Abstract
Surface electromagnetic waves (Dyakonov waves) 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, are considered. It is well known 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. In the present work, this system is investigated in the Sage computer algebra system. The built-in technique of exceptional ideals in Sage made it possible to describe the solution of a system of algebraic equations parametrically using a single parameter, with all the original quantities expressed in terms of this parameter using radicals. The remaining inequalities were only partially investigated analytically. For a complete study of the solvability of the system of equations and inequalities, a symbolic-numerical algorithm is proposed and implemented in Sage, and the results of computer experiments are presented. Based on these results, conclusions were drawn that require further theoretical substantiation.
Highlights
In the 1980s, a special class of solutions to Maxwell’s equations was theoretically discovered, namely, electromagnetic waves traveling along the interface between two dielectrics, the intensity of which rapidly decreases with distance from the interface [1]–[6]
We conducted a series of computer experiments, the results of which are given in the table 1
3) if the difference between the values εo, ε, εe remains constant, and the values themselves increase, the half-interval of the angle u variation, in which surface waves exist, decreases; 4) if the difference between the values of εo, ε, εe is increased by the same amount, the half-interval of u variation is practically unchanged
Summary
In the 1980s, a special class of solutions to Maxwell’s equations was theoretically discovered, namely, electromagnetic waves traveling along the interface between two dielectrics, the intensity of which rapidly decreases with distance from the interface [1]–[6]. As in the work of Dyakonov itself [2], the question of the existence of surface waves was reduced to the question of the existence of a solution to a certain system of algebraic equations and inequalities that cannot be solved analytically, which hinders further research. In this paper, it will be shown what computer algebra systems can give for these systems.
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