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 τ_p/τ_R < 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 l_p and l_sf. Unusual temporal distortion is exhibited in the SF pulse for some trajectories when l_p is present, F is large, and τ_p 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 (τ_dp – τ_dsf)/[τ_dp + τ_dsf], and the less likely the phase wave is to be exhibited. The SF is not shielded from any fluctuations in the pump pulse.

© 1986 Optical Society of America