Optical rotation and structure of ferrielectric smectic phases.

We analyze the measured optical rotation in three- and four-layer smectic ferrielectric phases within the matrix approach to the light propagation. We show that "perfect" three- and four-layer structures with 120 degrees and 90 degrees phase rotation of the director in neighboring layers give negligible optical rotation of polarized light travelling along the normal to the smectic layers. Significant optical rotation is obtained in deformed three- and four-layer smectic phases. The analysis of the measured optical rotatory power clearly shows that three-layer ferrielectric phases of [4-(1-methylheptyloxycarbonylphenyl)-octylbiphenyl-4-carboxylate] and 4-[(4-[[1(*)-methyl]heptycarboxy]phenyl)carboxy]phenyl-4'-decyloxy-1-benzencarbatioate (10OTBBB1M7) are deformed with the deformation angle of 35 degrees-45 degrees. The deformation angle in the four-layer smectic phase of 10OTBBB1M7 is 70 degrees-90 degrees. This is in reasonable agreement with other experiments and suggests the validity of the "deformed clock model."