A new, vectorial, approximate solution is presented for a particular class of problems: that of a vector wave propagated through a linear, isotropic, piecewise-homogeneous medium with irregular interfaces and boundaries. This class of problems lacks not only an exact method of solution but also a reliable method of approximation for tropospheric radio propagation at VHF and higher frequencies. A method is proposed that incorporates a recent expansion of the Helmholtz integral to evaluate the Stratton-Chu integral by the methods of stationary phase. To demonstrate its potential, the method is applied to two of the simplest thin-screen problems.
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