Singular point waveguide device based on coupling topology interface state

Abstract

The invention belongs to the technical field of optics, and particularly relates to a singular point waveguide device based on a coupling topology interface state, which comprises a second-order singular point waveguide device with a structure of S18S2NS18, a third-order singular point waveguide device with a structure of S18S2NS1NS28 and a fourth-order singular point waveguide device with a structure of S18S2N1S1N2S2N1S18, the metal patch S2 is obtained by translating a metal patch S1 for a half period along the x direction, the metal patch S1 and the metal patch S2 have different topological characteristics in the first photonic band gap, and when electromagnetic waves are incident from the x direction, an interface state mode existing between the metal patch S1 and the metal patch S2 can be excited so as to regulate and control the transmission behavior of the electromagnetic waves; the problem of PT phase change is solved, the problem of gain and loss balance in a microwave system is solved, and a single-frequency filtering function is realized.

Description

Technical Field

[0001] The invention belongs to the field of optical technology, and in particular relates to a singular point waveguide based on coupled topological interface states. Background Art

[0002] Optical topological interface states have attracted extensive research and attention due to their excellent transmission properties. For one-dimensional structures with central symmetry, the topological invariant of the energy band is usually characterized by the Zak phase, which can be quantified as 0 or π. According to the body-edge correspondence, topological interface states exist at the interface of two structures with different topological properties. The interface state mode composed of one-dimensional topological structure has many advantages, such as high localization of the mode and single mode.

[0003] In non-Hermitian optical systems, the eigenstates and eigenvectors of the system are degenerate at singular points. By accurately designing the gain and loss of the system, second-order singular points can be realized in binary coupled systems. A notable feature of singular points is that they are sensitive to perturbations, and are commonly used in biomolecule detection, nanoparticle detection, and phase sensing. By extending the binary coupled system to a multi-element system and introducing gain and loss in two of its resonant modes, singular points of different orders can be realized. Compared with second-order singular points, higher-order singular points are more sensitive to perturbations and can improve the detection performance of the device.

[0004] Currently, achieving multi-order singular points in a multi-element coupled system requires precise control of the coupling between modes and the gain and loss of the modes. However, in microwave systems, introducing the gain of the modes is challenging. In addition, the balance between gain and loss in the control system also requires a lot of experimental and computational resources. Therefore, using a simple method to achieve high-order singular points will help promote the development of non-Hermitian devices.

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a singular point waveguide based on topological interface states.

[0006] In order to achieve the purpose of the present invention, the present invention will be implemented by adopting the technical solution described below.

[0007] A singular point waveguide based on coupled topological interface states, the singular point waveguide comprising a second-order singular point waveguide, a third-order singular point waveguide and a fourth-order singular point waveguide, wherein:

[0008] The second-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N layers, and metal patches S1 with 8 layers arranged in sequence along a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N S1 8 ;in:

[0009] The metal patch S1 8 And metal patch S2 N Composition interface with metal patch S2 N And metal patch S1 8 The interfaces composed of them all have topological interface states;

[0010] When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 And metal patch S2 N Between the metal patch S2 N And metal patch S1 8 The interface state modes between them are used to regulate the transmission behavior of electromagnetic waves;

[0011] The third-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N layers, metal patches S1 with N layers, and metal patches S2 with 8 layers, which are arranged in sequence along a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N S1 N S2 8 ;in:

[0012] The metal patch S1 8 With metal patch S2 N Interface composed of metal patch S2 N With metal patch S1 N Composition interface and metal patch S1 N With metal patch S2 8 The interfaces composed of them all have topological interface states;

[0013] When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 And metal patch S2 N Between, metal patch S2 N And metal patch S1 N Between and metal patch S2 N And metal patch S1 8 The interface state modes between them can regulate the transmission behavior of electromagnetic waves.

[0014] The fourth-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N1 layers, metal patches S1 with N2 layers, metal patches S2 with N1 layers, and metal patches S1 with 8 layers, which are arranged in a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N1 S1 N2 S2N1 S1 8 ;in:

[0015] The metal patch S1 8 With metal patch S2 N1 Interface composed of metal patch S2 N1 With metal patch S1 N2 Composition of interface and metal patch S1 N2 With metal patch S2 N1 Composition interface and metal patch S2 N1 With metal patch S1 8 The interfaces composed of them all have topological interface states;

[0016] When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 With metal patch S2 N1 Between, metal patch S2 N1 With metal patch S1 N2 Between and metal patch S1 N2 With metal patch S2 N1 Between and metal patch S2 N1 With metal patch S1 8 The interface state modes between them can regulate the transmission behavior of electromagnetic waves.

