General electromagnetic eigenstates and the field of an oscillating dipole in a flatslab composite structure
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An exact calculation of the local electric field is described for the case of an external current or plane wave source in a setup of an Ï µ_1,µ_1 slab in an Ï µ_2,µ_2 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 the electric field in the system characterized by physical values of Ï µ_1, Ï µ_2, µ_1, and µ_2. 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 contribution of the high k TM eigenstates is enhanced when Ï µ_1=-Ï µ_2 and the contribution of the high k TE eigenstates is enhanced when µ_1=-µ_2 where the enhancement of the evanescent waves starts from lower k values as we approach a setup with both Ï µ_1=-Ï µ_2 and µ_1=-µ_2. We also show that the eigenfunctions for the setup where µ=1 everywhere correspond to configurations of 3D phased arrays.