Internal and External Resonances of Dielectric Disks

TL;DR

This paper analyzes the eigenvalues of dielectric microdisks, distinguishing internal and external resonances for TM and TE modes, especially in the small opening limit, and classifies these resonances by modal indices.

Contribution

It provides a detailed analysis of the behavior of resonances in dielectric microdisks, clarifying the distinction between internal and external modes for both polarizations in the small opening limit.

Findings

Internal and external resonances are clearly distinguished in the small opening limit.

Resonances can be classified by azimuthal and radial modal indices.

TE polarization shows overlapping internal and external resonances.

Abstract

Circular microresonators (microdisks) are micron sized dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analysed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal and external resonances can be found in the same region of the complex wavenumber plane. It is also shown that for both polarizations, the internal as well as external resonances can be classified by well defined azimuthal and radial modal indices.