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Large-Scale Self-Trapping of Optical Beams in the Paraxial Ray Approximation
Phys. Rev. 175, 256 – Published 5 November, 1968Erratum Phys. Rev. A 3, 2150 (1971)
DOI: https://doi.org/10.1103/PhysRev.175.256
Abstract
We present a systematic discussion of time-independent large-scale self-focusing in a paraxial ray "constant-shape" approximation. An equation is obtained for the variance of a self-focusing beam with a Gaussian transverse intensity profile as a function of axial distance. This equation, valid for an arbitrary nonlinear constitutive relation, is solved for several important situations, including the case of a saturable nonlinear refractive index. We also derive closed expressions for such a saturable index arising from reorientation of axially symmetric molecules in an external field, ignoring local-field effects. Self-focusing of an elliptically polarized beam is considered in the same approximation, and numerical results are presented which show that the self-focusing length is quite sensitive to small departures from circular polarization.
Erratum
Large-Scale Self-Focusing of Optical Beams in the Paraxial Ray Approximation
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