Method for realizing topological boundary state switching by using gyromagnetic photonic crystal

Abstract

The invention discloses a method for realizing topological boundary state switching by using a gyromagnetic photonic crystal. The method comprises the following steps: (1) obtaining a gyromagnetic photonic crystal formed by arranging cylindrical gyromagnetic columns, adjusting the radius of the gyromagnetic columns and an applied external magnetic field to obtain inversion of Mie resonance, realizing topological phase change, and obtaining three different topological phases; (2) on the basis of the three different topological phases obtained in the step (1), two gyromagnetic photonic crystals with different topological characteristics are spliced to obtain a heterogeneous photonic structure, and a one-way transmission chiral boundary state exists at a heterogeneous interface; and (3) for the heterogeneous photon structure, multiple Mie resonance inversion is adjusted through a magnetic field regulation and control method, and switching control of a topological boundary state is realized. According to the invention, a switchable topology boundary state is realized in the gyromagnetic photonic crystal, and a new idea and guiding significance are provided for design and application of a topology photonic device.

Description

Technical Field

[0001] The present invention relates to the technical field of topological photonic crystals, and in particular to a method for realizing topological boundary state switching by utilizing multiple Mie resonance inversion of gyromagnetic photonic crystals. Background Art

[0002] In recent decades, topological photonics has become a rapidly developing research field, providing a new strategy for the manipulation of electromagnetic waves in photonic devices. Through the study of gyromagnetic photonic crystals, researchers have found that by applying a magnetic field, chiral boundary states with backscattering suppression effects can be achieved, which have good robustness. This opens up new possibilities for the development of topologically protected optical transmission devices.

[0003] In the field of topological photonics, early studies focused on the properties of s-orbital energy bands. Subsequently, researchers introduced the concept of orbital freedom into energy band topology and conducted in-depth studies, achieving a wealth of physical effects, such as p-orbital high-order topological insulators and quadrupole topological insulators based on sp-orbital synthetic flux. In photonic crystal systems, the units that make up photonic crystals, namely artificial atoms, have Mie resonance modes that are highly similar to atomic orbitals. Incorporating orbital freedom into the study of topological photonic crystals has great potential for enriching energy band control strategies and promoting the development of new topological phases. Previous studies on the use of Mie resonance to control photonic crystal bands have almost all focused on time-reversal invariant systems. However, for optical systems with broken time-reversal symmetry, the topological phase transition caused by the manipulation of localized Mie resonance modes has not yet been fully revealed. Summary of the invention

[0004] The purpose of the present invention is to provide a method for realizing topological boundary state switching by utilizing multiple Mie resonance inversion of gyromagnetic photonic crystals. This method not only expands the research on Mie resonance mode manipulation in time reversal symmetry breaking systems (including magnetic systems), but also realizes the switching of chiral boundary states.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for realizing topological boundary state switching using gyromagnetic photonic crystals comprises the following steps:

[0007] (1) obtaining a gyromagnetic photonic crystal composed of cylindrical gyromagnetic columns, adjusting the radius of the gyromagnetic columns and the applied external magnetic field to obtain the reversal of the Mie resonance, realize the topological phase transition, and obtain three different topological phases;

[0008] (2) Based on the three different topological phases obtained in step (1), two of the gyromagnetic photonic crystals with different topological properties are spliced ​​to obtain a heterogeneous photonic structure, and a chiral boundary state with unidirectional transmission is present at the heterogeneous interface;

[0009] (3) For the heterogeneous photonic structure, multiple Mie resonance inversions are regulated by a magnetic field control method to achieve switching control of the topological boundary state.

[0010] The present invention explores the multiple Mie resonance inversion based on the "atoms" of two-dimensional gyromagnetic photonic crystals to realize the topological phase transition in the photonic Chern insulator. The present invention realizes the switchable topological boundary state in the gyromagnetic photonic crystal system by constructing a heterogeneous photonic structure composed of photonic crystals with different topological phases. The research results of the present invention provide a flexible method for the reconfigurable control of chiral boundary states based on the Mie resonance degree of freedom, and provide new ideas and guiding significance for the design and application of topological photonic devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 The basic structure of the two-dimensional gyromagnetic photonic crystal in the embodiment of the present invention is as follows: (a) A two-dimensional gyromagnetic photonic crystal with YIG as the basic unit structure arranged in a square lattice; the lattice constant of the structure is a=10mm, and the diameter of the YIG is d; the external magnetic field is along the +z direction. (b) The body energy bands corresponding to the structure when the external magnetic field H=2200Gauss and the geometric parameters d / a=0.32, 0.42, and 0.49; the Chern number of each energy band is marked in the figure, as well as the Mie resonance mode at the high symmetry point Γ of the second, third, and fourth energy bands; the band gap between the second and third energy bands is marked as gap1; the band gap between the third and fourth energy bands is marked as gap2. (c) Mie resonance s, p at the high symmetry point Γ - and p + Corresponding to E on a single YIG column z Mode distribution.

