This thesis is directed at an analysis of the effects produced by designed perturbations on the physical properties of micron-scale segments of waveguides. Considered are two forms of perturbations, both of which are intended to favorably after the output of the waveguides. The first type of perturbation, discussed in Chapter 2, consists of an alteration of the index of refraction in a segment of one or both channels of a two of a two channel directional coupler. The intent of this alteration is the correction of a possible error in the function of the device. The second type of perturbation, in Chapter 3, is an alteration of the geometry of a segment of a single channel waveguide. This alteration has the intent of creating a drastic change in the output of the channel as a function of length of the perturbed region or as a function of the incident wavelength.

The analyses in both cases are based on analytic solutions of Maxwell's equations subject to the boundary conditions defined by the geometries considered. The analyses have the advantage, with respect to strictly numerical computations based on computer codes such as BeamProp, of providing analytic formulas for the changes in output produced by the perturbations. Analytic formulas for output changes allow insight into the underlying mechanisms of the alterations and can significantly reduce computation time required to determine the effects produced by the perturbations.