Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation
D. Grischkowsky, M. M. T. Loy, P. F. Liao
Two-photon resonantly enhanced parametric generation processes have generally been described using time-dependent perturbation theory. In this paper we show that a theory of two-photon coherent effects can be used to derive and explain these nonlinear mixing processes. Our technique makes use of the adiabatic following (AF) approximation to obtain solutions to a vector model describing the two-photon resonance. We show that the usual results for the nonlinear susceptibilities correspond to the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}$ vector of Feynman, Vernon, and Hellwarth adiabatically following the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\gamma}}}$ vector in the small-angle limit. Consequently, the theory allows a natural extension to large angles, and power-dependent nonlinear susceptibilities are obtained. We then use these AF results for the polarization to study the propagation of pulses nearly resonant with a two-photon transition, and we demonstrate that the pulse reshaping is due to the two related effects of a nonlinear pulse velocity and self-phase modulation.
Physical Review A•Dec 1, 1975•302 citations