where Q is the quality factor and k is the wave vector. The wave vector of random BICs.

[0071] In embodiments of this disclosure, Figure 4A This demonstrates the symmetry-protected BICs and accidental BICs along the TM1 band as Sb2S3 transitions from an amorphous to a crystalline state. The process of directional merging. Here, a-Sb₂S₃ represents the amorphous state of Sb₂S₃, and c-Sb₂S₃ represents the crystalline state of Sb₂S₃. When the state of Sb₂S₃ transforms into a crystalline state, it is located at... Random BICs at point Γ move toward point Γ, forming merged BICs, achieving high Q values ​​over a wider frequency range.

[0072] Figure 4B The scaling rule for the Q-value change before and after merging BICs when Sb₂S₃ transitions from an amorphous to a crystalline state is shown in the figure. The figure illustrates the fitting of Q-values ​​for two different cases. For isolated, random BICs, the geometric decay of Q-values ​​follows... When Sb₂S₃ transforms into a crystalline state, the Q value of the merged BICs decays to The Q-value decay is significantly lower than that of isolated, accidental BICs.

[0073] Figure 5A The momentum space far-field polarization vector diagram of the Sb2S3 amorphous state according to an embodiment of the present disclosure is schematically shown.

[0074] Figure 5B The momentum space far-field polarization vector diagram of the Sb2S3 crystalline state according to an embodiment of the present disclosure is schematically shown.

[0075] like Figure 5A and 5B As shown, in some possible embodiments of this disclosure, step three further includes: calculating the far-field polarization of the phase change material in the amorphous and crystalline states in the metasurface structure of the phase change material based on the energy band, and generating the corresponding momentum space far-field polarization vector diagram based on the far-field polarization; step four: according to the momentum space far-field polarization vector diagram, controlling the phase change material to transform from the amorphous state to the crystalline state, so that the symmetry-protected continuous domain bound state and the accidental continuous domain bound state are merged.

[0076] In embodiments of this disclosure, based on the momentum space far-field polarization vector diagram, the phase change material is controlled to transform from an amorphous state to a crystalline state, thereby changing the refractive index of the phase change material; based on the change in the refractive index of the phase change material, the accidentally bound states in the continuous domain are controlled to move towards the center point of the Brillouin zone, so as to merge with the bound states in the symmetry-protected continuous domain. Figure 5A As shown, the topological charge of the symmetric protective BICs located at point Γ and the BICs along the x and y axes is +1, while the topological charge of the remaining BICs is -1. Figure 5B As shown, when Sb₂S₃ transforms into a crystalline state, isolated BICs distributed along the high symmetry axes X and M move closer to point Γ, forming a single merged BIC. This merging process causes accidental BICs with topological charges of +1 and -1 to annihilate each other, resulting in a merged BIC with a net topological charge of +1. Therefore, the momentum space exhibits an extended wave vector spectrum with a high Q value, implying that such merged BICs are more robust to external perturbations.

[0077] Figure 6 The diagram schematically illustrates the multipole response analysis of a phase change material metasurface structure at the resonance point according to an embodiment of the present disclosure.

[0078] like Figure 6 As shown, according to embodiments of this disclosure, the method further includes: performing multi-level decomposition of the metasurface structure of the phase change material to obtain components of various modes of the energy band; determining one of the dominant modes based on the components of each mode; and adjusting the phase change material in momentum space from an amorphous state to a crystalline state based on this mode to achieve better merging of BICs.

[0079] According to embodiments of this disclosure, the phase change material metasurface structure is decomposed into multiple levels to obtain the components of each mode of the energy band, including: calculating the polarization power of the phase change material metasurface structure based on the Cartesian coordinate system; and calculating the electric dipole power, magnetic dipole power, electric quadrupole power, magnetic quadrupole power, and toroidal dipole power based on the polarization power extension, as components of each mode.

[0080] In one possible embodiment of this disclosure, in order to further understand the physical origin of BIC resonances, a multilevel decomposition analysis (CMDT) of the modes in the band is performed based on a Cartesian coordinate system, and polarization is calculated based on the near-field distribution of the metasurface.

