Quasiadiabatic approximation for a dense collection of two-level atoms

Abstract

In dense media, the Lorentz local-field condition results in a generalization of the usual semiclassical Maxwell-Bloch formulation for two-level atoms in which the optical Bloch equations are recast in terms of macroscopic spatially averaged atomic variables. We derive an adiabaticlike, or stationary, approximation for the generalized Bloch equations in the ultratransient limit and establish validity criteria. The significance of this quasiadiabatic approximation is that a point response solution of the generalized Bloch equations is obtained in terms of the field strength, thereby allowing the atomic response to be expressed as a nonlinear susceptibility that can be used to predict and analyze propagation effects in dense media. The quasiadiabatic approximation is quite general, allowing for a combination of detuning, chirping, and a variety of local-field and mean-field effects. It spans the range 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 approximation is used to interpret previous numerical results for the resonant 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 quasiadiabatic 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 field of the cooperating atoms, rather than absorption, and transmission and reflection coefficients for thin films are derived. In the intermediate range of detunings, the intensity-dependent index of refraction can undergo a phase transition due solely to the variation of the field intensity during excitation by an ultrashort pulse. Propagation effects are investigated using a finite-difference time-domain method to integrate the generalized Bloch-Maxwell equations and the results of the numerical simulations are analyzed in the context of the nonlinear index of refraction obtained using the quasiadiabatic approximation.