Optical diffraction in twisted liquid-crystalline media-phase grating mode

We have calculated the diffraction of light perpendicular to the twist axis in a chiral smectic C liquid crystal. In contrast to a cholesteric liquid crystal, in a chiral smectic C liquid crystal we find extra orders which form the odd orders in the diffraction pattern. For an incident linearly polarized light, at a general azimuth, these odd orders are linearly polarized and the even orders are elliptically polarized. The intensities of the odd orders are always independent of the azimuth of the incident light, while this is possible for even orders only at a particular tilt angle of the chiral smectic C liquid crystal. Also, for the incident vibration parallel or perpendicular to the twist axis the odd orders are polarized in the orthogonal linear state with respect to incident vibration, while the even orders are in the same linear state.