Exceptional points in dielectric spheroid

TL;DR

This paper investigates how resonant frequencies and modes evolve in a dielectric spheroid with varying aspect ratio and refractive index, identifying exceptional points where modes coalesce for different azimuthal indices and polarizations.

Contribution

It introduces the concept of exceptional points in dielectric spheroids by analyzing the dependence of resonant modes on aspect ratio and refractive index, highlighting mode coalescence phenomena.

Findings

Exceptional points occur at specific aspect ratios and refractive indices.

Mode coalescence happens for azimuthal indices m=0 and m=1.

Resonant frequencies and modes coalesce at these exceptional points.

Abstract

Evolution of resonant frequencies and resonant modes as dependent on the aspect ratio is considered in a dielectric high index spheroid. Because of rotational symmetry of the spheroid the solutions are separated by the azimuthal index $m$. By the two-fold variation of a refractive index and the aspect ratio we achieve exceptional points (EPs) at which the resonant frequencies and resonant modes are coalesced in the sectors $m=0$ for both TE and TM polarizations and $m=1$.