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Raman conversion of femtosecond laser pulses via Bessel beam pump geometry

waist and curvature in the transverse xly-plane in dependence on the propagation coordinate z. Thus, in ansatz (1) the space-time coupling is explicitly taken into account. The complex function I$( z, -q) describes the temporal pulse shape. Note that by use of the Gaussian ansatz (1) a generalized time-dependent ABCDmatrix formalism for the beam parameters can be established analogous to Ref. 2. This dramatically reduces the huge numerical expense of directly three-dimensional modeling as done in Ref. 3 and enables the investigation of an sufficiently extended set of laser parameters to determine the ultimate limitations to the pulse duration in KLM lasers. The temporal pulse shape transformation by the solid-state gain medium is governed by the equation