Optical properties of short pitch cholesteric liquid crystals

The optical properties of short pitch cholesteric liquid crystals are theoretically analysed in the framework of an effective medium theory. It is shown that such properties are well described by a very simple homogeneous model, defined by an effective permittivity tensor having uniaxial symmetry, that is expanded in a power series of the ratio p/λ0 between the helix pitch and the light wavelength. The linear term is identically zero. This fact gives short pitch cholesterics very unusual properties for their optical activity, which is related to the scaling terms as (p/λ0)m, with m odd and greater than 1. Some problems related to the presence of these terms and concerning boundary effects are discussed but not fully resolved. The limits of validity of the different approximations, obtained by considering only a limited number of terms, are also found.