Four-photon coherent resonant propagation and transient wave mixing: Application to the mercury atom.

Abstract

Density-matrix formalism is applied to construct a model for third- and fifth-harmonic generation in a four-photon resonant medium. The transition rates and coherent superposition of states associated with the resonant levels are treated rigorously, while the adiabatic following approximation is used to calculate the contribution of all nonresonant levels to the interaction. Expressions for the quadratic and quartic Stark shift and multiphoton ionization emerge naturally from the theory. At the power level required for appreciable four-photon absorption, the intensity-dependent Stark shift and ionization become overwhelming and limit the efficiency of harmonic generation. Because of the Stark shift, an intense pulse suffers a ``self-detuning'' effect and propagates through the resonant medium with minimal absorption. The interference of the phase-dependent Raman scattering with the multiphoton transition is found to be responsible for the vanishing of ionization in the presence of the generated third-harmonic field, an effect which was observed in earlier experiments.