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Quantum Electronics

Precursor pulse and frequency modulation of quasi-resonance self-induced transparency pulses in the presence of irreversible relaxation

Andrey L. Vershinin, A E Dmitriev, Oleg M. Parshkov

Published Nov 30, 2003• 2 citations
Publisher

Abstract

The quasi-resonance interaction of a laser pulse with an inhomogeneously broadened quantum transition is numerically simulated under conditions corresponding to the experiment on the study of self-induced transparency in rubidium vapours. It is shown that the experimental shift of the pulse spectrum is caused by the initial stage of the formation of a precursor pulse and the influence of irreversible relaxation. It is found that the precursor pulse is more stable to the destructive action of relaxation than the 2π pulse and appears even in the case when the input pulse area is insufficient for the formation of the 2π pulse.

DOI
10.1070/qe2003v033n11abeh002537

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The quasi-resonance interaction of a laser pulse with an inhomogeneously broadened quantum transition is numerically simulated under conditions corresponding to the experiment on the study of self-induced transparency in rubidium vapours. It is shown that the experimental shift of the pulse spectrum is caused by the initial stage of the formation of a precursor pulse and the influence of irreversible relaxation. It is found that the precursor pulse is more stable to the destructive action of relaxation than the 2π pulse and appears even in the case when the input pulse area is insufficient for the formation of the 2π pulse.
The results of a numerical simulation of the evolution of a precursor pulse are presented. This pulse exists at the stage of the conversion of a quasi-resonance input pulse into a 2π pulse considered in the theory of self-induced transparency. Calculations have shown that the efficiency of precursor-pulse formation increases as the input laser pulse shortens and its area approaches π. The results of a numerical analysis of the known experiments on the observation of a precursor pulse in ruby crystals are also presented. In one of the cases considered, the calculation results cast some doubt on the interpretation of the experiment adopted earlier.
The interaction of a sufficiently intense 0 π pulse with the inhomogeneously broadened resonance quantum transition is studied numerically in the slowly varying envelope approximation. The formation of a single optical breather and evolution of the population of energy levels related to it are described. It is found that in the quasi-resonance case, two 2 π pulses of the same duration with different frequencies appear instead of the breather at a large distance. The frequency modulation also prevents the formation of the breather, giving rise to one 2 π pulse or two 2 π pulses of different frequencies and different durations. The results of numerical analysis of the known experiment on the observation of the 0 π pulse in a ruby crystal are presented. It is shown that due to the presence of irreversible relaxation in this experiment, an optical breather was detected at the stage of its transformation to a weak 0 π pulse.
The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .
The transient double resonance in the Λ-scheme is numerically investigated for short input laser pulses whose spectral widths exceed noticeably the Doppler width of quantum transitions. The case of the exact resonance is considered, when the frequencies of input pulses coincide with the central frequencies of quantum transitions, and the quasi-resonance case, when this coincidence is slightly violated. It is shown that a pulse with a lower frequency is shortened and considerably amplified during its propagation in a medium. A pulse with a higher frequency transforms to a pulse with a ridge envelope, which virtually does not decay during its propagation despite the presence of irreversible relaxation. Estimates were performed for quantum transitions in the 208 Pb atom.
The results of numerical modeling of 0pi-pulse evolution in the medium with inhomogeneous broadening of resonant quantum transition line are presented in this paper. The main attention is devoted to phenomena related with 0pi-breather formation as in the strong resonance conditions so as in the presence of small detuning from exact resonance (quasi-resonance case). To compare with existed experimental data the numerical modeling was carried out with adequate duration of input 0pi-pulse and with taking into account of quantum transition transverse relaxation. There is founded that existed in real experiment irreversible relaxation essentially effects on evolution of pulse. So the conclusion can be made that in analyzed experiment the 0pi-breather on the stage of its transformation into many 0pi-pulse was observed