| Generalized modal analysis techniques for the characterization and modeling of dissipationless planar waveguide structures and discontinuities encountered in microwave and optical integrated circuits, as well as of quantum waveguide structures and devices, are presented.; The frequency-dependent transmission properties of the curved microstrip bend are derived by utilizing a second-order perturbation analysis of the equivalent modified curved waveguide model and a mode-matching method which includes the higher order modes. An extension of the mode-matching method for characterization of microstrip right-angle bends and T junctions having a rectangular notch is formulated.; The modal solutions for an arbitrary graded-index dielectric slab waveguide are derived by applying the generalized telegraphist's equations to the equivalent inhomogeneous parallel-plate waveguide model with electric or magnetic walls. These modal solutions are employed in a mode-matching procedure to calculate the transmission properties of a step discontinuity in typical diffused optical dielectric slab waveguides. Power loss calculations for an abrupt offset in a diffused optical waveguide show a smooth increase in radiation loss whereas a sharp transition from almost zero to nearly total radiation loss is found for an abrupt change in diffusion depth.; In the analysis of quantum waveguide structures, the modal expansions of the wave function together with a mode-matching technique are utilized. The computed generalized scattering matrices (GSMs) of junctions and uniform waveguide sections are combined via an extended GSM technique to obtain the scattering parameters of composite quantum waveguide structures. Results for cascaded right-angle bends and periodic multi-waveguide structures in a split-gate configuration are presented assuming hard wall confinement. For the multisection structures, strong resonant behavior similar to that in resonant tunneling diodes is found. Calculated current-voltage characteristics for a double constriction in GaAs are shown, exhibiting a region of negative differential resistance for temperatures up to approximately 60K with a maximum peak-to-valley ratio of over 80:1. Finally, a uniform narrow constriction with an assumed parabolic-like lateral potential confinement is analyzed by utilizing the modal expansion techniques developed for dielectric waveguides. |
