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Nonlinear Optics

Time-Resolved Four-Wave Mixing in Optically Dense Medium

M. Belov, M. A. Selifanov, Edward A. Manykin

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Time-resolved four-wave mixing CTRFWMZ) is a powerful method to study dephasing processes in solids [1]. The self-diffraction or two-pulse scheme of this phenomenon is shown in Fig.1. Presently, a number of the experimental and theoretical works dealt with TRFWM is reported [2-8]. Recently, the novel results which demonstrate the anomalous response of TRFWM with a signal at negative time delays, were obtained [9-10]. This effect cannot be predicted on the basis of the traditional Bloch equation approach [2].

DOI
10.1364/nlo.1992.tud32

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Time-resolved four-wave mixing CTRFWMZ) is a powerful method to study dephasing processes in solids [1]. The self-diffraction or two-pulse scheme of this phenomenon is shown in Fig.1. Presently, a number of the experimental and theoretical works dealt with TRFWM is reported [2-8]. Recently, the novel results which demonstrate the anomalous response of TRFWM with a signal at negative time delays, were obtained [9-10]. This effect cannot be predicted on the basis of the traditional Bloch equation approach [2].
We investigate the phenomenon of self-diffraction in optically dense media for those cases where it is necessary to take into account the inverse effect of the medium on the field. Our study is based on a numerical analysis of the Maxwell–Bloch equations. This analysis reveals that, as the concentration of two-level systems increases, an anomalous response of four-wave mixing arises. This response is associated with the appearance of a self-diffraction signal in the negative-delay region and also with a faster decay of coherence in the system.
We show, both experimentally and theoretically, that short-pulse reshaping clue to propagation leads to the formation of negative-time-delay signals in four-wave mixing (FWM) and to apparent signal decay that is not given by the dephasing or the population-decay rates. Recently, pulse reshaping due to coherent propagation was used to estimate dephasing times in CD, and ZnP·. (Ref. 1), and negative time-delay response in FWM in quantum wells was reported and was explained in terms of higher-order susceptibilities interfering with the third-order FWM process.2
We show that four-wave mixing in optically dense media is very different than in an optically thin medium. In time-resolved degenerate four-wave mixing we experimentally observe ``negative'' time delay response, fast decay rates at short delay times, and broad shoulders at long delays. The observations are explained very well in terms of pulse propagation effects, and a theoretical framework is presented for the analysis of the nonlinear interaction. We treat both the incident and generated fields self-consistently, and solve for the interaction of short pulses with a resonantly absorbing medium. The implications for the extraction of relaxation rates from four-wave-mixing experiments involving ultrashort pulses in optically dense matter are discussed.
We present a time-resolved study of the diffracted pulse in degenerate four-wave mixing experiments with short-response-time materials. The first step is the validation of a theoretical model that takes into account the temporal characteristics of the energy level (relaxation time T1 and dephasing time T2) and of the incident pulse (duration and spectral phase) in a simple particular case. Two methods are used for characterizing the diffracted beam: the amplitude correlation with the reference pulse and the spectrum intensity measurements. We discuss the experimental results, which show good agreement with the theoretical model and evidence the strong influence of the incident pulse characteristics.
Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time T2{\mathit{T}}_{2}T2​. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.