Wave-vector-space method for wave propagation in bounded media

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Abstract
A method for solving wave propagation problems in bounded media that operates entirely in wave-vector space is presented. No boundary conditions are used in the solution in contrast to the real-space method. The transmission/reflection problem of an electromagnetic wave on a dielectric half-space is solved as an illustration of the method. The dispersion relations of vacuum and medium, Snell’s law, the reflection angle law, and the Fresnel reflection/transmission formulas are obtained from these procedures. Applications to wave-vector dispersion problems, where the method appears to be essential, are pointed out.