Mathematical Analysis of a Method to Compute Guided Waves in Integrated Optics

Resumo

In this article, we propose a new method to solve an eigenvalue problem (posed in $\B$) arising from the computation of guided modes in integrated optics electromagnetic waveguides under the weak guiding assumption. We consider an open stratified waveguide translationally invariant in the infinite propagation direction. Its cross-section is also supposed to be an unbounded and stratified medium where an appropiate perturbation of the refraction index has been introduced to ensure the existence of guided modes. The method presented here appears as a combination of analytical methods which take into account the unbounded and stratified character of the propagation medium and numerical computations which can be reduced to a neighborhood of the perturbation. In this report, we give a complete description of the method, present its main mathematical properties and achieve the convergence analysis with respect to the various approximation parameters.