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Physical Review A

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

F. P. Mattar, C. M. Bowden

Published Jan 1, 1983• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.27.345

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

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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.

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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

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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.

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

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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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 7, 1983•1 citation

Cooperative behavior among three-level systems: Transient effects of coherent optical pumping

C. M. Bowden, Chi C. Sung

The dynamical evolution of an excited-state population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the excited states by an externally applied ($c$-number) coherent pump. The intermediate and ground states are taken as nonradiatively coupled whereas the excited-to-intermediate-state transition is coupled to the radiation field which is treated quantum mechanically. It is found that stimulated Raman processes can significantly influence the dynamical evolution of population inversion and macroscopic polarization by producing coherence effects among the populations. We examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration. It is shown, using the mean-field approximation, that for uniform pumping and conditions such that the pump Rabi rate ${\ensuremath{\omega}}_{R}$, the characteristic collective radiation time ${\ensuremath{\tau}}_{R}$, and the pump pulse duration ${\ensuremath{\tau}}_{P}$ satisfy the inequalities, ${\ensuremath{\omega}}_{R}>\frac{1}{{\ensuremath{\tau}}_{R}}>\ensuremath{\gamma}$ and ${\ensuremath{\tau}}_{P}\ensuremath{\gtrsim}{\ensuremath{\tau}}_{R}$ ($\ensuremath{\gamma}$ is a characteristic internal dephasing rate for the molecules), the system is left in a state with classical transverse polarization when the pump pulse terminates. The system can evolve collectively from such a state only as superradiant (classical) evolution. For superfluorescent evolution which requires a state of preparation of complete inversion (zero transverse polarization), it is shown that the pump pulse must be effectively of area $\ensuremath{\pi}$ and that ${\ensuremath{\tau}}_{P}<{\ensuremath{\tau}}_{R}$. Our results show that when the former conditions are satisfied the delay time ${\ensuremath{\tau}}_{D}$ for collective free pulse evolution is a function of both ${\ensuremath{\tau}}_{P}$ and ${\ensuremath{\tau}}_{R}$. It is shown further that the pump pulse shape as well as temporal duration significantly affect the final state of preparation. The results of this work are interpreted in connection with recent reported results of experiments in superfluorescence and superradiance.

Physical Review A•Oct 1, 1978•58 citations

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
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.
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.
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.
The dynamical evolution of an excited-state population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the excited states by an externally applied (ccc-number) coherent pump. The intermediate and ground states are taken as nonradiatively coupled whereas the excited-to-intermediate-state transition is coupled to the radiation field which is treated quantum mechanically. It is found that stimulated Raman processes can significantly influence the dynamical evolution of population inversion and macroscopic polarization by producing coherence effects among the populations. We examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration. It is shown, using the mean-field approximation, that for uniform pumping and conditions such that the pump Rabi rate ${\ensuremath{\omega}}_{R}$, the characteristic collective radiation time ${\ensuremath{\tau}}_{R}$, and the pump pulse duration ${\ensuremath{\tau}}_{P}$ satisfy the inequalities, ${\ensuremath{\omega}}_{R}>\frac{1}{{\ensuremath{\tau}}_{R}}>\ensuremath{\gamma}$ and ${\ensuremath{\tau}}_{P}\ensuremath{\gtrsim}{\ensuremath{\tau}}_{R}$ ($\ensuremath{\gamma}$ is a characteristic internal dephasing rate for the molecules), the system is left in a state with classical transverse polarization when the pump pulse terminates. The system can evolve collectively from such a state only as superradiant (classical) evolution. For superfluorescent evolution which requires a state of preparation of complete inversion (zero transverse polarization), it is shown that the pump pulse must be effectively of area $\ensuremath{\pi}$ and that ${\ensuremath{\tau}}_{P}<{\ensuremath{\tau}}_{R}$. Our results show that when the former conditions are satisfied the delay time ${\ensuremath{\tau}}_{D}$ for collective free pulse evolution is a function of both ${\ensuremath{\tau}}_{P}$ and ${\ensuremath{\tau}}_{R}$. It is shown further that the pump pulse shape as well as temporal duration significantly affect the final state of preparation. The results of this work are interpreted in connection with recent reported results of experiments in superfluorescence and superradiance.
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)