Crystal symmetry and nonlinear optical properties

In an introductory section, the symmetry properties of some of the higher rank polar tensors relating to nonlinear optical polarization are briefly enumerated. It is noted that linear magneto-electric polarizability has been experimentally measured and that the reported results are in conformity with the theory. Symmetry properties of the higher rank axial tensors relating to nonlinear magneto-electric effect are enumerated and it is suggested that such an effect is possible in some crystals in the anti-ferromagnetic state. In all these studies, methods developed earlier by the author have been used.