Four-waves mixing (FWM) of co-propagating femtosecond laser pulses is widely used in various practical applications for diagnostic of a medium, for example. Using the problem invariants (conservation laws for four wave pulses interaction) it is possible to develop an analytical solution of the problem under consideration in the frame-work of plane wave approximation and long pulse duration approximation (point–wise model). This solution demonstrates an existence of various FWM modes under their co-propagation. Among them, there is a mode of wave propagation without unchanging intensities. In the case of pulse propagation with inhomogeneous beam profile, this mode results in occurrence of (or oscillating) spatial-temporal domain of unchangeable intensity during certain propagation distance, which depends on SOD (second order dispersion) and beam diffraction. Both these factors destroy this propagation mode. Nevertheless, a pulse with hyperbolic cosine shape may exhibit such propertty. We investigate an influence of a pulse shape as well as a beam profile.
Vyacheslav A. Trofimov and Igor E. Kuchik, "Co-propagating FWM of axial symmetric laser pulse with femtosecond duration," Proc. SPIE 10091, Laser Applications in Microelectronic and Optoelectronic Manufacturing (LAMOM) XXII, 1009108 (Presented at SPIE LASE: January 30, 2017; Published: 20 February 2017); https://doi.org/10.1117/12.2253652.
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