SHG and SFG (SWG) and THG are used widely in many practical applications such as a substance diagnostics, and imaging of various physical, chemical and biological processes as well as for laser radiation frequency conversion. One of very interesting phenomena under the frequency conversion takes place if a basic wave incident intensity is enough high: a synchronic mode of the laser pulse intensities changing along a propagation coordinate appears under certain conditions. First of all, we investigate this phenomenon using the frame-work of long pulse duration approximation and plane wave approximation without applying the basic wave energy non-depletion approximation. Applying an original approach we derive the solution of Schr¨odinger equations describing the THG via a SHG process and summary frequency wave generation (SFG) process for femtosecond pulses. Among many modes of the frequency conversion process under consideration we found out analytically the mode corresponding to synchronous intensities changing for the interacting waves. We derive conditions of such mode realization in dependence of the problem parameters. After that we verify our analytical consideration using a computer simulation of the problem on the base of the corresponding Schr¨odinger equations. Computer simulation shown also a new phenomenon at three-wave interaction: interacting wave intensities changing with two (or more) oscillation periods.
Vyacheslav A. Trofimov, Dmitry M. Kharitonov, and Mikhail V. Fedotov, "Self-trapping of intensities changing under SHG and SWG for high intensive femtosecond laser pulse," Proc. SPIE 10228, Nonlinear Optics and Applications X, 102280A (Presented at SPIE Optics + Optoelectronics: April 24, 2017; Published: 16 May 2017); https://doi.org/10.1117/12.2267496.
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