  This work continues a series of papers where we propose an algorithm for
quasioptical modeling of electromagnetic beams with and without mode
conversion. The general theory was reported in the first paper of this series,
where a parabolic partial differential equation was derived for the field
envelope that may contain one or multiple modes with close group velocities. In
the second paper, we presented a corresponding code PARADE (PAraxial RAy
DEscription) and its test applications to single-mode beams. Here, we report
quasioptical simulations of mode-converting beams for the first time. We also
demonstrate that PARADE can model splitting of two-mode beams. The numerical
results produced by PARADE show good agreement with those of one-dimensional
full-wave simulations and also with conventional ray tracing (to the extent
that one-dimensional and ray-tracing simulations are applicable).
