VFD approach to the computation TE and TM modes in circular waveguide on TM grid

Finite differences, i.e., the direct discretization of the vector eigenmodes equation, can be a very effective approach to the computation of waveguide modes, as long as the discretization grid matches exactly the grid boundary. We describe here the implementation of such approach for a circular waveguide, using a polar grid, both for TE and TM modes. The resulting matrix eigenvalue problems turns out to be a constrained one, which can be solved using a QR-based methods.