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NUMERICAL SIMULATIONOFOH-PULSE EVOLUTIONINTHE MEDIUMWITHGREATINHOMOGENEOUSBROADENINGOF RESONANTTRANSITION LINE

A E Dmitriev, Oleg M. Parshkov

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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.

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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 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
Transient regime ofcommon-upper-level scheme double resonance isstudied numerically. Itwas shown that inthepresence ofresonance detunings inchannels ofinteraction andwith taking into account ofin- homogeneous broadening ofresonant transition lines theprocess ofstationary gained signal pulse forming isac- companied withsignal carrier frequency pulling tothevalue that iscorresponding somecondition. Thisrelates frequency detunings with transition central frequencies anddiffers fromsuch conditions forRamanscattering. In somecases. Satisfaction ofthis condition provides theeffective conversion ofpumppulse energy into signal one.Depends onfrequency detuning values one-ortwo-pulse structure will arise insignal channel. Tovary these detunings itispossible tomanipulate ofsignal pulse magnitudes andoftimeshift between them. Keywords: double resonance, inhomogeneous broadening, resonance detunings Non-stationary regime ofdouble resonance isaroused whendurations ofexcitant pulses areconsiderably less than times ofirreversible relaxation ofquantum transitions andthenef- fects ofrelaxation processes areexcluded infact. Analytical results oftheory ofnonlinear stage ofnon-stationary double resonance produced uptonowadays related mainly withcase ofspectrally homogeneous medium. Realmediae.g. diluted gases duetoDoppler effect have inhomogeneously broadened lines ofspectral transitions. Theobjective ofthis work-nu- merical simulation ofprocess non-stationary double resonance with taking into account ofde- tunings ofpulse carrier frequencies fromcentral lines ofquantum transitions andofDoppler broadening ofspectral lines. Ourconsideration isrestricted bythesupposition that width of inhomogeneously broadened line oftransition withgreater frequency isgreatly overpass the spectral widths ofinteracting pulses onentrance surface ofresonant medium. Andthenwe consider only A-configuration ofquantum transitions. Onwards thelevels ofA-configuration will belabeled according toenergy growth as1, 2,3.Frequencies ofappropriated quantum transitions ofstable (moving) atomdesignated as
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 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 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.