The rigorous descriptions of linear and nonlinear guided wave theory are given together with a geometrical description that helps in the understanding of the physical phenomena taking place. The nonlinear waveguide discussed in this dissertation is composed of a linear thin film and substrate with a cladding material whose refractive index varies with the intensity of the light. Experimentally, this was accomplished, by placing an oriented liquid crystal (highly nonlinear but extremely slow) on top of a thin film glass waveguide. When the liquid crystal used was K15, light-induced mode cutoff was observed. The TE(,0) mode became leaky as the guided wave power was increased. This was a consequence of the light-induced increase in refractive index due to thermal effects. This behaviour was studied as a function of temperature. Light by light modulation was also accomplished with this setup. The theory of the linear and nonlinear prism coupler and the first experimental investigations on the nonlinear prism coupler are given. The nonlinear prism coupler used was obtained by depositing a small amount of MBBA liquid crystal in the gap beween the input coupling prism and the thin film. The basic properties of the nonlinear prism coupler were demonstrated experimentally and the results obtained were verified to have their origin in the temperature component of the nonlinear index of refraction. Good qualitative agreement between the theory developed and experiments were obtained. Bistability and switching in a thin film waveguide with a K18 liquid crystal cladding has been demonstrated for the first time. These experiments made use of the interesting phenomena associated with the nematic to isotropic phase transition. Such behaviour was satisfactorily explained by the intense light scattering associated with the critical opalescence that accompanies such a phase transition in a liquid crystal. Both the TE(,0) and the TM(,0) modes were found to exhibit such behaviour.

A theory is presented which describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. A complete characterization of the different behavior of the channel is given in the proper parameter space. In the dominant region, the nonlinear wavepacket representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton's equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase planes of the equivalent potential. This theory provides therefore, the nonlinear Snell's Laws of refleciton or transmission since the particle dynamics gives the critical angle of total reflection and in the case of transmission, the corresponding angle of transmission. This theory also gives the stability characteristics of nonlinear surface waves, which had only been partially established in the past through numerical simulations. Finally, some applications of the theory are presented such as the design of an all-optical power adjustable spatial scanning element and an all optical switch. Extensions of the theory to waveguides with multiple interfaces are also given and possible new directions are also suggested.

The small dispersion limit of the focusing nonlinear Schroödinger equation (fNLS) exhibits a rich structure with rapid oscillations at microscopic scales. Due to the non self-adjoint scattering problem associated to fNLS, very few rigorous results exist in the semiclassical limit. The asymptotics for reectionless WKB-like initial data was worked out in [KMM03] and for the family q(x, 0) = sech^(1+(i/∈)μ in [TVZ04]. In both studies the authors observed sharp breaking curves in the space-time separating regions with disparate asymptotic behaviors. In this paper we consider another exactly solvable family of initial data, specifically the family of centered square pulses, q(x; 0) = qx[-L,L] for real amplitudes q. Using Riemann- Hilbert techniques we obtain rigorous pointwise asymptotics for the semiclassical limit of fNLS globally in space and up to an O(1) maximal time. In particular, we find breaking curves emerging in accord with the previous studies. Finally, we show that the discontinuities in our initial data regularize by the immediate generation of genus one oscillations emitted into the support of the initial data. This is the first case in which the genus structure of the semiclassical asymptotics for fNLS have been calculated for non-analytic initial data.

Large amplitude interfacial waves are an important feature of annular gas-liquid two-phase flow. They act as a source of entrainment for liquid droplets. They occur for liquid flow rates above a critical value which depends on the gas flow rate. This thesis examines the formulation of a mathematical model to describe the behaviour of these nonlinear waves. Attention is focussed on the case of vertical upwards flow with reference to the experimental conditions for the rig at AERE Harwell. A comprehensive account is given of the limitations and similarities of mathematical models proposed by earlier research workers and their applicability to vertical two-phase flow. The most suitable approaches are found to be kinematic wave theory and an integral method. Experiments have been carried out at AERE Harwell to determine the relationship between liquid flux and film thickness required by kinematic wave theory and also to test some of the theory's predictions. There is a discussion of the difficulties involved in modelling the stresses exerted by the turbulent gas core on disturbance waves. The applicability of Benjamin's 'quasi-laminar' theory is considered. A linear stability analysis indicates that the interface is always unstable. The linear theory cannot provide a criterion for disturbance wave inception. Alternative explanations for wave inception are suggested. The SMAC (Simplified Marker And Cell) numerical method has been developed to model the time dependent behaviour of large amplitude waves in vertical annular two-phase flow. Finally, it is proposed that any realistic mathematical model for disturbance waves should be based upon kinematic wave theory and should take account of wave-breaking.

No description available.

Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains xxvii, 375 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 139-152).

Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 181-188). Also available on the World Wide Web.

Thesis (Ph. D.)--University of California, San Diego, 1997. / Vita. Includes bibliographical references (leaves 102-106).

Proefschrift-Delft. / "Stellingen": [4] p. inserted. Summary in Dutch. Bibliography: p. 79-80.

Thesis (Ph. D.)--University of Delaware, 2005. / Principal faculty advisor: Victor V. Klemas, College of Marine Studies. Includes bibliographical references.