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The time-dependent Maxwell system describing electromagnetic wave propagationin inhomogeneous isotropic media in the one-dimensional case reduces to aVekua-type equation for bicomplex-valued functions of a hyperbolic variable,see arXiv:1001.0552. In arXiv:1410.4873 using this reduction a representationof a general solution of the system was obtained in terms of a couple ofDarboux-associated transmutation operators arXiv:1111.4449. In arXiv:1508.02738a Fourier-Legendre expansion of transmutation integral kernels was obtained.This expansion is used in the present work for obtaining an exact solution ofthe problem of the transmission of a normally incident electromagnetictime-dependent plane wave through an arbitrary inhomogeneous layer. The resultcan be used for efficient computation of the transmitted modulated signals. Inparticular, it is shown that in the classical situation of a signal representedin terms of a trigonometric Fourier series the solution of the problem can bewritten in the form of Neumann series of Bessel functions with exact formulasfor the coefficients. The representation lends itself to numerical computation.

Time-dependent one-dimensional electromagnetic wave propagation in  inhomogeneous media: exact solution in terms of transmutations and Neumann  series of Bessel functions