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Physical Review Letters

Transverse Effects in Superfluorescence

F. P. Mattar, H. M. Gibbs, S. L. McCall, Michael S. Feld

Published Apr 27, 1981• 68 citations
Publisher

Abstract

Dynamic diffraction coupling is examined in superfluorescence with use of a semiclassical model in which diffraction and transverse density variations are rigorously included. The Cs data are correctly simulated for the first time.
DOI
10.1103/physrevlett.46.1123

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Abstract : The interaction of a light beam with matter has varying degrees of dependence on the transverse profile of the beam. Two topics are considered here. The first topic, superfluorescence, involves the coherent emission generated by an initially inverted two-level medium. Calculations in the past have included either quantum fluctuations in the initial conditions or transverse effects, but never both. The calculations presented here include both transverse effects and quantum fluctuations. The results of the theoretical calculations are in good agreement with previous experimental results, both quantitatively in terms of time delay averages and distributions and also qualitatively in terms of pulse shapes. The second topic considered, optical bistability, involves devices which exhibit two stable output light intensities (a high and a low branch) over a limited range of input light intensities. Simulations performed here show the effect of diffraction, measured in terms of the Fresnel number, on how much of the device becomes bistable. It was found that for small Fresnel number cases, the entire device become bistable. For high Fresnel number cases, only part of the device becomes bistable while the rest of the device remains low transmitting. The results of an experiment performed are consistent with the simulations. (Author)

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Recent work is reviewed where dynamic diffraction coupling is examined in Superfluorescence SF with use of a one-way semiclassical model in which diffraction and transverse density variations are rigorously included. The Cs data are correctly simulated for the first time in conjunction with both an average tipping angle and quantum fluctuation (either longitudinal or transverse) at the initiating stage. This comprehensive review also encompasses rigorously the effects of pump dynamics on the SF evolution. The terminology is unified. Specification of certain pump beam initial conditions at a given frequency results in specific SF characteristics at another frequency as recently observed in CH3F and Ba. Pump dynamics are studied in both the average value of the tipping angle and quantum fluctuation at the initiation stage.
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.
Abstract : The interaction of a light beam with matter has varying degrees of dependence on the transverse profile of the beam. Two topics are considered here. The first topic, superfluorescence, involves the coherent emission generated by an initially inverted two-level medium. Calculations in the past have included either quantum fluctuations in the initial conditions or transverse effects, but never both. The calculations presented here include both transverse effects and quantum fluctuations. The results of the theoretical calculations are in good agreement with previous experimental results, both quantitatively in terms of time delay averages and distributions and also qualitatively in terms of pulse shapes. The second topic considered, optical bistability, involves devices which exhibit two stable output light intensities (a high and a low branch) over a limited range of input light intensities. Simulations performed here show the effect of diffraction, measured in terms of the Fresnel number, on how much of the device becomes bistable. It was found that for small Fresnel number cases, the entire device become bistable. For high Fresnel number cases, only part of the device becomes bistable while the rest of the device remains low transmitting. The results of an experiment performed are consistent with the simulations. (Author)