Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba
TL;DR
This paper develops a numerical method for solving electromagnetic wave transmission in inhomogeneous media using hyperbolic pseudoanalytic functions and transmutation operators, enabling efficient computation of transmitted signals.
Contribution
It introduces a novel approach linking Maxwell's equations to Vekua-type equations and employs transmutation operators for efficient numerical solutions.
Findings
Effective numerical method for wave transmission problems
Successful illustration with computational examples
Enhanced efficiency in calculating transmitted signals
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.