An exact calculation of the local electric field E(r) is described for the case of a monochromatic (∼ e−iωt) source or incident field in an ∈1, ∈2 composite structure. For this purpose we expand the local electric field E(r) in a complete set of eigenstates of the full Maxwell equations. The eigenvalues appear as special, non-physical values of ∈1 when ∈2 is given. These eigenstates are then used to write an exact expansion for the physical values of E(r) in the system characterized by physical values of ∈1(ω) and ∈2(ω). The application of this approach to the analysis of a Veselago Lens is discussed. In that case the ∈1 constituent has the shape of a flat slab in the otherwise uniform ∈2 constituent. The eigenstates of the full Maxwell equations for this structure are easy to find. This will allow an in depth analysis of the Veselago Lens to be developed, including the possibility of attaining an optical image with sub-wavelength resolution
David J. Bergman and Asaf Farhi, "Perfect optical imaging of a Veselago Lens: Eigenstate-based analysis," Proc. SPIE 9547, Plasmonics: Metallic Nanostructures and Their Optical Properties XIII, 954706 (Presented at SPIE Nanoscience + Engineering: August 09, 2015; Published: 28 August 2015); https://doi.org/10.1117/12.2190259.
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