[0017] in:

[0018] The metal patch S2 is obtained by translating the metal patch S1 along the x direction for half a period;

[0019] The metal patches S1 and S2 have different topological properties within the first photonic band gap.

[0020] As a preferred solution of the present invention, the second-order singular point waveguide is configured by adjusting the metal patch S2 N The number of layers N is used to control the metal patch S1 8 And metal patch S2 N There exists a topological interface state between the metal patch S2 N And metal patch S1 8 The coupling strength between the existing topological interface states makes the two peaks of the transmission curve merge into one;

[0021] As a preferred solution of the present invention, the third-order singular point waveguide is configured by adjusting the metal patch S1 N And metal patch S2 N The number of layers N is used to control the metal patch S1 8 And metal patch S2 N The topological interface state between the metal patch S2 N And metal patch S1N The topological interface state between the metal patch S2 N And metal patch S1 8 The coupling strength between the topological interface states makes the three peaks of the transmission curve merge into one, and the metal patch S2 N And metal patch S1 N The electric field strength of the topological interface state between the metal patch S1 8 And metal patch S2 N The topological interface state and metal patch S2 exist between N And metal patch S1 8 The electric field strength of the topological interface state between times;

[0022] As a preferred solution of the present invention, the fourth-order singular point waveguide is configured by adjusting the metal patch S2 N1 , Metal patch S1 N2 And metal patch S2 N1 The number of layers is used to adjust the metal patch S1 8 And metal patch S2 N1 The topological interface state between the metal patch S2 N1 And metal patch S1 N2 There are topological interface states and metal patch S1 between them N2 And metal patch S2 N1 The topological interface state between the metal patch S2 N1 And metal patch S1 8 The coupling strength between the existing topological interface states causes the three peaks of the transmission curve to merge into one and then split into two.

[0023] As a preferred solution of the present invention, the basic unit of the singular point waveguide is composed of a top metal plate, a dielectric substrate and a bottom metal plate, wherein:

[0024] The length and width of the dielectric substrate are P x =5mm,P y =10mm, thickness is t=2mm;

[0025] The length and width of the bottom metal plate are l=5mm, w=3mm, and the thickness is 0.035mm;

[0026] The length and width of the top metal plate are l=5mm, w=3mm, and the thickness is 0.035mm. Two symmetrical rectangular gaps with lengths and widths of l1=1.2mm and l2=0.6mm are respectively arranged at its upper and lower boundaries.

[0027] As a preferred solution of the present invention, the topological characteristics of the metal patches S1 and S2 are characterized by Zak phase, wherein the Zak phase is expressed as:

[0028]

[0029] Where n represents the nth energy band, Λ represents the period of the structure, and u k represents the wave function of the system at the k point in the Brillouin zone.

[0030] As a preferred solution of the present invention, the topological characteristics of the metal patch S1 show the characteristics of a conventional insulator, and its topological invariant in the first photonic band gap is 0;

[0031] The topological characteristics of the metal patch S2 show topological insulator characteristics, and its topological invariant in the first photonic band gap is π.

[0032] As a preferred solution of the present invention, the singular point waveguide is equivalent to a multi-mode coupling model, wherein the dynamic equations of the interface state are:

[0033]

[0034] Among them, a i (i=1…N) topological modes of different interfaces, ω0 represents the working frequency of the topological interface state, τ i represents the coupling coefficient from the input port to the left interface state, τ o represents the mode of the output port and the right interface state, κ i Indicates mode a i and mode a i-1 The coupling strength between them.

[0035] As a further embodiment of the present invention, when τ i =τ o By adjusting the coupling coefficient between modes, the system can realize singular points of different orders at the critical point of PT phase transition.

