Space-group theory of photonic bands

TL;DR

This paper develops a comprehensive space group theory for photonic bands, revealing how symmetry constraints influence band structures and topological degeneracies in three-dimensional photonic crystals.

Contribution

It introduces a detailed theoretical framework for understanding photonic band dispersions across all 230 space groups, including singularities at zero frequency and momentum.

Findings

Identifies minimal band connectivities for all space groups.

Shows topological degeneracies occur in space groups without band gaps between certain bands.

Provides guidelines for symmetry-based photonic crystal design.

Abstract

The wide-range application of photonic crystals and metamaterials benefits from the enormous design space of three-dimensional sub-wavelength structures. In this work, we study the space group constraints on photonic dispersions for all 230 space groups with time-reversal symmetry. Our theory carefully treats the unique singular point of photonic bands at zero frequency and momentum, which distinguishes photonic bands from their electronic counterpart. The results are given in terms of minimal band connectivities at zero~($M$) and non-zero frequencies~($M'$). Topological band degeneracies are guaranteed to be found in space groups that do not allow band gaps between the second and third photonic bands~($M>2$). Our work provides theoretical guidelines for the choice of spatial symmetries in photonics design.