Orthogonality and amplitude spectrum of radiation modes along open-boundary waveguides

The continuous spectrum of radiation modes along open-boundary dielectric waveguides of arbitrary cross-section shape is considered. Orthogonality of the spectral components of these radiation modes is established in a general manner. This development is based on the Lorentz reciprocity theorem, and it is demonstrated that orthogonality is a direct consequence of (1) satisfaction of Maxwell's equations by spectral-component fields and (2) satisfaction of the radiation condition by total radiation-mode fields. The amplitude spectrum of continuous radiation modes, maintained by impressed excitatory electric currents immersed in either the waveguide core or cladding regions, is determined. These results are of general use in the study of discontinuities along open-boundary dielectric waveguides.