[0036] As a preferred solution of the present invention, the input end is coupled to the metal patch S1 8 And metal patch S2 N or S1 N1 The energy of the interface composed of the metal patch S1 8 And metal patch S2 N or S2 N1 The gain of the topological interface state between the metal patch S2 N or S2 N1 And metal patch S1 8 The energy coupled out of the topological interface state can be used as the metal patch S2 Nor S2 N1 And metal patch S1 8 The loss of topological interface states between them.

[0037] As a preferred solution of the present invention, the high-order singular point can be obtained by measuring the transmission efficiency of the device with a vector network analyzer:

[0038] When the system is in the PT symmetric phase, the transmission curve has multiple transmittance peaks within the energy gap range, corresponding to multiple eigenstates of the system;

[0039] When the system is at the PT phase transition point, multiple transmission peaks of the transmission curve merge into one, that is, the system supports singular points of different orders;

[0040] When the system is in the PT phase breaking state, the peak value of the transmittance of the transmission curve will decrease.

[0041] As a preferred solution of the present invention, the singular point waveguide is a metal configuration, and can be expanded to other working frequency bands by changing the structural size and material of the metal configuration.

[0042] Beneficial Effects

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1. Invented a high-order singular point waveguide based on coupled topological boundary states, which solves the problem that traditional singular point waveguides need to introduce a specific amount of gain or loss to achieve PT phase transition;

[0045] 2. The coupling between the input and output ports and the interface state mode is used as the gain and loss of the system, which solves the problem of difficulty in controlling the gain and loss balance in microwave systems;

[0046] 3. The topological waveguide only supports a single interface state mode at the interface of the structure, and can realize a single frequency filtering function within a specific frequency range. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Figure (a) shows the basic unit of the present invention. The structure is arranged periodically along the x direction, and the lattice constants of the structure are P x and P y , (b) shows the corresponding band structure when the structure is not deformed, (c) shows the corresponding band structure and the electric field distribution at the boundary of the Brillouin zone when the structure is deformed (b = 1.75 mm), and (d) shows the corresponding band structure and the electric field distribution at the boundary of the Brillouin zone when the structure is deformed (b = 0.75 mm);

[0048] Figure 2(a) shows a topological waveguide structure with a single interface and the prepared sample, (b) shows the eigenfrequency of the topological waveguide, (c) shows the transmission curve of the topological waveguide obtained by simulation, (d) shows the relationship between the quality factor of the topological interface state and the number of S1 and S2 layers, (e) shows the equivalent model of the single-interface topological waveguide and the transmission curve obtained by simulation and numerical simulation, and (f) shows the experimentally measured transmission curve of the single-interface topological waveguide.

[0049] Figure 3 Figure (a) is a schematic diagram of the structure of a high-order singular point waveguide based on coupled topological interface states and an equivalent coupled waveguide model; Figure (b) shows the eigenfrequency diagram of the system when the coupling strength between the input and output ports and the topological interface states is τ = 0.4; Figure (c) shows the relationship between the real part of the eigenfrequency of the system and τ and κ; Figure (d) shows the relationship between the imaginary part of the eigenfrequency of the system and τ and κ;

[0050] Figure 4 Figure (a) shows the transmission curve of the topological interface state under different coupling conditions obtained by simulation; Figure (b) shows the transmission curve of the topological interface state under different coupling conditions obtained by experimental measurement; Figure (c) shows the electric field distribution at the peak of the transmission curve; Figure (d) shows the electric field intensity distribution at the peak of the transmission curve;

[0051] Figure 5 (a) is a schematic diagram of the structure of the third-order singular point waveguide based on the coupled topological interface state and the equivalent coupled waveguide model, (b) shows the eigenfrequency diagram of the system when the coupling strength between the input and output ports and the topological interface state is τ = 0.4, (c) shows the relationship between the real part of the eigenfrequency of the system and τ and κ, and (d) shows the relationship between the imaginary part of the eigenfrequency of the system and τ and κ;

[0052] Figure 6 (a) shows the transmission curve of the topological interface state under different coupling conditions obtained by simulation, (b) shows the transmission curve of the topological interface state under different coupling conditions obtained by experimental measurement, (c) shows the electric field distribution at the peak of the transmission curve, and (d) shows the electric field intensity distribution at the peak of the transmission curve.

