Quasi-modes in open cavities formulated as a boundary-value problem with application to laser resonators

Quasi-modes in open cavities, such as laser resonators, are formulated as a scaler mixed boundary-value problem. Using this approach, we seek to unify the derivations of the Fox-Li and Weinstein versions of laser resonator theory. Having obtained a rigorous theory, we analyze both analytically and numerically the long-wavelength limit of the lower-order quasi-modes, using a triple series to solve the mixed boundary-value problem. When the wavelength is very small compared with the size of the cavity (the usual laser resonator condition), we derive an integral equation governing the wave function and link it to the Fox-Li integral equation of laser resonator theory. The orthogonality and normalization of the various wave functions are also investigated. (C) 1997 Optical Society of America.