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.