Generation of optical harmonics in atoms

A method is suggested for the calculation of the nonlinear susceptibility corresponding to the generation of second and third optical harmonics in atomic gases. The method is based on the use of the Green's function of an atomic optical electron in the computation of the composite matrix elements. The results are given of a numerical calculation of χ(–3ω;ω,ω,ω) and χ(–2ω;0,ω,ω) for hydrogen, alkali atoms, and inert gases at the frequencies of ruby and neodymium laser radiations and their second harmonics. A two-photon resonance in the generation of the third harmonics is considered.