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Physical Review Letters

Observation of Self-Steepening of Optical Pulses with Possible Shock Formation

D. Grischkowsky, E. Courtens, John A. Armstrong

Published Aug 13, 1973• 147 citations
Publisher

Abstract

Near-resonant light pulses were steepened by passage through Rb vapor. The rise time changed from typically 4 nsec to less than 1 nsec, and complicated envelopes developed. The self-steepening, well described by adiabatic following, results from (i) an intensity-dependent pulse velocity, (ii) self-phase modulation combined with strong groupvelocity dispersion. Numerical integration gives quantitative agreement with observations and indicates shock formation on the leading edge.

DOI
10.1103/physrevlett.31.422

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Near-resonant light pulses were steepened by passage through Rb vapor. The rise time changed from typically 4 nsec to less than 1 nsec, and complicated envelopes developed. The self-steepening, well described by adiabatic following, results from (i) an intensity-dependent pulse velocity, (ii) self-phase modulation combined with strong groupvelocity dispersion. Numerical integration gives quantitative agreement with observations and indicates shock formation on the leading edge.
Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split 2P12^{2}P_{\frac{1}{2}}2P21​​ resonance line (7948 \AA{}) of rubidium were observed to propagate through dilute rubidium vapor as slowly as (114)c(\frac{1}{14})c(141​)c. These slow pulse velocities showed that most of the energy in the propagating wave was contained by the vapor as coherent atomic excitation. The observed pulse velocities vp{v}_{p}vp​ are in good agreement with the equation ${v}_{p}=\frac{d\ensuremath{\omega}}{\mathrm{dk}}$ for the group velocity obtained from linear-dispersion theory. Also, the experimental results are quantitatively explained by adiabatic following, in which the pseudomoments of the atoms remain aligned along the effective field of the laser light. The adiabatic-following model allows for a direct comparison of our results with the work on self-induced transparency. For high-intensity light, adiabatic following predicts a nonlinear pulse velocity and the possibility of observing self-steepening.
Evolution under two-photon near-resonance conditions of an adiabatic Gaussian pulse is considered in Rb vapour. Theoretical results show strong self-phase modulation and pulse deformation with increasing distance of propagation and intensity at a fixed detuning. At sufficiently large distances of propagation and/or input intensity pulse deformation is seen to develop into (two-photon) optical shocks. At a higher intensity double shock fronts are predicted to occur. The previously anticipated existence of an upper bound for the output maximum and of the vanishing of the self-phase modulation at the 'interaction time' between the output and the input profiles are shown explicitly to hold for the cases considered. A quasi free-wave like evolution occurs at asymptotically higher intensities.
Ultrafast laser pulses with complex envelopes (amplitude and frequency modulated) are used to excite an optically dense column of rubidium vapor. Pulse reshaping, stimulated emission dynamics, and residual electronic excitation in the Rb vapor are all shown to depend strongly on the laser pulse shape. Pulses that produce adiabatic passage in the optically thin limit exhibit more complex behavior in optically thick samples, including an unexpected dependence on the sign of the frequency sweep. Numerical solutions of the Maxwell-Bloch equations are shown to account for our results.