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

Propagation, Transverse, Diffraction Effects, And Coherent Pump Dynamics In Three-Level Superfluorescence And Light Control By Light

F. P. Mattar, C. M. Bowden

Published Jun 16, 1983• 0 citations
Publisher

Abstract

Calculational results and analysis are presented and discussed for the effects of coherent pump dynamics, propagation, transverse and diffraction effects on superfluorescent (SF) emission from an optically-pumped three-level system. The full, co-propagational aspects of the injected pump pulse together with the SF which evolves are explicitly treated in the calculation. It is shown that the injection pulse initial characteris-tics can have a strong effect on the SF emission.

DOI
10.1117/12.934375

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Calculational results and analysis are presented and discussed for the effects of coherent pump dynamics, propagation, transverse and diffraction effects on superfluorescent (SF) emission from an optically-pumped three-level system. The full, co-propagational aspects of the injected pump pulse together with the SF which evolves are explicitly treated in the calculation. It is shown that the injection pulse initial characteris-tics can have a strong effect on the SF emission.
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.
Abstract : In this paper, we present calculational results and analysis for the effects of coherent pump dynamics, propagation, transverse and diffraction effects on SF emission from an optically-pumped three-level system. The full nonlinear, co-propagational aspects of the injuect pump pulse, together with the SF which evolves are explicitly treated in the calculation. Not only do our results relate strongly to previous calculations and experimental results in SF, but we introduce and demonstrate a new concept in nonlinear light-matter interactions, which we call light control by light. We show how characteristics of the Sf can be controlled by specifying certain characteristics of the injection pulse. This leads to possible applications in laser pulse control and shaping, nonlinear optical information encoding, and unique pulsed LADAR and millimeter wavelength sources.
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.
We develop a theory to take into account the effects in coherent propagation of a small overlapping of the pump and probe pulses in a three-level system. The Maxwell equations reduce to coupled equations for variables which are related to the time-integrated field envelopes. We make comparisons of the propagation results to the Burnham-Chiao theory for a two-level amplifier and can predict when this theory breaks down. An application to superfluorescence is presented where a lengthening of the delay time is found. We treat Doppler broadening and find simplified equations in two cases: (a) a very broad line and (b) a very narrow line where the initial and final states are degenerate. For the broad-line case, with an appropriate choice of initial parameters, we can make the probe pulse approach any desired area for certain configurations of the levels.
This paper is devoted to understanding the temporal synchronization of the two-color superfluorescence output powers. Following McCall and Feld et al., the monochromatic superfluorescence can be described in terms of a semi-classical propagational model that shares the same equations as Self-Induced Transparency (SIT). Thus it became important to understand double SIT that was discovered by McCall and Hahn (MH) to correctly interpret co-propagating beams with coherent exchange of energy and nonlinear phase evolution. A further motivation would be to elucidate pump and Stokes synchronization as well as pump depletion effect on Stokes buildup in Raman forward amplifier. In this work, we describe how the diffraction affects the longitudinal and transverse reshaping associated affects the simultaneous resonant propagation of two different-wavelength optical pulses in a three-level medium. The pulse lengths are shorter than any of the relaxation times, thus, the interaction is coherent. The material response has an inertial characteristic, which precludes its description with two instantaneous susceptibilities, and requires instead the density matrix formulism. A semi-classical formulism, as introduced by Konopnicki and Eberly (KE), is adopted in which two paraxial Maxwell field equations are closely intertwined in the generalized three-level Bloch equations.