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Proceedings Paper

General eigenstates of Maxwell's equations in a two-constituent composite medium
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Paper Abstract

Eigenstates of Maxwell’s equations in the quasistatic regime were used recently to calculate the response of a Veselago Lens1 to the field produced by a time dependent point electric charge.2, 3 More recently, this approach was extended to calculate the non-quasistatic response of such a lens. This necessitated a calculation of the eigenstates of the full Maxwell equations in a flat slab structure where the electric permittivity ϵ1 of the slab differs from the electric permittivity ϵ2 of its surroundings while the magnetic permeability is equal to 1 everywhere.4 These eigenstates were used to calculate the response of a Veselago Lens to an oscillating point electric dipole source of electromagnetic (EM) waves. A result of these calculations was that, although images with subwavelength resolution are achievable, as first predicted by John Pendry,5 those images appear not at the points predicted by geometric optics. They appear, instead, at points which lie upon the slab surfaces. This is strongly connected to the fact that when ϵ1/ϵ2 = −1 a strong singularity occurs in Maxwell’s equations: This value of ϵ1/ϵ2 is a mathemetical accumulation point for the EM eigenvalues.6 Unfortunately, many physicists are unaware of this crucial mathematical property of Maxwell’s equations. In this article we describe how the non-quasistatic eigenstates of Maxwell’s equations in a composite microstructure can be calculated for general two-constituent microstructures, where both ϵ and μ have different values in the two constituents.

Paper Details

Date Published: 3 November 2016
PDF: 5 pages
Proc. SPIE 10028, Plasmonics II, 100280B (3 November 2016); doi: 10.1117/12.2246455
Show Author Affiliations
David J. Bergman, Tel Aviv Univ. (Israel)
Asaf Farhi, Tel Aviv Univ. (Israel)


Published in SPIE Proceedings Vol. 10028:
Plasmonics II
Hongxing Xu; Satoshi Kawata; David J. Bergman; Xing Zhu, Editor(s)

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