Hybrid method of plane-wave and cylindrical-wave expansions for distributed Bragg-reflector pillars: formalism and its application to topological photonics

Abstract

A hybrid computational method of plane-wave and cylindrical-wave expansions for distributed Bragg-reflector (DBR) pillars is proposed. The plane-wave expansion is employed to represent the one-dimensional periodic structure of the DBR. The cylindrical-wave expansion is employed to describe the scattering by circular pillars with the DBR structure inside. This formalism enables us to calculate the radiation fields, $t$-matrices, scattering cross sections, photonic band structures, and quality factors of the DBR pillars. Furthermore, optical properties of arrayed DBR pillars are also investigated with the aid of the multiple-scattering method. Using this formalism, we demonstrate explicitly that high $Q$ photonic band modes including the so-called bound states in continuum are obtained both in isolated and arrayed DBR pillars. We also present a novel formation of gapless Dirac-cone surface states in a three-dimensional photonic crystal composed of a two-dimensional periodic arrangement of core-shell DBR pillars.

15 pages, 8 figures

References in corpus (7)

• Topological Photonics
• Topological Photonics
• Strongly Correlated Two-Photon Transport in One-Dimensional Waveguide Coupled to A Two-Level System
• Three-Dimensional All-Dielectric Photonic Topological Insulator
• Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity
• Gapless surface states originated from accidentally degenerate quadratic band touching in a three-dimensional tetragonal photonic crystal
• The Design for a Nanoscale Single-Photon Spin Splitter

Cited by in corpus (1)

• Crystallographic splitting theorem for band representations and fragile topological photonic crystals