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A new equation for self-focusing in the presence of small beam nonparaxiality is derived. Analysis of this equation shows that nonparaxiality remains small as the beam propagates. Nevertheless, nonparaxiality arrests self-focusing when the beam width becomes comparable to its wavelength. A series of focusing-defocusing cycles of decreasing magnitude follows, ending with a final defocusing stage.
Gadi Fibich (Mon,) studied this question.