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 resul ts of E. Braun, L. Faucheux, and A. Libchaber in which the liquid crys tal sample is studied in three geometries - film, pipe, and droplet. T hen, after a very brief glimpse at the history of liquid crystals, a t heoretical model of the interacting system is described. In a one tran sverse dimensional idealization, we investigate the pipe and film conf igurations. In these cases the model reduces to a coupled system of no nlinear pde's - an elliptic sine-Gordon equation for the director fiel d coupled to a Schroedinger equation for the electromagnetic field. Pr operties and qualitative behavior of this coupled system are described , both numerically and theoretically. As an illustrative example of bo undary layer analysis of such coupled light-nematic systems, we descri be calculations in the film geometry in some detail. Results of this a nalysis include: (i) an extension of the Frederiks bifurcation analysi s 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 w hich governs the inner structure of the laser beam. We conclude the pa per with a summary of similar boundary layer calculations for light-ne matic systems in other geometries.