Gap-dependent mass of a photon in a photonic topological insulator

By using an analogy with axioniclike systems, we study light propagation in a 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 the appearance of nonzero effective photon mass $m^{*}\left(\delta \right)\propto \frac{\sqrt{\delta }}{\delta +2}$.

Figure 1

The proposed system: a photonic crystal composed of two layers with distinctive electric ($\epsilon$), magnetic ($\mu$), and topological ($\theta$) properties.

Figure 2

The band diagram $\omega \left(k\right)$ of a photonic crystal based on topological insulators for different values of the gap-related parameter $\delta$ according to Eq. (21).

Figure 3

The dependence of normalized effective photon mass on the gap-related parameter $\delta$ according to Eq. (23).