On the computation of eigenmodes of integrated optical components (Q1817737)

For the propagation of light in a waveguide, the author first describes the reduction of the Maxwell equations to an eigenproblem for the scalar Helmholtz equation with a complex coefficient which may vary in space. Next, multigrid algorithms for such problems are discussed. Here, at the end, he turns to the advantages of the approach of Deuflhard and coworkers (including the author) to solve a sequence of projected Schur problems. Finally, as numerical example, a waveguide consisting of 3 specific materials is considered which leads, in general, to a nonselfadjoint problem. This is solved using the proposed methodology by an adaptive multigrid method and in dependence on a material parameter.