Exceptional points in perturbed dielectric spheres: A resonant-state expansion study

TL;DR

This paper uses the resonant-state expansion to rigorously analyze exceptional points in perturbed dielectric spheres, revealing their spectral properties, chirality effects, and potential observability in optical spectra.

Contribution

It introduces a non-perturbative RSE approach to study EPs in dielectric spheres, providing analytical and numerical insights into their spectral degeneracies and chirality effects.

Findings

Analytical expression for an exceptional arc of EPs in perturbed WGMs

Observation of opposite and equal chirality in WGM pairs at EPs

Manifestation of chirality in circular dichroism and optical spectra

Abstract

Exceptional points (EPs) in open optical systems are rigorously studied using the resonant-state expansion (RSE). A spherical resonator, specifically a homogeneous dielectric sphere in a vacuum, perturbed by two point-like defects which break the spherical symmetry and bring the optical modes to EPs, is used as a worked example. The RSE is a non-perturbative approach encoding the information about an open optical system in matrix form in a rigorous way, and thus offering a suitable tool for studying its EPs. These are simultaneous degeneracies of the eigenvalues and corresponding eigenfunctions of the system, which are rigorously described by the RSE and illustrated for perturbed whispering-gallery modes (WGMs). An exceptional arc, which is a line of adjacent EPs, is obtained analytically for perturbed dipolar WGMs. Perturbation of high-quality WGMs with large angular momentum and their EPs are found by reducing the RSE equation to a two-state problem by means of an orthogonal transformation of a large RSE matrix. WGM pairs have opposite chirality in spherically symmetric systems and equal chirality at EPs. This chirality at EPs can be observed in circular dichroism measurements, as it manifested itself in a squared-Lorentzian part of the optical spectra, which we demonstrate here analytically and numerically in the Purcell enhancement factor for the perturbed dipolar WGMs.