Three-dimensional shaft insulator, multi-port isolator and design method thereof

Abstract

The invention provides a three-dimensional shaft insulator constructed based on gyromagnetic photonic crystals, which comprises A-layer photonic crystals, B-layer photonic crystals and interlayer coupling layers, the A-layer photonic crystals and the B-layer photonic crystals are alternately stacked, and the top layer and the bottom layer are the A-layer photonic crystals; the A-layer photonic crystal and the B-layer photonic crystal are formed by arranging gyromagnetic medium columns in a square lattice mode and have the same lattice constant, and the gyromagnetic medium columns in the B-layer photonic crystal and the A-layer photonic crystal are staggered by a half period in the x direction and the y direction; the magnetic fields applied to the gyromagnetic medium columns in the B-layer photonic crystal and the A-layer photonic crystal are equal and opposite in magnitude; and the interlayer coupling layer is provided with an AB interlayer coupling layer and a BA interlayer coupling layer with inversion symmetry. The three-dimensional shaft insulator has a non-coplanar chiral prism state and can realize non-reciprocal transmission of energy. Furthermore, the invention also provides a multi-port isolator and a design method thereof based on the three-dimensional shaft insulator, and the obtained multi-port isolator has the characteristics of high isolation degree and low loss in a microwave frequency band.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic wave technology, and in particular relates to the design of constructing a three-dimensional axion insulator and a multi-port isolator using gyromagnetic photonic crystals. Background Art

[0002] In recent years, the research on topological insulators has been continuously deepened, and the search for new topological quantum matter and topological phase transitions has always been the central theme of modern physics and materials science. Three-dimensional axion insulators represent a unique class of magnetic topological phases, which are quantum anomalous Hall effect insulators that combine two-dimensional and three-dimensional topological magnetic high-order phases. In axion insulators, axion electrodynamics exhibits novel topological magneto-electric phenomena such as quantized Faraday and Kerr rotations and half-integer surface Hall response.

[0003] The axion insulator is an exotic topological phase with zero Chern number but a finite topological Chern-Simons term, which is produced 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 behaves as an insulator in the body but conducts at the edges. The reversal of magnetization intensity will flip the energy flow direction of the boundary state energy. A three-dimensional axion insulator can be constructed by stacking Chern insulators with opposite magnetization intensity alternately and applying weak coupling between layers. The boundary state energy between adjacent layers with opposite magnetization intensity is oppositely annihilated, so that non-coplanar chiral edge state transmission can occur in the axion insulator with a finite odd number of layers, and its edge state transmission is topologically robust.

[0004] An isolator is a device designed based on a non-reciprocal system. There are three main ways to implement a non-reciprocal system, namely breaking time reversal symmetry, building a nonlinear system, and building an active time-varying modulation system. The most commonly used method is to break time reversal symmetry. The main way to break time reversal symmetry is to apply a magnetic field to the system to destroy the symmetry of the tensor of magnetic permeability or dielectric constant. The current mainstream microwave band isolators realize non-reciprocal transmission in a two-dimensional system. For example, the gyromagnetic material YIG is coupled with a microstrip line to achieve non-reciprocal transmission, or the defect state of a photonic crystal is combined with a gyromagnetic medium to achieve non-reciprocal transmission. However, these isolators currently lack topological robustness, and energy scattering and loss caused by body defects may occur during energy transmission. Summary of the invention

[0005] In order to solve the above problems, the present invention provides a three-dimensional axion insulator constructed using gyromagnetic photonic crystals, which has non-coplanar chiral edge states, thereby innovatively realizing a three-dimensional axion insulator with an antiferromagnetic structure in the magneto-optical photonic crystal system, enriching the regulation of non-reciprocal transmission of photons. Furthermore, the present invention also provides a multi-port isolator and a design method thereof based on the above three-dimensional axion insulator, and the designed multi-port isolator has the characteristics of high isolation and low loss in the microwave frequency band.

