Quality factor of dielectric optical resonators

Abstract

We show analytically that the quality ($Q$) factor of magnetic and electric Mie modes in a lossless dielectric spherical resonator with high refractive index ($n\gg 1$) scales as $n^{2j+1}$ and $n^{2j+3}$ respectively, where $j$ denotes the multipolar order. We numerically validate these results and show that our high-$n$ analytical relation is accurate for the dipolar modes when $n>5$. For higher multipolar orders, the analytical relation becomes valid for increasingly lower $n$. We study the dependence of the $Q$ factor on absorption losses and determine a general functional form that describes the $Q$ factor for all Mie modes for any complex refractive index. Finally, we observe that this functional form predicts a multipolar-dependent singular value of optical gain which gives rise to a lasing condition with an infinite $Q$ factor.

4 figures

References in corpus (4)

• High-Q supercavity modes in subwavelength dielectric resonators
• Excitation of single multipolar modes with engineered cylindrically symmetric fields
• The role of the angular momentum of light in Mie scattering. Excitation of dielectric spheres with Laguerre-Gaussian modes
• Polarizability Expressions for Predicting Resonances in Plasmonic and Mie Scatterers

Cited by in corpus (1)

• Computational discovery of high-refractive-index van der Waals materials: The case of HfS${}_2$