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 bounding surfaces. 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 electric field and compare the computed curves with the experimental data. The theoretical and experimental results are found to be in good agreement.

We study both theoretically and experimentally the electro-optical properties of vertically aligned deformed helix ferroelectric liquid crystals (VADHFLC) with subwavelength pitch that are governed by the electrically induced optical biaxiality of the smectic helical structure. The key theoretical result is that the principal refractive indices of homogenized VADHFLC cells exhibit the quadratic nonlinearity and such behavior might be interpreted as an orientational Kerr effect caused by the electric-field-induced orientational distortions of the FLC helix. In our experiments, it has been observed that, for sufficiently weak electric fields, the magnitude of biaxiality is proportional to the square of electric field in good agreement with our theoretical results for the effective dielectric tensor of VADHFLCs. Under certain conditions, the 2π phase modulation of light, which is caused by one of the induced refractive indices, is observed without changes in ellipticity of incident light.