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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). Using this relation we solve the problem of thetransmission through an inhomogeneous layer of a normally incidentelectromagnetic time-dependent plane wave. The solution is written in terms ofa pair of Darboux-associated transmutation operators (see arXiv:1111.4449), andcombined with the recent results on their construction (see arXiv:1208.6166,arXiv:1306.2914) can be used for efficient computation of the transmittedmodulated signals. We develop the corresponding numerical method and illustrateits performance with examples.

Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations