Method of Auxiliary Sources With an Excitation Source: The Auxiliary-Current Vector Norm

The method of auxiliary sources with an excitation source (MAS-ES) is a reliable method for determining the eigenvalues
$k$
in hollow, 2-D waveguides. This is done using a
$k$
-dependent response function
$F(k)$
, defined as the mean-square value of the magnitude of the field at a number of random points within the waveguide: plotting
$F(k)$
for a fine grid of
$k$
yields a response curve with sharp peaks at the positions of the eigenvalues. In this work, it is shown that the eigenvalues can be determined, more simply, by means of the auxiliary currents vector norm (ACVN). We explain our method analytically for the simple problem of the circular waveguide, apply it numerically to more complicated geometries, and compare our results to those of a finite element method (FEM)-based commercial software. We introduce a Hankel-function lookup procedure, which greatly reduces computational times, and discuss the rather peculiar effect of divergence/oscillations of the auxiliary currents.