Abstract

Transverse phenomena have been emphasized in works dealing with self-focusing or defocusing of optical pulses, but these works usually have been concerned with the effects of non-strictly resonant non-linearities in the quasi-steadystate limit, as in common transparent media. Self-lensing due to an intensity dependent index of refraction explains the main part of these phenomena. In the present paper, we give the main results of a systematic numerical study of coherent on-resonance self-focusing of laser pulse in atomic media. When cylindrical symmetry is assumed, this study reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena, first described by McCall and Hahn. From this interpretation and the well-known Maxwell-Bloch equations, we derived what is, to our knowledge, the first theoretical quantitative model for coherent on-resonance large-scale self-focusing that is to say, focusing of the beam as a whole. Our main results include the above mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. These theoretical predictions are shown to correspond closely to the numerical simulations and experimental results. The parametric dependence of the focusing distance on the input pulse peak power is quite different from what can be obtained in the usual. The relative predominance of either the large-scale self-focusing or self-induced transparency phenomenon is discussed. Both numerical and theoretical descriptions are compared with the results of an experiment involving nanosecond dye laser pulses interacting with a degenerate inhomogeneously broadened two-level system provided by a fundamental transition in a ¹⁶⁹Tm vapor.

© 1994 IEEE