QUASI-ADIABATIC APPROXIMATION FOR A DENSE COLLECTION OF 2-LEVEL ATOMS

In dense media, the Lorentz local-field condition results in a general ization of the usual semiclassical Maxwell-Bloch formulation for two-l evel atoms in which the optical Bloch equations are recast in terms of macroscopic spatially averaged atomic variables. We derive an adiabat iclike, or stationary, approximation for the generalized Bloch equatio ns in the ultratransient limit and establish validity criteria. The si gnificance of this quasiadiabatic approximation is that a point respon se solution of the generalized Bloch equations is obtained in terms of the held strength, thereby allowing the atomic response to be express ed as a nonlinear susceptibility that can be used to predict and analy ze propagation effects in dense media. The quasiadiabatic approximatio n is quite general, allowing for a combination of detuning, chirping, and a variety of local-field and mean-field effects. It spans the rang e from cases for which local-field effects can be neglected, as in the usual adiabatic approximation, to cases in which local-field effects cause a large inversion-dependent frequency renormalization. The appro ximation is used to interpret previous numerical results for the reson ant interaction of ultrashort pulses with dense media and it is shown that dense media can exhibit behavior analogous to adiabatic following and adiabatic inversion. The nonlinear index of refraction in the qua siadiabatic limit is purely real for large detunings. However, at and near resonance, the nonlinear index is purely imaginary. The imaginary index relates to coherent reflectivity arising from the reaction fiel d of the cooperating atoms, rather than absorption, and transmission a nd reflection coefficients for thin films are derived. In the intermed iate range of detunings, the intensity-dependent index of refraction c an undergo a phase transition due solely to the variation of the field intensity during excitation by an ultrashort pulse. Propagation effec ts are investigated using a finite-difference time-domain method to in tegrate the generalized Bloch-Maxwell equations and the results of the numerical simulations are analyzed in the context of the nonlinear in dex of refraction obtained using the quasiadiabatic approximation.