Investigation of resonant modes in thin microcavities by using electromagnetic theory

A biharmonic differential equation for 3D thin microcavities with uniform thickness is investigated by use of electromagnetic theory, whose exact solution is determined to govern the electromagnetic field distribution inside the thin microcavities. The resonant field patterns of a thin microdisk and thin rectangular microcavity are obtained accordingly. The governing equation can be verified by comparing the results of the thin microdisk presented with the approximate ones in the literature. The fourth-order partial differential equation and its exact solution should be useful in possible applications of the thin microcavities for optical resonators in laser optics and optical devices.