The effect of an absorbed layer on the resonant frequencies and Q-factors of spherical microresonators

Abstract

We investigate two approaches to the calculation of the resonant frequency shift and Q-factor modification in a microresonator due to adsorption of a homogeneous isotropic dielectric layer on its surface. The first approach is based on the analytical solution of the characteristic equation for a spherical microresonator in the approximation of a thin dielectric layer on its surface. The second, more general approach, uses the adiabatic invariant. We demonstrate it to be equivalent to the well-known perturbation-theory technique and use it for the case of a spherical microresonator. Both approaches yield the same result and confirm the previous data. The obtained complex part of the frequency shift allows one to calculate the variation in the Q-factor of a microresonator with a lossy layer.