Marburger formula

Although the Kerr effect involves the intensity, the occurrence of self-focusing is determined by the beam power rather than the beam intensity. However, once the self-focusing occurs, the beam diameter, and hence its intensity, determines the non-linear focal length, i.e. the point where the beam will collapse. The location Z of the non-linear focus for a power P is given by the empirical Marburger formula [38] ... 

J. H. Marburger, E. L. Dawes, Dynamical formation of a small-scale filament, Physical Review Letters 21, 556 (1968). Note that the radius considered in the classical writing of the Marburger formula is the half width at e 1,/2, not at 1/ e or 1 /e2 as usual. 

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