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This work continues a series of papers where we propose an algorithm for quasi-optical 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 quasi-optical 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). [ABSTRACT FROM AUTHOR]

This work opens a series of papers where we develop a general quasi-optical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multicomponent wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ ("quasioptical equation") on the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. We also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radio frequency wave beams in magnetized plasma based on this theory. [ABSTRACT FROM AUTHOR]