Semi-classical theory of two-photon resonant third-harmonic generation

A semi-classical density matrix theory based on the Method of Averages is used to derive an expression for the third-harmonic generation intensity I^3ω as a function of the fundamental intensity I^ω in the neighbourhood of a two-photon resonance. The result takes account of optical Stark shifts, two-photon saturation and both homogeneous and inhomogeneous broadening. At high intensities, I^3ω∝I^ω, in contrast to the case where optical Stark shifts are ignored for which I^3ω∝(I^ω)^-1.