Vector Finite Difference approach to the computation of TM waveguide modes

We describe here a Vector Finite Difference approach to the evaluation of waveguide eigenvalues and modes. The VFD is applied using a 2D cartesian grid, in the waveguide section. A suitable Taylor expansion of the vector mode function, allows to take exactly into account the boundary condition for a large class of waveguide. The FD approximation results in a constrained eigenvalue problem, that we solve using a decomposition method. This approach has been evaluated comparing our results to the analytical TM modes of a rectangular waveguide.