[0053] Figure 7 (a) is a schematic diagram of the structure of the fourth-order singular point waveguide based on the coupled topological interface state and the equivalent coupled waveguide model, (b) is the transmission curve of the electromagnetic wave of the topological interface state under different coupling conditions, (c) is the real part of the system eigenfrequency under different coupling conditions, and (d) is the imaginary part of the system eigenfrequency under different coupling conditions;

[0054] Figure 8Figure (a) is a schematic diagram of the structure of the second-order singular point waveguide described in the present invention, Figure (b) is a schematic diagram of the structure of the third-order singular point waveguide described in the present invention, and Figure (c) is a schematic diagram of the structure of the fourth-order singular point waveguide described in the present invention. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0056] As an embodiment of the present invention, Figure 8 As shown, a singular point waveguide based on coupled topological interface states, the singular point waveguide includes a second-order singular point waveguide, a third-order singular point waveguide and a fourth-order singular point waveguide, wherein:

[0057] like Figure 8 As shown in Figure (a), the second-order singular point waveguide is a topological metasurface structure composed of 8 layers of metal patches S1, N layers of metal patches S2 and 8 layers of metal patches S1 arranged in a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N S1 8 ;in:

[0058] The metal patch S1 8 And metal patch S2 N Composition interface with metal patch S2 N And metal patch S1 8 The interfaces composed of them all have topological interface states;

[0059] When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 And metal patch S2 N Between the metal patch S2 N And metal patch S1 8 The interface state modes between them are used to regulate the transmission behavior of electromagnetic waves;

[0060] like Figure 8 As shown in FIG. 1(b), the third-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N layers, metal patches S1 with N layers, and metal patches S2 with 8 layers, which are arranged in a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N S1 N S2 8 ;in:

[0061] The metal patch S1 8 With metal patch S2 N Interface composed of metal patch S2N With metal patch S1 N Composition interface and metal patch S1 N With metal patch S2 8 The interfaces composed of them all have topological interface states;

[0062] When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 And metal patch S2 N Between, metal patch S2 N And metal patch S1 N Between and metal patch S2 N And metal patch S1 8 The interface state modes between them can regulate the transmission behavior of electromagnetic waves.

[0063] like Figure 8 As shown in Figure (c), the fourth-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N1 layers, metal patches S1 with N2 layers, metal patches S2 with N1 layers, and metal patches S1 with 8 layers, which are arranged in a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N1 S1 N2 S2 N1 S1 8 ;in:

[0064] The metal patch S1 8 With metal patch S2 N1 Interface composed of metal patch S2 N1 With metal patch S1 N2 Composition of interface and metal patch S1 N2 With metal patch S2 N1 Composition interface and metal patch S2 N1 With metal patch S1 8 The interfaces composed of them all have topological interface states;

[0065] When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 With metal patch S2 N1 Between, metal patch S2 N1 With metal patch S1 N2 Between and metal patch S1 N2 With metal patch S2 N1 Between and metal patch S2 N1 With metal patch S1 8 The interface state modes between them can regulate the transmission behavior of electromagnetic waves.

[0066] in:

[0067] The metal patch S2 is obtained by translating the metal patch S1 along the x direction for half a period;

[0068] The metal patches S1 and S2 have different topological properties within the first photonic band gap.

[0069] As an embodiment of the present invention, Figure 1 As shown in Figure (a), it consists of two layers of metal patches and a dielectric substrate in the middle. The lattice constant of the photonic crystal is P x =5mm, P y =10mm, the width of the top metal patch is w=3mm, and the length and width of the empty rectangle at the boundary of the metal patch are l1=1.2mm and l2=0.6mm respectively. The distance between the rectangular vacant part and the center of the structure is b, which can be used to control the topological characteristics of the structure. In addition, the thickness of the top and bottom metal structures is 0.035mm. The thickness and dielectric constant of the intermediate dielectric substrate are t=2mm and ε=4.2 respectively.

[0070] As an embodiment of the present invention, Figure 1 As shown in Figure (b), when b = 1.25 mm, the structure is x =0.75π / P x to k x =π / P x Since the left and right parts of the structure have central and translational symmetry, it is equivalent to expanding the Brillouin zone of the structure by two times, so the energy band of the structure will fold from the boundary of the Brillouin zone to the center, resulting in the degeneration of the energy band at the boundary of the Brillouin zone. By changing the size of b, the translational symmetry of the left and right sides of the structure can be broken, thereby opening the degenerate point of the energy band at the boundary of the Brillouin zone and realizing the topological phase transition.

