Classical Approach to Third-Order Non-Linear Susceptibilities

Abstract

The important quantitiy in any nonlinear light scattering phenomenon is the nonlinear molecular susceptibility where N indicates Nth order dependence on the inducing electric field and the subscripts i, j , k , l, … denote directions in a Cartesian coordinate system indicating polarization directions of the generated and incident radiation. In general, ∼ denotes a vector, ≈ denotes a tensor of rank two and ≈ will identify tensors of rank greater than two. The susceptibility X^(N) is a tensor of rank N+1. Third order effects include Coherent Stokes and Anti-Stokes Raman Scattering, the a.c. and d.c. Kerr effects, third harmonic generation, self-focussing, self-phase modulation, stimulated Brillouin scattering, stimulated Raman scattering, Raman induced Kerr effect and inverse Raman.