Theory of second-harmonic generation in nematic liquid crystals

In recent years the observation of optical second-harmonic generation (SHG) in nematic liquid crystal (NLC) MBBA [N-(4-methoxybenzylidene)-4’-n-butylaniline] raised again the question of whether NLC’s possess centrosymmetry. Lyakhov et al. [Izv. Akad. Nauk SSSR 45, 917 (1981)] suggested that these observations can only be explained by considering the NLC as noncentrosymmetric and optically biaxial. In this paper it is shown phenomenologically that even with $D_{\infty h}$ symmetry, SHG arising from ee→e, oo→e, and oe→o interactions can occur in an aligned NLC. With curvature strains SHG arising from ee→o, ee→e, oe→o, oe→e, oo→o, and oo→e interactions are all possible. Several experimental observations are satisfactorily explained by the present calculation. The order of magnitude of the effective susceptibilities estimated from a quadrupole-moment mechanism agrees with the values obtained by Arakelyan et al. [Mol. Cryst. Liq. Cryst. 71, 137 (1981)] and by Barnik et al. [Mol. Cryst. Liq. Cryst. 98, 1 (1983)]. One may conclude that it is possible to explain the occurrence of SHG in NLC’s without having to invoke noncentrosymmetry of the system.