[0012] Figure 2 The evolution of the eigenfrequency at point Γ when adjusting the geometric parameters and external magnetic field of the photonic crystal in the embodiment of the present invention: (a) When there is no external magnetic field, the evolution of the eigenfrequency at point Γ with the geometric parameter d / a. (b) When the geometric parameter d / a = 0.44, the evolution of the eigenfrequency at point Γ with the external magnetic field. (c) The phase diagram corresponding to the photonic crystal structure; the figure marks the regions corresponding to three different topologies, which are marked as topological phase I, topological phase II, and topological phase III.

[0013] Figure 3 The projected energy bands of the two-dimensional gyromagnetic photonic crystal supercell in the embodiment of the present invention are as follows: (a) The projected energy bands of the supercell constructed by the topological phase I (d / a = 0.32, H = 2200 Gauss), the supercell has 8 periods in the y direction and the x direction is a periodic boundary condition. (b) The boundary states at 1, 2, 3 and 4 in Figure (a) correspond to E zMode distribution and energy flow distribution. (c) Projected energy band of the supercell constructed by topological phase II (d / a = 0.42, H = 2200 Gauss). (d) The E corresponding to the boundary states at 1 and 2 in Figure (c). Z Mode distribution and energy flow distribution.

[0014] Figure 4 1 and 2 show the transmission spectrum and mode field distribution of microwave transmission of the heterogeneous photonic structure under point source excitation in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The following is a further explanation of the technical solution of the present invention in conjunction with the accompanying drawings, but 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.

[0016] The present invention provides a method for realizing topological boundary state switching by using multiple Mie resonance inversion of gyromagnetic photonic crystal, which specifically comprises the following steps:

[0017] (1) A gyromagnetic photonic crystal composed of cylindrical gyromagnetic columns is obtained. By adjusting the radius of the gyromagnetic columns in the photonic crystal and the applied external magnetic field, the Mie resonance can be reversed, a topological phase transition can be achieved, and three different topological phases can be exhibited. The corresponding boundary states can be observed in the band gap of the photonic crystal body energy band.

[0018] (2) Based on the three different topological phases obtained in step (1), two of the gyromagnetic photonic crystals with different topological properties are spliced ​​to form a heterogeneous photonic structure, and a chiral boundary state with unidirectional transmission is present at the heterogeneous interface;

[0019] (3) Based on the heterogeneous photonic structure of step (2), the multiple Mie resonance inversion can be regulated by magnetic field control method to achieve switching control of topological boundary states.

[0020] In step (1), the gyromagnetic photonic crystal is composed of cylindrical gyromagnetic columns arranged in air, the dielectric constant of the air is ε0=1; the dielectric constant of the gyromagnetic columns is ε=13ε0.

[0021] like Figure 1 As shown in (a), the present invention provides a square lattice gyromagnetic photonic crystal structure composed of yttrium iron garnet ferrite (YIG) columns. The distance between the centers of adjacent square cells is the lattice constant a=10mm, and the diameter of the YIG column is d. When there is no external magnetic field, the relative permeability of YIG is μ=1. When an external magnetic field of magnitude H is applied along the +z direction, the gyromagnetic permeability of YIG is as follows:

[0022]

[0023] in ω m =γM s ,ω0=γH. Among them, γ=1.76×10 11 s -1 T -1 is the gyromagnetic ratio, M s =1780Gauss is the saturation magnetization, ω is the operating frequency, and H is the external magnetic field strength. All numerical calculations in the present invention use the Electromagnetic Waves, Frequency Domain module in the finite element calculation software COMSOL. The ratio of the diameter of the column to the lattice constant is set to 0.32, and an external magnetic field with an intensity of 2200Gauss is applied to it along the z direction. Figure 1 (b) shows the band structure of the unit cell, and the bands are separated from each other. Using the band gap Chern number to characterize the topological properties of the band gap, it can be found that there are non-trivial band gaps between the second and third and third and fourth bands, marked as gap1 and gap2, and the corresponding band gap Chern numbers are 1 and -1 respectively. z Field distribution, from low frequency to high frequency corresponds to s, p - and p + Three Mie resonance modes. Here p - and p + is a degenerate p x and p y The result of the mode splitting under the influence of a magnetic field.

[0024] The present invention found that by continuously adjusting the geometric parameters and external magnetic field in the two-dimensional gyromagnetic photonic crystal, the photonic crystal presents three different topological phases. Specifically, by increasing the ratio of the column diameter to the lattice constant, the band gap between the second and third energy bands will close, forming a Dirac cone at the Γ point. By continuing to increase the column diameter, the band gap will reopen. From the band structure, it can be found that the second and third energy bands have s and p at the Γ point. - The reversal of the mode. Further increasing the column diameter, the s and p bands also occur between the third and fourth energy bands. + The corresponding band gap Chern numbers of gap1 and gap2 change from 1, -1 to 0, -1 and then to 0, 0, showing three different topological phases. Figure 1 (c) is the Mie resonance s at the high symmetry point Γ, p - and p + Corresponding to E on a single YIG column z Mode distribution.

