A method for computing guided waves in integrated optics. Part II: Numerical approximation and error analysis

In this paper, we are interested in the numerical approximation of the method for computing guided modes in integrated optics introduced in our earlier paper [Gomez Pedreira and Joly, SIAM J. Numer. Anal., 39 (2001), pp. 596-623]. We saw that the main step of the computation of the guided modes consists of computing the eigenvalues of a compact operator K depending on the frequency and the wavenumber beta. This second paper is devoted to the discretization of this problem and to the corresponding convergence analysis. In particular, we derive error estimates in the eigenvalue approximation, which will be of exponential accuracy.