[0006] The first aspect of the present invention discloses an axion insulator constructed based on gyromagnetic photonic crystals, comprising alternately stacked A-layer photonic crystals and B-layer photonic crystals, and an interlayer coupling layer for interlayer coupling of photonic crystals, and the top and bottom layers of the axion insulator are both A-layer photonic crystals; the A-layer photonic crystals and the B-layer photonic crystals are both composed of gyromagnetic dielectric columns arranged in a square lattice form; the B-layer photonic crystals and the A-layer photonic crystals have the same lattice constant, and the gyromagnetic dielectric columns in the B-layer photonic crystals are staggered by half a period in the x-direction and the y-direction; the magnetic field applied to the gyromagnetic dielectric columns in the B-layer photonic crystals is equal to and opposite to the magnetic field applied to the gyromagnetic dielectric columns in the A-layer photonic crystals; the interlayer coupling layer includes an AB interlayer coupling layer and a BA interlayer coupling layer with inversion symmetry.

[0007] As an optional solution, the gyromagnetic medium column is made of ferrite material; the ferrite material includes 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 non-ferromagnetic metal; a magnet is embedded in the perforated metal plate, and the magnet completely overlaps with the projection of the gyromagnetic medium columns in the A layer photonic crystal and the B layer photonic crystal in the xy plane; 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 include special-shaped coupling holes located in the projection of the square lattice on the xy plane and circular coupling holes located at the four vertices of the projection of the square lattice on the xy plane; the special-shaped coupling holes are composed of T-shaped holes and semicircular holes that are interconnected and inclined at a preset angle, and the center of the circular coupling hole is located at the vertex.

[0012] As an optional scheme, the A-layer photonic crystal includes multiple A-layer square lattices, and the B-layer photonic crystal includes multiple B-layer square lattices; the interlayer coupling layer has multiple interlayer coupling units; the axion insulator includes multiple supercells arranged along the z direction, and the supercell is composed of elementary cells; the elementary cells include A-layer square lattices, AB interlayer coupling units, B-layer square lattices, and BA interlayer coupling units stacked from top to bottom.

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

[0014] An isolator body is provided: the isolator body is a three-dimensional axion insulator constructed using a gyromagnetic photonic crystal according to the first aspect of the present invention or any one of its optional solutions, and the three-dimensional axion insulator has a loop for non-reciprocal energy transmission composed of non-coplanar chiral edges; boundary conditions are set: an absorption boundary for blocking the loop is set on the surface of the isolator body, and an ideal semiconductor boundary is set on other surfaces of the isolator body except the absorption boundary, so as to obtain a channel for non-reciprocal energy transmission composed of non-coplanar chiral edges; the absorption boundary is made of absorbing material, and the perfect conductor boundary is made of non-ferromagnetic metal;

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

[0016] As an optional scheme, the multi-port isolator design method also includes boundary modification: opening a second coupling hole for enhancing coupling at the boundary of the interlayer coupling layer of the three-dimensional axion insulator; the second coupling hole includes rectangular holes arranged at equal intervals at two boundaries of the interlayer coupling layer and square holes arranged at four top corners of the interlayer coupling layer.

[0017] As an optional scheme, the three-dimensional axion insulator is a cuboid or a cube; the input port is arranged at the vertex of the cuboid or the cube away from the absorption boundary on the channel; the output port is arranged at the vertex of the cuboid or the cube downstream of the input port and there are at least two output ports.

[0018] The third aspect of the present invention discloses a multi-port isolator designed using the second aspect of the present invention or any one of its optional schemes; it includes an isolator body, an input port, an output port, an absorbing boundary, an ideal conductor boundary, and a channel for non-reciprocal energy transmission formed by non-coplanar chiral edges of the isolator body.

[0019] The isolator comprises an isolator body, an input port, an output port, an absorption boundary, an ideal electric conductor boundary, and a channel for non-reciprocal energy transmission formed by non-coplanar chiral edges of the isolator body.

