SELF-FOCUSED OPTICAL STRUCTURES IN A NEMATIC LIQUID-CRYSTAL

In recent experiments investigating the nonlinear interaction between light and nematic liquid crystals, Braun et al. (1993) observed comple x optical beam structures that were generated by the strong self-focus sing of laser light. For a simplified partial differential equation (P DE) model which captures the essential coupling between optical refrac tion and nematic deformation, we demonstrate two of the experimentally observed features-undulation and filamentation.For the mathematical a nalysis, we develop a novel asymptotic representation for this strongl y coupled nonlinear system which exploits the natural separation of sc ales at which these optical structures are created by the self-focussi ng process. This approach uses geometrical optics, paraxial optics, an d scale-separation to identify tractable outer and inner problems. The outer problem describes the undulation of the beam, and is given by a free-boundary problem for the distortion of the nematic crystal. The inner problem describes the filamentation of the beam, and is given by a nonlocal-nonlinear Schrodinger (NLS) equation for evolution of the light wave. For the outer problem, we demonstrate analytically the exi stence of small amplitude undulations of the beam. Large amplitude und ulations are studied numerically. For the inner problem, waveguide mod es are constructed. Simulations of the nonlocal NLS show that the inte raction of these modes generates filamentary beam structures. Thus the PDE model, when reduced asymptotically into two decoupled systems at two distinct spatial scales, produces a theoretical corroboration of t he unusual nonlinear optical behavior of undulation, as well as a nonl inear mechanism for filamentation.