A non-hermitian topological photonic crystal functional waveguide

Abstract

The application provides a non-Hermite topological photonic crystal functional waveguide which is composed of two non-Hermite Kagome photonic crystals containing gain-loss medium columns inside and outside, and comprises an external topological trivial non-Hermite Kagome photonic crystal (1) and an internal topological non-trivial triangular non-Hermite Kagome photonic crystal (2). Based on a high-order topological insulator model of the non-Hermite Kagome photonic crystal, the non-Hermite topological photonic crystal functional waveguide is constructed, perfect spatial selection of a topological corner state is realized, and the non-Hermite topological photonic crystal functional waveguide can be applied to the fields of topological optical storage and optical calculation.

Description

Technical Field

[0001] This invention belongs to the field of photonic crystal integrated waveguide technology, specifically relating to a non-Hermitian topological photonic crystal functional waveguide. Background Technology

[0002] In the past decade, topological insulators have become a hot topic in scientific research both domestically and internationally, and have been extensively studied in condensed matter physics and other extended systems due to their strong robustness and anti-backscattering ability. In particular, the topological angular states in higher-order topological insulators of photonic crystals are protected by time-reversal or space-reversal symmetry, which can be used to develop micro- and nano-lasers with ultra-small mode volume, high quality factor, and low threshold, as exemplified by the patent application "A novel topological photonic crystal structure and a method for fabricating optical waveguides (CN202011436792.9)".

[0003] In recent years, the combination of non-Hermitian physics and topological physics has opened up a new direction: "non-Hermitian topological physics." Non-Hermitian topological physics is dedicated to exploring the influence of the presence of non-Hermitianness on the topological state of a system. Taking photonic crystal topological insulators as an example, studies have shown that the presence of non-Hermitianness can change or even completely destroy the original topological body edge and body angle correspondence of the system. In 2019, ZW Zhang et al. proposed a non-Hermitian photonic crystal model based on a two-dimensional cubic lattice. Their research found that when different spatiotemporal inversion symmetry settings are used, the topological angular states simultaneously excited at the four corners of the two-dimensional cubic lattice photonic crystal will be replaced by complex conjugate diagonal states or pseudo-hinge angular states (Phys. Rev. Lett. 122(19), 195501(2019)). This lays the foundation for the development of novel non-Hermitian topological photonic crystal functional waveguides.

[0004] Research on non-Hermitian topological photonic crystal functional waveguides is still in its early stages compared to conventional topological photonic crystal functional waveguides, requiring extensive further investigation. In the work of ZW Zhang et al., although the introduction of non-Hermitianness disrupts the symmetry distribution of topological angular states, these angular states still spatially overlap, meaning perfect spatial selectivity is not achieved. Developing a non-Hermitian topological photonic crystal functional waveguide with perfect spatial selectivity holds promise for significant applications in topological optical storage and optical computing. Summary of the Invention

[0005] The purpose of this invention is to provide a non-Hermitian topological photonic crystal functional waveguide that enables perfect spatial selection of topological angle states.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A non-Hermitian topological photonic crystal functional waveguide is composed of two non-Hermitian Kagome photonic crystals containing gain-loss dielectric pillars, including an outer topologically trivial non-Hermitian Kagome photonic crystal and an inner topologically non-trivial triangular non-Hermitian Kagome photonic crystal.

[0008] Furthermore, the cell of the photonic crystal contains three pairs of dimer dielectric pillars, including three dark-colored gain dielectric pillars and three light-colored loss dielectric pillars. The gain and loss materials are based on single-crystal silicon or gallium arsenide doped with gain coefficients γ and loss coefficients -γ, respectively. The gain and loss dielectric pillars are mirror-symmetrical along the vertical direction.

[0009] Furthermore, the lattice constant of the Kagome photonic crystal is a, the radius of the dielectric pillars is r = a / 12, the distance between the dimer dielectric pillars is m = 0.2a, and the initial distance from the dimer center to the lattice center is b = 0.5a. The externally topologically trivial non-Hermitian Kagome photonic crystal (1) and the internally topologically non-trivial triangular non-Hermitian Kagome photonic crystal are multiplied by scaling factors t1 and t2, respectively, where 0.6 <t1<1,1<t2<1.4。

[0010] Compared with the prior art, the significant advantage of this invention is that the non-Hermitian topological photonic crystal functional waveguide proposed in this invention can achieve perfect spatial selection of topological angle states. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the non-Hermitian topological photonic crystal functional waveguide structure of the present invention.

[0012] Figure 2 This is a diagram of the band structure and high-symmetry point intrinsic mode of the non-Hermitian Kagome photonic crystal of the present invention.

[0013] Figure 3 This is a diagram of the topological characteristic frequencies and topological angle modes of the non-Hermitian Kagome photonic crystal of this invention. Detailed Implementation

[0014] This invention is based on a novel non-Hermitian Kagome photonic crystal, which achieves perfect spatial selection of two angular states (Type I and Type II) by introducing symmetrical gain loss.