[0071] As an embodiment of the present invention, Figure 1 As shown in Figure (c), the band structure of the system when b = 1.75 mm is shown. Since the structure has central symmetry, the topological characteristics of the first band can be judged by comparing the eigenstates of the structure at the center and the boundary of the Brillouin zone. When the eigenstates of the structure at the center and the boundary of the Brillouin zone have the same symmetry distribution, the band exhibits topologically mediocre characteristics. The eigenstates of the first band of S1 at the center of the Brillouin zone have a coupled symmetric distribution, which is the same as the eigenstates of the structure at the boundary of the Brillouin zone (see Figure 1 (c) in the figure), so S1 exhibits conventional insulator characteristics within the first energy gap range.

[0072] As an embodiment of the present invention, Figure 1As shown in Figure (d) in the figure, the band structure of the system when b = 0.75 mm is shown. Since S2 can be obtained by translating S1 half a period along the x direction, S1 and S2 have the same band structure. However, the eigenstate of the first band of S2 at the boundary of the Brillouin zone exhibits an odd symmetric distribution (see Figure 1 (d) in the figure), therefore S2 and S1 exhibit different topological characteristics within the first energy gap range.

[0073] According to the body-edge correspondence, the topological interface state exists at the interface between two structures with different topological properties. Figure 2 As shown in Figure (a), the metasurface structure composed of S1 and S2 (including 9 layers of S1 and 9 layers of S2) and the prepared experimental sample. Figure 2 As shown in Figure (b), the eigenfrequency distribution of the system near the energy gap, where the black and red points represent the bulk and interface modes, respectively. The electric field distribution of the bulk and interface states is shown in Figure 2 As shown in Figure (b), the electric field corresponding to the interface state is mainly concentrated near the interface of the structure and decays rapidly on both sides of the structure; while the electric field corresponding to the bulk state is distributed over the entire surface of the structure, as shown in Figure (b). Figure 2 As shown in Figure (c), the transmission curve of the topological interface state near the energy gap, where the frequency of the transmission peak is related to Figure 2 The characteristic frequency of the interface state is consistent with that in (b). The quality factor (3dB bandwidth) of the interface state is Q = f / BW 3dB ≈100. In this topological waveguide, the transmittance curve of the system is related to the number of layers of the structure, such as Figure 2 Figure (d) shows the relationship between the peak transmittance and the quality factor and the number of S1 and S2 structures. The transmission efficiency is inversely proportional to the number of structures, while the quality factor is proportional to the number of structures.

[0074] This topological interface state can be equivalent to a coupled waveguide system (see Figure 2 (e) in the figure), where the dynamic equation of the topological interface state (resonant cavity) can be expressed as:

[0075]

[0076] Where ω0 represents the resonant frequency of the topological interface state, τ l represents the intrinsic loss of the mode, τ i The coupling between the input port and the interface state, τ o Represents the coupling between the output port and the interface state. According to the coupled mode theory, the relationship between the input and output ports is:

[0077] S-=c s S + +c a a(6

[0078]

[0079] where c s ,c s They represent the direct coupling between the output port and the input port and the coupling between the boundary state and the output port. +2 = 0) and ignoring the intrinsic loss of the interface state, the reflection and transmission coefficients of the system can be expressed as:

[0080]

[0081] like Figure 2 As shown in Figure (e), S1 15 S2 15 The transmission efficiency of the waveguide is obtained by electromagnetic simulation software and equation (9). Figure 2 As shown in Figure (f), the experimentally measured transmission efficiency of the waveguide shows that the topological interface states are well excited within the energy gap.

