Three-dimensional axial insulator, multi-port isolator and method of designing the same

Abstract

The application provides a three-dimensional axial insulator based on a gyromagnetic photonic crystal, comprising alternately stacked A-layer and B-layer photonic crystals and an interlayer coupling layer, and the top layer and the bottom layer are both A-layer photonic crystals; the A-layer and B-layer photonic crystals are both arranged in a square lattice form by gyromagnetic medium columns and have the same lattice constant, and the gyromagnetic medium columns in the B-layer and A-layer photonic crystals are staggered by half a period in the x direction and the y direction; the magnetic fields applied to the gyromagnetic medium columns in the B-layer and A-layer photonic crystals are equal in magnitude and opposite in direction; the interlayer coupling layer has inversion symmetry, and the interlayer coupling layer is an AB interlayer coupling layer and a BA interlayer coupling layer. The three-dimensional axial insulator has a non-coplanar chiral edge state and can realize non-reciprocal transmission of energy. Further, the application also provides a multi-port isolator and a design method thereof based on the three-dimensional axial insulator, and the obtained multi-port isolator has the characteristics of high isolation and low loss in the microwave frequency band.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic waves, and particularly relates to a design of a three-dimensional axion insulator and a multi-port isolator constructed by using a gyromagnetic photonic crystal. BACKGROUND

[0002] In recent years, the research on topological insulators is deepening, and finding new topological quantum substances and topological phase transitions has been a central theme in modern physics and materials science. Three-dimensional axion insulators represent a unique magnetic topological phase, which is a two-dimensional three-dimensional topological magnetic high-order phase quantum anomalous Hall effect insulator. In the axion insulator, the axion electromagnetism shows novel topological magnetic electricity such as quantized Faraday and Kerr rotation and half-integer surface Hall response phenomena.

[0003] The axion insulator is a singular topological phase with a zero Chern number but a finite topological Chern-Simons term, which is generated by breaking the time reversal symmetry of the surface of a three-dimensional topological insulator. The construction of the three-dimensional axion insulator is derived from the two-dimensional Chern insulator, which has a bulk that behaves as an insulator and an edge that conducts electricity, and the reversal of the magnetization will reverse the energy flow direction of the boundary state. The three-dimensional axion insulator can be constructed by alternately stacking Chern insulators with opposite magnetization and applying weak coupling between the layers. The boundary state energy of adjacent layers with opposite magnetization is opposite and is annihilated, so that non-coplanar chiral edge states can appear in the axion insulator with a finite odd number of layers, and the edge state transmission has topological robustness.

[0004] An isolator is a device designed based on a non-reciprocal system, and the realization of a non-reciprocal system mainly has three ways, i.e., breaking time reversal symmetry, constructing a nonlinear system, and constructing an active time-varying modulation system. The most commonly used one is to break the time reversal symmetry. The main way to break the time reversal symmetry is to apply a magnetic field to the system to break the symmetry of the tensor of magnetic permeability or dielectric constant. The current mainstream microwave band isolator realizes non-reciprocal transmission in a two-dimensional system. For example, a gyromagnetic material YIG is coupled with a microstrip line to realize non-reciprocal transmission, or a defect state of a photonic crystal is combined with a gyromagnetic medium to realize non-reciprocal transmission. However, the current isolators do not have topological robustness, and energy scattering, loss and other problems caused by bulk defects may occur in the energy transmission process. SUMMARY

[0005] To solve the above problems, the application provides a three-dimensional axial insulator constructed by a gyromagnetic photonic crystal, which has a non-coplanar chiral edge state, so that a three-dimensional axial insulator with an anti-ferromagnetic structure is realized in a magneto-optical photonic crystal system, and the regulation of non-reciprocal transmission of photons is enriched. Further, the application also provides a multi-port isolator and a design method thereof based on the three-dimensional axial insulator.

