# Gap dependent mass of photon in photonic topological insulator

## TL;DR

This paper derives an explicit expression for the band structure of photonic topological insulators, showing that a topological phase difference induces a finite gap and an effective photon mass that depends on this gap.

## Contribution

It introduces a novel explicit formula linking the topological phase difference to the photon mass in photonic topological insulators.

## Key findings

- Finite spectral gap opens with nonzero topological phase difference
- Effective photon mass depends on the size of the spectral gap
- Photon mass scales as the square root of the gap

## Abstract

By using an analogy with axionic like systems, we study light propagation in periodic photonic topological insulator (PTI). The main result of this paper is an explicit expression for the PTI band structure. More specifically, it was found that for nonzero values of the topological phase difference $\gamma=\theta_2-\theta_1$ a finite gap $\delta \propto\gamma^2$ opens in the spectrum which is equivalent to appearance of nonzero effective photon mass $m^{*}(\delta)\propto \frac{\sqrt{\delta}}{\delta +2}$.