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Abstract
We present a theoretical study of two-wave mixing in smectic A liquid crystals (SALC) due to the resonant interaction of the electromagnetic (EM) waves through the second sound (SS), which is a new type of the cubic non-linearity. It is shown that a parametric amplification of one EM wave by the other occurs. Explicit expressions for the EM and SS wave amplitudes are obtained, which appear to be of the kink and transverse spatial soliton form, respectively. It is also shown that the SS wave creates flexoelectric polarization and space charge. The estimated gain is one or two orders of magnitude greater than the gain for the stimulated Brillouin scattering in isotropic organic liquids. The theoretical results obtained may be used as a basis for an experimental investigation of SS high frequency behaviour.