[0006] The first aspect of the application discloses an axial insulator constructed based on a gyromagnetic photonic crystal, which comprises alternately stacked A-layer photonic crystals and B-layer photonic crystals, and an interlayer coupling layer for coupling between the photonic crystal layers, and the top layer and the bottom layer of the axial insulator are both A-layer photonic crystals; the A-layer photonic crystals and the B-layer photonic crystals are both arranged in a square lattice form by gyromagnetic medium columns; the B-layer photonic crystals and the A-layer photonic crystals have the same lattice constant, and the gyromagnetic medium columns in the B-layer photonic crystals are staggered by half a period in the x direction and the y direction from the gyromagnetic medium columns in the A-layer photonic crystals; the magnetic field applied to the gyromagnetic medium columns in the B-layer photonic crystals is opposite to the magnetic field applied to the gyromagnetic medium columns in the A-layer photonic crystals; and the interlayer coupling layer comprises AB interlayer coupling layers and BA interlayer coupling layers with inversion symmetry.

[0007] As an optional solution, the gyromagnetic medium column is a ferrite material; the ferrite material comprises spinel ferrite, garnet ferrite and magnetoplumbite ferrite.

[0008] As an optional solution, the gyromagnetic medium column is a yttrium iron garnet ferrite medium column.

[0009] As an optional solution, the interlayer coupling layer is a perforated metal plate made of a non-ferromagnetic metal; a magnet is embedded on the perforated metal plate, the projection of the magnet in the x-y plane is completely coincident with the gyromagnetic medium columns in the A-layer photonic crystals and the B-layer photonic crystals; and the perforated metal plate is also provided with coupling holes arranged corresponding to the square lattice.

[0010] As an optional solution, the non-ferromagnetic metal is copper or aluminum.

[0011] As an optional solution, the coupling holes comprise special-shaped coupling holes located in the x-y plane projection of the square lattice and circular coupling holes located at the four vertices of the x-y plane projection of the square lattice; the special-shaped coupling holes are composed of T-shaped holes and semicircular holes with a preset angle, and the center of the circular coupling hole is located at the vertex.

[0012] As an alternative, the A-layer photonic crystal comprises a plurality of A-layer square lattices, the B-layer photonic crystal comprises a plurality of B-layer square lattices; the interlayer coupling layer has a plurality of interlayer coupling units; the axial insulator comprises a plurality of supercells arranged along the z direction, and the supercell is composed of a primitive cell; the primitive cell comprises an A-layer square lattice, an AB interlayer coupling unit, a B-layer square lattice, and a BA interlayer coupling unit arranged in a top-down stack.

[0013] The second aspect of the present application discloses a multi-port isolator design method, comprising the following steps:

[0014] Providing an isolator body: the isolator body is a three-dimensional axial insulator constructed based on a gyromagnetic photonic crystal according to the first aspect of the present application or any one of the optional solutions thereof, and the three-dimensional axial insulator has a loop for non-reciprocal energy transmission composed of non-coplanar chiral prisms; setting boundary conditions: setting an absorbing boundary on the surface of the isolator body to block the loop, and setting an ideal electrical conductor boundary on the surface of the isolator body other than the absorbing boundary, to obtain a channel for non-reciprocal energy transmission composed of non-coplanar chiral prisms; the absorbing boundary is made of wave-absorbing material, and the ideal electrical conductor boundary is made of non-ferromagnetic metal;

[0015] Port setting: at least two ports are provided on the channel, and the ports include input ports and output ports.

[0016] As an alternative, the multi-port isolator design method further comprises boundary modification: a second coupling hole for enhancing coupling is opened on the boundary of the interlayer coupling layer of the three-dimensional axial insulator; the second coupling hole includes rectangular holes arranged at equal intervals on two boundaries of the interlayer coupling layer and square holes arranged at four corners of the interlayer coupling layer.

[0017] As an alternative, the three-dimensional axial insulator is a cuboid or a cube; the input port is arranged at a vertex of the cuboid or the cube away from the absorbing boundary on the channel; the output port is arranged at a vertex of the cuboid or the cube downstream of the input port, and the output port has at least two.

[0018] The third aspect of the present application discloses a multi-port isolator designed according to the second aspect of the present application or any one of the optional solutions thereof; comprising an isolator body, input ports, output ports, an absorbing boundary, an ideal electrical conductor boundary, and a channel for non-reciprocal energy transmission composed of non-coplanar chiral prisms of the isolator body.

