Polarization field and orientational order in liquid crystals

Optical birefringence is a conveniently measurable quantity that is often used for determining the orientational order in uniaxial liquid crystals. The orientational order parameter is given by S = αe − α0/ α|| − α⊥ where αe and α0 are the polarizabilities of the medium corresponding to the extraordinary and ordinary refractive indices, α|| and α⊥ are the corresponding values for a perfectly oriented medium with S = 1