Topological quasi-flat-band metal metasurface waveguide structure, design method and electromagnetic device

Abstract

The application belongs to the field of waveguides, and particularly relates to a topological quasi-flatband metal metasurface waveguide structure, a design method and an electromagnetic device. The application provides a design method of a topological quasi-flatband metal metasurface waveguide structure, which comprises parallel plate waveguides and metal scatterers which jointly constitute a two-dimensional metal metasurface. The metal scatterers in different regions between two parallel metal plates of the parallel plate waveguides are rotated in different directions to form a valley Hall topological phase and a topological edge state. The size of all the metal scatterers is scaled while the rotation angle of each metal scatterer is kept unchanged to adjust the amplitude of an equivalent mass term in an equivalent Hamiltonian until the dispersion of the topological edge state is compressed into a quasi-flatband, and the topological edge state forms a deterministic spatially anchored edge mode along a preset interface section. The rotation angle of the metal scatterer is decoupled from the equivalent mass term, so that independent, stable and engineeringable adjustment of the topological phase characteristics and the dispersion compression capability can be realized.

Description

Technical Field

[0001] This application belongs to the field of waveguides, and in particular relates to topological quasi-flat band metallic metasurface waveguide structures, design methods and electromagnetic devices. Background Technology

[0002] For parallel-plate waveguides (PPWs), by forming a subwavelength gap between the upper and lower metal plates, the electromagnetic response can be confined within an equivalent two-dimensional system, primarily supporting transverse magnetic (TM) mode propagation within a certain frequency band. Therefore, they are suitable for constructing two-dimensional metallic metasurface waveguides, frequency-selective structures, and on-chip interconnect proof-of-concept devices. By introducing periodic metallic scattering units within the parallel-plate waveguide, the propagation constant, local distribution, and dispersion characteristics of electromagnetic modes can be effectively controlled, providing a foundation for constructing artificial electromagnetic materials with specific band structures.

[0003] Quasi-flat bandgap typically corresponds to a smaller group velocity and a longer electromagnetic wave residence time, which can lead to stronger local field enhancement and slow wave effects, thereby improving filter selectivity, coupling efficiency, and sensing sensitivity. However, existing methods for realizing quasi-flat bandgap often rely on fine destructive interference mechanisms, strictly coupled unit cell networks, or specific symmetry conditions. They are quite sensitive to processing errors, unit cell perturbations, boundary roughness, and zigzag routing, and are prone to problems such as operating frequency drift, mode leakage, increased crosstalk, or transmission instability.

[0004] Topological electromagnetic structures or topological photonic structures, such as topological phase systems built based on the valley-Hall mechanism, can form interface edge states between two regions with different topological properties and exhibit good suppression capabilities against certain types of scattering or defect perturbations, thus possessing high geometric robustness and transmission stability. However, conventional topological edge states usually still have relatively obvious dispersion characteristics, with relatively long local lengths and large mode volumes, which are not conducive to achieving deterministic spatial anchoring at the interface segment level and low crosstalk multiplexing at multiple frequencies, and also make it difficult to simultaneously meet the requirements of slow-wave enhancement and defect-tolerant transmission.

[0005] In the analysis of topological metasurfaces and topological photonic crystals, the area near the Dirac point is often used. k · p The equivalent theory describes the band dispersion and band gap formation mechanism. This theory shows that when an appropriate perturbation is applied to the cell geometry, a band gap can be opened near the Dirac point, and the equivalent mass term in the equivalent Hamiltonian characterizes the band gap size and local topological phase characteristics; the specific formula for the equivalent Hamiltonian is: ,in, For the valley degree of freedom is When the momentum shift is The equivalent Hamiltonian at the location; Dirac speed; This is the momentum offset. for x Momentum shift in direction. for y Momentum shift in direction; For valley degrees of freedom, , to represent two inequivalent valleys in the valley Hall topological phase; m This is the equivalent mass term caused by the breaking of inversion symmetry; This represents the Pauli matrix. Changes in the sign of the equivalent mass term typically correspond to transitions between different topological phases, while the magnitude of the equivalent mass term affects the localization of interface states and dispersion compression capability. Existing technologies struggle to achieve independent, stable, and engineerable adjustment of topological phase characteristics and dispersion compression capability.

[0006] Therefore, there is an urgent need to provide a new metallic metasurface waveguide structure that can adjust the amplitude of the equivalent mass term near the Dirac point while maintaining the topological relative contrast and topological inversion relationship, so as to effectively compress the dispersion of the interface edge states, thereby realizing topological quasi-flat band, strong spatial localization of edge states, multi-frequency multiplexing, and defect-tolerant routing. Summary of the Invention

[0007] To address the problems in the background art, the first aspect of this application provides a design method for a topological quasi-flat band metallic metasurface waveguide structure, comprising:

[0008] Multiple periodically arranged metal scatterers with triple rotational symmetry are arranged between two parallel metal plates of a parallel plate waveguide, so that the two parallel metal plates and all metal scatterers together constitute a two-dimensional metal metasurface. The two parallel metal plates have adjacent preset first and second regions, and the metal scatterers are distributed in the first and second regions. All the metal scatterers have the same initial rotation angle.

[0009] The metal scatterer in the first region is rotated along the first direction by a first preset angle to form a first topological domain, and the metal scatterer in the second region is rotated along the second direction opposite to the first direction by a second preset angle to form a second topological domain, in order to break the spatial inversion symmetry and open the band gap near the Dirac point to form a Valley Hall topological phase. At the same time, topological edge states are generated at the interface between the first topological domain and the second topological domain.

