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

TL;DR

This paper introduces a hybrid computational method combining plane-wave and cylindrical-wave expansions to analyze distributed Bragg-reflector pillars, enabling detailed study of their optical properties and topological photonic states.

Contribution

The paper develops a novel formalism integrating plane-wave and cylindrical-wave expansions for DBR pillars, facilitating accurate calculations of their optical and topological properties.

Findings

High Q photonic band modes including bound states in continuum identified.

Explicit demonstration of gapless Dirac-cone surface states in 3D photonic crystals.

Effective analysis of arrayed DBR pillars using multiple-scattering method.

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.