[0081] Among them, polarization power Represented as:

[0082] ,

[0083] The first five orders of the multi-level components, including the electric dipole (ED), magnetic dipole (MD), electric quadrupole (EQ), magnetic quadrupole (MQ), and toroidal dipole (TQ), are respectively represented as:

[0084] ;

[0085] ;

[0086] ;

[0087]

[0088] ;

[0089] in The dielectric constant of free space, and These are the relative permittivity of the metasurface structure of the phase material and the surrounding medium, respectively. Let r represent the total electric field inside the metasurface, and r denote the surface element. Represents circumferential frequency. Let i represent the total volume integral, and let i represent the imaginary part.

[0090] In the embodiments of this disclosure, the components of each mode of the TM1 band were obtained based on the above multipole decomposition analysis. Among them, the cyclic dipole mode is dominant, has weak coupling with the incident light, and has a relatively large Q value, which can better merge the BICs in momentum space.

[0091] According to embodiments of this disclosure, in order to study the stability of the phase change material metasurface structure to defects, the momentum space far-field diagrams of the phase change material metasurface under three manufacturing errors, with Sb2S3 in both amorphous and crystalline states, were calculated to verify the robustness of the phase change material metasurface structure.

[0092] Figure 7A The diagram schematically illustrates the momentum space far-field plot of a phase change material metasurface structure according to an embodiment of the present disclosure under the defect of etched square holes smaller than the design value for the Sb2S3 amorphous state.

[0093] Figure 7B The diagram schematically illustrates the momentum space far-field plot of a phase change material metasurface structure according to an embodiment of the present disclosure under the defect of etched square holes smaller than the design value for Sb2S3 crystal.

[0094] like Figure 7A , 7B As shown, when Sb2S3 transforms from an amorphous state to a crystalline state, the C4v symmetry of the phase change material metasurface remains unchanged, and the merging situation still exists.

[0095] Figure 8A The momentum space far-field plot of the phase change material metasurface structure according to an embodiment of the present disclosure is shown in the case of Sb2S3 amorphous state under etched square holes twisted into parallelogram holes.

[0096] Figure 8B The momentum space far-field plot of the Sb2S3 crystal state under the condition that the etched square hole is twisted into a parallelogram hole defect is schematically shown for a phase change material metasurface structure according to an embodiment of the present disclosure.

[0097] like Figure 8A , 8B The figure shows the momentum space far-field diagrams of Sb₂S₃ in both amorphous and crystalline states when a square hole is etched and twisted into a parallelogram hole on a phase change material metasurface. In this case, the C of the phase change material metasurface... 4v The symmetry is broken, but the vertical symmetry remains unchanged. Figure 8B It can be seen that this deformation does not affect the merging of BICs.

[0098] Figure 9A The momentum space far-field plot of the phase change material metasurface structure according to an embodiment of the present disclosure is shown in the form of Sb2S3 amorphous state under prism hole defects with inconsistent widths above and below the etched square hole twist.

[0099] Figure 9B The momentum space far-field plot of the phase change material metasurface structure according to an embodiment of the present disclosure is shown in the form of Sb2S3 crystal under the defect of etched square holes twisted into prism holes with inconsistent widths at the top and bottom.

[0100] likeFigure 9A , 9B The figures show the momentum space far-field diagrams of Sb₂S₃ in its amorphous and crystalline states when the etched square holes are twisted into prismatic holes with inconsistent widths at the top and bottom. In this case, the mirror symmetry is destroyed, and radiation in two perpendicular directions cannot be suppressed simultaneously, resulting in a finite Q value.

[0101] In the three cases mentioned above, the Q value of merged BICs is significantly greater than that of random BICs over a wider wave vector range. Therefore, compared to random BICs, merged BICs can maintain a higher Q value even in the presence of manufacturing defects.

[0102] Those skilled in the art will understand that the features described in the various embodiments and / or claims of this disclosure can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. In particular, the features described in the various embodiments and / or claims of this disclosure can be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0103] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of this disclosure is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A method for merging bound states in a continuous domain, characterized in that, include: Obtain the band structure of metasurface structures in phase change materials; Determine the band structure that simultaneously possesses symmetry-protected continuous-domain bound states and accidental continuous-domain bound states; Based on the energy band, the far-field polarization of the phase change material in the metasurface structure of the phase change material in the amorphous and crystalline states is calculated, and the corresponding momentum space far-field polarization vector diagram is generated based on the far-field polarization. Based on the momentum space far-field polarization vector diagram, the phase change material is controlled to transform from the amorphous state to the crystalline state, thereby merging the symmetry-protected continuous domain bound state and the accidental continuous domain bound state.

