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Macroscopic Method of Quantization of Evanescent Electromagnetic Fields with Taken into Account of Medium Dispersion
Masahiro AGU Jingbo LI
IEICE TRANSACTIONS on Electronics
Publication Date: 1998/08/25
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Microwave and Millimeter Wave Technology
evanescent field, dispersion, orthogonality, quantization,
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Macroscopic method for quantization of the evanescent fields brought about by total reflection is presented. Here, a semi-infinite space is assumed to be filled with a transparent dispersive dielectric with dielectric constant ε(ω) to the left of the plane z = 0, and be empty to the right of the plane. The wave is assumed to be incident from the left, and so the whole field is composed of the triplet of incident, reflected, and transmitted waves labeled by a continuous wave vector index. The transmitted wave in free space may be evanescent. The triplet is shown exactly without using slowly varying field approximation in dispersive medium to form orthogonal mode for different wave vectors, which provides the basis for the quantization of the triplet with taken into account of medium dispersion. The exact orthogonal relation reduces to the well known one if the dielectric is nondispersive, ε/ω = 0. By using the field expansion in terms of the orthogonal triplet modes, the total field energy is found to be the sum of the energies of independent harmonic oscillators. A discussion is also made on the wave momentum of evanescent field.