Propagation of light beams at the interface separating nonlinear diffusive dielectrics.
AdvisorNewell, Alan C.
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PublisherThe University of Arizona.
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AbstractDiffusion effects on the stationary TE nonlinear surface waves and guided waves and the beam propagation characteristics at the interface separating two or more nonlinear diffusive Kerr-like media are studied extensively. The shape of the nonlinear surface and guided waves are computed for differing diffusion mechanisms and diffusion lengths. Stability of these waves is determined using the beam propagation method. The power and the shape of the nonlinear surface or guided waves are seen to be sensitive to the scaled diffusion length. However, many features including the stability criteria from the diffusionless case remain in the presence of the diffusion. An equivalent particle theory, describing the propagation of a self-focused light channel at the interface of two nonlinear dielectric media, is extended to include diffusion of the nonlinear excitation within each medium. The theory replaces the computationally intensive beam propagation problem by a much simpler Newtonian dynamical problem of studying the motion of an equivalent particle in an effective potential. This simpler Newtonian dynamical problem provides quantitative information on the asymptotes of the reflected, transmitted or trapped channels as well as the stability of the latter as a function of increasing diffusion length. The main results are that increased diffusion makes light transmission more difficult and tends to wash out the local equilibria of the equivalent potential representing unstable or stable TE nonlinear surface waves. The dynamics of two beams interacting at an interface separating two nonlinear dielectrics is studied. Using the two-soliton solution of the nonlinear Schrodinger equation (NLS) and performing a perturbation analysis, ordinary differential equations (ODE) approximation for the two beam interaction dynamics are derived. The numerical results of the ODE model are verified by comparison with numerical solutions of the governing full partial differential equation (PDE). This ODE model is reduced to a simple form to carry out a useful analysis for a special case where a single beam propagating as a trapped surface wave acts as a power controllable switch to direct a second beam incident at a finite angle to the interface. In this case the shape of the effective potential for the second beam is obtained and predicts the behavior of such a beam using the equivalent particle theory.
Degree ProgramApplied Mathematics