[0010] Keeping the rotation angle of each metal scatterer constant, the size of all metal scatterers is scaled to adjust the amplitude of the equivalent mass term in the equivalent Hamiltonian until the dispersion of the topological edge state is compressed into a quasi-flat band, and the topological edge state forms a deterministically spatially anchored edge guiding mode along the preset interface segment.

[0011] In some embodiments, when scaling the metal scatterer, the metal scatterer is scaled isotropically.

[0012] In some embodiments, each of the metal scatterers is composed of three cylinders aggregated together, and the dimensions of the metal scatterer include the radius of the cylinders. r The offset distance from the center of the cylinder to the center of the metal scatterer d and the height of the cylinder h ;

[0013] When isotropically scaling a metallic scatterer, a scaling factor is introduced to adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. b And based on the scaling factor b For radius r Offset distance d and height h Perform isotropic scaling.

[0014] In some embodiments, when scaling the metal scatterer, the height dimension of the metal scatterer is kept constant, while the remaining dimensions of the metal scatterer are scaled proportionally.

[0015] In some embodiments, each of the metal scatterers is composed of three cylinders aggregated together, and the dimensions of the metal scatterer include the radius of the cylinders. r The offset distance from the center of the cylinder to the center of the metal scatterer d and the height of the cylinder h ;

[0016] Maintaining height when isotropically scaling a metallic scatterer h The scaling factor remains unchanged and is used to adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. b Based on the scaling factor b For radius r and offset distance d Perform proportional scaling.

[0017] In some embodiments, a single metal scatterer and a corresponding hexagonal prism portion on a parallel metal plate together form a single metal scattering unit, the lattice constant of which is... Offset distance , 0.4≥ k ≥0.3.

[0018] In some embodiments, the path of the interface corresponding to the preset interface segment is a straight line, a polygonal line, or a Z-shape.

[0019] The second aspect of this application provides a first topological quasi-flat band metallic metasurface waveguide structure, which is designed using the above-mentioned topological quasi-flat band metallic metasurface waveguide structure design method.

[0020] The third aspect of this application provides a second type of topological quasi-flat band metallic metasurface waveguide structure, including a parallel plate waveguide formed by two parallel metal plates, and a plurality of periodic arrays arranged between the two parallel metal plates to form a two-dimensional metallic metasurface together with the two parallel metal plates. The metallic scatterers have triple rotational symmetry. The space between the two parallel metal plates includes a first topological domain and a second topological domain. The metallic scatterers are distributed in the first topological domain and the second topological domain. The rotation directions of the metallic scatterers in the first topological domain and the metallic scatterers in the second topological domain are opposite.

[0021] Each of the aforementioned metallic scatterers is composed of three cylinders aggregated together, each cylinder having a radius of... Offset distance from the center of each cylinder to the center of the metal scatterer ,in, for b The radius of the cylinder when =1, for b When =1, the offset distance from the center of each cylinder to the center of the metal scatterer b The scaling factor is used to adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. b Satisfy the following: compress the dispersion of the topological edge states into a quasi-flat band, and enable the topological edge states to form a deterministically spatially anchored edge guide mode along a preset interface segment.

[0022] The fourth aspect of this application provides an electromagnetic device including the above-described topological quasi-flat band metallic metasurface waveguide structure.

[0023] It has at least the following beneficial effects:

[0024] (1) This application proposes for the first time a decoupled parameterized design of the rotation angle and the equivalent mass term of the metal scatterer. Both the rotation angle and the equivalent mass term of the metal scatterer can be adjusted independently. Without changing the topological opening mechanism determined by the rotation angle, the equivalent mass term can be adjusted by adjusting the size of the metal scatterer. m It plays a dominant role in the equivalent Hamiltonian, compressing the dispersion of the interface topological edge states into a topological quasi-flat band, thereby achieving lower group velocity, stronger locality, and deterministic spatial anchoring on the interface segment, which is conducive to obtaining narrowband selectivity and slow wave enhancement effects.

[0025] (2) The interface edge state in this application has both topological defect tolerance transmission capability and quasi-flat band enhanced slow wave characteristics. Under the conditions of bent interface and local defects, it can still maintain low backscattering and relatively stable guided wave transmission, thereby improving the reliability in engineering applications.

[0026] (3) This application is easy to process and assemble, and can be applied to microwave, millimeter wave, terahertz and other frequency bands. It has good engineering portability and application prospects. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the topological quasi-flat band metallic metasurface waveguide structure according to an embodiment of this application.

[0028] Figure 2 This is a perspective view of the topological quasi-flat band metallic metasurface waveguide structure according to an embodiment of this application.

[0029] Figure 3 for Figure 2 A perspective view of a single metal scattering unit.

[0030] Figure 4 for Figure 3 A schematic diagram of the structure of a medium-sized metal scatterer.

[0031] Figure 5 This is a schematic diagram comparing the positive and negative α angles of a metallic scatterer.

[0032] Figure 6 Scale factor b Used only for adjusting the radius of each cylinder r and the center of each cylinder To the center of the metal scatterer offset distance d When, the scaling factor b A comparison diagram showing the values ​​of 0.6, 0.8, and 1.0.

[0033] Figure 7 Scale factor b Distance from the metal scatterer to the edge of the hexagonal lattice at a value of 1.0 L A schematic diagram.

[0034] Figure 8 height of the cylinder h constant scaling factor b A schematic diagram comparing the unit cell band structure and the dispersion curves of the interface edge states at 0.6, 0.8 and 1.0, where the upper part is the unit cell band structure and the lower part is the dispersion curve of the edge states.

