Abstract
The paraxial wave equation, as is well known, predicts the catastrophic collapse of self-focusing beams. It is pointed out that this collapse is due to the loss of validity of the paraxial wave equation in the neighborhood of a self-focus. If nonparaxiality of the beam propagation is taken into account, on the other hand, a lower limit of the order of one optical wavelength is imposed on the diameter of a self-focus. A nonparaxial algorithm for the Helmholtz equation is applied to the self-focusing of Gaussian and ring-shaped beams. The self-focusing is noncatastrophic, and the results give insight into filament formation and beam breakup resulting from the self-focusing of optical beams.
© 1988 Optical Society of America
Full Article | PDF ArticleMore Like This
Vladimir Tikhonenko, Jason Christou, and Barry Luther-Daves
J. Opt. Soc. Am. B 12(11) 2046-2052 (1995)
Timo A. Laine and Ari T. Friberg
J. Opt. Soc. Am. B 17(5) 751-757 (2000)
A. W. McCord, R. J. Ballagh, and J. Cooper
J. Opt. Soc. Am. B 5(6) 1323-1334 (1988)