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On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem) | E.M. Ovsiyuk
; V.M. Red'kov
; | Date: |
1 Sep 2011 | 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
ho. | Source: | arXiv, 1109.0126 | Services: | Forum | Review | PDF | Favorites |
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