Light interacting with liquid crystals

In this paper we describe laser light interacting with nematic liquid crystals. The paper begins with a summary of recent experimental results of E. Braun, L. Faucheux, and A. Libchaber in which the liquid crystal sample is studied in three geometries - film, pipe, and droplet. Then, after a very brief glimpse at the history of liquid crystals, a theoretical model of the interacting system is described. In a one transverse dimensional idealization, we investigate the pipe and film configurations. In these cases the model reduces to a coupled system of nonlinear pde's - an elliptic sine-Gordon equation for the director field coupled to a Schroedinger equation for the electromagnetic field. Properties and qualitative behavior of this coupled system are described, both numerically and theoretically. As an illustrative example of boundary layer analysis of such coupled light-nematic systems, we describe calculations in the film geometry in some detail. Results of this analysis include: (i) an extension of the Frederiks bifurcation analysis to electric fields with spatial variation; (ii) the determination of the transverse scale at which self-focusing saturates in this nematic; (iii) the derivation of a nonlocal nonlinear Schroedinger equation which governs the inner structure of the laser beam. We conclude the paper with a summary of similar boundary layer calculations for light-nematic systems in other geometries.