[0035] Figure 9 height of the cylinder h constant scaling factor bA schematic diagram showing the distribution of the first and second topological domains when =1.

[0036] Figure 10 To and Figure 9 The electromagnetic field simulation distribution diagram corresponding to the topological domain distribution.

[0037] Figure 11 height of the cylinder h constant scaling factor b When =1, the interface edge state formed by splicing the first and second topological domains The parameter test chart.

[0038] Figure 12 height of the cylinder h constant scaling factor b A schematic diagram comparing the electromagnetic field simulations of the Z-shaped bending interface routing structure with and without point defects when the value is 1.

[0039] Figure 13 height of the cylinder h constant scaling factor b The electromagnetic field simulation distribution diagram corresponding to the topological domain distribution when ω = 0.95.

[0040] Figure 14 height of the cylinder h constant scaling factor b The electromagnetic field simulation distribution diagram corresponding to the topological domain distribution when =0.9.

[0041] Figure 15 height of the cylinder h With scaling factor b When the scaling factor changes b The electromagnetic field simulation distribution diagram corresponding to the topological domain distribution when ω = 0.95.

[0042] Figure 16 height of the cylinder h With scaling factor b When the scaling factor changes b Electromagnetic field simulation diagram of the Z-shaped bending interface routing structure when the value is 0.95.

[0043] Figure 17 height of the cylinder h With scaling factor b When the scaling factor changes b The electromagnetic field simulation distribution diagram corresponding to the topological domain distribution when =0.9.

[0044] Figure 18 height of the cylinder h With scaling factor b When the scaling factor changes bElectromagnetic field simulation diagram of the Z-shaped bending interface routing structure when the value is 0.9.

[0045] Explanation of key component symbols: 100 topological quasi-flat band metallic metasurface waveguide structure, 10 parallel plate waveguide, 11 first metal plate, 12 second metal plate, 20 metal scattering unit, 21 metal scatterer, 22 cylinder, 30 first topological domain, 40 second topological domain, 50 interface, 60 point defect.

[0046] The following detailed description, in conjunction with the accompanying drawings, will further illustrate this application. Detailed Implementation

[0047] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0048] Examples of design methods for topological quasi-flat band metallic metasurface waveguide structures

[0049] The design method in this embodiment is used to design any of the topological quasi-flat band metallic metasurface waveguide structures in this application. Specifically, the design can be carried out according to the following steps.

[0050] Step S21, refer to Figures 1-3 As shown, a parallel plate waveguide 10 is designed using a first metal plate 11 and a second metal plate 12 arranged in parallel. Metal scatterers 21 with the same initial rotation angle are arranged between the two parallel metal plates of the parallel plate waveguide 10. The two parallel metal plates have adjacent first and second regions. The metal scatterers 21 are arranged in the first and second regions, and all metal scatterers 21 are arranged in a periodic array, together with the two parallel metal plates, forming a two-dimensional metallic metasurface. In this document, for ease of description, a single first metal plate 11 or a single second metal plate 12 is sometimes referred to as a "parallel metal plate" or "metal plate," and the first metal plate 11 and the second metal plate 12 together are sometimes referred to as "two parallel metal plates" or "two metal plates," etc.

[0051] Step S22, refer to Figures 1-5 As shown, the metal scatterer 21 in the first region is rotated by a first preset angle along the first direction to form a first topological domain 30, and the metal scatterer 21 in the second region is rotated by a second preset angle along the second direction opposite to the first direction to form a second topological domain 40. This is used to break the spatial inversion symmetry and open a band gap near the Dirac point to form a Valley Hall topological phase. At the same time, a topological edge state is generated at the interface 50 where the first topological domain 30 and the second topological domain 40 meet.

[0052] In some embodiments, the initial rotation angle is 0, and the first preset angle and the second preset angle are exactly the same. In other embodiments, the initial rotation angle can be 1°, 2°, or other values, in which case the first preset angle and the second preset angle are different. However, in both of these embodiments, the final relative rotation angles of the metal scatterers 21 within the first topological domain 30 and the second topological domain 40 are the same.

[0053] Step S23: Keep the rotation angle of each metal scatterer 21 unchanged to maintain the topological relative ratio and topological anti-rotation relationship. Scale the size of all metal scatterers 21 to adjust the size of the metal scatterers 21, thereby adjusting the amplitude of the equivalent mass term in the equivalent Hamiltonian, until the dispersion of the topological edge state is compressed into a quasi-flat band, and the topological edge state forms a deterministically spatially anchored edge guided mode along a preset interface segment, thereby obtaining the topological quasi-flat band metal metasurface waveguide structure 100.

[0054] The specific formula for the equivalent Hamiltonian is as follows: ,in, For the valley degree of freedom is When the momentum shift is The equivalent Hamiltonian at the location; Dirac speed; This is the momentum offset. for x Momentum shift in direction. for y Momentum shift in direction; For valley degrees of freedom, , to represent two inequivalent valleys in the valley Hall topological phase; m The effective Dirac mass term, also known as the equivalent mass term, is caused by the breaking of inversion symmetry. This represents the Pauli matrix.

[0055] It should be noted that the above steps are merely exemplary, and those skilled in the art can adjust the order of the steps and the matters involved in each step according to actual needs.

[0056] like Figures 1-3 As shown, the topological quasi-flat band metallic metasurface waveguide structure 100 includes a parallel-plate waveguide (PPW) 10, which includes two parallel metal plates, namely a first metal plate 11 and a second metal plate 12, with the first metal plate 11 located above the second metal plate 12.