[0020] Compared with the prior art, the present invention has the following significant advantages:

[0021] The present invention constructs a three-dimensional axion insulator similar to antiferromagnetic materials in electronic systems under the gyromagnetic photonic crystal system, realizing non-coplanar chiral edge states. Such non-coplanar chiral edge states are topologically non-trivial and can realize robust non-reciprocal transmission, which has guiding significance for the design of related optical integrated devices such as non-reciprocal devices.

[0022] Furthermore, the present invention provides a multi-port isolator based on the three-dimensional axion insulator. The isolator operates in the microwave frequency band and has multiple high-isolation ports, which can provide unidirectional transmission and reverse isolation for the connection of multiple devices at the same time. At the same time, the isolator is based on the topological non-trivial prism state of the axion insulator, and its energy transmission is robust, which makes it have broad application prospects, such as better stability under high noise conditions.

[0023] The present invention not only enriches the research on three-dimensional topological insulators, but also provides new ways and methods for regulating and applying topological edge states. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 : (a) is a schematic diagram of the arrangement of YIG dielectric columns in the A-layer photonic crystal, and the square box in the figure indicates the square lattice of the A-layer; (b) is a schematic diagram of the arrangement of YIG media in the B-layer photonic crystal, and the square box in the figure indicates the square lattice of the B-layer; (c) is a structural schematic diagram of the smallest repeating unit of the three-dimensional axion insulator, namely the primitive unit cell, and the direction of the arrow on the dielectric column indicates the direction of the magnetic field applied to the dielectric column; (d) is a structural schematic diagram of the interlayer copper plate unit.

[0025] The attached drawings are marked as follows: ① represents a YIG dielectric column; ② represents a perforated copper plate; ③ represents a circular magnet; red represents the N pole of the magnet; and blue represents the S pole of the magnet.

[0026] Figure 2 :(a) is a schematic diagram of the chiral edge state of the photon axion insulator, and the arrow line indicates the energy flow along the axis. (b) is the projected energy band of the axion insulator in the kx, ky, and kz directions. The green and blue dots in the figure correspond to Figure 2 (a) The edge state in the figure, the small black dots represent the projected body state and surface state.

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

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

[0029] The following is an explanation of the technical solution and specific implementation scheme of the present invention in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0030] The present invention constructs a three-dimensional axion insulator (abbreviated as "axion insulator") in a gyromagnetic photonic crystal, and realizes a microwave frequency band multi-port isolator (abbreviated as "multi-port isolator") based on the non-reciprocal edge state transmission characteristics of the axion insulator. In addition, the present invention also verifies the principle and results of the relevant performance of the axion insulator through numerical calculation and simulation.

[0031] The three-dimensional axion insulator has non-coplanar chiral edge state transmission characteristics, which is obtained based on the calculation of its projected energy bands in the kx, ky, and kz directions in momentum space, and the calculation of the projected energy bands is obtained by calculating the eigenstates of the supercell. The supercell includes an A-layer gyromagnetic photonic crystal (abbreviated as "A-layer photonic crystal"), an AB interlayer coupling layer, a B-layer gyromagnetic photonic crystal (abbreviated as "B-layer photonic crystal"), and a BA interlayer coupling layer arranged from top to bottom.

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

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

[0034] like Figure 3 As shown in (b), magnets are embedded in the interlayer copper plate. The embedded magnets correspond to the positions of the YIG medium columns in the A-layer photonic crystal and the B-layer photonic crystal respectively and have the same diameter, that is, the projections on the xy plane completely overlap. However, the magnetic fields of the magnets embedded in the A-layer photonic crystal and the magnets embedded in the B-layer photonic crystal are equal in magnitude and opposite in direction. The interlayer copper plate is also provided with coupling holes for interlayer coupling. The structure of the coupling holes can be found in the introduction of the copper plate unit section.

