  Electro-optical properties of deformed helix ferroelectric liquid crystal
(DHFLC) cells are studied by using a general theoretical approach to
polarization gratings in which the transmission and reflection matrices of
diffraction orders are explicitly related to the evolution operator of
equations for the Floquet harmonics. In the short-pitch approximation, a DHFLC
cell is shown to be optically equivalent to a uniformly anisotropic biaxial
layer where one of the optical axes is normal to the substrates. For in-plane
anisotropy, orientation of the optical axes and birefringence are both
determined by the voltage applied across the cell and represent the parameters
that govern the transmittance of normally incident light passing through
crossed polarizers. We calculate the transmittance as a function of the applied
voltage and compare the computed curves with the experimental data. The
theoretical and experimental results are found to be in good agreement.
