Investigation of surface electromagnetic waves at the boundary with an anisotropic medium in CAS Sage

Abstract

The report touches upon the topic of surface electromagnetic waves that propagating along a plane interface between an isotropic substance with a constant dielectric constant and an anisotropic crystal, whose dielectric tensor has a symmetry axis directed along the interface. It is well known among specialists in this field that the question of the existence of such surface waves is reduced to the question of the existence of a solution to a certain system of algebraic equations and inequalities. Since this system has not been solved analytically so far, the question remains controversial and open. Therefore, as a research task, we made an attempt to find out what the Sage computer algebra system can give in solving this issue.
The technique of exceptional ideals built into Sage made it possible to solve a system of algebraic equations about the existence of Diakonov waves parametrically using a single parameter, with all the original quantities expressed in terms of this parameter using radicals. At the same time, the remaining inequalities were only partially investigated analytically.
In this paper, a symbolic-numerical algorithm is proposed and implemented in Sage for a complete study of the solvability of a system of equations and inequalities, testing of this algorithm is carried out, and the results of computer experiments are presented. Based on these results, conclusions were drawn that require further theoretical substantiation.

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Kroytor Oleg
Kroytor O. K.
Russia

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