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 li near hyperbolic system of first order partial differential equations with p iecewise constant coefficients. In this paper we investigate spectral prope rties of an operator H defined by this boundary value problem. We prove tha t H generates a C-0-group of bounded operators in a suitable Hilbert space U, that ail but finitely many eigenvalues of H are simple and have negative real parts and that there exists a basis in U consisting of root functions of H, where all but finitely many of these root functions are eigenfunctio ns. Mathematics Subject Classification (1991). 35P20, 35L40.