published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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The problem of electromagnetic wave propagation across the junction of two similar planar dielectric waveguides is analysed, within the Kirchhoff approximation, by expanding the field into transverse variations of all possible modes. It is proven that the expansion can represent any solution for any planar dielectric waveguide. The spectral function is introduced into the representation, and this helps resolve some of the theoretical problems in passing from the limit of closed waveguides to open waveguides. Using the spectral function and the Gel'fand-Levitan integral equation some new exact solutions to novel dielectric planar waveguides can be found. Examples of waveguiding by total internal reflection or by Bragg reflection (which are physically very different processes) can be generated by changing a single parameter in the formulation. Usually the representation for an open dielectric waveguide requires the matrix spectral function. However the Gel'fand-Levitan reconstruction is defined for scalar spectral functions. A technique for constructing the spectral matrix and the scattering solutions from two spectral functions is demonstrated. This technique uses a variational formulation of a scattering experiment. The connection between a dielectric structure and the characteristics of propagation on it is obscure. However the connection between these characteristics and the spectral function is much clearer. It is sometimes possible to make predictions about the properties of the waveguide by looking at its spectral function only. Since the connection between the spectral function and the dielectric structure is well established by inverse spectral theory, introducing the spectral function has been of help in establishing the desired connection between the dielectric structure and the characteristics of propagation on it. Such considerations suggest one of the above waveguides is sensitive to small perturbations and could be used as an electro-optic modulator. Detailed calculations confirm the hypothesis. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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There is often a need to interpolate data that is obtained through experiment or computational analysis, because the data is difficult or expensive to obtain. An example is the scattering parameters of microwave devices, obtained through computationally intensive finite element (FE) analysis. Cauchy interpolation is an established solution to this problem. In this thesis it is extended to interpolate data over a multi-parameter space, when the data available includes not just the function to be interpolated, but also its derivatives with respect to each parameter. The finite element method (FEM) provides such derivatives. The new algorithm is applied to a simple RLC circuit test case, and to real data from a 3D FE analysis of a rectangular waveguide component, in a 4-parameter space. Results show the effectiveness of the approach taken.

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

In this thesis a numerical technique is developed determining the propagation constant in waveguides and transmission lines. The technique accounts for both dielectric and conductor losses in a guide having an arbitrary cross section and uses a full-wave solution process. A set of coupled, vector integral equations which characterize the system are derived. The equations enforce the necessary boundary conditions on the tangential electric and magnetic fields at the boundaries separating the conductors and dielectrics. The method of moments (MOM) technique is used to cast the equations into a numerically solvable form. Computed results for various waveguide structures are compared to known or perturbed results for three well-known structures. However, the program is more general and may be applied to other cross-sections. Finally, possible future extensions of the work is presented. / Master of Science