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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

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

This dissertation describes various nonlinear grating coupling phenomena in InSb waveguides. InSb exhibits an opto-thermal, diffusive nonlinearity at 9.6μm. This nonlinearity strongly modifies the growth of a guided wave via the grating coupling of an incident, Gaussian signal. In particular, optical limiting and bistability in the coupled power were demonstrated for a detuned grating coupler. The limits on the detunings were also investigated. The experimental results showed qualitative agreement with a theory based upon a diffusive nonlinearity in the grating coupling process. Also demonstrated and theoretically explained was a new form of "butterfly" bistability in the output coupled signal from a nonlinear waveguide. In this situation, nonlinear interference effects in the substrate modified the proportion of power outcoupled into the cover and the substrate. The effects of a thermal nonlinearity on the response of a distributed feedback grating (DFB) were also studied. The DFB reflection response of an incident guided wave was modified either by varying the power of the incident guided wave or that of a second guided wave. Also, the effects of the DFB reflection were shown to enhance the bistable input grating coupling process by providing an additional feedback. This enhancement resulted in a smaller incident switching power required to obtain bistability in the input coupler.

The effect of linear absorption on TE0 nonlinear guided waves and the effect of linear absorption, input-beam misalignment and nonlinear saturation on soliton emission from a nonlinear waveguide have been numerically investigated using the beam propagation method. In the first case the distribution of the absorption is found to have a dramatic effect on the propagation of the nonlinear guided waves. In the second case results reminiscent of the lossless case are found to survive in the presence of these complications.

Thesis (Ph. D.)--Ohio State University, 1980. / Includes bibliographical references (leaves 77-79). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Generalized modal analysis techniques for the characterization and modeling of dissipationless planar waveguide structures and discontinuities encountered in microwave and optical integrated circuits, as well as of quantum waveguide structures and devices, are presented. The frequency-dependent transmission properties of the curved microstrip bend are derived by utilizing a second-order perturbation analysis of the equivalent modified curved waveguide model and a mode-matching method which includes the higher order modes. An extension of the mode-matching method for characterization of microstrip right-angle bends and T junctions having a rectangular notch is formulated. The modal solutions for an arbitrary graded-index dielectric slab waveguide are derived by applying the generalized telegraphist's equations to the equivalent inhomogeneous parallel-plate waveguide model with electric or magnetic walls. These modal solutions are employed in a mode-matching procedure to calculate the transmission properties of a step discontinuity in typical diffused optical dielectric slab waveguides. Power loss calculations for an abrupt offset in a diffused optical waveguide show a smooth increase in radiation loss whereas a sharp transition from almost zero to nearly total radiation loss is found for an abrupt change in diffusion depth. In the analysis of quantum waveguide structures, the modal expansions of the wave function together with a mode-matching technique are utilized. The computed generalized scattering matrices (GSMs) of junctions and uniform waveguide sections are combined via an extended GSM technique to obtain the scattering parameters of composite quantum waveguide structures. Results for cascaded right-angle bends and periodic multi-waveguide structures in a split-gate configuration are presented assuming hard wall confinement. For the multisection structures, strong resonant behavior similar to that in resonant tunneling diodes is found. Calculated current-voltage characteristics for a double constriction in GaAs are shown, exhibiting a region of negative differential resistance for temperatures up to approximately 60K with a maximum peak-to-valley ratio of over 80:1. Finally, a uniform narrow constriction with an assumed parabolic - like lateral potential confinement is analyzed by utilizing the modal expansion techniques developed for dielectric waveguides. / Graduation date: 1991

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.