[0015] like Figure 1 As shown, this invention discloses a novel complex non-Hermitian Kagome photonic crystal, comprising: Figure 1 (a) The topologically nontrivial 1-region and the topologically trivial 2-region constitute a two-dimensional photonic crystal supercell. A single primitive cell is as follows: Figure 1 (b) and Figure 1As shown in (c), a spacetime inversion-symmetric system is constructed using three dimer pillars embedded in an air background, comprising three dark-colored gain dielectric pillars and three light-colored loss dielectric pillars. The gain and loss materials are based on single-crystal silicon or gallium arsenide doped with gain and loss coefficients of γ and -γ, respectively. The gain and loss dielectric pillars are mirror-symmetric along the perpendicular direction. The lattice constant of the Kagome photonic crystal is a, the radius of the dielectric pillars is r, and the distance between the dimer dielectric pillars is m. The initial distance from the dimer center to the lattice center is b. The external topologically trivial non-Hermitian Kagome photonic crystal and the internal topologically non-trivial triangular non-Hermitian Kagome photonic crystal are multiplied by scaling factors t1 and t2, respectively. This study is based on TM polarization.

[0016] Example 1

[0017] With t1 = 0.7 and t2 = 1.3, the gain and loss material is based on single-crystal silicon doped with dielectric constant ε = 12 ± γi, γ = 0.1. The lattice constant of the Kagome photonic crystal is a = 0.69 μm, the radius of the dielectric pillars is r = a / 12, and the distance between the dimer pillars is m = 0.2a.

[0018] Example 2

[0019] With t1 = 0.75 and t2 = 1.25, the gain and loss material is based on doped single-crystal silicon, and its dielectric constant can be expressed as ε = 12 ± γi, γ = 0.15. The lattice constant of the Kagome photonic crystal is a = 0.81 μm, the radius of the dielectric pillars is r = a / 12, and the distance between the dimer pillars is m = 0.2a.

[0020] Example 3

[0021] With t1 = 0.8 and t2 = 1.2, the gain and loss material is based on gallium arsenide doping, and its dielectric constant can be expressed as ε = 11.4 ± γi, γ = 0.05. The lattice constant of the Kagome photonic crystal is a = 0.73 μm, the radius of the dielectric pillars is r = a / 12, and the distance between the dimer pillars is m = 0.2a.

[0022] The effectiveness of this invention can be further illustrated and verified by the following simulation results:

[0023] Taking the model in Example 1 as an example, the band structure of the non-Hermitian Kagome photonic crystal in this invention was obtained through simulation calculations. Figure 2 (c) and Figure 2 As shown in (d), the topologically nontrivial photonic crystal (t1 = 1.3) and the topologically trivial photonic crystal (t2 = 0.7) in this invention are relative to... Figure 2In the unscaled case shown in (a), the first and second bands are open and have the same band structure, but have eigenmodes with opposite charge distributions at the high symmetry point K, such as... Figure 2 As shown in (b).

[0024] Further calculations yielded the characteristic frequency map of the non-Hermitian Kagome photonic crystal supercell, such as... Figure 3 As shown. From Figure 3 As can be seen in (a), two modes of angular states (type I and type II) can be found in the supercell bandgap of the non-Hermitian Kagome photonic crystal in this invention. The degeneracy of these two angular states is broken, and they are distributed at the three vertices of the internal topologically nontrivial triangular non-Hermitian Kagome photonic crystal, achieving perfect spatial selection.

[0025] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A non-Hermite topological photonic crystal functional waveguide, characterized by, It is composed of two non-Hermite Kagome photonic crystals containing gain-loss medium columns inside and outside, including an outer topologically trivial non-Hermite Kagome photonic crystal (1) and an inner topologically non-trivial triangular non-Hermite Kagome photonic crystal (2); The cell of the photonic crystal contains three pairs of dimer medium columns, including three gain medium columns and three loss medium columns, the gain-loss material is doped based on monocrystalline silicon or gallium arsenide, the gain coefficient and the loss coefficient are γ and-γ respectively, and the gain medium column and the loss medium column constitute a mirror symmetry along the vertical direction; The lattice constant of the Kagome photonic crystal (1) is a, the radius of the dimer medium column is r=a / 12, the distance between the dimer medium columns is m=0.2a, the initial distance from the center of the dimer medium column to the center of the lattice is b=0.5a, and the distance from the dimer medium column of the outer topologically trivial non-Hermite Kagome photonic crystal (1) and the inner topologically non-trivial triangular non-Hermite Kagome photonic crystal (2) to the center of the lattice is equal to the initial distance multiplied by the scaling coefficient t1 and t2 respectively, where 0.6<t1<1 and 1<t2<1.

4.

2. The non-Hermite topological photonic crystal functional waveguide according to claim 1, wherein, Set t1=0.7, t2=1.3, the gain-loss material is doped based on monocrystalline silicon, the dielectric constant is represented as ε=12±γi, γ=0.1, the lattice constant of the Kagome photonic crystal is a=0.69μm, the radius of the dimer medium column is r=a / 12, and the distance between the dimer medium columns is m=0.2a.

3. The non-Hermite topological photonic crystal functional waveguide according to claim 1, wherein, Set t1=0.75, t2=1.25, the gain-loss material is doped based on monocrystalline silicon, the dielectric constant is represented as ε=12±γi, γ=0.15, the lattice constant of the Kagome photonic crystal is a=0.81μm, the radius of the dimer medium column is r=a / 12, and the distance between the dimer medium columns is m=0.2a.

4. The non-Hermite topological photonic crystal functional waveguide according to claim 1, wherein, Set t1=0.8, t2=1.2, the gain-loss material is doped based on gallium arsenide, the dielectric constant is represented as ε=11.4±γi, γ=0.05, the lattice constant of the Kagome photonic crystal is a=0.73μm, the radius of the dimer medium column is r=a / 12, and the distance between the dimer medium columns is m=0.2a.

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