Nonlinear Optical Response of Nematic Droplets
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NONLINEAR OPTICAL RESPONSE OF NEMATIC DROPLETS
STEVEN M. RISSER AND KIM F. FERRIS Pacific Northwest Laboratory, Box 999, K2-44, Richland, WA 99352
ABSTRACT We have used a finite element method to calculate the nonlinear polarization of small nematic droplets, for both the radial and bipolar director configurations. The nonlinear polarization of droplets with a radial director is concentrated along the droplet axis, while for the bipolar droplets, the nonlinear polarization is more uniform across the droplet. The nonlinear polarization of the bipolar configuration has also been shown to be sensitive to the angle between the droplet axis and the applied field. INTRODUCTION Polymer dispersed liquid crystals (PDLC), which consist of small nematic droplets imbedded in a polymer matrix, have many possible applications in optical and electro-optical devices[l). In the nematic phase, the liquid crystal molecules preferentially align parallel to the director. PDLCs function by using an external field to modulate the refractive index of the nematic droplets, which alters the droplet scattering and the transparency of the PDLC films. There are two methods to alter the refractive index of these droplets: 1) reorient the director within the droplets, and 2) couple a large external field to the nonlinear polarizability of the nematic molecules to increase the refractive index. The first method is used in current PDLC devices, while the second may be useful for power limiter applications. Because of the large optical nonlinearities of the nematic molecules, PDLCs may also find applications as switchable third harmonic generation (THG) devices. Both the linear and nonlinear polarizability of nematic molecules are highly anisotropic. The linear dielectric susceptibility tensor can be directly related to both this anisotropy and the local nematic director, and so may exhibit large spatial variation[2]. For typical liquid crystal molecules, the nonlinear polarizability will have only a component along the director. Because general analytic solutions for the local field and polarization do not exist, we have developed a numerical method to calculate the local field and polarization in nematic droplets. In this paper we will use this method to show the dependence of nonlinear polarization on the director configuration and applied field orientation. Mat. Res. Soc. Symp. Proc. Vol. 228. @1992 Materials Research Society
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METHODS The microscopic polarization of a medium is given by P
= X l(r)(r) -E(r) + X( 2)(r)-E(r) + X 3 )(r) .E(r) + ..
(1)
The first term is the linear polarizability, while the second, third, and higher order terms define the nth order nonlinear polarizability. The local electric field, E, is equal to the sum of the applied and induced fields, where the induced electric field is due to the polarization throughout the whole volume. Although an analytic solution for the local field and linear polarization of the radial director has been found[3], the use of other director configurations, or the inclusion of a no
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