Quantum theory of whispering gallery modes in a cylindrical optical microcavity

The quantum interpretation of whispering gallery modes in a cylindrical optical microcavity is presented in analogy with quantum mechanical theory. The formulas for the resonance shifts caused by a small change in correlative refractive index are derived. Then they are applied to two applications of the cylindrical microcavity to probe the change of surrounding medium and the nonlinear effect of cavity's surface.