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Physical review. B, Condensed matter

Theory of pulse propagation and wave-mixing processes under intense resonant excitation

Samy S. Montasser, J. Miletic, B. Hönerlage

Published Sep 15, 1989• 4 citations
Publisher

Abstract

We study the temporal and spatial evolution of a pump, test, and signal field generated in a four-wave-mixing process for resonant excitation of a nonlinear medium by nanosecond pulses. The propagation effects for the pulses are taken into account beyond the usual mean-field approximation. The model is then applied to a three-level system, describing CuCl at low temperatures. A great deal of new information concerning the temporal and spatial structures of the different fields propagating through the sample is obtained. We show, for instance, that the temporal shapes of the interacting fields are well established after propagation through the first few micrometers of the sample. Beyond this, they propagate with a diminishing amplitude. We also show that these structures are due to the dephasing of the fields throughout their propagation as well as to the temporal evolution of the absorption and generation function of the sample.

DOI
10.1103/physrevb.40.6163

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We study the temporal and spatial evolution of a pump, test, and signal field generated in a four-wave-mixing process for resonant excitation of a nonlinear medium by nanosecond pulses. The propagation effects for the pulses are taken into account beyond the usual mean-field approximation. The model is then applied to a three-level system, describing CuCl at low temperatures. A great deal of new information concerning the temporal and spatial structures of the different fields propagating through the sample is obtained. We show, for instance, that the temporal shapes of the interacting fields are well established after propagation through the first few micrometers of the sample. Beyond this, they propagate with a diminishing amplitude. We also show that these structures are due to the dephasing of the fields throughout their propagation as well as to the temporal evolution of the absorption and generation function of the sample.
Abstract Using nanosecond laser pulses the time behaviour is investigated of degenerate four‐wave mixing close to the biexcitonic resonance in CuCl. The signal emission presents different time evolutions depending on excitation conditions. Its generation rate shows intensity changes and retardation effects. These effects are explained by an attenuation of the pump pulse through a time‐dependent nonlinear absorption and, at the resonance, by a loss of coherence related to collisions with bi‐excitons.
We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.
The optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is T2{\mathit{T}}_{2}T2​, the apparent decay rate 2/Ta{\mathit{T}}_{\mathit{a}}Ta​ of a time resolved four-wave mixing signal is given by 2/Ta{\mathit{T}}_{\mathit{a}}Ta​=(2/T2{\mathit{T}}_{2}T2​)(1+\ensuremath{\alpha}L/2).
We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.
Maxwell's equations for the apparently complicated generation and propagation of femtosecond four-wave-mixing signals in optically thick samples can be solved by triple Fourier transformation into the three-dimensional (3D) frequency domain. Given the linear absorption and refractive-index spectra, the propagation problem can be solved in three dimensions under the assumption that nonlinear distortions of the excitation pulses can be neglected. A propagation function exactly incorporates the linear evolution of the excitation pulses, the nonlinear generation of the signal, and the linear propagation of the signal. A quantitative treatment of the directional filtering of the 3D susceptibility that arises from excitation with noncollinear pulses and selective interference detection of signal in one phase-matched direction is developed. This 3D treatment is used to examine the influence of phase-matching bandwidth, directional filtering, and sample absorption on femtosecond four-wave-mixing signals in the rectangular and square boxcars phase-matching geometries.
We study the evolution in time and in one space coordinate of picosecond laser pulses interacting with a nonlinear medium modeled by three quantum states. This is done by solving numerically the equation of evolution of the density matrix elements together with the Maxwell equation. The nonperturbative treatment of the density matrix allows us to understand the contribution of the different optical transitions and populations to the pulse deformation during its propagation. We apply the model to CuCl where the quantum levels are the fundamental, the excitonic, and the biexcitonic states. Near the two-photon resonance, the pulse is strongly altered and the excitonic and biexcitonic levels show a population inversion. A modulation of the amplitude and a superbroadening of the phase occur during the propagation.