Abstract
This chapter considers different nematic and cholesteric phases from the experimental and theoretical points of view. Besides the usual uniaxial nematic phases, lyotropic mixtures with more than two components may also display biaxial nematic mesophases. This particular mesophase has three different refraction indices depending on the orientation of the electric field of the light rays with respect to the symmetry axes of the structure. The classical example of the potassium laurate/decanol/water mixture is given as an introductory example of a lyotropic system displaying three nematic phases (two uniaxial phases, calamitic and discotic, and a biaxial phase). X-ray diffraction, linear and nonlinear optical experiments are discussed to support the characterization of these structures. A phenomenological Landau model is presented to describe the nematic phase diagram. Cholesteric phases are discussed both experimentally and theoretically.
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