Integral equations and discretizations for waveguide apertures

We present integral equations and their discretizations for calculating the fields radiated from arbitrarily shaped antennas fed by cylindrical waveguides of arbitrary cross sections. We give results for scalar fields in two dimensions with Dirichlet and Neumann boundary conditions and for (vector) electric and magnetic fields in three dimensions. The discretized forms of the equations are cast in identical format for all four cases. Feed modes can be TM, TE, or transverse electromagnetic (TEM). A method for numerically computing the modes of an arbitrarily shaped, cylindrical waveguide aperture is also given.