[0025] Figure 2 The evolution of the eigenfrequency at point Γ when the geometric parameters and the external magnetic field are continuously adjusted. Figure 2As shown in (a), when no external magnetic field is applied, that is, when the time reversal symmetry is not broken, p x and p y The mode is degenerate. Around d / a = 0.4, the s and p modes are reversed, but since the magnetic field is 0, there is no band gap between the s and p energy bands. Figure 2 As shown in (b), if d / a is kept constant and only the external magnetic field is adjusted, s and p occur successively at the Γ point. - Mode and s and p + The reversal between modes indicates that the system has undergone two topological phase transitions. By adjusting the two parameters d / a and magnetic field strength at the same time, Figure 2 (c) gives a more intuitive phase diagram. Each point on the dotted line represents the Dirac cone at the Γ point. The Dirac cone between topological phase I and topological phase II is s and p - The Dirac cone between topological phase II and topological phase III is formed by accidental degeneration of s and p + It is formed by accidental degeneration.

[0026] Figure 3 is the projected energy band of the two-dimensional gyromagnetic photonic crystal supercell. Construct a supercell with 8 cells along the y direction and periodic boundary conditions along the x direction. In order to avoid leakage of boundary states, the upper and lower boundaries are set as PEC boundaries. When d / a = 0.32, H = 2200 Gauss, that is, the photonic crystal belongs to topological phase I, such as Figure 3 As shown in (a) in the figure, there are boundary states in both gap1 and gap2. Figure 3 (b) is the E corresponding to the edge states at 1, 2, 3 and 4 z Field distribution and energy flow distribution, the edge state in gap1 transmits unidirectionally to the right at the upper boundary and unidirectionally to the left at the lower boundary, while the edge state in gap2 presents a chirality completely opposite to gap1. The electric field distribution also shows that the edge state is well localized at the upper and lower boundaries, and decays exponentially toward the bulk region. When d / a=0.42, H=2200Gauss, that is, when the photonic crystal belongs to topological phase II, there are chiral edge states only in gap2, and there are no edge states in gap1, which is a mediocre band gap. These results are consistent with the previously calculated band gap Chern number.

[0027] like Figure 4As shown, this embodiment constructs a heterostructure formed by splicing photonic crystals with different topological phases, and studies the transmission behavior of the boundary state at the heterogeneous interface under point source excitation. The structure is composed of two photonic crystals with different topological phases, with a gap of 6 mm in the middle; the point source is placed at the heterogeneous interface; all four boundaries are set as scattering boundary conditions. The simulated transmission spectrum shows that within the frequency range of gap2, there are boundary states with unidirectional transmission to the right at the interface of topological phase II and topological phase III, which is consistent with the difference of their band gap Chern numbers being 1. The band gap Chern numbers of topological phase I and topological phase II are topologically equivalent, both of which are -1, so there are no boundary states at their interfaces. Based on this result, the present invention proposes a method for manipulating the topological properties of photonic crystals by using the multiple Mie resonance inversion of gyromagnetic photonic crystals to realize topological boundary state switching, which has potential application value in the design of photonic crystal devices.

Claims

1. A method for realizing topological boundary state switching using gyromagnetic photonic crystals, characterized in that: The method comprises the following steps: (1) obtaining a gyromagnetic photonic crystal composed of cylindrical gyromagnetic columns, adjusting the radius of the gyromagnetic columns and the applied external magnetic field to obtain the reversal of the Mie resonance, realize the topological phase transition, and obtain three different topological phases; (2) Based on the three different topological phases obtained in step (1), two of the gyromagnetic photonic crystals with different topological properties are spliced ​​to obtain a heterogeneous photonic structure, and a chiral boundary state with unidirectional transmission is present at the heterogeneous interface; (3) For the heterogeneous photonic structure, multiple Mie resonance inversions are regulated by a magnetic field control method to achieve switching control of the topological boundary state.

2. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 1, characterized in that: In step (1), the gyromagnetic photonic crystal is yttrium iron garnet ferrite.

3. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 2, characterized in that: When there is no external magnetic field, the relative magnetic permeability of the gyromagnetic photonic crystal is μ=1. When an external magnetic field of magnitude H is applied along the +z direction, the gyromagnetic permeability of the gyromagnetic photonic crystal is as follows: in ω m =γM s ,ω0=γH; where γ=1.76×10 11 s -1 T -1 is the gyromagnetic ratio, M s =1780Gauss is the saturation magnetization intensity, ω is the operating frequency, and H is the external magnetic field intensity.

4. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 1, characterized in that: In step (1), the gyromagnetic photonic crystal has a square lattice.

5. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 1, characterized in that: In step (1), the gyromagnetic poles are arranged in air, and the dielectric constant of the air is ε0=1; the dielectric constant of the gyromagnetic poles is ε=13ε0.

6. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 1, characterized in that: In step (1), the distance between two adjacent gyromagnetic columns is lattice constant a=10 mm.

7. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 1, characterized in that: In step (2), the distance between the two gyromagnetic photonic crystals with different topological properties is b=6 mm.

8. The method for realizing topological boundary state switching using gyromagnetic photonic crystals according to claim 1, characterized in that: In step (3), a point source is placed at the heterointerface.

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