[0082] like Figure 3 As shown in Figure (a), the second-order singular point waveguide based on coupled topological interface states and the equivalent coupled waveguide model. The dynamic simulation of the system is shown in formulas (2) to (4). Assuming that the system is at the critical point of PT symmetry, the reflection coefficient of the system is zero, that is, r = 0, and the Hamiltonian of the system can be expressed as:

[0083]

[0084] The two resonant cavity models are respectively regarded as resonant modes with gain (ω0+jτ i ), and the resonant mode with loss (ω0-jτ o ). For simplicity, the coupling efficiency between the output and output ports and the interface states is considered equal, that is, τ i =τ o =τ. Figure 3 Figure (b) shows the eigenfrequency of the system when τ = 0.4. In addition, Figure 3 Figures (c) and (d) in the figure show the relationship between the eigenfrequency of the system and the coupling coefficients τ and κ, respectively. The results show that when τ = κ, the real part and the imaginary part of the eigenvalue of the system are equal, that is, the system has a second-order singular point (indicated by the black dotted line).

[0085] Figure 4 Figure (a) shows the second-stage singular point waveguide (S1 8 S2 N S1 8 ) transmission efficiency, when N = 5, the waveguide has two transmission peaks, corresponding to Figure 3 (b) shows two eigenstates when the coupling mode is strong. At this time, the system is in the PT symmetric phase. When N = 16, the two transmission peaks of the system merge into one, corresponding to Figure 3 The critical point of the PT phase change in Figure (b) is where the system supports a second-order singular point; when N=20, the peak value of the single transmission peak decreases, and the system is in a PT symmetry breaking phase. Figure 4 Figure (b) is the experimentally measured transmittance curve, showing the change of the waveguide transmission peak from 2 to 1. It is worth noting that compared with the simulation results, the frequency of the transmission peak has shifted, which may be caused by the manufacturing error of the sample and the experimental measurement error. Figure 4 Figures (c) and (d) show the electric field distribution of the system at the peak of transmittance. At the second-order singular point, the energy at the two interfaces is equal.

[0086] Figure 5 Figure (a) shows the third-order singular point waveguide based on coupled topological interface states and the equivalent coupled waveguide model. The dynamic simulation of the system is shown in formulas (2) to (4). Assuming that the system is at the critical point of PT symmetry, the reflection coefficient of the system is zero, that is, r = 0, and the Hamiltonian of the system can be expressed as:

[0087]

[0088] The three resonant cavity models are respectively regarded as resonant modes with gain (ω0+jτ i ), the neutral resonant mode (ω0) and the resonant mode with loss (ω0-jτ o ). For simplicity, the coupling efficiency between the output and output ports and the interface states is considered equal, that is, τ i1 =τ o3 =τ. In addition, the coupling efficiency between interface state modes is also equal, that is, κ1=κ2=κ. Figure 5 Figure (b) shows the eigenfrequency of the system when τ=0.4. Figure 5 Figures (c) and (d) in Figure 1 show the relationship between the eigenfrequency of the system and the coupling coefficients τ and κ, respectively. The results show that when When , the real part and imaginary part of the system eigenvalue are equal, that is, the system has a third-order singular point (indicated by the black dotted line).

[0089] Figure 6 Figure (a) shows the third-order singular point waveguide (S1 8 S2 N S1 N S2 8 ) transmission efficiency, when N = 6, the waveguide has three transmission peaks, corresponding to Figure 5The three eigenstates in (b) when the coupling strength is strong indicate that the system is in the PT symmetric phase; when N = 16, the three transmission peaks merge into one, corresponding to the PT phase transition point of the system. At this time, the system supports a third-order singular point; when N = 21, the peak value of a single transmission peak decreases. At this time, the system is in the PT symmetry breaking phase. Figure 6 Figure (b) is the experimentally measured transmittance curve, showing the change of the waveguide transmission peak from 3 to 1. It is worth noting that compared with the simulation results, the frequency of the transmission peak has shifted, which may be caused by the manufacturing error of the sample and the experimental measurement error. Figure 6 Figures (c) and (d) in the figure show the electric field distribution of the system at the peak transmittance. At the third-order singular point, the energy of the interface state in the middle is about the energy of the interface states on the left and right sides. times, corresponding to the eigenvector of the third-order singular point,

[0090] Figure 7 Figure (a) shows the fourth-order singular point waveguide (S1) based on coupled topological interface states. 8 S2 N1 S1 N2 S2 N1 S1 8 ), and the equivalent coupled waveguide model. The Hamiltonian of this system can be expressed as:

[0091]

