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Quantum Electronics

Numerical simulation of the evolution of an intense 0πpulse and formation of an optical breather at the inhomogeneously broadened resonance quantum transition

Oleg M. Parshkov

Published Sep 30, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe2007v037n09abeh013431

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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 numerical simulations are outlined for the evolution of a 0π pulse in a medium with an inhomogeneously broadened quantum transition neglecting irreversible relaxation. A rule is formulated for the prediction of the 0π-pulse structure at long distances, which relies on the notion of the 0π-pulse area as the area under the curve of the modulus of its envelope. Analytical relations between the duration, the peak value, and the propagation velocity are given for the 0π pulse of the breather type.
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
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 formation and collisions of breathers excited by laser radiation at the inhomogeneously broadened J = 0 → J = 1 quantum transition are studied by numerical simulations in the slowly varying envelope approximation. Conditions are obtained under which laser pulses with the initial shape quite simply realised in experiments can be transformed into elliptically polarised breathers in the medium, each of the components of their field being a breather described by the theory of self-induced transparency at a nondegenerate quantum transition. It is shown that the collision of such breathers is not elastic in the general case and leads to the appearance of more general types of resonance breather-like pulses. Taking into account relaxation processes, the possibility of the formation of a breather at the 6p 2 3 P 0 → 6p7s 3 P 1 transition in the 208 Pb isotope is investigated. It is found that relaxation in some case not only causes the pulse decay but also changes the eccentricity of its polarisation ellipse.
Theresults ofnumerical modeling ofOn-pulse evolution inthemediumwithinhomogeneous broadening ofresonant quantum transition line arepresented inthis paper.'The mainattention isdevoted to phenomena related withOn-breather formation asinthestrong resonance conditions soasinthepresence of small detuning fromexact resonance (quasi-resonance case). Tocompare with existed experimental data the numerical modeling wascarried outwith adequate duration ofinput On-pulse andwith taking into account of quantum transition transverse relaxation. There isfounded that existed inreal experiment irreversible relaxation essentially effects onevolution ofpulse. Sotheconclusion canbemadethat inanalyzed experiment theOi- breather onthestage ofits transformation into wanyOIL-pulse wasobserved.
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.