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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Fresnel Variation Of Deterministic And Quantum Initiation In Two And Three Level Superfluorescencet

Farrès P. Mattar

Published Nov 7, 1983• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.934815

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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.
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.
Delay statistics of amplified quantum initiation of SF are reported as manifestly important in both the pump/SF partial and total overlap regimes for τp/τR < 1 (pump pulse length to cooperative radiation time ratio) as a function of the Fresnel number F for a given atomic density N. The Mattar et al. formulation1 is adopted with phase, transverse variations, and copropagation in conjunction with the Bowden and Sung2 initiation through Langevin forces of bivariate normally distributed amplitudes and uniformly random phase in both pump and SF transitions lp and lsf. Unusual temporal distortion is exhibited in the SF pulse for some trajectories when lp is present, F is large, and τp is shortened. However, when diffraction strengthens, i.e., decreases, the communication between adjacent shells improves and significantly reduces the statistics uncertainty associated with the delay difference σ (τdp – τdsf)/[τdp + τdsf], and the less likely the phase wave is to be exhibited. The SF is not shielded from any fluctuations in the pump pulse.
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.
A model is presented for the dynamical evolution of superfluorescence from an optically pumped three-level system. The full propagation, transverse, and diffraction effects are taken into account. With the use of a previously developed algorithm, a computational simulation was constructed from this model and results are presented and discussed. In particular, it is shown that the injected coherent pump-pulse initial characteristics, such as on-axis area, temporal and radial width and shape, can have significant deterministic effects on the superfluorescent pulse delay time, peak intensity, temporal width, and shape. Thus, by specifying certain initial properties of the injected pump pulse, the superfluorescent pulse can be shaped and altered. The results predict the conditions under which an injected light pulse of a given frequency can be used to generate, shape, and control a second light pulse of a different frequency via a nonlinear medium, thus demonstrating a new aspect of the phenomenon of light control by light.