An adiabaticlike approximation is derived for the optical Bloch equations, extended for dense media, and used to interpret recent numerical results for the resonant interaction of ultrashort pulses with dense media. It is shown that dense media can exhibit behavior analogous to adiabatic following and adiabatic inversion. In particular, we show that dense collections of two-level systems can be adiabatically inverted by intrinsic self-chirping.
An adiabaticlike approximation is derived for the optical Bloch equations, extended for dense media, and used to interpret recent numerical results for the resonant interaction of ultrashort pulses with dense media. It is shown that dense media can exhibit behavior analogous to adiabatic following and adiabatic inversion. In particular, we show that dense collections of two-level systems can be adiabatically inverted by intrinsic self-chirping.
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.
We performed a numerical investigation of the dynamics of the optical Bloch equations, extended for near dipole-dipole (NDD) interactions in dense collections of two-level systems. As a function of peak field strength, the inversion that remains in the medium following excitation by an ultrashort optical pulse has step-like transitions between the ground state and the excited state. The medium is left fully inverted if the peak Rabi frequency (peak field strength written in units of frequency) is equal to the NDD interaction strength. Remarkably, this result is independent of pulse area. About this point is a region of peak field strength for which the dense medium is left fully, or nearly fully, inverted. On the weak side of this region, the dense medium is left in the ground state. On the strong side of this region, the medium alternates between absorbing (ground state) and amplifying (inverted) as a function of peak field strength. This response can be used to measure the strength of the NDD interaction, for coherent optical pumping, and also constitutes a new and unique intrinsic optical switch, which, unlike optical bistability, does not have hysteresis and is independent of dissipation from incoherent effects.
We investigate ultrashort pulse propagation in a dense medium of two-level atoms. We numerically solve the coupled nonlinear Maxwell-Bloch equations by assuming that the fields are slowly varying in time only. We find that while intrinsic optical switching of the atomic inversion persists in extended media, self-phase-modulation effects, coherent energy transfer, and reflections can be large even for films that are only a small fraction of a wavelength thick. If the propagation distance is sufficiently large, a physical boundary that separates fully excited atoms from atoms in the ground state can be created within the medium. In turn, this leads to a rapid spatial modulation of the nonlinear polarization, and a deterioration of the intrinsic optical switching mechanism. We then show that, although the slowly varying envelope approximation in space may be preempted by the fast longitudinal variation of the field and atomic variables, the mean-field approximation remains valid in the regime of ultrafast optical switching, provided the film thickness is sufficiently small such that the medium is nearly uniformly excited. These results are generated by utilization of our calculational method that fully accounts for the longitudinal dynamics of the fields, including reflections.
In this work the authors will present analytical results that explain the numerical simulations of M. E. Crenshaw et al.1 on the extended optical Bloch equations that include near dipole–dipole interactions. These simulations have shown the possibility of an ultrafast switch, caused by an incident unaltered pulse in a thin dense medium of two-level atoms. The switching parameter, defined as Ω 0 ε , is a ratio of the Rabi frequency to the strength of the near dipole–dipole interaction Our analysis will show an exact solution for the first switching condition, Ω 0 ε ≈ 1 . Furthermore, an asymptotic analysis will show that to leading order in the asymptotic expansion, only three possible final states of the medium occur. These states, if characterized by the population inversion w, are total inversion (w f = 1), no inversion (w f = -1), or half inversion (w f = 0). For the case w f = 0, a reduced system in a phase plane is derived. This reduced system will help us understand this self-transparent behavior. We will conclude by presenting the results on the stability analysis in parameter space.
We performed a numerical investigation of the dynamics of the Bloch equations, extended for dense media (media having many atoms within a cubic resonance wavelength), for optical pulses whose duration is much less than an induced-dipole dephasing time. We find a signature of near dipole-dipole interaction which may provide a useful method for validating the first-principles model, for measuring the strength of the interaction, and for coherent pumping. Further, we demonstrate a new and unique optical switching mechanism which may lead to the development of important devices.
According to the semi-classical theory of light-matter interaction,the Bloch equations with chirped terms were established in a dense two-level medium,and an accurate and efficient fourth-order Runge-Kutta method was applied for solving the equations.After numerical simulation,the interactions between a chirped ultra-short pulse and dense resonant two-level medium were investigated,and the influences of local-field effects and chirp on Bloch vectors were gained.The numerical results show that,the evolutions of Bloch vectors and the final state of inversion are strongly modulated by the local-field effects correction coefficient and chirp parameter,which provides a method to achieve stable population inversion of control by adjusting the linear chirp parameter and local-field correction coefficient.