Theory of third-harmonic generation in metal vapors under two-photon resonance conditions

Abstract

The density-matrix formalism is used to develop the theory of two-photon-resonant third-harmonic generation in metal vapors taking into account saturation, ionization, laser-induced Stark shifts, and variations in the wave-vector mismatch as a result of population redistribution. It is shown that for third-harmonic generation in the ultraviolet and the vacuum-ultraviolet regions, where $3\omega$ exceeds the ionization limit of the metal vapor, two-photon-resonant three-photon ionization will be the main limiting process. This will also be true for four-wave parametric processes. For efficient energy conversion, the two-photon-resonant metal vapor must be phase matchable to allow large vapor density and cell length. Otherwise, the low incident intensity limits, set by the saturation and the ionization effects, cannot be efficiently converted in only one coherence length. The theory is applied to two-photon-resonant tripling of the ruby laser in cesium vapor.