Spectral properties of coupled wave operators

Essential features of two-section DFB semiconductor lasers can be described by a boundary value problem for the so-called coupled wave equations, a linear hyperbolic system of first order partial differential equations with piecewise constant coefficients. In this paper we investigate spectral properties of an operator H defined by this boundary value problem. We prove that H generates a C 0-group of bounded operators in a suitable Hilbert space \(\Cal{U}\), that all but finitely many eigenvalues of H are simple and have negative real parts and that there exists a basis in \(\Cal{U}\) consisting of root functions of H, where all but finitely many of these root functions are eigenfunctions.