[0057] like Figures 1-5As shown, the topological quasi-flat band metal metasurface waveguide structure 100 also includes a metal scatterer 21 disposed between the first metal plate 11 and the second metal plate 12. The metal scatterer 21 is located within the first topological domain 30 and the second topological domain 40, and the metal scatterer 21 is arranged in a periodic array and cooperates with the first metal plate 11 and the second metal plate 12 to form a two-dimensional metal metasurface. The metal scatterer 21 has triple rotational symmetry.

[0058] After arranging each metal scatterer 21 in the same orientation between the two metal plates, as follows: Figure 5 As shown, the metal scatterer 21 in the first topological domain 30 is rotated by a first preset angle along a first direction, and the metal scatterer 21 in the second topological domain 40 is rotated by a second preset angle along a second direction opposite to the first direction. This allows each metal scatterer 21 to have a rotation angle around its own central axis, which is used to break the spatial inversion symmetry and open the band gap near the Dirac point, thereby forming a Valley Hall topological phase on the metal metasurface. Therefore, the area near the Dirac point can be used. k · p The equivalent theory describes the band dispersion and band gap formation mechanism, and uses the equivalent Hamiltonian. The equivalent mass term in the equation characterizes the band gap size and local topological phase characteristics.

[0059] It should be noted that the first and second preset angles of rotation are the rotation angles. The first direction refers to the direction of rotation clockwise or counterclockwise relative to the plane containing the first metal plate 11 or the second metal plate 12, and the second direction refers to the direction of rotation counterclockwise or clockwise relative to the plane containing the first metal plate 11 or the second metal plate 12. This application does not specifically limit the first and second directions. For example, if the metal scatterer 21 in the first topological domain 30 rotates clockwise, then the metal scatterer 21 in the second topological domain 40 rotates counterclockwise.

[0060] At the same time, such as Figure 2 , Figure 9 and Figure 12 As shown, the metal scatterer 21 in the first topological domain 30 and the metal scatterer 21 in the second topological domain 40 rotate in opposite directions. An interface 50 is formed at the junction of the first topological domain 30 and the second topological domain 40, so that the two topological domains have different topological phases and the signs of the equivalent mass terms corresponding to the two topological domains on both sides of the interface 50 are opposite, thereby generating a topological edge state at the interface 50.

[0061] like Figure 5 , Figure 9 and Figure 12As shown, the metal scatterer 21 in the first topological domain 30 is rotated counterclockwise by a positive rotation angle α (i.e., the rotation angle is +α), and the metal scatterer 21 in the second topological domain 40 is rotated clockwise by a negative rotation angle α (i.e., the rotation angle is -α). This reverses the topological signs of the two topological domains and creates a topological edge state at the boundary between them. For example, if the initial rotation angle is 0, the rotation angle α of the metal scatterer 21 in the first topological domain 30 and the second topological domain 40 is the same, both being 6°.

[0062] This application has the following beneficial effects:

[0063] (1) This application proposes a decoupled parameterized design of rotation angle and equivalent mass term of metal scatterer 21. The rotation angle of metal scatterer 21 can be adjusted independently in step S22, and the magnitude of equivalent mass term of metal scatterer 21 can be adjusted independently in step S23. Thus, without changing the topological opening mechanism determined by rotation angle, the local scattering intensity and the coupling strength between metal scatterers 21 can be independently adjusted by the equivalent mass term of metal scatterer 21, thereby realizing the systematic control of bandgap amplitude and dispersion compression degree.

[0064] (2) In this application, by adjusting the size of the metal scatterer 21, the equivalent mass term can be made more efficient. m It plays a dominant role in the equivalent Hamiltonian, compressing the dispersion of the interface topological edge states into a topological quasi-flat band, thereby achieving lower group velocity, stronger locality, and deterministic spatial anchoring on the interface segment, which is conducive to obtaining narrowband selectivity and slow wave enhancement effects.

[0065] It should be noted that in step S23, the metal scatterer 21 can be scaled using one of the following two methods.

[0066] Method 1: When scaling the metal scatterer 21, keep the height dimension of the metal scatterer 21 unchanged, and only scale the other dimensions of the metal scatterer 21 proportionally.

[0067] Method 2: When scaling the metal scatterer 21, the metal scatterer 21 is scaled isotropically, that is, the height dimension of the metal scatterer 21 is also scaled.

[0068] To facilitate understanding by those skilled in the art, the following description uses the example of a metal scatterer 21 being composed of three cylinders 22 aggregated together.

[0069] When scaling the metal scatterer 21 using method one, the height of each cylinder 22 is... h The radius of each cylinder 22 The center of each cylinder 22 To the center of the metal scatterer 21 offset distance ,in, b To adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. Scale factor, for b The maximum radius of cylinder 22 when =1 for b When =1, the center of each cylinder 22 To the center of the metal scatterer 21 Maximum offset distance, scaling factor b Satisfy the following: compress the dispersion of the topology edge states into a quasi-flat band, and enable the topology edge states to form deterministically spatially anchored edge guiding modes along a preset interface segment, thereby realizing deterministic spatial anchoring, frequency reuse, and defect-tolerant routing of the topology quasi-flat band and interface edge states.

[0070] like Figure 3 and Figure 4 As shown, a single metal scatterer 21 and its corresponding hexagonal prism portion on each metal plate together constitute a single metal scattering unit 20. A single metal scattering unit 20 constitutes a hexagonal lattice. The lattice constant of the metal scattering unit 20 is... =40 mm, meaning the distance between the two parallel sides of the hexagonal prism portion of the metal plate is 40 mm, and the thickness of the first metal plate 11 and the second metal plate 12 is... =5 mm, in b When = 1, the radius of a single cylinder 22 in the metal scatterer 21 =9.2mm, offset distance In the formula, k =0.3, the height of a single cylinder 22 h =10 mm. For example... Figure 7 As shown, in b =1, k When = 0.3, the distance from the metal scatterer 21 to the edge of the hexagonal lattice 2.01 mm.

