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

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 microres onator 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 wellknown perturbationtheory 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.