[0035] From the perspective of the xy plane, the supercell is composed of several elementary primitive cells. The elementary primitive cells can be regarded as composed of the A-layer square lattice, the AB interlayer coupling unit, the B-layer square lattice, and the BA interlayer coupling unit stacked from top to bottom. The A-layer square lattice of each layer together constitutes the A-layer photonic crystal, and the B-layer square lattice of each layer together constitutes the B-layer photonic crystal. The AB interlayer coupling units are connected to each other to form the AB interlayer coupling layer. Similarly, the BA layer coupling units are connected to each other to form the BA interlayer coupling layer.

[0036] like Figure 1 As shown in (c), each layer of the square lattice in the elementary primitive cell includes two 1 / 2YIG dielectric columns. In the two layers of the square lattice, the 1 / 2YIG dielectric columns are staggered, and the center of the projection of the four 1 / 2YIG dielectric columns on the xy plane coincides with the center point of the projection of the four sides of the square lattice on the xy plane. It can be seen that the B layer square lattice can be obtained by moving the YIG dielectric columns in the A layer square lattice by half a period in the x direction and the y direction respectively, that is, the YIG dielectric columns in the B layer photonic crystal are staggered by half a period in the x direction and the y direction with the YIG dielectric columns in the A layer photonic crystal. The period of the elementary primitive cell in the xy plane is a, and the period in the z direction is 2h = 10mm.

[0037] In this embodiment, both the AB interlayer coupling unit and the BA interlayer coupling unit are interlayer copper plate units embedded with magnets, referred to as "copper plate units". Figure 3 As shown in (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 inclined at 225°, that is, the angle between the center line of the T-shaped hole and the x-axis is 225°. The T-shaped hole can be formed by drawing a rectangle in the copper plate unit, the rectangle is 2m long and m wide, Draw an arc (1 / 4 circle) with a radius of r1 in the rectangle with two vertices in the length direction as the center. Keep the part of the rectangle that coincides with the arc and dig out the rest to get a T-shaped hole. The length of the rectangle is 2m and the width is m. Furthermore, a semicircular hole connected to the T-shaped hole is provided at the top, and the radius of the semicircular hole is r2. 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 called a special-shaped coupling hole. Figure 1 As shown in (d). On the four sides of the copper plate unit, 1 / 2 circular magnets with a radius of r are embedded in the positions corresponding to the 1 / 2YIG dielectric columns. The AB interlayer copper plate (unit) and the BA interlayer copper plate (unit) have inversion symmetry. Therefore, the AB interlayer copper plate (unit) is rotated 180° with the center of the primitive cell (unit center) as the axis to obtain the BA interlayer copper plate (unit). The special-shaped coupling holes of the BA interlayer copper plate (unit) are tilted 45°. Furthermore, a 1 / 4 circle with a radius of r2 can be dug out at the four vertices of the copper plate unit to enhance the coupling between layers.

[0038] Combination Figure 1 (d) and Figure 3 As shown in (b), from the xy plane, the perforated copper plate serving as the interlayer coupling layer includes a circular magnet (composed of 1 / 2 circular magnets with a radius of r) and a number of array-arranged special-shaped coupling holes and circular coupling holes. The circular magnet is located at the position corresponding to the YIG dielectric column, which is 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 holes in the perforated copper plate unit may also be in other structural forms, as long as they can satisfy that there is only an edge state within a certain microwave frequency band in the projected energy band.

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

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

[0042]

[0043] in, ω m =γM s ,ω0=γH0,

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

[0045] In order to simplify the calculation, the damping coefficient is set to 0 (α = 0). Without considering the dispersion, according to formula (1), μ r = ±0.71604, Then the gyromagnetic permeability of YIG is obtained Since the gyromagnetic permeability changes little near the operating frequency of the present invention, that is, the operating frequency is in the range of 11-11.5 GHz, the permeability can be approximately regarded as the permeability at an operating frequency of 11.2 GHz.