[0071] Of course, in other embodiments, those skilled in the art can also set the size of the rotation angle α and the scaling factor according to actual needs. b Size and k The size, 30°≥α>0, 1≥ b ≥0.6, 0.4≥ k ≥0.3, and the value of α can also be 1°, 3°, 10°, 20° or 30°, etc. b The value can also be 0.6, 0.8, 0.9 or 0.95, etc., preferably 0.9~1. k The polymerization coefficient is used to polymerize the three cylinders together. kThe value can also be 0.3, 0.35 or 0.4, etc. Figure 6 It shows b A comparison diagram showing the values ​​of 0.6, 0.8, and 1.0.

[0072] In the above embodiments, the height of the metal scatterer 21 can be kept constant, that is, the distance between the first metal plate 11 and the second metal plate 12 can be kept constant. The remaining dimensions of the metal scatterer 21 are scaled proportionally to change the equivalent mass term of the metal scatterer 21. When the metal scatterer 21 is composed of three cylinders 22 aggregated together, the scaling factor... b The change does not affect the height of cylinder 22 h Therefore, the distance between the first metal plate 11 and the second metal plate 12 remains unchanged and is always equal to the distance between them. h .

[0073] Scale factor b Independent of the rotation angle α, the scaling factor b This is used to adjust the local scattering intensity and the coupling strength between the metallic scatterer 21, thereby adjusting the dispersion compression and bandgap amplitude of the band structure without altering the symmetry breaking and opening mechanism determined by the rotation angle. This is achieved by using the area near the Dirac point. k · p When the equivalent theory describes the band dispersion and band gap formation mechanism, the rotation angle is mainly used to determine the band gap opening and topological inversion relationship, and the scaling factor... b It is mainly used to adjust the amplitude of the equivalent mass term in the equivalent Hamiltonian. .

[0074] By increasing the scaling factor b This can increase the size of the metal scatterer 21, thereby enhancing the equivalent mass term. m The dominant role of the dispersion behavior at the interface edge states causes the system to enter the equivalent mass term. m The dominant region can compress the topological edge state dispersion at interface 50 into a quasi-flat band feature that is "approximately flat and retains weak dispersion", thereby achieving slow wave enhancement and strong localization, while retaining the coupling channel for interface guided wave transmission.

[0075] By adjusting the scaling factor b It can shorten the local length of the interface edge state, reduce the group velocity, and enable the electromagnetic energy to achieve deterministic spatial anchoring and slow wave enhancement along the preset interface segment. At the same time, while maintaining the transmissibility of the interface edge state, it can also achieve engineering control of the operating frequency and spatial distribution of the interface edge state.

[0076] Figure 8 China compared bThe figure shows the unit cell band structure and the dispersion curves of the interface edge states at ω = 0.6, 0.8, and 1.0. The upper figure is the unit cell band structure, and the lower figure is the corresponding dispersion curve of the interface edge states. Figure 8 It can be seen that in the scaling factor b As the dispersion gradually increases, the edge state dispersion is compressed from the conventional dispersion state towards the quasi-flat band. The group velocity of the edge state decreases, the local length shortens, and the electromagnetic energy is more concentrated in the preset interface region, thereby achieving deterministic spatial anchoring and slow wave enhancement on the preset interface segment. Preferably, the quasi-flat band interface state maintains a limited but relatively small group velocity within the operating frequency band to balance local enhancement and interface transmission capability.

[0077] The topological quasi-flat band metallic metasurface waveguide structure in this application can be applied to microwave slow wave enhancement, narrowband filtering and multiplexing, sensing, and programmable wave field manipulation. It can be applied to the microwave frequency band and can also be extended to the millimeter wave, terahertz and other frequency bands.

[0078] In some embodiments, the first metal plate 11 and the second metal plate 12 forming the parallel plate waveguide 10 can be made of aluminum or copper; the metal scatterer 21 can also be made of aluminum or copper. In the microwave frequency band, aluminum and copper can be regarded as ideal conductors or near-ideal conductors; when the inter-plate gap of the parallel plate waveguide 10 is on the order of subwavelength, the electromagnetic response in the operating frequency band is confined to an equivalent two-dimensional system, mainly supporting the propagation of transverse magnetic (TM) modes.

[0079] The aforementioned "two-dimensional metallic metasurface" refers to an ultrathin artificial electromagnetic surface composed of metal scattering units 20 arranged in an ordered array of periodic lattices (square lattices, hexagonal lattices, etc.) in a two-dimensional plane, which can flexibly control the phase, amplitude, polarization, and mode of incident electromagnetic waves.

[0080] It should be noted that the aforementioned "topological quasi-flat band" or "quasi-flat band" refers to the following: the dispersion curve of the interface edge state on the high symmetry path in the first Brillouin zone exhibits significant compression characteristics, the slope of which decreases significantly within the corresponding high symmetry point and its neighborhood, and it appears as an approximately horizontal interface state band in the band diagram.

[0081] The aforementioned “quasi-flat band” does not require the group velocity to be strictly zero. Rather, it is preferred to maintain a limited but small group velocity in the operating frequency band at the interface edge states. This is to achieve slow wave enhancement and strong localization while still retaining the weak coupling transmission capability required for propagation along the interface 50, thereby distinguishing it from the non-topologically restricted modes caused by trivial localization or Anderson localization.

