Wannier Function Methods for Topological Modes in 1D Photonic Crystals

TL;DR

This paper employs Wannier functions to analyze and model topological phase transitions in one-dimensional photonic crystals, providing a quantitative approach to defect state localization and topological characterization.

Contribution

It introduces a method to construct and apply Wannier functions for topological analysis in photonic systems, advancing the understanding of topological phases in 1D photonic crystals.

Findings

Successfully constructed exponentially localized Wannier functions for photonic systems

Developed an accurate model for topological phase transitions in 1D photonic crystals

Quantified localization of topological defect states

Abstract

In this work, we use Wannier functions to analyze topological phase transitions in one dimensional photonic crystals. We first review the construction of exponentially localized Wannier functions in one dimension, and show how to numerically construct them for photonic systems. We then apply these tools to study a photonic analog of the Su-Schrieffer-Heeger model. We use photonic Wannier functions to construct a quantitatively accurate approximate model for the topological phase transition, and compute the localization of topological defect states. Finally, we discuss the implications of our work for the study of band representations for photonic crystals.