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arXiv · 1109.0126

On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem)

E. M. Ovsiyuk·V. M. Red'kov
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Abstract

Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space models within the tetrad formalism, have been found in Lobachevsky space. The problem reduces to a second order differential equation which can be associated with an 1-dimensional Schrodinger problem for a particle in external potential field U(z) = U_{0} e^{2z}. In quantum mechanics, curved geometry acts as an effective potential barrier with reflection coefficient R=1; in electrodynamic context results similar to quantum-mechanical ones arise: the Lobachevsky geometry simulates a medium that effectively acts as an ideal mirror. Penetration of the electromagnetic field into the effective medium, depends on the parameters of an electromagnetic wave, \omega, k_{1}^{2} + k_{2}^{2}, and the curvature radius \rho.

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E. M. Ovsiyuk, V. M. Red'kov. 2011-09-01. On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem). https://arxiv.org/abs/1109.0126

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