2. The method for merging bound states in a continuous domain according to claim 1, characterized in that, The symmetry-protected continuum bound state is located at the center point of the Brillouin zone, and the accidental continuum bound state is located on a high symmetry axis other than the center point of the Brillouin zone.

3. The method for merging bound states in a continuous domain according to claim 2, characterized in that, Based on the momentum space far-field polarization vector diagram, by controlling the phase transition material to transform from the amorphous state to the crystalline state, the symmetry-protected continuous domain bound state and the accidental continuous domain bound state are merged, including: Based on the momentum space far-field polarization vector diagram, the refractive index of the phase change material is changed by controlling the phase change material to transform from the amorphous state to the crystalline state. Based on the change in refractive index of the phase change material, the accidental continuous domain bound state is controlled to move towards the center point of the Brillouin zone in order to merge with the symmetry-protected continuous domain bound state.

4. The method for merging bound states in a continuous domain according to claim 1, characterized in that, Also includes: Based on the energy band, calculate the quality factor of the phase change material in the amorphous and crystalline states in the metasurface structure of the phase change material; According to the quality factor, when the phase change material transforms from the amorphous state to the crystalline state, the merging direction of the symmetry-protected continuous domain bound state and the accidental continuous domain bound state is obtained.

5. The method for merging bound states in a continuous domain according to claim 4, characterized in that, The quality factor of the phase change material in the amorphous state is: ， The quality factor of the phase change material in the crystalline state is: ， Where Q is the quality factor and k is the wave vector. The wave vector is a bound state in an accidental continuous domain.

6. The method for merging bound states in a continuous domain according to claim 1, characterized in that, Also includes: The metasurface structure of the phase change material is decomposed into multiple levels to obtain the components of each mode of the energy band. The dominant mode is determined based on the components of each mode, and the bound states of the continuous domain are merged according to the dominant mode.

7. The method for merging bound states in a continuous domain according to claim 6, characterized in that, The phase change material metasurface structure is decomposed into multiple levels to obtain the components of each mode of the energy band, including: The polarization power of the metasurface structure of the phase change material was calculated based on the Cartesian coordinate system. The electric dipole power, magnetic dipole power, electric quadrupole power, magnetic quadrupole power, and toroidal dipole power are calculated based on the polarization power extension and used as components of each mode.

8. The method for merging bound states in a continuous domain according to claim 1, characterized in that, Also includes: Based on the momentum space far-field polarization vector diagram, the robustness of the metasurface structure of the phase change material is verified by controlling the phase change material to transform from the amorphous state to the crystalline state, thereby merging the symmetry-protected continuous domain bound state and the accidental continuous domain bound state.

9. The method for merging bound states in a continuous domain according to claim 1, characterized in that, Obtaining the band structure of metasurface structures of phase change materials, including: Establish a geometric model of the metasurface structure of the phase change material; Periodic boundary conditions are set in a two-dimensional plane to simulate the periodicity of the metasurface structure of the phase change material in the two-dimensional plane. An electromagnetic wave is incident vertically to simulate the propagation of electromagnetic waves in a vertical direction. A matching layer is constructed in the vertical direction to absorb electromagnetic waves propagating along the vertical direction; In the numerical simulation software, based on the geometric model, the periodic boundary conditions, and the matching layer, the electromagnetic wave propagation of the phase change material metasurface structure is numerically simulated to obtain the band structure.

10. A metasurface structure of a phase change material, characterized in that, include: Si3N4 layer; Two Sb2S3 thin film layers cover both sides of the Si3N4 layer, respectively, so that when the Sb2S3 in the two Sb2S3 thin film layers changes from amorphous to crystalline, the symmetry-protected continuous domain bound state and the accidental continuous domain bound state simultaneously present on the energy band of the metasurface structure of the phase change material form a merged continuous domain bound state.

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