In this research, we are concerned with obtaining characteristics of a scattering object from transient input-output data. The input is a transient pulse with broad bandwidth. The output is the field scattered by the object. Specifically, we consider two classical structures: First a single lossless dielectric slab backed by a perfect conductor; second, a double-layer lossless dielectric slab backed by a perfect conductor. We begin with two generic solution forms: First, the ray-optic form, which emphasizes local object features; second, the singularity expansion method (SEM) form, which emphasizes object resonances. Using these two forms, we generate a variety of solutions for each structure. For the single slab, we obtain five solution forms for the transient response as follows: The ray-optic, the SEM, two hybrids, and one closed. We find that the input signal plays an important role in the results. We believe the specific hybrid solutions for the slab are new. For the double slab, we find four solution forms as follows: Two ray-optic and two quasi-hybrid. The quasi-hybrid solutions involve a ray-optic expansion in one slab and SEM in the other. We believe the quasi-hybrid forms are new and lead to some interesting comparisons with work by other researchers. As a result of critical study of the various solution types, we reach some conclusions concerning determination of parameters that classify an object (the parametric inverse problem). We find that a given SEM pole set does not always correspond to a unique object. In addition, we show that it is often not possible to relate SEM poles to object size or constitution. Because of these facts, it is necessary to add knowledge of the specific form factor of the object to permit classification. We include some conclusions concerning object identification and point out some areas for future research.

Dielectric waveguides are becoming important for their numerous applications in integrated optics. The study of dielectric waveguides by analytical techniques is not sufficient for many variations in waveguide shape, anisotropy, and inhomogeneity commonly encountered in waveguide materials. This work studies the finite element method as an accurate tool for the numerical modeling of dielectric waveguides. Other commonly used numerical techniques are also considered. The implementation of the finite element method is discussed. The finite element technique is also modified to incorporate the lack of fixed-potential boundary conditions in dielectric waveguides. The results of the simulations are documented for several experimental and analytical test cases. Measurements were made on waveguides fabricated in-house using the plasma-enhanced chemical vapor deposition (PECVD) films of silicon oxynitride. The light source was a 6328 A helium-neon laser. The results of the finite element simulations are compared with the experimental results and with other previously documented numerical and analytical results from the literature. The finite element method developed here is shown to be in good agreement with these results and will be useful in solving for the modes of novel waveguide designs. / Graduation date: 1993