Transition from Dirac points to exceptional points in anisotropic waveguides

TL;DR

This paper investigates how Dirac points in anisotropic waveguides transition into exceptional points when non-Hermitian effects are introduced, revealing new hybrid leaky states and their dependence on anisotropy.

Contribution

It demonstrates the transition from Dirac to exceptional points in anisotropic waveguides and characterizes the conditions and nature of these exceptional points.

Findings

Dirac points occur at specific propagation directions in anisotropic waveguides.

Introducing leakage transforms Dirac points into exceptional points connected by a Fermi arc.

Exceptional points are always out of the anisotropy symmetry planes.

Abstract

We uncover the existence of Dirac and exceptional points in waveguides made of anisotropic materials, and study the transition between them. Dirac points in the dispersion diagram appear at propagation directions where the matrix describing the eigenvalue problem for bound states splits into two blocks, sorting the eigenmodes either by polarization or by inner mode symmetry. Introducing a non-Hermitian channel via a suitable leakage mechanism causes the Dirac points to transform into exceptional points connected by a Fermi arc. The exceptional points arise as improper hybrid leaky states and, importantly, are found to occur always out of the anisotropy symmetry planes.