Stimulated light scattering in smectic A liquid crystals

Abstract

The non-linear interaction of arbitrary polarized light with smectic layer deformations in smectic A liquids (S_A) is considered. It is shown that the combined effect of anisotropy, fluidity and a characteristic kind of deformation cause a number of specific non-linear optical phenomena. Two-wave mixing in S_A transforms into a partly degenerate four-wave mixing (FWM) when the polarization and the direction of propagation of the coupled electromagnetic (EM) waves are arbitrary. The interference of the EM waves gives rise to a dynamic grating of layer deformations without a change of mass density of S_A. In the resonant case a propagating mode of a second sound (SS) is excited. The non-linear phenomena are analysed by solving the self-consistent system of the Maxwell equations for the non-linear anisotropic inhomogeneous medium and the hydrodynamic equations of S_A in the external EM field. The explicit expressions of the EM and SS waves amplitudes are obtained. It is shown that the coupled fundamental EM waves undergo the parametric amplification and the phase cross-modulation, and their amplitudes as well as the SS wave amplitude are spatially localized. The energy transfer between the coupled EM waves is non-reciprocal. The scattering of the fundamental EM waves by the dynamic grating results in the appearance of additional harmonics with combination frequencies and wavevectors. The light induced dynamic grating also generates a longitudinal electric field due to the flexoelectric effect.