Nonlinear atomic susceptibilities

Abstract

Starting with well known formulae for nth-order atomic susceptibilities, irreducible spherical tensor techniques and Racah algebra are used to put these in a form suitable for the treatment of complex nonlinear processes, e.g. where fine and hyperfine interactions can be included and the interacting fields can have quite general polarizations. By way of illustration the susceptibilities are calculated in detail for third harmonic generation and Raman scattering in alkali vapours, taking into account the effect of spin-orbit coupling.