Strong Self-focusing: An Aberrational Approach

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Abstract
A beamwidth expression derived using the methods of Kelley and Wang in the paraxial approximation for the regime of ‘strong’ optical self-defocusing is incompatible with the application of Talanov's lens transformation. The correct description of a pre-focused beam should appear when this transformation is applied to the transmitted field of the corresponding unfocused beam, hence a perturbation technique that is more powerful than that hitherto used is required. By use of the analytic method of Lugovoi, it is shown that a new continued-fraction formalism is generally adequate for this purpose. An improved approximation for the axial intensity and the beamwidth parameter has been found for a defocusing medium.