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Journal of Optics B Quantum and Semiclassical Optics

Competition between homogeneous, inhomogeneous and transversal effects in 130Te2 superfluorescence

Jaafar Meziane, Etienne Boursey, Koutaiba Amezian, Mohammed Benzirar

Published Oct 17, 2002• 0 citations
Publisher

Abstract

A semi-classical approach is used to analyse how transverse effects and relaxation due to homogeneous and inhomogeneous broadening affect the dynamics of superfluorescence. Results are discussed in order to match our Te 2 data.
DOI
10.1088/1464-4266/4/6/303

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Superfluorescence emission profiles are computed using one-way coupled Maxwell-Bloch equations. Transverse effects are included in the full three-spatial-dimension case as well as in the cylindrical-symmetry case. Initiating quantum fluctuations are approximated by a random polarization source with a completely random phase and root-mean-square tipping angle of 2N\frac{2}{\sqrt{N}}N​2​, where NNN is the number of atoms in each volume element. These fluctuations reduce the tail of the output obtained with transverse effects alone. In fact, the fluctuations in output pulse shapes encompass the Cs data of Gibbs, Vrehen, and Hikspoors. The standard deviation for the delay time is found to be (12.5\ifmmode\pm\else\textpm\fi{}4)% for Fresnel number of 0.8 compared with the value (10\ifmmode\pm\else\textpm\fi{}2)% recently measured by Vrehen and der Weduwe, also for Cs. Inhomogeneous-broadening effects are also included in some simulations.
Using proven computational methods developed to efficiently treat transverse and longitudinal dynamic reshaping associated with single-stream propagation effects in cooperative light-matter interactions, a realistic superfluorescence (SF) theory was constructed in close collaboration with experimentalists. A semi-classical model based on the Maxwell-Bloch equa-tions (which rigorously encompasses diffraction, transverse density variations and inhomoge-neous broadening) is used. Furthermore, the medium initiation is stimulated by a coherent pulse of an area θ0 which varies radially, propagates along the rod axis and tips the indi-vidual Bloch vectors over an angle θ0 from its upright position. This effective initiation is treated in using either (a) an homogeneous average tipping angle or (b) instantaneous longitudinal and transverse fluctuations. The Cs datas are correctly simulated for the first time.* Important remark At this time, I wish to express my appreciation and give credit to Gibbs, McCall and Feld for their many contributions in the form of numerous relevant discussions, preparatory ana-lytical work and help in selecting details of realistic models based on their close contact with laboratory results. In addition, Dr Gibbs' participation in carrying the calculations accelerated the rate of progress in my research. Let me take this occasion to thank Dr. Gibbs, Dr. McCall and Dr. Feld for their energetic and enthousiastic collaboration.
A probability distribution W(t)W(t)W(t) for the delay time ttt of superfluorescent pulses is defined in terms of a functional integral, which is evaluated exactly. Although the linearized early-stage dynamics is used, full agreement is obtained with previous numerical and experimental results for the variance of ttt and, more generally, for the shape of W(t)W(t)W(t). The effect of inhomogeneous broadening of the atomic levels, showing that decrease of the dephasing time T2∗{{T}_{2}}^{*}T2​∗ leads to substantial increase of the mean and variance of ttt, is also analyzed.