[0046] It should be noted that all numerical calculations in the present invention are implemented using the Electromagnetic Waves, Frequency Domain module in the finite element calculation software COMSOL. Before calculating the projected energy bands in the kx, ky, and kz directions, a supercell must be constructed. Figure 2 (b) is the projected energy band in the kx, ky, and kz directions calculated by the software. In the projected energy band diagram, the green and blue points correspond to Figure 2 (a) The edge states in the figure, the small black dots represent the projected bulk states and surface states. The projected energy band in the ky direction reflects the edge states transmitted along the y direction, that is, the edge states on edge C1 and edge C4; the projected energy band in the kx direction reflects the edge states transmitted along the x direction, that is, the edge states on edge C2 and edge C5; the projected energy band in the kz direction reflects the edge states transmitted along the z direction, that is, the edge states on edge C3 and edge C6. Moreover, the frequency range with only edge states in the band gap is 11 to 11.5 GHz.

[0047] Among them, when calculating the projected energy band in the kx direction, the supercell is constructed by arraying the primitive cells for 5 periods in the y direction and 7.5 periods in the z direction (that is, 15 layers in the z direction); the boundary of the yz plane is set as a periodic boundary, and the xy plane and xz plane are set as perfect conductor boundaries; scanning different kx calculations can obtain the projected energy band in the kx direction.

[0048] Similarly, when calculating the projected energy band in the ky direction, a supercell is constructed with an array of 5 periods in the x direction and 7.5 periods in the z direction; the boundary of the xz plane is set as a periodic boundary, and the xy plane and yz plane are set as ideal conductor boundaries; scanning different ky calculations can obtain the projected energy band in the ky direction.

[0049] Similarly, when calculating the projected energy band in the kz direction, a supercell is constructed with an array of 5 periods in the x direction and 5 periods in the y direction. The boundary of the xy plane is set as a periodic boundary, and the xz plane and yz plane are set as perfect conductor boundaries. Scanning different kz calculations can obtain the projected energy band in the kz direction.

[0050] Based on the above-mentioned axion insulator constructed under the gyromagnetic photonic crystal system, it has a full band gap, and there are non-coplanar chiral edge states within the band gap frequency range, that is, energy is only transmitted unidirectionally on a specific edge of the axion insulator to form a loop. According to the calculated projected energy band, we can obtain the transmission direction of the chiral edge state of the axion insulator model. The schematic diagram of the chiral edge state transmission is shown in Figure 2 (a), where edges C1-C6 are edges with chiral edges, edges T7-T12 are ordinary edges, and energy is transmitted unidirectionally along edges C1-C6 to form a loop. This completes the construction of the axion insulator model and the energy band calculation in the gyromagnetic photonic crystal system.

[0051] Furthermore, based on the non-coplanar chiral prism state of the axion insulator, a multi-port isolator in the microwave band is also constructed in the present invention. In another embodiment, the YIG dielectric column is arranged according to a square lattice, so that the A-layer square lattice constituting the primary unit cell is arrayed in 4 periods in the x direction and 3 periods in the y direction, forming a Figure 1 (a) shows the A-layer photonic crystal; the YIG medium columns are arranged in a square lattice, so that the B-layer square lattice constituting the primary unit cell is arrayed in 3 periods in the x direction and 4 periods in the y direction, forming a Figure 1 (b) The B-layer photonic crystal shown. In the z direction, the A-layer photonic crystal and the B-layer photonic crystal are alternately stacked in odd layers, and the top and bottom layers are both A layers. In this embodiment, the A-layer photonic crystal and the B-layer photonic crystal are alternately stacked in 7 layers, and equal and opposite magnetic fields are applied to the A-layer photonic crystal and the B-layer photonic crystal. The A-layer photonic crystal and the B-layer photonic crystal are separated by a perforated copper plate embedded with a magnet. The copper plate between the AB layers is as shown in FIG. Figure 3 (b) shows a square perforated copper plate with a side length of L = 57.5 mm and an embedded magnet, where circles of different colors represent different magnetic poles of the magnet, with light colors representing N poles and dark colors representing S poles. This completes the construction of the isolator body.

