Third-harmonic-generation study of orientational order in nematic liquid crystals

Relationships between the optical third-harmonic-generation susceptibility ${\chi }_{\mathrm{ijkl}}^{\mathrm{}\left(3\right)\mathrm{}}$(-3ω;ω,ω,ω) and the nonvanishing order parameters 〈$P_2$〉 and 〈$P_4$〉 for a nematic-liquid-crystal phase are presented. Third-harmonic-generation experiments were performed on the nematic N-(p-methoxybenzylidene)-p-butylaniline (MBBA) using the wedge-maker fringe method as a function of polarization and temperature to demonstrate the simultaneous determination of 〈$P_2$〉 and 〈$P_4$〉. The results are in agreement with previous experimental results from nuclear magnetic resonance and Raman scattering studies. Local-field corrections are considered, and based on the data, local-field factors do not appear to depend on the long-range anisotropy of the macroscopic medium.