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Annual Meeting Optical Society of America

Quantum fluctuations, phase wave, pump depletion, and diffraction dynamics in three-level superfluorescence

F. P. Mattar, E. Friedman

Published Jan 1, 1986• 0 citations

Abstract

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.

DOI: 10.1364/oam.1986.tum9

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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.

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.

We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ensuremath{\ge} 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.

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Numerical simulations of an extended sample of three-level atoms with slow dipole dephasing exhibit a superfluorescent pulse shortly after incoherent pumping begins. The operator Maxwell-Bloch equations are simulated by classical Langevin equations. The counterpropagating fields are solved for in the (one-dimensional) limit of the Fresnel number near unity, with open-end boundary conditions. An initial, ``quiet'' buildup of the inversion is followed by superfluorescence. Oscillation of the populations, coherences, and fields is observed. The superfluorescence delay time is compared with analytical predictions made in the linear regime. A transition to amplified spontaneous emission is found as the pump rate is decreased.

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.