Nonlinear optical response from periodic molecular structures

Abstract

The explicit expressions of all independent components of the molecular crystal nonlinear susceptibility (NS) tensor (of any order) are given through the independent components of hyperpolarizability (HP) tensors of the constituting molecules. This expression has a polynomial form of convolutions of HP components and includes local field tensor components; each product contains from 1 to k−1 HP cofactors of all preceding ranks, and k is NS rank. The Bloembergen-Armstrong formula for the first NS and Hurst-Munn for the second NS are particular cases of this expression. The reciprocal equation for molecular HP in terms of crystal NS is also presented. The Lorentz formula of the phenomenological reaction field theory is derived from the microscopic crystal Hartree-Fock HP equations with the Madelung polarization potential included. The derivation is based on the expansion of the Madelung polarization interaction over the inter-ion distances. The second order term of this expansion is expressed through the Lorentz tensor components. The expansion is obtained due to a convenient method of calculation of the Madelung crystal sums. This technique enabled to reformulate for a molecular crystal the existing computational quantum methods for lone molecules. In particular, Hartree-Fock equations for HP of molecules are adjusted for the optical properties of molecular crystals and layers. The illustrative examples, demonstrating various aspects of the mentioned techniques, are presented.