Transient Sum-Frequency Generation in Resonant Three-Level Media

摘要

Nonlinear optical interactions are typically described in terms of the nonlinear optical susceptibility, which is obtained by calculating the steady-state response of the material system to applied optical fields. However, experiments are often conducted using pulsed lasers, and when the pulse length is comparable to or smaller than the relaxation times of the medium, the steady-state treatment of the nonlinear response must be modified to include transient effects. Transient effects in nonlinear optics have been discussed by Grischkowsky and by Courtens and Szoke, primarily for the case of a two-level system, and by Tai for the case of third-harmonic generation. This paper presents an analysis of resonantly enhanced sum-frequency generation (SFG) involving pulsed lasers. The density-matrix equations of motion are solved using second-order, time-dependent perturbation theory with the inclusion of transient effects. The energy and spectrum of the generated radiation are calculated as functions of laser detunings, laser pulse lengths, and temporal overlap of the laser pulses. The tuning characteristics and output pulse characteristics are found to differ qualitatively depending on whether or not the excitation pulses satisfy the adiabatic following criteria generalized for the case of a three-level atom.