[0019] The third aspect of the present application discloses a multi-port isolator designed according to the second aspect of the present application or any one of the optional solutions thereof; comprising an isolator body, input ports, output ports, an absorbing boundary, an ideal electrical conductor boundary, and a channel for non-reciprocal energy transmission composed of non-coplanar chiral prisms of the isolator body. The third aspect of the present application discloses a multi-port isolator designed according to the second aspect of the present application or any one of the optional solutions thereof; comprising an isolator body, input ports, output ports, an absorbing boundary, an ideal electrical conductor boundary, and a channel for non-reciprocal energy transmission composed of non-coplanar chiral prisms of the isolator body.

[0020] Compared with the prior art, the present application has the following remarkable advantages:

[0021] The present application constructs a three-dimensional axial insulator similar to the anti-ferromagnetic material in the electronic system under the gyromagnetic photonic crystal system, and realizes the non-coplanar chiral edge state.

[0022] Further, the present application provides a multi-port isolator based on the three-dimensional axial insulator, which works in the microwave frequency band and has multiple high-isolation ports, and can simultaneously provide unidirectional transmission and reverse isolation effect for the connection of multiple devices.

[0023] The present application not only enriches the research of three-dimensional topological insulators, but also provides a new way and method for regulating and applying topological edge states. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 (a) is an arrangement schematic diagram of YIG dielectric columns in the A layer photonic crystal, and the square box in the figure schematically shows the square lattice of the A layer; (b) is an arrangement schematic diagram of YIG dielectric in the B layer photonic crystal, and the square box in the figure schematically shows the square lattice of the B layer; (c) is a structure schematic diagram of the minimum repeating unit, i.e. the primitive unit cell, of the three-dimensional axial insulator, and the arrow direction on the dielectric column represents the direction of the magnetic field applied on the dielectric column; (d) is a structure schematic diagram of the interlayer copper plate unit.

[0025] The figure legend is: ① represents YIG dielectric column; ② represents open-hole copper plate, ③ represents circular magnet, red represents N pole of the magnet, and blue represents S pole of the magnet.

[0026] Figure 2 (a) is a schematic diagram of the chiral edge state of the photonic axial insulator, and the arrow line represents the energy flow along the axial direction; (b) is the kx, ky, kz direction projection band of the axial insulator, and the green and blue dots in the figure correspond to the Figure 2 The edge state in the (a) figure, and the small black dots represent the projected bulk state and surface state.

[0027] Figure 3 (a) is a structure schematic diagram of the multi-port isolator; (b) is a schematic diagram of an optimal interlayer copper plate design scheme of the AB layer.

[0028] Figure 4(a) is the calculation result of the isolation degree of the port 1, 2 of the isolator; (b) is the calculation result of the isolation degree of the port 1, 3 of the isolator; (c) is the calculation result of the isolation degree of the port 1, 3 of the isolator. DETAILED DESCRIPTION

[0029] The technical solutions and specific embodiments of the present application are described below in conjunction with the drawings, but are not limited thereto, and any modification or equivalent replacement of the technical solutions of the present application without departing from the spirit and scope of the technical solutions of the present application shall be covered in the protection scope of the present application.

[0030] The present application utilizes a three-dimensional axial insulator (hereinafter referred to as "axial insulator") constructed in a gyromagnetic photonic crystal, and realizes a microwave frequency band multi-port isolator (hereinafter referred to as "multi-port isolator") based on the non-reciprocal edge state transmission characteristics of the axial insulator. Moreover, the present application also verifies the principle and results of the related performance of the axial insulator through numerical calculation and simulation.

[0031] The three-dimensional axial insulator has a non-coplanar chiral edge state transmission characteristic, which is calculated according to the projection energy band in the kx, ky, kz direction in the momentum space, and the projection energy band is calculated according to the supercell calculation eigenstate. The supercell includes an A layer gyromagnetic photonic crystal (hereinafter referred to as "A layer photonic crystal") arranged by stacking from top to bottom, an AB interlayer coupling layer, a B layer gyromagnetic photonic crystal (hereinafter referred to as "B layer photonic crystal"), and a BA interlayer coupling layer.

