Modal analysis applied to quantum waveguide structures and discontinuities

Modal expansions of the wave function together with a mode-matching method are utilized to analyze quantum waveguide structures and discontinuities. The modal expansion in the discontinuity region is simplified by employing a decomposition technique. The numerical behavior of the method is illustrated for a step discontinuity. It is shown that the computational cost is significantly reduced when the mode ratio is approximately 1.5 times the corresponding ratio in widths. Assuming an infinite lateral potential confinement, conductance calculations for a single and double bend configuration are compared to the idealized uniform quantum waveguide and display a reduction in the overall slope. The infinite lateral potential (hard wall) confinement is compared to a more realistic parabolic-like potential (soft wall) confinement for the case of a uniform narrow constriction. Utilizing the method of moments, the lateral eigensolutions for soft wall confinement are expanded in infinite square-well eigenfunctions. Conductance calculations for the uniform narrow constriction show a small increase in the resonant structure for soft wall confinement compared to hard wall confinement.