Quantum theory of electromagnetic waveguide dispersion

The microscopic basis of the linear dispersion in any physical model of a linear waveguide in one or more spatial dimensions is studied. The model is the quantized version of the classical Drude-Lorentz single-electron oscillator model, in a linearized continuum limit. It uses the multipolar gauge which eliminates complications due to Coulomb interactions and contact terms. It includes all the propagation effect by virtue of the transformation to a multipolar interaction, in which the coupling is to the polarization rather than to the electronic momentum. A straightforward procedure for exactly diagonalizing the Hamiltonian using Cauchy's theorem is demonstrated