Mode theory of an axially symmetric laser with a gradient profile of active medium

Abstract

Results are presented of a rigorous mode theory for a laser with gradient profile of active medium excitation density. The method used to solve the eigenvalue problem is based on Maxwell's wave equation and on impedance boundary conditions of the resonance type at the open resonator ends. The case considered refers to a a laser resonator equipped with plane parallel circular mirrors of finite size. The rigorous solution of the eigenvalue problem is obtained for a bounded parabolic profile of the active medium. The transcendental eigenvalue equation is investigated and distributions of the active resonator eigenfunctions are found. The asymptotic behaviour of the rigorous solutions is investigated. A multilayers approximation method is used to solve the eigenvalue problem when the active medium has an arbitrary excitation density profile.