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

David J. Bergman, Asaf Farhi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 ε12 = -1 a strong singularity occurs in Maxwell's equations: This value of ε12 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.

Original languageEnglish
Title of host publicationPlasmonics II
EditorsHongxing Xu, Xing Zhu, David J. Bergman, Satoshi Kawata
ISBN (Electronic)9781510604759
StatePublished - 2016
EventPlasmonics II - Beijing, China
Duration: 12 Oct 201614 Oct 2016

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferencePlasmonics II


  • Bi-orthogonal basis in Hilbert space
  • Eigenfunction
  • Expansion of the electric field
  • Negative refractive index


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