An Alternative Representation for Green's Functions Used in Rectangular Waveguide Slot Analysis

The representation of the Green's functions normally used in rectangular waveguide analysis is based on Fourier series analyses in the two transverse directions. This paper presents an alternative form particularly suited for broad wall slot analysis. It is based on a Fourier transform in the direction along the guide and a Fourier series in one of the transverse directions. It is superior to the conventional form because it simplifies the z-dependence of the Green's functions, thus simplifying the convolution of these functions with method of moments basis and testing functions. This paper also shows how to use the alternative representation to find the conventional series representation of the convolutions. For many slot geometries this approach is actually easier than the conventional method. The alternative form also has educational benefit because the boundary conditions, relating magnetic current and the tangential electric field in any plane parallel to the broad wall, are more readily seen.