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Journal Articles SIAM Journal on Mathematical Analysis Year : 2022

A mathematical study of a hyperbolic metamaterial in free space

Abstract

Wave propagation in hyperbolic metamaterials is described by the Maxwell equations with a frequency dependent tensor of dielectric permittivity, whose eigenvalues are of different signs. In this case the problem becomes hyperbolic (Klein-Gordon equation) for a certain range of frequencies. The principal theoretical and numerical difficulty comes from the fact that this hyperbolic equation is posed in a free space, without initial conditions provided. The subject of the work is the theoretical justification of this problem. In particular, this includes the construction of a radiation condition, a well-posedness result, a limiting absorption principle and regularity estimates on the solution.
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Dates and versions

hal-03164619 , version 1 (10-03-2021)

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Patrick Ciarlet, Maryna Kachanovska. A mathematical study of a hyperbolic metamaterial in free space. SIAM Journal on Mathematical Analysis, 2022, 54 (2), pp.2216-2250. ⟨10.1137/21M1404223⟩. ⟨hal-03164619⟩
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