Generalized transmission ellipsometry for twisted biaxial dielectric media: Application to chiral liquid crystals

We report on the application, for the first time to our knowledge, of spectroscopic generalized ellipsometry to liquid crystal materials. We have measured the three normalized elements of the Jones transmission matrix t at various sample temperatures within the spectral range from 340 to 1700 nm (0.73 to 3.65 _eV) on thin cells filled with twisted nematic mixtures 4-cyano-4’-pentylbiphenyl (5CB) and 4-cyano-4’-(2 methyl)-butylbiphenyl (CB15) (Ref. 4). The Berreman 4 × 4 matrix for electromagnetic plane waves in a biaxial medium homogeneously twisted along the sample normal is derived and presented. Analytic expressions in the case of light propagation along the helical axis permit the calculation of the transmission and reflection coefficients simultaneously without numerical approximations. This solution is valid for any biaxial configuration of chiral liquid crystals, including the case of absorption. We have fully analyzed the measured Jones transmission matrix elements and obtained the geometrical sample properties and, as a function of the photon energy and the temperature, the refractive indices n_o, and n_e of the chiral liquid crystals. We found that within the experimental error the main refractive indices of the mixtures 5CB and CB15 are those of pure 5CB at the same reduced temperatures. The handedness of the optical activity of the samples can be obtained immediately from the phase information of the Jones transmission matrix coefficients.