Two-stage mode finder for waveguides with a 2D cross-section

We present a fast and efficient method to find the vectorial eigenmodes of waveguides with an arbitrary 2D cross-section. The method can deal with both material losses and radiation losses (through perfectly matched layer boundary conditions). In the first stage of the method, a coarse estimate of the propagation constants is found using a plane-wave method. In the second stage, these estimates are refined using a mode-matching method.