# Analytical study of mode degeneracy in non-Hermitian photonic crystals with TM-like polarization

## TL;DR

This paper analytically investigates mode degeneracy in non-Hermitian photonic crystals with $C_{4v}$ symmetry, revealing conditions for Dirac-cone like dispersion, its properties, and topological transitions, using coupled-wave-theory.

## Contribution

It provides an analytical framework for understanding accidental triple degeneracy and Dirac-cone like dispersion in non-Hermitian photonic crystals, highlighting their linearity, isotropy, and topological features.

## Key findings

- Derivation of conditions for accidental triple degeneracy.
- Identification of Dirac-cone like dispersion with good linearity and isotropy.
- Observation of topological band transitions without Berry phase accumulation.

## Abstract

We present an analytical study of the mode degeneracy in non-Hermitian photonic crystals (PC) with $C_{4v}$ symmetry, from the perspective of the coupled-wave-theory (CWT). The wave couplings and leakages within the non-Hermitian PCs are depicted, and the condition of accidental triple degeneracy is derived which leads to a Dirac-cone like dispersion. We prove that, similar to the real Dirac-cone, the Dirac-cone like band in non-Hermitian PC possesses good linearity and isotropy in the vicinity of the $\Gamma$ point. Moreover, some topological transit of the band may occur when the parameters adiabatically evolve. However, the Berry phase remains zero at the $\Gamma$ point, indicated the Dirac-like-cone dosen't obey Dirac equation and it is only Dirac-cone.