Spherical tensor analysis of polar liquid crystals with biaxial and chiral molecules

With the help of spherical tensor expression, an irreducible calculus of a Lth-rank macroscopic susceptibility χ for a polar liquid crystal (PLC) of biaxial and chiral molecules written as the average of molecular hyperpolarizability tensor β associated with their spherical orientational order parameters 〈 Y lm 〉 ( 0 ⩽ l ⩽ L ) is presented. Comprehensive formulas of L = 1 , 2 have been obtained and the latter explains the optical activity and spontaneous splay texture observed in bent-core PLC. The expression of L = 3 specifies for the molecules with D 2 symmetry which can be applied to analyze the nonlinear optical second harmonic generation (SHG) observed in proteins, peptides, and double-stranded DNA at interfaces.