[0032] As shown in Figure 1 As shown in (a), the A layer photonic crystal is arranged by gyromagnetic medium columns in a square lattice, the gyromagnetic medium columns are made of ferrite materials, the ferrite materials mainly include spinel ferrite, garnet ferrite and magnetoplumbite ferrite, and the magnetic permeability of these materials is in tensor form under the condition of an external magnetic field. The present application preferably uses YIG (yttrium iron garnet ferrite) as the material of the gyromagnetic medium column, which has low magnetic loss and good stability, so that it has unique advantages in high frequency signal processing. As shown in Figure 1 As shown in (b), the B layer photonic crystal can also be arranged by YIG (yttrium iron garnet ferrite) medium columns in a square lattice form, but it is worth noting that the YIG medium columns in the AB two layer photonic crystal are staggered and opposite magnetic fields of the same size are applied. The lattice constants of the AB two layer photonic crystals are the same, and the geometric sizes of each YIG medium column in the AB two layer photonic crystals are also the same. For example, in the present embodiment, the lattice constant a is set to 15.5 mm, the diameter of the YIG medium column is set to d = 2r = 5 mm, r is the radius of the YIG medium column, and the height of the YIG medium column h1 = 4 mm.

[0033] The interlayer coupling layer includes AB interlayer coupling layer (A layer on top, B layer on bottom, and the coupling direction is from A layer to B layer) for coupling between A layer photonic crystal and B layer photonic crystal, and BA interlayer coupling layer (B layer on top, A layer on bottom, and the coupling direction is from B layer to A layer) for coupling between B layer photonic crystal and A layer photonic crystal. The AB interlayer coupling layer and the BA interlayer coupling layer can be realized by using a perforated metal plate made of non-ferromagnetic metal such as copper or aluminum in cooperation with a magnet. In the embodiment, the perforated copper plate with embedded magnets is used as the interlayer coupling layer of the photonic crystal, and is also called interlayer copper plate. The thickness of the perforated copper plate is h2=1mm. The size and shape of the perforated holes of the perforated copper plate control the coupling strength between the layers. The AB interlayer copper plate and the BA interlayer copper plate have inversion symmetry, that is, the AB interlayer copper plate can be obtained by rotating the BA interlayer copper plate by 180° in the plane.

[0034] As shown in Figure 3 As shown in FIG. 2(b), the interlayer copper plate has embedded magnets, and the embedded magnets are respectively opposite to the positions of the YIG dielectric columns in the A layer photonic crystal and the B layer photonic crystal and have the same diameter, that is, the projections in the x-y plane are completely coincident. However, the magnetic field of the magnet embedded in the A layer photonic crystal is equal to the magnetic field of the magnet embedded in the B layer photonic crystal, and the magnetic field directions are opposite. The interlayer copper plate also has coupling holes for interlayer coupling. The structure of the coupling holes can be referred to the introduction of the copper plate unit.

[0035] From the x-y plane, the supercell is composed of a plurality of primitive cells. The primitive cell can be regarded as being composed of an A layer square lattice, an AB interlayer coupling unit, a B layer square lattice, and a BA interlayer coupling unit arranged from top to bottom. The A layer square lattices of each layer together form the A layer photonic crystal, and the B layer square lattices of each layer together form the B layer photonic crystal. The AB interlayer coupling units are connected together to form the AB interlayer coupling layer, and the BA interlayer coupling units are connected together to form the BA interlayer coupling layer.

[0036] As shown in Figure 1 As shown in FIG. 2(c), each square lattice in the primitive cell includes two 1 / 2 YIG dielectric columns. In the two square lattices, the 1 / 2 YIG dielectric columns are staggered, and the centers of the projections of the four 1 / 2 YIG dielectric columns in the x-y plane coincide with the centers of the projections of the four edges of the square lattice in the x-y plane. It can be seen that the YIG dielectric column in the A layer square lattice is moved by half a period in the x direction and the y direction to obtain the B layer square lattice, that is, the YIG dielectric column in the B layer photonic crystal is staggered by half a period in the x direction and the y direction with the YIG dielectric column in the A layer photonic crystal. The period of the primitive cell in the x-y plane is a, and the period in the z direction is 2h=10mm.

