Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals

TL;DR

This paper demonstrates how breaking symmetry in a 2D photonic crystal can create complete bandgaps by manipulating degeneracies and line node singularities, advancing the design of photonic materials.

Contribution

It introduces a systematic method to break degeneracies in photonic crystals, enabling the formation of complete bandgaps through symmetry manipulation.

Findings

Complete bandgap formation due to level repulsion along line nodes

Symmetry breaking leads to Dirac points and inverted bandgaps

Numerical framework based on multigrid finite element method

Abstract

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experimentations are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.