An exact calculation of the local electric field E(r) is described for the case of an external current or plane wave source in a setup of an E1, μ1 slab in an E2, μ2 medium. For this purpose we first calculate all the general eigenstates of the full Maxwell equations. These eigenstates are then used to develop an exact expansion for the physical values of E(r) in the system characterized by physical values of E1, E2, μ1, and μ2. Results are compared with those of a previous calculation of the local field where μ = 1 everywhere. Numerical results are shown for the eigenvalues in practically important configurations where attaining an optical image with sub-wavelength resolution has practical significance. We show that the k ≫ k2 components are enhanced for the TM field when E1/E2 = −1 and for the TE field when μ1/μ2 = −1 where the enhancement of the evanescent waves starts from lower k values as we approach a setup with both E1/E2 = −1 and μ1/μ2 = −1. We also show that the eigenfunctions for the setup where μ = 1 everywhere correspond to configurations of 3D phased arrays.
Asaf Farhi and David J. Bergman, "General eigenstates of Maxwell's equations in a two-constituent composite medium and their application to a calculation of the local electric field in a flat-slab microstructure," Proc. SPIE 9921, Plasmonics: Design, Materials, Fabrication, Characterization, and Applications XIV, 99210E (Presented at SPIE Nanoscience + Engineering: August 28, 2016; Published: 17 September 2016); https://doi.org/10.1117/12.2236639.
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