[0037] In this embodiment, the AB interlayer coupling unit and the BA interlayer coupling unit are both interlayer copper plate units embedded with magnets, which are referred to as "copper plate units" for short. As shown in Figure 3 (b), the interlayer copper plate unit is the smallest repeating unit on the interlayer copper plate. The copper plate unit is a square with a side length of a, and is provided with a coupling hole. In this embodiment, the coupling hole includes a T-shaped hole with an inclination of 225°, that is, the included angle between the center line of the T-shaped hole and the x-axis is 225°. The T-shaped hole can be formed in the following manner: a rectangle is drawn in the copper plate unit, the length of the rectangle is 2m, and the width is m, A circular arc (1 / 4 circle) with a radius of r i is drawn in the rectangle with the two vertices in the length direction of the rectangle as the centers, the part of the rectangle coinciding with the circular arc is retained, and the remaining part is removed, that is, a T-shaped hole is obtained, wherein the length of the rectangle is 2m, and the width is m, Further, a semicircular hole with a radius of r2 is provided at the top of the T-shaped hole and communicates with the T-shaped hole. The center of the semicircular hole is located at the center point of the long side of the rectangle and coincides with the center point of the copper plate unit. The T-shaped hole and the semicircular hole are connected to form a whole, which can be referred to as a special-shaped coupling hole, as shown in Figure 1 (d). On the four sides of the copper plate unit, a 1 / 2 circular magnet with a radius of r is embedded at a position opposite to the 1 / 2 YIG medium column. The AB interlayer copper plate (unit) and the BA interlayer copper plate (unit) have inversion symmetry, so that the BA interlayer copper plate (unit) can be obtained by rotating the AB interlayer copper plate (unit) by 180° about the primitive cell center (unit center). The special-shaped coupling hole of the BA interlayer copper plate (unit) is inclined by 45°. Further, a 1 / 4 circle with a radius of r2 can be removed from each of the four vertices of the copper plate unit to enhance the interlayer coupling.

[0038] As shown in Figure 1 (d) and Figure 3 (b), from the x-y plane, the open-hole copper plate serving as the interlayer coupling layer includes a circular magnet (composed of two 1 / 2 circular magnets with a radius of r), and a plurality of arrayed special-shaped coupling holes and circular coupling holes. The circular magnet is located at a position opposite to the YIG medium column, that is, at the center of the four sides of the square lattice. The center of the semicircular hole in the special-shaped coupling hole is located at the center of the interlayer copper plate unit, and the center of the circular coupling hole is the four vertices of the square interlayer copper plate unit.

[0039] It can be understood that in other embodiments, the coupling hole in the open-hole copper plate unit can also have other structural forms, as long as it can satisfy the condition that there is a certain microwave frequency band in the projected energy band that only has a corner state.

[0040] The three-dimensional axial insulator is obtained by alternately stacking the A layer photonic crystal and the B layer photonic crystal, and the layers are separated by an interlayer coupling layer, the interlayer coupling layer has an odd number of layers, and the top layer and the bottom layer are both A layer photonic crystals. The three-dimensional axial insulator constructed by the photonic crystal with such an antiferromagnetic structure has a topological band gap, that is, electromagnetic waves cannot propagate in the body within the band gap frequency range, but electromagnetic waves can be allowed to have robust transmission on the surface, which is specifically manifested as non-coplanar chiral edge state transmission.

[0041] Based on the three-dimensional axial insulator proposed in the embodiment of the present application, according to the actual material parameters and the magnetic field strength in the experiment, the parameters are set as follows: the saturation magnetization (M s ) of YIG is 0.182T, the relative dielectric constant ε is 15 (without considering the dielectric loss of the material), a permanent magnet magnetic field device is used to apply a magnetic field to the three-dimensional axial insulator, when the external magnetic field H0 in the z direction is ±1920Oe, the gyromagnetic permeability of YIG is as follows:

[0042]

[0043] Wherein, ω m = γM s , ω0 = γH0,

[0044] In the formula, i represents an imaginary unit; γ represents a gyromagnetic ratio, which is a constant (γ = 1.759 x 10 11 s -1 T -1 ); M s is the saturation magnetization; ω is the operating angular frequency, the operating frequency f in the embodiment of the present application is 11.2GHz, and the operating angular frequency is ω = 2πf; H0 is the external magnetic field strength; and α represents the damping coefficient.

[0045] In order to simplify the calculation, the damping coefficient is set to 0 (α = 0), and without considering dispersion, according to formula (1), μ r = ± 0.71604, and the gyromagnetic permeability of YIG is obtained.

