Maxwell equations in Lobachevsky space and modeling the medium with reflecting properties
Автор: Kuzmich A., Buryy A., Ovsiyuk E.
Журнал: Известия Коми научного центра УрО РАН @izvestia-komisc
Рубрика: Научные статьи
Статья в выпуске: 5 (71), 2024 года.
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Lobachevsky geometry simulates a medium with special constitutive relations Di = ϵ0ϵikEk, Bi = μ0μikHk, where two matrices coincide: ϵik(x) = μik(x). The situation is specified in quasi-Cartesian coordinates (x, y, z) in Lobachevsky space, they are appropriate for modeling a medium nonuniform along the axis z. Exact solutions of the Maxwell equations in complex form of Majorana-Oppenheimer have been constructed. The problem reduces to a second-order differential equation for a certain primary function which can be associated with the one-dimensional Schrödinger problem for a particle in external potential field U(z) = U0e2z. In the frames of the quantum mechanics, Lobachevsky geometry acts as an effective potential barrier with reflection coefficient R = 1; in electrodynamic context, this geometry simulates a medium that effectively acts as an ideal mirror distributed in space. Penetration of the electromagnetic field into the effective medium along the axis z depends on the parameters of an electromagnetic waves ω, k2 1 + k2 2 and the curvature radius ρ of the used Lobachevsky model. The generalized quasi-plane wave solutions f(t, x, y, z) = E + iB and the relevant system of equations are transformed into the real form, which permit us to relate geometry characteristics with expressions for effective tensors of electric and magnetic permittivities.
Maxwell equations, majorana-oppenheimer formalism, lobachevsky geometry, exact solutions, effective constitutive relations
Короткий адрес: https://sciup.org/149146266
IDR: 149146266 | DOI: 10.19110/1994-5655-2024-5-58-63
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