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Soviet Journal of Quantum Electronics

Reduction in the duration of small-area pulses during coherent propagation across an absorber

O. P. Varnavskiǐ, Valerie V. Golovlev, A. N. Kirkin, A. M. Mozharovskiǐ, N. V. Sidoruk

Published Jul 31, 1986• 0 citations
Publisher

Abstract

A study was made of coherent propagation of small-area pulses across a resonant absorber. At least five-fold reduction in the duration of subnanosecond pulses with a steep leading edge (τe ≲ 20 psec) was observed as a result of passage through a ruby rod cooled to 100 K. This reduction in the duration was due to the finite time needed to establish absorption. The experimental results were in agreement with a numerical solution of a system of Maxwell-Bloch equations describing the interaction of a field of a pulse with a resonant medium.

DOI
10.1070/qe1986v016n07abeh007222

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A study was made of coherent propagation of small-area pulses across a resonant absorber. At least five-fold reduction in the duration of subnanosecond pulses with a steep leading edge (τe ≲ 20 psec) was observed as a result of passage through a ruby rod cooled to 100 K. This reduction in the duration was due to the finite time needed to establish absorption. The experimental results were in agreement with a numerical solution of a system of Maxwell-Bloch equations describing the interaction of a field of a pulse with a resonant medium.
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This article presents a study of the propagation of small-area pulses of coherent light through matter. It is found that the small-area pulses exactly obey an area theorem which, in the case of an attenuating medium, requires that the pulse area decay to zero exponentially with increasing distance of propagation. This, however, does not necessarily imply that the pulse energy decays exponentially. Instead, it is found that pulses of duration comparable to or shorter than the transverse relaxation time of the medium T2{T}_{2}T2​ (including both homogeneous and inhomogeneous broadening) propagate with low energy loss. The results are explained in terms of simple physical arguments which indicate that the pulse envelope should oscillate between positive and negative values, causing the area to decrease without a comparable decrease in the pulse energy. Analytic solutions are presented for the case of a pulse whose envelope varies as ${t}^{k}{e}^{\ensuremath{-}t}$ for t>0t>0t>0, a rectangular pulse, an ultrashort pulse (i.e., pulse width much less than T2{T}_{2}T2​), and the leading portion of a step-function pulse. The propagation of a small-area Gaussian pulse is studied numerically.
An investigation of the propagation properties of a short pulse in a resonant absorber with a homogeneously broadened transition is presented with two main questions in mind: 1) the influence of the input pulse area on the transitory regime and on the steady-state propagation; 2) the effects of atomic coherence on the pulse shaping and the time delay of the leading edge of the pulse. The transitory regime of a propagating pulse is investigated and the stability of some asymptotic wave form confirmed. As expected, the transversal relaxation mechanism affects critically the major features of the coherent interaction. A detailed analysis of this problem is also presented.
Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.