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Final Report

Transverse and quantum effects in light control by light; (A) parallel beams: Pump dynamics for three level superfluorescence; and (B) counterflow beams: An algorithm for transverse, full transient effects in optical bi-stability in a Fabryperot cavity

F. P. Mattar

Published Jan 1, 1983• 0 citations
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Abstract

Abstract : Computational methodologies were developed to treat rigorously (1) transverse boundary in an inverted (amplifying) media; (2) to treat quantum fluctuations in an initial boundary condition in the light-matter interactions problem; (3) construct a two-laser three-level code to study light control by light effect; (4) construction of a data base that (a) would manage the production of different types of laser calcualtions: cylindrical, cylindrical with atomic frequency broadening, cartesian geometry; (all of the above with quantum mechanical initiation), (b) allow parametric comparison within the same type of calculations, by establishing a unifying protocol of software storage, of the various refinements of the model could be contrasted among themselves and with experiment; (5) construct an algorithm for counterbeam transient studies for optical bistability and optical oscillator studies. (A) Transverse propagation effects in an inverted medium were studied. Special care had to be taken to treat the boundary reflection conditions. If ill-posed, they can obscure the emergence of any new physical results. The two transverse effects considered are (1) the 'spatial averaging' associated with the inial atomic inversion density being radially dependent (since the pump which inverts the sample has typically a Gaussian-like profile); and (2) the 'diffraction coupling' (which permits the various parts of the cylindrical cross-section to communicate, interact and emit at the same time). The first effect is important for large Fresnel numbers, whereas the second predominant for small Fresnel numbers.

Related papers

Transverse effects in optical bistability and superfluorescence

Edward Watson

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)

•Jan 1, 1982•1 citation

Coherent pump dynamics, propagation, transverse, and diffraction effects in three-level superfluorescence and control of light by light

F. P. Mattar, C. M. Bowden

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.

Physical Review A•Jan 1, 1983•27 citations

Effects Of Propagation, Transverse Mode Coupling, Diffraction, And Fluctuations On Superfluorescence Evolution

Farrès P. Mattar

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 30, 1981•1 citation

Quantum fluctuations and transverse effects in superfluorescence

E. A. Watson, H. M. Gibbs, F. P. Mattar +4 more

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 $\frac{2}{\sqrt{N}}$, where $N$ 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.

Physical Review A•Mar 1, 1983•50 citations

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

F. P. Mattar, C. M. Bowden

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 16, 1983•0 citations

MICOM Program in Light Control by Light.

Charles M. Bowden

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.

army•Jun 18, 1982•0 citations
Abstract : Computational methodologies were developed to treat rigorously (1) transverse boundary in an inverted (amplifying) media; (2) to treat quantum fluctuations in an initial boundary condition in the light-matter interactions problem; (3) construct a two-laser three-level code to study light control by light effect; (4) construction of a data base that (a) would manage the production of different types of laser calcualtions: cylindrical, cylindrical with atomic frequency broadening, cartesian geometry; (all of the above with quantum mechanical initiation), (b) allow parametric comparison within the same type of calculations, by establishing a unifying protocol of software storage, of the various refinements of the model could be contrasted among themselves and with experiment; (5) construct an algorithm for counterbeam transient studies for optical bistability and optical oscillator studies. (A) Transverse propagation effects in an inverted medium were studied. Special care had to be taken to treat the boundary reflection conditions. If ill-posed, they can obscure the emergence of any new physical results. The two transverse effects considered are (1) the 'spatial averaging' associated with the inial atomic inversion density being radially dependent (since the pump which inverts the sample has typically a Gaussian-like profile); and (2) the 'diffraction coupling' (which permits the various parts of the cylindrical cross-section to communicate, interact and emit at the same time). The first effect is important for large Fresnel numbers, whereas the second predominant for small Fresnel numbers.
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)
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.
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.
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.
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.