Parametric amplification of light as a result of frequency-degenerate interaction of two waves in a liquid crystal

New mechanisms of the cubic nonlinearity of absorbing liquid crystals are proposed. These mechanisms can result in parametric amplification in the case of frequency-degenerate interaction of waves. Amplification is based on the dependence of the pitch of a helix of a cholesteric liquid crystal on temperature or on the concentration of an isomer which is formed as a result of absorption of incident radiation. The possibility of amplification as a result of a gyrothermal effect in nematic liquid crystals is considered. Typical pump intensities required for the observation of these effects amount to a few watts per square centimeter.