[0046] It should be noted that the calculation of all numerical values in the present application is realized by using the Electromagnetic Waves, Frequency Domain module in the COMSOL finite element calculation software. Before calculating the projection band in the kx, ky and kz directions, an supercell needs to be constructed,Figure 2 (b) is the projected band in kx, ky, kz direction calculated by the software. In the projected band diagram, the green and blue dots correspond to Figure 2 (a) the ribbons in the figure, the small black dots represent the projected bulk and surface states, the projected band in ky direction reflects the ribbon state transmitted along y direction, i.e. the ribbon state on ribbon C1, C4; the projected band in kx direction reflects the ribbon state transmitted along x direction, i.e. the ribbon state on ribbon C2, C5; the projected band in kz direction reflects the ribbon state transmitted along z direction, i.e. the ribbon state on ribbon C3, C6. Moreover, the frequency range with only ribbon state in the band gap is 11-11.5 GHz.

[0047] Wherein, when calculating the projected band in kx direction, the supercell is constructed by arraying the primitive cell in y direction for 5 periods and in z direction for 7.5 periods (i.e. 15 layers in z direction); the boundary of y-z plane is set as periodic boundary, and the boundaries of x-y plane and x-z plane are set as ideal electrical conductor boundary; scanning different kx can obtain the projected band in kx direction.

[0048] Similarly, when calculating the projected band in ky direction, the supercell is constructed by arraying in x direction for 5 periods and in z direction for 7.5 periods; the boundary of x-z plane is set as periodic boundary, and the boundaries of x-y plane and y-z plane are set as ideal electrical conductor boundary; scanning different ky can obtain the projected band in ky direction.

[0049] Similarly, when calculating the projected band in kz direction, the supercell is constructed by arraying in x direction for 5 periods and in y direction for 5 periods; the boundary of x-y plane is set as periodic boundary, and the boundaries of x-z plane and y-z plane are set as ideal electrical conductor boundary; scanning different kz can obtain the projected band in kz direction.

[0050] Based on the above constructed axion insulator in the gyromagnetic photonic crystal system, there is a full band gap, and there is a noncoplanar chiral ribbon state in the band gap frequency range, i.e. the energy only unidirectionally transmits on the specific ribbon of the axion insulator to form a loop. According to the calculated projected band, we can obtain the transmission direction of the chiral ribbon state of the axion insulator model, and the schematic diagram of the chiral ribbon state transmission is as Figure 2 (a), wherein the ribbons C1-C6 are ribbons with chiral ribbon state, and the ribbons T7-T12 are ordinary ribbons, and the energy transmission is unidirectional along the ribbons C1-C6 to form a loop. Thus, the construction of the axion insulator model and the band calculation in the gyromagnetic photonic crystal system are completed.

[0051] Further, based on the non-coplanar chiral edge state of the axial insulator, a multi-port isolator in the microwave band is also constructed in the present application. In another embodiment, the YIG medium columns are arranged in a square lattice, so that the square lattice of layer A constituting the primitive unit cell is arrayed in 4 periods in the x direction and 3 periods in the y direction, forming a photonic crystal of layer A as shown in Figure 1 (a); the YIG medium columns are arranged in a square lattice, so that the square lattice of layer B constituting the primitive unit cell is arrayed in 3 periods in the x direction and 4 periods in the y direction, forming a photonic crystal of layer B as shown in Figure 1 (b). In the z direction, the photonic crystals of layer A and layer B are alternately stacked in odd layers, and the top layer and the bottom layer are both layer A. In this embodiment, the photonic crystals of layer A and layer B are alternately stacked in 7 layers, and equal and opposite magnetic fields are applied to the photonic crystals of layer A and layer B. The layers of the photonic crystals of layer A and layer B are separated by a square open copper plate embedded with magnets, as shown in Figure 3 (b), which is a square open copper plate embedded with magnets with a side length of L = 57.5 mm, where different colors of circles represent different poles of the magnets, light color represents N pole, and dark color represents S pole. Thus, the construction of the isolator body is completed.

[0052] Further, in order to enhance the coupling between layers and the transmission of energy in the z direction, the boundaries of the square open copper plate can be modified to improve the transmission efficiency of energy along the edge state. As shown in Figure 3 (b), the modification method given in this embodiment is to dig a rectangular coupling hole with a length of 4.4r and a width of r every interval of lattice constant a on the left boundary and the upper boundary; then dig a square coupling hole with a side length of 1.5r at each corner of the square open copper plate, and the coupling holes inside the square open copper plate and Figure 1 (d) are arranged in the same way. Rotating the AB interlayer copper plate (i.e., the AB interlayer coupling layer) by 180° along the center can obtain the BA interlayer copper plate (i.e., the BA interlayer coupling layer).

