Fluctuations and Light Scattering in a Compressible Cholesteric Liquid Crystal

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Abstract
The normal modes of a compressible cholesteric liquid crystal are determined from the hydro-dynamical equations of Ericksen and Leslie for the case of the propagation vector parallel to the helical axis. Besides the overdamped twisting and viscous-splay modes present in the incompressible case we find a sound wave mode which couples to orientation and produces a propagating twist wave. The results are not restricted to wavelengths large compared to a pitch. The sound wave contributes six lines to the Brillouin spectrum at frequencies ± cq, ± c(q ± 2q0), where c is the sound velocity, q the momentum transfer and q0 = π/P0 where P0 is the pitch. The twist wave contributes only to the latter four lines and its intensity dominates near the condition for Bragg scattering.