| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 107 === In this thesis, the two dimensional parity-time symmetric photonic crystal are used to construct topological edge state. Let dielectric materials of unit cell satisfy parity-time symmetric invariant to become parity time symmetric photonic crystals. However, from the analysis of band structure, when the imaginary part of electric permittivity is smaller than some critical value, it is a unbroken parity-time symmetric phase, and eigenvalues are all real. But, when the imaginary part of electric permittivity is greater than the critical value, it is a broken parity-time symmetric phase, and eigenvalues are imaginary conjugate pairs. The local frequency bands will merge into a flat band, and can learn about the position of exceptional points from band structure.
When band structure is a parity-time symmetric phase, it can adjust structure parameter of double Dirac cone in the band structure to find out appreciative trivial phase and topological phase structure with band inversion. However, let the trivial phase and topological phase structure of the two different topological properties to be combined to form the supercell structure, it can keep the genuine time-reversal symmetry by breaking the pseudo time-reversal symmetry, and realize the quantum spin Hall effect. Because the lattice structure of two different topological properties are combined together, it can lead to form the topological edge state. The topological edge state can propagate in the interface of the two different structures, and it can march in the orbit with obtuse and acute angle. Meanwhile, it possess ability to suppress the backscattering.
Keywords: parity-time symmetry, photonic crystals, Unbroken parity-time symmetric phase, Broken parity-time symmetric phase, quantum spin Hall effect, topological edge state
|
|---|
