An Approximate Method for Solving the Wave Equation in an Inhomogeneous Medium

A technique is described for obtaining approximate solutions to the wave equation when a dielectric variation exists in the direction of propagation. The method consists of approximating the true dielectric variation with several adjacent slabs having exponentially varying characteristics. Solutions in each region include Bessel function of purely imaginary order. A variety of these previously untabulated functions are presented so that the solutions in each slab can be joined at the boundaries. The method offers the possibility of an analytical determination of fields in many cases which would otherwise require a more extensive solution technique.