In this paper we study the electromagnetic (EM) wave propagation in a perfect magnetic medium with continuously varying magnetic permeability m(z) in one direction. We consider the inhomogeneity to be arbitrary and described by an infinite power series of z and use the Frobenious method to solve the governing differential equation of the problem in the frequency domain. We also give special attention to the first cut-off frequency of the main mode TM11 and we propose a good estimation for it by means of the mean value of the magnetic permeability profile. The results from the mathematical analysis are applied to solve the direct problem of wave propagation in a system of three waveguides having two homogeneous filling materials and one that exhibits such inhomogeneous characteristics. We finally confront the inverse problem of magnetic permeability reconstruction by handling simulation data and a genetic optimization algorithm.
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