[0082] The aforementioned “quasi-flat band” can be determined by band diagrams or dispersion curves. For the “quasi-flat band”, its interface state band exhibits an approximately horizontal band segment near the high symmetry point of the first Brillouin zone, and the band segment still retains the finite non-zero group velocity used to maintain the interface waveguide transmission.

[0083] By using the aforementioned quasi-flat band interface state that is "approximately flat but retains finite group velocity", this application can achieve deterministic spatial anchoring in the interface segment while maintaining the usable transmission capability and bending routing capability of the interface waveguide.

[0084] The aforementioned “preset interface segment” refers to the boundary region between the two parallel metal plates of the parallel plate waveguide and between the first topological domain 30 and the second topological domain 40. It is a specific narrow interface formed by extending along a pre-set transmission path and used to constrain the propagation of the topological edge state. Its extension direction is consistent with the pre-set propagation direction of the topological edge state. It is the core region for the topological edge state to achieve deterministic spatial anchoring and form an edge guiding mode.

[0085] Furthermore, the path of the interface 50 corresponding to the preset interface segment can be a straight line, a polygonal line, a Z-shape, or a path with multiple bends, etc., which can be set according to actual needs by those skilled in the art. Specifically, the interface between the positive-rotation metal scatterer in the first topological domain 30 and the anti-rotation metal scatterer in the second topological domain 40 can be controlled, and the shape of this interface matches the shape of the preset interface segment. For example, as Figure 9 and Figure 10 As shown, the path of interface 50 is a triangle; in Figure 12 In the middle, the path of interface 50 is Z-shaped, which includes two bends; when there are two, three or more first topological domains 30 and second topological domains 40, the preset interface segment can also be other shapes. For example, there are two first topological domains 30 and two second topological domains 40, with the two first topological domains 30 located at the upper left corner and the lower right corner respectively, and the two second topological domains 40 located at the upper right corner and the lower left corner respectively, to form a cross-shaped preset interface segment.

[0086] like Figure 9 and Figure 10 As shown, the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor is... b =1, and when the frequency of the electromagnetic wave selected in the experiment is 12.36 GHz, the electromagnetic simulation results show that near the operating frequency point corresponding to the topological quasi-flat band, the electromagnetic energy mainly propagates along the interface 50 between the first topological domain 30 and the second topological domain 40, and exhibits strong spatial localization characteristics and low group velocity.

[0087] like Figure 10 and Figure 11As shown, the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor is... b When =1, the frequency of the electromagnetic wave is 12.36 GHz. The working frequency band of the interface edge state obtained by near-field scanning and parameter measurement corresponds well with the electromagnetic simulation results.

[0088] In the scaling factor b When the size of the metal scatterer 21 changes, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metal metasurface waveguide structure 100 will also change.

[0089] For example, such as Figure 13 As shown, the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor is... b =0.95, height of cylinder 22 =10 mm, and the electromagnetic wave frequency is 10.95 GHz. The electromagnetic simulation results show that near the operating frequency point corresponding to the topological quasi-flat band, the electromagnetic energy mainly propagates along the interface 50 between the first topological domain 30 and the second topological domain 40, and exhibits strong spatial localization characteristics and low group velocity.

[0090] For example, such as Figure 14 As shown, the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor is... b =0.9, height of cylinder 22 =10 mm, and when the frequency of the electromagnetic wave is 9.85 GHz, the electromagnetic simulation results show that near the operating frequency point corresponding to the topological quasi-flat band, the electromagnetic energy mainly propagates along the interface 50 between the first topological domain 30 and the second topological domain 40, and exhibits strong spatial localization characteristics and low group velocity.

[0091] In summary, regarding the scaling factor b When the size of the metal scatterer 21 changes, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100 also changes. In this paper, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100 is simply referred to as the frequency of the electromagnetic wave.

[0092] like Figure 12As shown, local defects can be introduced near interface 50 to verify defect-tolerant transmission and robust routing performance. These local defects can be formed by: (1) removing local units; (2) changing the local scaling factor. b (3) Change the local geometric parameters. Figure 12 The above method (1) was adopted to remove a metal scatterer 21 located near the interface 50 to form a point defect 60, thereby constructing a local structural defect perturbation. The point defect 60 can be set near the bend of the interface 50 or near the straight section of the interface 50, so as to examine the transmission behavior of the topological quasi-flat band edge states under the condition of local structural defect.

[0093] according to Figure 10 and Figure 12 It can be seen that the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor... b =1, and when the frequency of the electromagnetic wave selected for the experiment is 12.36 GHz, the electromagnetic simulation results show that while achieving quasi-flat band slow wave enhancement, this application still has good defect-tolerant transmission capability and robust routing performance. Even if a point defect 60 is generated, it does not affect the interface edge state from still transmitting around the Z-shaped interface 50, and continues to transmit along the interface 50 after passing through the area where the point defect 60 is located.

[0094] Subsequently, the transmission characteristics under the two conditions of no point defect and point defect can be compared through transmission response testing, parameter measurement or near-field scanning results to characterize the backscattering suppression capability, interface localization capability and stable waveguide capability of the interface edge state under the condition of local structure absence.

[0095] The topological quasi-flat band metallic metasurface waveguide structure 100 designed using method one has the following advantages:

[0096] (1) This application is the first to propose the rotation angle and scaling factor. b Decoupled parametric design, rotation angle α and scaling factor b Each can be individually controlled, without altering the topological opening mechanism determined by the rotation angle, using a scaling factor. b The local scattering intensity and the coupling strength between the metal scatterers 21 are independently adjusted, thereby achieving systematic control of the bandgap amplitude and dispersion compression.