[0053] After the boundary modification, the boundary conditions are set. Since the transmission of the non-coplanar chiral edge state is a loop, in this embodiment, the surfaces where edges C1 and C6 are located are set as absorbing boundaries, which aims to block the backflow of energy to form a loop, so that the energy of the isolator can only be transmitted in one direction along the channel formed by edges C2-C5, and cannot form a loop. In the actual construction of the isolator, placing a wave-absorbing material on the surfaces where edges C1 and C6 are located can achieve the effect of absorbing boundary. The remaining surfaces outside the absorbing boundary are set as ideal electrical conductor boundaries to realize the transmission of energy along the edges. In the actual construction of the isolator, the ideal electrical conductor boundary can be realized by placing a metal plate made of non-ferromagnetic metal such as copper plate or aluminum plate on the surface.

[0054] It can be understood that in other embodiments, other surfaces can also be selected to set the absorbing boundary, for example, the surfaces where the edges C3 and C4 are located, as long as the absorbing boundary can block the energy from flowing back to form a loop. Preferably, after setting the absorbing boundary, the two edges C3 and C6 in the z direction with high isolation are not affected by the absorbing boundary.

[0055] After the boundary condition is set, the port setting needs to be performed. Since the energy is transmitted along the edges C2-C5, considering the influence of the absorbing boundary, the intersection of the edges C2 and C3 can be set as the input port of the energy, so that the energy is transmitted along the edges C3-C5. Since the isolator has high isolation in the z direction, according to the path of energy propagation, the output port can be set at any position on the edges C4 and C5.

[0056] According to Figure 2 (a), an edge of the top surface of the cube is selected as a port, and three edges of the bottom surface are selected as three other ports, and specifically, one input port and three output ports can be set. As shown in Figure 3 (a), port 1 is the input port of the energy, and ports 2-4 are all output ports of the energy. The energy transmission direction is along the edges C3-C5, the y-z surface where the port 4 is located is set as the absorbing boundary to prevent the energy from returning to the port 1 to form a loop, and the remaining surfaces are all ideal electrical conductor boundaries, thereby a four-port microwave frequency band isolator with high isolation can be constructed.

[0057] According to Figure 2 (b), the calculation of the projected energy band, the frequency range with chiral edge state transmission in the band gap interval is 11-11.5 GHz, and therefore, the working frequency of the isolator is 11-11.5 GHz.

[0058] Figure 4 The transmission isolation between different ports is calculated: as shown in Figure 4 (a), the isolation between the port 1 and the port 2 of the isolator is 43 dB, and the transmission direction is from the port 1 to the port 2, which is the reverse isolation; as shown in Figure 4 (b), the isolation between the port 1 and the port 3 of the isolator is 46 dB, and the transmission direction is from the port 1 to the port 3, which is the reverse isolation; as shown in Figure 4 (c), the isolation between the port 1 and the port 4 of the isolator is 58 dB, and the transmission direction is from the port 1 to the port 4, which is the reverse isolation.

[0059] The application utilizes a design of a class anti-ferromagnetic gyromagnetic photonic crystal, i.e. two kinds of square lattices with opposite magnetic field and staggered arrangement are stacked, and successfully realizes the construction of a three-dimensional axion insulator in a photonic crystal system. Through the calculation of the energy band structure of the axion insulator, it is proved that the constructed three-dimensional axion insulator has a non-reciprocal transmission loop of non-coplanar chiral edge state. Further, based on the topological non-trivial edge state non-reciprocal transmission property of the three-dimensional axion insulator, the application also proposes a multi-port isolator with robustness and high isolation in the microwave frequency band. As can be seen, the application not only realizes the axion insulator in the magneto-optical photonic crystal system, but also designs a multi-port and high-isolation isolator by using the non-coplanar edge state transmission of the axion insulator. Therefore, the application has guiding significance for the design of non-reciprocal devices and other related optical integrated devices.

[0060] Finally, it should be noted that although the embodiments of the application are described above in combination with the drawings, the application is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the guidance of this specification without departing from the scope protected by the claims of the application, and these all belong to the protection of the application.

