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.
© 2008 Optical Society of America
Original Manuscript: January 10, 2008
Manuscript Accepted: March 12, 2008
Published: May 27, 2008
Vol. 3, Iss. 7 Virtual Journal for Biomedical Optics
Iwao Teraoka and Stephen Arnold, "Variational principle in whispering gallery mode sensor responses," J. Opt. Soc. Am. B 25, 1038-1045 (2008)