[0097] (2) In this application, by adjusting the scaling factor b This enables equivalent quality items mIt plays a dominant role in the equivalent Hamiltonian, compressing the dispersion of the interface topological edge states into a topological quasi-flat band, thereby achieving lower group velocity, stronger locality, and deterministic spatial anchoring on the interface segment, which is conducive to obtaining narrowband selectivity and slow wave enhancement effects.

[0098] (3) The interface edge state in this application has both topological defect tolerance transmission capability and quasi-flat band enhanced slow wave characteristics. Under the conditions of bent interface and local defects, it can still maintain low backscattering and relatively stable guided wave transmission, thereby improving the reliability in engineering applications.

[0099] (4) This application is easy to process and assemble, can be applied to microwave frequency bands, and can be extended to millimeter wave, terahertz and other frequency bands through scale scaling and material replacement, and has good engineering transferability and application prospects.

[0100] When scaling the metal scatterer 21 using method two, the height of each cylinder 22 The radius of each cylinder 22 The center of each cylinder 22 To the center of the metal scatterer 21 offset distance ,in, For the maximum height of each cylinder 22, in b When =1, =10 mm. In the scaling factor... b When it changes, the scaling factor b The change affects the height of cylinder 22 h Therefore, the spacing between the first metal plate 11 and the second metal plate 12 varies with the scaling factor. b Change and always equal h .

[0101] In some embodiments, such as Figure 15 As shown, the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor is... b =0.95, height of cylinder 22 =9.5 mm, and the electromagnetic wave frequency is 10.95 GHz. The electromagnetic simulation results show that near the operating frequency point corresponding to the topological quasi-flat band, the electromagnetic energy mainly propagates along the interface 50 between the first topological domain 30 and the second topological domain 40, and exhibits strong spatial localization characteristics and low group velocity.

[0102] like Figure 16As shown, under the premise of keeping the above conditions unchanged, the electromagnetic simulation results show that while achieving quasi-flat band slow wave enhancement, this application still has good defect-tolerant transmission capability and robust routing performance, enabling electromagnetic waves to be transmitted along the interface 50.

[0103] In some embodiments, such as Figure 17 As shown, the materials of the first metal plate 11, the second metal plate 12, and the metal scatterer 21 are copper or aluminum. The metal scatterer 21 in the first topological domain 30 rotates forward by an angle α, and the metal scatterer 21 in the second topological domain 40 rotates backward by an angle α. The scaling factor is... b =0.9, height of cylinder 22 =9 mm, and when the frequency of the electromagnetic wave is 9.84 GHz, the electromagnetic simulation results show that near the operating frequency point corresponding to the topological quasi-flat band, the electromagnetic energy mainly propagates along the interface 50 between the first topological domain 30 and the second topological domain 40, and exhibits strong spatial localization characteristics and low group velocity.

[0104] like Figure 18 As shown, under the premise of keeping the above conditions unchanged, the electromagnetic simulation results show that while achieving quasi-flat band slow wave enhancement, this application still has good defect-tolerant transmission capability and robust routing performance, enabling electromagnetic waves to be transmitted along the interface 50.

[0105] In method two, the scaling factor b The value is 0.6 to 1, preferably 0.9 to 1, such as 0.6, 0.7, 0.8, 0.85, 0.9, 0.95 or 1.

[0106] It should be noted that, as Figures 13-18 As shown in (1) b =0.9, h In the electromagnetic simulation experiment corresponding to 10 mm, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100 is 9.85 GHz; in (3) b =0.9, h In the electromagnetic simulation experiment corresponding to 9 mm, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100 is 9.84 GHz; in (2) b =0.95, h In the electromagnetic simulation experiment corresponding to 10 mm, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100 is 10.95 GHz; in (4) b =0.95, h In the electromagnetic simulation experiment corresponding to 9.5 mm, the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100 is 10.95 GHz. In summary, compared to (1)b =0.9, h =10 mm; (2) b =0.95, h =10 mm; (3) b =0.9, h =9 mm and (4) b =0.95, h The simulation results of the four sets of electromagnetic simulation experiments, with a value of 9.5 mm, show that... h The change has little effect on the operating frequency of the electromagnetic wave corresponding to the topological quasi-flat band metallic metasurface waveguide structure 100, and can be almost ignored.

[0107] The topological quasi-flat band metallic metasurface waveguide structure 100 designed using method two has the aforementioned beneficial effects (1)(2)(3)(4) of the topological quasi-flat band metallic metasurface waveguide structure 100 designed using method one, which will not be elaborated here.

[0108] Of course, in other embodiments, the metal scatterer 21 can also be other materials possessing triple rotational symmetry (i.e., Structures with symmetrical properties, such as a structure formed by the aggregation of three triangular prisms, or a structure formed by the aggregation of three elliptical cylinders, etc.

[0109] In this application, preferably, the gap between the parallel board waveguides 10 can be filled with perforated dielectric foam or equivalent low-loss dielectric filling material to suppress parasitic air gap resonance and stabilize effective background environmental parameters, thereby improving device consistency, resistance to environmental disturbances and test repeatability.

[0110] Examples of topological quasi-flat band metallic metasurface waveguide structures

[0111] The topological quasi-flat band metallic metasurface waveguide structure 100 in this application is designed using the design method of the topological quasi-flat band metallic metasurface waveguide structure in this application. Its specific structure and beneficial effects are the same as those of the topological quasi-flat band metallic metasurface waveguide structure 100 described above, and will not be repeated here.

