Laser diffraction by periodic dynamic patterns in anisotropic fluids

Abstract

This paper describes the application of a laser diffraction technique to the study of electroconvection in nematic liquid crystal cells. It allows a real-time quantitative access to pattern wave lengths and amplitudes. The diffraction profile of the spatial periodic pattern is calculated and compared quantitatively to experimental intensity profiles. For small director tilt amplitudes ϕ, the phase grating generated in normally incident undeflected light and the first order term correction from light deflection is derived analytically. It yields an I ∝ ϕ 4 dependence of the diffracted intensity I on the amplitude of director deflections. For larger director tilt amplitudes, phase and amplitude modulations of deflection of light in the inhomogeneous director field are calculated numerically. We apply the calculations to the determination of the director deflection and measure growth and decay rates of the dissipative patterns under periodic excitation. Real time analysis of pattern amplitudes under stochastic excitation is demonstrated. PACS. 4 2.70.Df (Liquid Crystals), 47.20.-k (Hydrodynamic instability), 78.20.-e (Optical Properties of bulk materials and thin films).

Decay of spatially periodic patterns in a nematic liquid crystal

“…(2) and (3) is not self-adjoint, one has to solve the adjoint problem as well. Finally the contribution of the different modes to the intensity of the fringes has to be calculated following-e.g., the methods presented in [10,11]. A corresponding detailed analysis is presently under way.…”

“…where J n is a Bessel function of the first kind of order n, while the quantities B n and Q depend on the refractive indices, the angle of incidence, and the shape of the director profile [11,12]. In the limit of small m , which is relevant for our study, we have I n ϰ m 2n .…”

“…Thus the I n for small n prevail. For symmetry reasons only the even-order fringes are visible (at least for small deformations) at normal light incidence [8][9][10][11]. For oblique incidence [11,12], however, the oddorder fringes (in particular n =1) become accessible, which thus present a sensitive tool to monitor variations of EC pattern amplitudes near the threshold.…”

Preparation of subharmonic patterns in nematic electroconvection

“…Most of the involved material parameters are known from independent experiments. Some unknown parameters, like the conductivity that varies slightly for individual cells, were determined by fitting threshold voltages and wave numbers at single-frequency square-wave excitation to the measured characteristics [10,11]. In detail, ʈ = 5.6, Ќ = 6.0, ʈ = 260 s −1 , ʈ / Ќ = 1.5, ␣ 1 = 0.2 g cm −1 s −1 , ␥ 1 =−␥ 2 = 3.67 g cm −1 s −1 , 1 =4 g cm −1 s −1 , 2 = 0.4 g cm −1 s −1 , K 11 = 14.9ϫ 10 −7 g cm s −2 , K 33 = 13.76ϫ 10 −7 g cm s −2 (cgs units).…”

“…In detail, ʈ = 5.6, Ќ = 6.0, ʈ = 260 s −1 , ʈ / Ќ = 1.5, ␣ 1 = 0.2 g cm −1 s −1 , ␥ 1 =−␥ 2 = 3.67 g cm −1 s −1 , 1 =4 g cm −1 s −1 , 2 = 0.4 g cm −1 s −1 , K 11 = 14.9ϫ 10 −7 g cm s −2 , K 33 = 13.76ϫ 10 −7 g cm s −2 (cgs units). The pattern dynamics is recorded using laser diffraction [11]. The He-Ne laser beam (wavelength L = 632.85 nm) is diffracted by phase and amplitude gratings formed by the periodically distorted director field.…”