[0092] The four resonant cavity models are respectively regarded as resonant modes with gain (ω0+jτ i ), two neutral resonant modes (ω0) and a resonant mode with loss (ω0-jτ o ). For simplicity, the coupling efficiency between the output and output ports and the interface states is considered equal, that is, τ i =τ o =τ. Figure 7 Figure (b) shows the transmission curve of the fourth-order singular point waveguide. As N2 increases, the peak value of the system transmittance changes from three to one and then to two. Figure 7 Figure (c) shows the changes in the real part of the eigenstate of the system under different coupling conditions (the red, black and blue curves correspond to κ1 = 0.09, κ1 = 0.096 and κ1 = 0.11, respectively). The black curve shows the process of the system changing from PT symmetry to PT symmetry breaking. Figure 7 Figure (d) shows the relationship between the imaginary part of the system's eigenfrequency and the topological interface state coupling. The results show that at the fourth-order singular point, both the real and imaginary parts of the system's eigenfrequency are degenerate.

[0093] The technical solution of the present invention is described in detail above in conjunction with the embodiments / drawings, but the present invention is not limited to the above technical solution. For ordinary technicians in this technical field, after knowing the contents recorded in the present invention, they can make several equivalent changes and substitutions without departing from the principle of the present invention. These equivalent changes and substitutions should also be regarded as belonging to the protection scope of the present invention.

Claims

1. A singular point waveguide based on coupled topological interface states, characterized in that: The singular point waveguide includes a second-order singular point waveguide, a third-order singular point waveguide and a fourth-order singular point waveguide, wherein: The second-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N layers, and metal patches S1 with 8 layers arranged in sequence along a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N S1 8 ;in: The metal patch S1 8 And metal patch S2 N Composition interface with metal patch S2 N And metal patch S1 8 The interfaces composed of them all have topological interface states; When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 And metal patch S2 N Between the metal patch S2 N And metal patch S1 8 The interface state modes between them are used to regulate the transmission behavior of electromagnetic waves; The third-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N layers, metal patches S1 with N layers, and metal patches S2 with 8 layers, which are arranged in sequence along a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N S1 N S2 8 ;in: The metal patch S1 8 With metal patch S2 N Interface composed of metal patch S2 N With metal patch S1 N Composition interface and metal patch S1 N With metal patch S2 8 The interfaces composed of them all have topological interface states; When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 And metal patch S2 N Between, metal patch S2 N And metal patch S1 N Between and metal patch S2 N And metal patch S1 8 The interface state modes between them can then regulate the transmission behavior of electromagnetic waves; The fourth-order singular point waveguide is a topological metasurface structure composed of metal patches S1 with 8 layers, metal patches S2 with N1 layers, metal patches S1 with N2 layers, metal patches S2 with N1 layers, and metal patches S1 with 8 layers, which are arranged in a straight line from the input end to the output end. The topological metasurface structure is expressed as S1 8 S2 N1 S1 N2 S2 N1 S1 8 ;in: The metal patch S1 8 With metal patch S2 N1 Interface composed of metal patch S2 N1 With metal patch S1 N2 Composition of interface and metal patch S1 N2 With metal patch S2 N1 Composition interface and metal patch S2 N1 With metal patch S1 8 The interfaces composed of them all have topological interface states; When electromagnetic waves are incident from the x direction, they can excite the metal patch S1. 8 With metal patch S2 N1 Between, metal patch S2 N1 With metal patch S1 N2 Between and metal patch S1 N2 With metal patch S2 N1 Between and metal patch S2 N1 With metal patch S1 8 The interface state modes between them can regulate the transmission behavior of electromagnetic waves. in: The metal patch S2 is obtained by translating the metal patch S1 along the x direction for half a period; The metal patches S1 and S2 have different topological properties within the first photonic band gap.

