Orthogonal Relations for Quantization of Evanescent Electromagnetic Wave in Parallel Plate Waveguide Partly Filled with Dispersive Dielectrics

By considering a typical one-dimensional evanescent wave given as a cut-off mode in a parallel plate waveguide, we show a normalization procedure for the quantization of the evanescent wave. The waveguide is assumed to be partly filled with lossless dispersive dielectric medium. New orthogonal relations between the wave modes with arbitrary propagation constants in the waveguide are derived, and normalized wave amplitude is introduced for field quantization. The normalization depends on the dispersive property of the dielectric medium in the waveguide. The wave energy density in the waveguide including that of incident, reflected and evanescent waves is shown to be given by the sum of the energies of independent harmonic oscillators with different frequencies.