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Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

Optical nonlinearity and bistability in liquid crystals

Y. Ron Shen

Published Dec 18, 1984• 24 citations
Publisher

Abstract

Abstract Molecular reorientation and laser heating induced by an optical field can yield significant changes in the refractive indices in a nematic liquid crystal. A c.w. laser beam is intense enough to induce a phase retardation much larger than 2pi in a nematic film less than 100 pm thick. Optical bistability in such a film sandwiched between mirrors can be readily observed. Coupling between the two mechanisms for induced refractive indices can lead to interesting results in the bistable operation.

DOI
10.1098/rsta.1984.0114

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Abstract Molecular reorientation and laser heating induced by an optical field can yield significant changes in the refractive indices in a nematic liquid crystal. A c.w. laser beam is intense enough to induce a phase retardation much larger than 2pi in a nematic film less than 100 pm thick. Optical bistability in such a film sandwiched between mirrors can be readily observed. Coupling between the two mechanisms for induced refractive indices can lead to interesting results in the bistable operation.
We present a quantitative theoretical and experimental study of the transverse dependence of nematic liquid crystal axis reorientation by a laser beam of beam sizes that are comparable to the liquid crystal film thickness. As a result of the interplay between the boundary torques and the torques exerted by the molecules outside the laser beam on the molecules within the laser beam, interesting nonlocal effects arise. The natures of the torque balance equations and the solutions for the reorientation profile are very different for laser polarizations that are normal, or obliquely inclined, to the director axis. If the laser polarization is perpendicular to the director axis there is a threshold intensity for reorientation to occur. The relative width of the reorientation profile (with respect to the laser beam waist) can be larger (or smaller) than unity depending on whether the laser beam size is smaller (or larger) than the film thickness. On the other hand, if the beam polarization is not normal to the director axis, the width of the response is always larger than the laser beam waist. These nonlocal behaviors have profound effects on transverse optical bistability switching behaviors and switching intensities.
We have studied theoretically and experimentally the nonlinear Fabry-Perot transmission of a cavity with a thin nematic liquid-crystal film. Various modes of operation have been observed, using a moderate-power cw laser. In the limit of small reorientation angles, the optically induced molecular reorientation of the birefringent crystal and the nonlinear phase shift is solved for a homeotropically aligned crystal. Multiple-valued Fabry-Perot transmission is obtained by solving the nonlinear equations that couple the optical phase shift with the cavity transmission. The time-independent nature of the process and the explicit quantitative expressions involving the nematic liquid-crystal parameters allow a direct comparison between the thoery and experimental results. Good quantitative agreement is demonstrated.