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

Abstract

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

12 pages, 3 figures

References in corpus (4)

• Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems
• Spectral parameter power series for perturbed Bessel equations
• Construction of transmutation operators and hyperbolic pseudoanalytic functions
• Transmutations for Darboux transformed operators with applications