Laser diffraction by periodic dynamic patterns in anisotropic fluids

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 $\phi$, the phase grating generated in normally incident undeflected light and the first order term correction from light deflection is derived analytically. It yields an $I\propto\phi^4$ 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.