Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions, and transmutations
- Faculty of Engineering, Autonomous University of Queretaro, Cerro de las Campanas s/n, col. Las Campanas Querétaro, Qro. CP 76010 (Mexico)
- Department of Mathematics, CINVESTAV del IPN, Unidad Querétaro, Libramiento Norponiente # 2000 Fracc. Real de Juriquilla Querétaro, Qro., CP 76230 (Mexico)
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 Kravchenko and Ramirez [Adv. Appl. Cliord Algebr. 21(3), 547–559 (2011)]. 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 [Kravchenko, V. V. and Torba, S. M., J. Phys. A: Math. Theor. 45, 075201 (2012)], and combined with the recent results on their construction [Kravchenko, V. V. and Torba, S. M., Complex Anal. Oper. Theory 9, 379-429 (2015); Kravchenko, V. V. and Torba, S. M., J. Comput. Appl. Math. 275, 1–26 (2015)] can be used for efficient computation of the transmitted modulated signals. We develop the corresponding numerical method and illustrate its performance with examples.
- OSTI ID:
- 22596834
- Journal Information:
- Journal of Mathematical Physics, Vol. 57, Issue 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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