Claims

1. An axion insulator constructed based on a gyromagnetic photonic crystal, characterized in that, The photonic crystal structure comprises alternating A-layer photonic crystal and B-layer photonic crystal, and interlayer coupling layer for coupling between photonic crystal layers, and the top layer and the bottom layer of the axial insulator are both A-layer photonic crystal; The A-layer photonic crystal and the B-layer photonic crystal are both arranged in square lattice form by gyromagnetic medium columns; the B-layer photonic crystal and the A-layer photonic crystal have the same lattice constant, and the gyromagnetic medium columns in the B-layer photonic crystal and the gyromagnetic medium columns in the A-layer photonic crystal are staggered by half a period in the x direction and the y direction; The magnetic field applied to the gyromagnetic medium column in the B-layer photonic crystal is opposite to the magnetic field applied to the gyromagnetic medium column in the A-layer photonic crystal; The interlayer coupling layer comprises AB interlayer coupling layer and BA interlayer coupling layer with inversion symmetry.

2. The shaft subinsulator of claim 1, wherein The gyromagnetic medium column is a ferrite material; the ferrite material comprises spinel ferrite, garnet ferrite and magnetoplumbite ferrite.

3. The shaft subinsulator of claim 2, wherein The gyromagnetic medium column is a yttrium iron garnet ferrite medium column.

4. The shaft subinsulator of claim 1, wherein The interlayer coupling layer is a perforated metal plate made of non-ferromagnetic metal; the perforated metal plate is embedded with a magnet, the projection of the magnet and the gyromagnetic medium column in the A-layer photonic crystal and the B-layer photonic crystal in the x-y plane completely coincide; the perforated metal plate is also provided with a coupling hole corresponding to the square lattice.

5. The shaft subinsulator of claim 4, wherein The coupling hole comprises a special-shaped coupling hole located in the x-y plane projection of the square lattice and a circular coupling hole located at the four vertices of the x-y plane projection of the square lattice; the special-shaped coupling hole is composed of a T-shaped hole and a semicircular hole with a preset angle, and the center of the circular coupling hole is located at the vertex.

6. The shaft sub-insulation of any of claims 1 to 5, wherein, The A-layer photonic crystal comprises a plurality of A-layer square lattices, and the B-layer photonic crystal comprises a plurality of B-layer square lattices; the interlayer coupling layer has a plurality of interlayer coupling units; The axial insulator comprises a plurality of supercells arranged along the z direction, and the supercell is composed of a primitive cell; The primitive cell comprises an A-layer square lattice, an AB interlayer coupling unit, a B-layer square lattice and a BA interlayer coupling unit arranged in a top-down stack.

7. A method of designing a multi-port isolator, the method comprising: The method comprises the following steps: Providing an isolator body: the isolator body is an axial insulator constructed based on the gyromagnetic photonic crystal according to any one of claims 1 to 6, and the axial insulator has a loop for non-reciprocal transmission of energy composed of non-coplanar chiral edges; Setting boundary conditions: setting an absorbing boundary on the surface of the isolator body to block the loop, and setting an ideal electrical conductor boundary on the surface of the isolator body other than the absorbing boundary to obtain a channel for non-reciprocal transmission of energy composed of non-coplanar chiral edges; the absorbing boundary is made of wave-absorbing material, and the ideal electrical conductor boundary is made of non-ferromagnetic metal; Setting ports: setting at least two ports on the channel, the ports comprising input ports and output ports.

8. The multi-port isolator design method of claim 7, wherein, Further comprising boundary modification: opening a second coupling hole for enhancing coupling on the boundary of the interlayer coupling layer of the axial insulator; the second coupling hole comprises rectangular holes arranged at equal intervals on two boundaries of the interlayer coupling layer and square holes arranged at four corners of the interlayer coupling layer.

9. The multi-port isolator design method of claim 7 or 8, wherein, The shaft sub-insulator is a cuboid or a square; the input port is arranged at a cuboid or square vertex away from the absorbing boundary on the channel; the output port is arranged at a cuboid or square vertex downstream of the input port and has at least two.

10. A multi-port isolator, characterized by, The multi-port isolator design method is designed by any one of claims 7 to 9; including an isolator body, an input port, an output port, an absorbing boundary, an ideal electric conductor boundary, and a channel for non-reciprocal energy transmission composed of non-coplanar chiral edges of the isolator body.

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