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Soviet Journal of Quantum Electronics

Self-diffraction in optically dense media

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

Published Nov 30, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1992v022n11abeh003661

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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 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.
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 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
Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.
Analytic and numerical solutions of the Maxwell–Bloch equations, including transverse and timedependent phase variations, predict on-resonance self-focusing (SF) and elucidate its formation due to the combined effect of diffraction and inertial response of the medium. This new SF can be characterized by a simple parameter in terms of the beam and medium parameters. Recently, two independent experiments on SF in Na and Ne demonstrated convincingly this new SF effect for spatially nonuniform self-induced transparency pulses propagating in thick resonant absorbers.