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Physical Review A

Spatiotemporal evolution and multiple self-focusing of ultrashort pulses in a resonant two-level medium

Yueping Niu, Keyu Xia, Ni Cui, Shangqing Gong, Ruxin Li

Published Dec 30, 2008• 14 citations
Publisher

Abstract

The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis $2n\ensuremath{\pi}$ sech pulse, local delay makes the temporal split $2\ensuremath{\pi}$ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split $2\ensuremath{\pi}$ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.

DOI
10.1103/physreva.78.063835

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The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis 2n\ensuremathπ2n\ensuremath{\pi}2n\ensuremathπ sech pulse, local delay makes the temporal split 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.
The spatiotemporal evolution of an ultrashort pulse pair is investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly-varying envelope approximation and rotating-wave approximation. For each pulse, the temporal effect causes the breakup while the transverse effect leads to instability and reshaping. The split pulse pair always remains out-of-phase or in-phase depending on the relative phase of the incident pulse pair. When the incident pulse pair is in-phase, fusion can appear in the ultrashort regime under proper parameter conditions.
The semiclassical Maxwell–Bloch equations beyond the slowly varying envelope approximation (SVEA) are derived in order to study the propagation of the ultrashort pulse in a two-level medium. The evolutions of the pulse shape, the group velocity and the pulse peak of 2[Formula: see text] ultrashort pulse are investigated as well as the pulse splitting of 4[Formula: see text] ultrashort pulse. By comparing the numerical results with those obtained using the SVEA, the error introduced by the approximation is quantitatively evaluated with respect to the pulse width and the applicable condition of the SVEA is discussed consequently. The envelope solutions presented by us allow clear observation on the evolution of the envelope.
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
Analytical and numerical methods are used to study the transverse reshaping that occurs when ultrashort optical pulses propagate through media resonant to the pulse-carrier frequency. The field is described by the scalar quasi-optic equation, and the material system by the full Bloch equations describing a distribution of homogeneously broadened two-level molecules. Transverse derivatives in the field equation provide the coupling leading to the development of radially dependent frequency variations and phase curvature. We have studied the origin and evolution of transverse energy flow and investigated the conditions under which this leads to significant coherent self-focusing. The physical mechanisms responsible for the onset and development of the focusing phenomenon are discussed and related to other types of self-confinement of optical pulses.
By solving the Maxwell-Bloch equations beyond the slowly varying envelope approximation (SVEA), we investigate the interaction of ultrashort pulse with two-level medium. When the pulse width decreases to the order of the optical period, the evolutions of the 2π, 4π and 6π ultrashort pulses deviate from the results obtained using the SVEA and present some new features, such as the frequency shift occurring on the trailing edge of the pulse. Moreover, a factor is defined to quantify the envelope deviation between the cases of the SVEA and the non-SVEA in order to quantitatively evaluate the error caused by the SVEA, then we discuss the applicable condition of the approximation.