Theory of paraxial self-focusing

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Abstract
The phenomena of steady‐state self‐focusing and self‐trapping have been analyzed in the paraxial approximation through a formalism utilizing a generalization of the angular‐spectrum representation of electromagnetic beams. The method discards the a priori quasioptic approximation used in all previous theories; the effect of power loss from paraxial regions into beam aberrations during focusing and defocusing has also been incorporated. Results on self‐trapping suggest greater dominance of nonlinear effects over beam‐diffraction effects than predicted by earlier paraxial theories particularly in the region of nonlinear saturation. These results are in qualitative agreement with the moment theory of self‐trapping. The present theory indicates certain periodic focusing solutions much different from the earlier paraxial theory.