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16 February 2025
 
  » arxiv » 1109.0126

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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
AbstractLobachewsky 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
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