Date of Award

Spring 1-1-2015

Document Type


Degree Name

Master of Science (MS)


Applied Mathematics

First Advisor

Alan R. Mickelson

Second Advisor

Gregory Beylkin

Third Advisor

Mark Hoefer

Fourth Advisor

Christian Ketelsen


A qualitative study on the ray and wave dynamics of light in optical waveguides with separatrix geometry is presented herein. The thesis attempts to answer the question as to what happens in slab waveguides with a transverse refractive index distribution similar to the effective index distribution of a dual tapering waveguide. Discontinuous perturbations along the optical axis to the slab waveguide are also studied. A low-order method is used in this study. Light is found to be guided due to an interaction of the input signal with dynamical equilibria within the waveguide geometry. Dynamical systems and quantum separatrix crossing theory are utilized to explain paraxial propagation paths and modal power spectra of the segmented waveguide. Light confinement in the guide is reliant on the large number of degenerate higher-order modes present. Alternate solution methods are also discussed.