[0112] Examples of electromagnetic devices

[0113] Waveguide structures are commonly used in various electromagnetic devices, such as superwaveguide lenses, mode converters, polarization controllers, narrowband filters, frequency-selective surface integrated devices, waveguide phased array antenna feed structures, leaky antennas, refractive index biosensors, terahertz modulators, terahertz absorption devices, optical isolators, optical power dividers, optical couplers, waveguide gratings, and other electromagnetic devices.

[0114] In this application, the topological quasi-flat band metallic metasurface waveguide structure described herein can also be used in the above-mentioned electromagnetic devices to replace existing waveguide structures, thereby enabling the electromagnetic devices to have all the beneficial effects of the topological quasi-flat band metallic metasurface waveguide structure embodiments, which will not be elaborated here.

[0115] The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the above preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application should not depart from the spirit and scope of the technical solutions of this application.

Claims

1. A design method for a topologically quasi-flat band metallic metasurface waveguide structure, characterized in that, include: Multiple periodically arranged metal scatterers with triple rotational symmetry are arranged between two parallel metal plates of a parallel plate waveguide, so that the two parallel metal plates and all metal scatterers together constitute a two-dimensional metal metasurface. The two parallel metal plates have adjacent preset first and second regions, and the metal scatterers are distributed in the first and second regions. All the metal scatterers have the same initial rotation angle. The metal scatterer in the first region is rotated along the first direction by a first preset angle to form a first topological domain, and the metal scatterer in the second region is rotated along the second direction opposite to the first direction by a second preset angle to form a second topological domain, in order to break the spatial inversion symmetry and open the band gap near the Dirac point to form a Valley Hall topological phase. At the same time, topological edge states are generated at the interface between the first topological domain and the second topological domain. Keeping the rotation angle of each metal scatterer constant, the size of all metal scatterers is scaled to adjust the amplitude of the equivalent mass term in the equivalent Hamiltonian until the dispersion of the topological edge state is compressed into a quasi-flat band, and the topological edge state forms a deterministically spatially anchored edge guiding mode along the preset interface segment.

2. The design method for topological quasi-flat band metallic metasurface waveguide structures as described in claim 1, characterized in that, When scaling a metal scatterer, the metal scatterer is scaled isotropically.

3. The design method for a topologically quasi-flat band metallic metasurface waveguide structure as described in claim 2, characterized in that, Each of the metal scatterers is composed of three cylinders, and the dimensions of the metal scatterer include the radius of the cylinders. r The offset distance from the center of the cylinder to the center of the metal scatterer d and the height of the cylinder h ; When isotropically scaling a metallic scatterer, a scaling factor is introduced to adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. b And based on the scaling factor b For radius r Offset distance d and height h Perform isotropic scaling.

4. The design method for a topologically quasi-flat band metallic metasurface waveguide structure as described in claim 1, characterized in that, When scaling the metal scatterer, keep the height dimension of the metal scatterer unchanged, and scale the other dimensions of the metal scatterer proportionally.

5. The design method for a topologically quasi-flat band metallic metasurface waveguide structure as described in claim 4, characterized in that, Each of the metal scatterers is composed of three cylinders, and the dimensions of the metal scatterer include the radius of the cylinders. r The offset distance from the center of the cylinder to the center of the metal scatterer d and the height of the cylinder h ; Maintaining height when isotropically scaling a metallic scatterer h The scaling factor remains unchanged and is used to adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. b Based on the scaling factor b For radius r and offset distance d Perform proportional scaling.

6. The design method for a topologically quasi-flat band metallic metasurface waveguide structure as described in claim 3 or 5, characterized in that, A single metal scatterer and the corresponding hexagonal prism portion on a parallel metal plate together form a single metal scattering unit. The lattice constant of the metal scattering unit is... Offset distance , 0.4≥ k ≥0.

3.

7. The design method for a topologically quasi-flat band metallic metasurface waveguide structure as described in claim 1, characterized in that, The path of the interface corresponding to the preset interface segment is a straight line, a broken line, or a Z-shape.

8. A topologically quasi-flat band metallic metasurface waveguide structure, characterized in that, It was designed using the topological quasi-flat band metallic metasurface waveguide structure design method described in any one of claims 1 to 7.

9. A topologically quasi-flat band metallic metasurface waveguide structure, characterized in that, The device includes a parallel plate waveguide formed by two parallel metal plates, and a metal scatterer arranged in a periodic array between the two parallel metal plates, which together with the two parallel metal plates form a two-dimensional metal metasurface. The metal scatterer has triple rotational symmetry. The space between the two parallel metal plates includes a first topological domain and a second topological domain. The metal scatterer is distributed in the first topological domain and the second topological domain. The metal scatterer in the first topological domain and the metal scatterer in the second topological domain rotate in opposite directions. Each of the aforementioned metallic scatterers is composed of three cylinders aggregated together, each cylinder having a radius of... Offset distance from the center of each cylinder to the center of the metal scatterer ,in, for b The radius of the cylinder when =1, for b When =1, the offset distance from the center of each cylinder to the center of the metal scatterer b The scaling factor is used to adjust the magnitude of the equivalent mass term in the equivalent Hamiltonian. b Satisfy the following: compress the dispersion of the topological edge states into a quasi-flat band, and enable the topological edge states to form a deterministically spatially anchored edge guide mode along a preset interface segment.

10. An electromagnetic device, characterized in that, Including the topological quasi-flat band metallic metasurface waveguide structure as described in claim 8 or 9.

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