[0052] Furthermore, in order to enhance the coupling between layers and the energy transmission in the z direction, the boundary of the square perforated copper plate can be modified to improve the efficiency of energy transmission along the edge state. Figure 3 As shown in (b), the modification method provided in this embodiment is: a rectangular coupling hole with a length of 4.4r and a width of r is dug out at each distance of the lattice constant a between the left boundary and the upper boundary; then a square coupling hole with a side length of 1.5r is dug out at each of the four corners of the square perforated copper plate, and the coupling holes inside the perforated copper plate are Figure 1 The same setting is used in (d). The AB interlayer copper plate (also known as the AB interlayer coupling layer) is rotated 180° along the center to obtain the BA interlayer copper plate (also known as the BA interlayer coupling layer).

[0053] After the boundary modification is completed, the boundary conditions are set. Since the transmission of non-coplanar chiral edge states is a loop, in this embodiment, an absorption boundary is set on the surface where the edges C1 and C6 are located. The purpose is 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 the edges C2-C5, and a loop cannot be formed. In the actual isolator construction, the effect of the absorption boundary can be achieved by placing absorbing materials on the surface where the edges C1 and C6 are located. The remaining surfaces outside the absorption boundary are set as ideal conductor boundaries to achieve energy transmission along the edges. In the construction of the actual isolator, the ideal conductor boundary can be achieved by placing a metal plate made of non-ferromagnetic metals such as copper plates and aluminum plates on the surface.

[0054] It is understandable that in other embodiments, other surfaces may be selected to set the absorption boundary, for example, the surface where the edge C3 and the edge C4 are located, as long as the backflow of the energy can be blocked to form a loop. Preferably, after setting the absorption boundary, the two edges C3 and C6 in the z direction with high isolation are not affected by the absorption boundary as much as possible.

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

[0056] according to Figure 2 (a) shows the prismatic propagation path. In this embodiment, one corner of the top surface of the cube is selected as a port, and three corners of the bottom surface are selected as the other three ports. Specifically, one input port and three output ports can be set. Figure 3 As shown in (a), port 1 is the energy input port, and ports 2-4 are all energy output ports. The energy transmission direction is along the edges C3-C5. The yz plane where port 4 is located is set as an absorption boundary to prevent the energy from returning to port 1 to form a loop. The remaining planes are all ideal electrical conductor boundaries, thus forming a four-port microwave frequency band isolator with high isolation.

[0057] according to Figure 2 According to the calculation of the projected energy band in (b), the frequency range of chiral edge state transmission in the band gap is 11 to 11.5 GHz. Therefore, the operating frequency of the isolator is 11 to 11.5 GHz.

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

[0059] The present invention utilizes the design of antiferromagnetic gyromagnetic photonic crystals, that is, stacking two square lattices with opposite magnetic fields and staggered arrangements, to successfully realize the construction of a three-dimensional axion insulator in a photonic crystal system. The present invention calculates the band structure of the axion insulator and confirms that the constructed three-dimensional axion insulator has a non-reciprocal transmission loop with non-coplanar chiral edge states. Furthermore, based on the properties of topological non-trivial edge state non-reciprocal transmission of three-dimensional axion insulators, the present invention also proposes a multi-port isolator with robustness and high isolation in the microwave band. It can be seen that the present invention not only innovatively realizes the axion insulator in the magneto-optical photonic crystal system, but also designs a multi-port, high-isolation isolator using the non-coplanar edge state transmission of the axion insulator. Therefore, the present invention has guiding significance for the design of related optical integrated devices such as non-reciprocal devices.

[0060] Finally, it should be noted that although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and instructive, rather than restrictive. Under the guidance of this specification, a person of ordinary skill in the art can also make many forms without departing from the scope of protection of the claims of the present invention, all of which belong to the scope of protection of the present invention.

