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