2. The singular point waveguide based on coupled topological interface states according to claim 1, characterized in that: The second-order singular point waveguide is constructed by adjusting the metal patch S2 N The number of layers N is used to control the metal patch S1 8 And metal patch S2 N There exists a topological interface state between the metal patch S2 N And metal patch S1 8 The coupling strength between the existing topological interface states makes the two peaks of the transmission curve merge into one; The third-order singular point waveguide is constructed by adjusting the metal patch S1 N And metal patch S2 N The number of layers N is used to control the metal patch S1 8 And metal patch S2 N The topological interface state between the metal patch S2 N And metal patch S1 N The topological interface state between the metal patch S2 N And metal patch S1 8 The coupling strength between the topological interface states makes the three peaks of the transmission curve merge into one, and the metal patch S2 N And metal patch S1 N The electric field strength of the topological interface state between the metal patch S1 8 And metal patch S2 N The topological interface state and metal patch S2 exist between N And metal patch S1 8 The electric field strength of the topological interface state between times; The fourth-order singular point waveguide is formed by adjusting the metal patch S2 N1 , Metal patch S1 N2 And metal patch S2 N1 The number of layers is used to adjust the metal patch S1 8 And metal patch S2 N1 The topological interface state between the metal patch S2 N1 And metal patch S1 N2 There are topological interface states and metal patch S1 between them N2 And metal patch S2 N1 The topological interface state between the metal patch S2 N1 And metal patch S1 8 The coupling strength between the existing topological interface states causes the three peaks of the transmission curve to merge into one and then split into two.

3. The singular point waveguide based on coupled topological interface states according to claim 1, characterized in that: The basic unit of the singular point waveguide is composed of a top metal plate, a dielectric substrate and a bottom metal plate, wherein: The length and width of the dielectric substrate are P x =5mm,P y =10mm, thickness is t=2mm; The length and width of the bottom metal plate are l=5mm, w=3mm, and the thickness is 0.035mm; The length and width of the top metal plate are l=5mm, w=3mm, and the thickness is 0.035mm. Two symmetrical rectangular gaps with lengths and widths of l1=1.2mm and l2=0.6mm are respectively arranged at its upper and lower boundaries.

4. The singular point waveguide based on coupled topological interface states according to claim 1, characterized in that: The topological characteristics of the metal patches S1 and S2 are characterized by the Zak phase, wherein the Zak phase is expressed as: Where n represents the nth energy band, Λ represents the period of the structure, and u k represents the wave function of the system at the k point in the Brillouin zone.

5. The singular point waveguide based on coupled topological interface states according to claim 4, characterized in that: The topological characteristics of the metal patch S1 show the characteristics of a conventional insulator, and its topological invariant in the first photonic band gap is 0; The topological characteristics of the metal patch S2 show topological insulator characteristics, and its topological invariant in the first photonic band gap is π.

6. The singular point waveguide based on coupled topological interface states according to claim 2, characterized in that: The singular point waveguide is equivalent to a multi-mode coupling model, in which the dynamic equations of the interface state are: Among them, a i (i=1...N) topological modes of different interfaces, ω0 represents the working frequency of the topological interface state, τ i represents the coupling coefficient from the input port to the left interface state, τ o represents the mode of the output port and the right interface state, κ i Indicates mode a i and mode a i-1 The coupling strength between them.

7. The singular point waveguide based on coupled topological interface states according to claim 6, characterized in that: When τ i =τ o By adjusting the coupling coefficient between modes, the system can realize singular points of different orders at the critical point of PT phase transition.

8. The singular point waveguide based on coupled topological interface states according to claim 6, characterized in that: Coupling from the input to the metal patch S1 8 And metal patch S2 N or S1 N1 The energy of the interface composed of the metal patch S1 8 And metal patch S2 N or S2 N1 The gain of the topological interface state between the metal patch S2 N or S2 N1 And metal patch S1 8 The energy coupled out of the topological interface state can be used as the metal patch S2 N or S2 N1 And metal patch S1 8 The loss of topological interface states between them.

9. The singular point waveguide based on coupled topological interface states according to claim 2, characterized in that: The singular point can be obtained by measuring the transmission efficiency of the device with a vector network analyzer: When the system is in the PT symmetric phase, the transmission curve has multiple transmittance peaks within the energy gap, corresponding to the number of eigenstates of the system; When the system is at the PT phase transition point, the multiple transmission peaks of the transmission curve merge into one; When the system is in the PT phase breaking state, the peak value of the transmittance of the transmission curve will decrease.

10. The singular point waveguide based on coupled topological interface states according to claim 1, characterized in that: The singular point waveguide is a metal configuration, and can be expanded to other working frequency bands by changing the size and material of the metal configuration structure.

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