Mode theory of plane Fabry-Pérot resonator with inhomogeneous active medium

A new method of the eigenvalue problem solution for a resonator with inhomogeneous active medium is given. The approach is based on Maxwell's wave equation and impedance boundary conditions of resonance-type at open resonator ends. A resonator equipped with mirrors in the form of infinite long strips is studied as an example. A rigorous solutions for the cases of stepped and bounded parabolic active medium profiles are obtained. Transcendental eigenvalue equations are investigated, distributions of field amplitude of active resonator modes are found. Asymptotic behavior of rigorous solutions is investigated. A multilayer approximation method is proposed for the eigenvalue problem solution for a resonator with an arbitrary gradient profile of active medium. The testing of this method was carried out with the rigorous solutions for the bounded parabolic profile.