Claims

1. An axion insulator constructed based on gyromagnetic photonic crystal, characterized in that: It includes alternately stacked A-layer photonic crystals and B-layer photonic crystals, and an interlayer coupling layer for interlayer coupling of the photonic crystals, and the top layer and the bottom layer of the axion insulator are both A-layer photonic crystals; The A-layer photonic crystal and the B-layer photonic crystal are both formed by gyromagnetic dielectric columns arranged in a square lattice form; the B-layer photonic crystal and the A-layer photonic crystal have the same lattice constant, and the gyromagnetic dielectric columns in the B-layer photonic crystal and the gyromagnetic dielectric 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 equal to and opposite to the magnetic field applied to the gyromagnetic medium column in the A-layer photonic crystal; The interlayer coupling layers include an AB interlayer coupling layer and a BA interlayer coupling layer having inversion symmetry.

2. The axion insulator according to claim 1, characterized in that The gyromagnetic medium column is made of ferrite material; the ferrite material includes spinel ferrite, garnet ferrite and magnetoplumbite ferrite.

3. The axion insulator according to claim 2, characterized in that: The gyromagnetic medium column is a yttrium iron garnet ferrite medium column.

4. The axion insulator according to claim 1, characterized in that: The interlayer coupling layer is a perforated metal plate made of non-ferromagnetic metal; a magnet is embedded in the perforated metal plate, and the projection of the magnet on the xy plane completely overlaps with the gyromagnetic medium columns in the A-layer photonic crystal and the B-layer photonic crystal; the perforated metal plate is also provided with coupling holes arranged corresponding to the square lattice.

5. The axion insulator according to claim 4, characterized in that: The coupling holes include special-shaped coupling holes located in the projection of the square lattice on the xy plane and circular coupling holes located at the four vertices of the projection of the square lattice on the xy plane; the special-shaped coupling holes are composed of T-shaped holes and semicircular holes that are interconnected and inclined at a preset angle, and the center of the circular coupling hole is located at the vertex.

6. The axion insulator according to any one of claims 1 to 5, characterized in that: The A-layer photonic crystal includes a plurality of A-layer square lattices, and the B-layer photonic crystal includes a plurality of B-layer square lattices; the interlayer coupling layer has a plurality of interlayer coupling units; The axion insulator comprises a plurality of super-primitive cells arranged along the z direction, wherein the super-primitive cells are composed of primary primitive cells; The primary primitive cell includes an A-layer square lattice, an AB interlayer coupling unit, a B-layer square lattice, and a BA interlayer coupling unit which are stacked from top to bottom.

7. A multi-port isolator design method, characterized in that: The steps include: An isolator body is provided: the isolator body is a three-dimensional axion insulator constructed using a gyromagnetic photonic crystal according to any one of claims 1 to 6, the three-dimensional axion insulator having a loop for non-reciprocal energy transmission composed of non-coplanar chiral edges; Boundary condition setting: setting an absorption boundary for blocking the loop on the surface of the isolator body, and setting an ideal semiconductor boundary on other surfaces of the isolator body except the absorption boundary, so as to obtain a channel for non-reciprocal energy transmission composed of non-coplanar chiral edges; the absorption boundary is made of absorbing material, and the perfect electrical conductor boundary is made of non-ferromagnetic metal; Port setting: at least two ports are set on the channel, and the ports include an input port and an output port.

8. The multi-port isolator design method according to claim 7, characterized in that: It also includes boundary modification: a second coupling hole for enhancing coupling is opened at the boundary of the interlayer coupling layer of the three-dimensional axion insulator; the second coupling hole includes rectangular holes arranged at equal intervals at two boundaries of the interlayer coupling layer and square holes arranged at four top corners of the interlayer coupling layer.

9. The multi-port isolator design method according to claim 7 or 8, characterized in that: The three-dimensional axion insulator is a cuboid or a cube; the input port is arranged at the vertex of the cuboid or the cube away from the absorption boundary on the channel; the output port is arranged at the vertex of the cuboid or the cube downstream of the input port and there are at least two output ports.

10. A multi-port isolator, characterized in that: The multi-port isolator is designed by the multi-port isolator design method described in any one of claims 7 to 9; it includes an isolator body, an input port, an output port, an absorbing boundary, an ideal electrical conductor boundary, and a channel for non-reciprocal energy transmission formed by non-coplanar chiral edges of the isolator body.

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