Multigrid eigenvalue solver for mode calculation of planar optical waveguides

We present a multigrid algorithm suited to solve the discretized eigenvalue problem resulting from Maxwell's equations in the case of a planar optical waveguide homogeneous in one coordinate direction. The discretization scheme provides a full-vector solution for lossy or anisotropic media. It is possible to calculate higher order eigenmodes. The multigrid algorithm turns out to be a very powerful tool to find the solution in a short time with a moderate need of storage capacity even for very fine discretizations. This is demonstrated for the case of a rib waveguide.