Analytical expression for the fringe intensities of a nematic grating excited electrohydrodynamically in the dielectric mode

Abstract

A formula has been derived for predicting the intensities of the first-order fringes that result from the illumination of a periodically reoriented nematic liquid-crystal layer that is excited electrohydrodynamically in the dielectric mode. The agreement between the predictions of the derived formula and those of the more rigorous theory is excellent. It turns out that the intensities of the first-order fringes are proportional to the square of the maximum angle formed between the director and its orientation direction in the undistorted state. It also turns out that these intensities are highly sensitive functions of the incidence angle of the monochromatic light beam that is illuminating the nematic layer; they exhibit two pronounced maxima that correspond to two different incidence angles that are determined by the material and distortion parameters as well as by the wavelength of the illuminating beam. The derived formula is an essential tool for monitoring the motion of the nematic director during electrohydrodynamic excitation in the dielectric mode.