Variational principle in whispering gallery mode sensor responses
I. Teraoka & S. Arnold
J. Opt. Soc. Am. B, 25, 1038 -1045 (2008).

We present a variational method for whispering gallery modes (WGMs) and apply it to sensor responses of
WGMs in a spherical resonator to two types of perturbation for which we know the exact answers. The perturbations
are adsorption of a thin dielectric layer and a uniform change in the surroundings’ refractive index.
The variational method gives the perturbed wave function and, if a suitable trial function is chosen, the resonance
wavelength shift up to the second order in the perturbation. The linear part is identical to the result of
the first-order perturbation theory.