Quality factor of dielectric optical resonators
arxiv(2024)
摘要
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 ≫ 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.
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