Abstract:
The inverse-scattering analysis of the nonlinear Schrödinger equation (NSE) is shown to provide powerful insights into a beam breakup and filamentation dynamics of high-power laser pulses. In the highly nonlinear regime, in which a laser beam tends to break up into multiple filaments as a part of its nonlinear dynamics, the scattering-space waves representing real-space NSE fields are shown to obey the scalar wave equation for the field in a fictitious waveguide with an index profile as dictated by the Kerr lens induced by the laser beam. Despite the drastic differences in the ways the inverse-scattering framework and the Bespalov-Talanov theory of beam filamentation treat nonlinear beam dynamics, the angular spectrum of beam instabilities and the transverse size of filaments in both frameworks can be understood on strikingly similar grounds—in terms of wave-vector matching, reflecting the wave-by-wave scattering nature of the emerging filamentary beam structure.
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