Four-dimensional eikonal theory of linear mode conversion

The problem of linear mode conversion in nonuniform media is solved for general geometry, in that the dispersion functions Da(k,x),Db(k,x) of the two, orthogonally polarized, coupled modes a,b have spatial gradients Da/x,Db/x which need not be parallel. The transmission ratio is found to be exp(-22/B), where is the coupling coefficient, and B is the Poisson Bracket {Da,Db}=(Da/X)(Db/k) Db) -(DaK)(Db/X) /x). The further generalization to weak dissipation and ray divergence is included.