Interacting Step Discontinuities in Planar Dielectric Waveguides

Planar dielectric waveguides play an important role in electro-optics. In many laser configurations and integrated optical components, grooves are etched in the planar surface or overlays are deposited on it. The step is an idealization of such a discontinuity. This paper has two aims. First, the field problem of an arbitrary large step under multimode excitation is solved by means of a rigorous variational approach. Step discontinuities however are seldom isolated. Mostly a cascade is employed. The second aim of the paper is to show how appropriately generalized methods of network theory can be applied to the rigorous analysis of such cascades, either finite or infinite, periodic or aperiodic.