SHG is used in many practical applications such as a substance diagnostics, and imaging of various processes as well as for frequency conversion. Well known that the frequency doubling is used also for a generation of tripled frequency wave due to mixing of optical radiation at basic frequency with optical radiation at doubled frequency. In this case an important role plays a relation between phases of interacting waves with basic frequency and doubled frequency. Therefore, a derivation of the corresponding law for phase evolutions is an urgent problem. Below we provide such derivation for a SHG of high intensive femtosecond pulse with taking into account an influence of a cubic nonlinear response on the frequency doubling. Using the frame-work of long pulse duration approximation and plane wave approximation as well as an original approach we derive the solution of Schrodinger equations describing the SHG for femtosecond pulse without using the basic wave energy non-depletion approximation. It should be stressed, that the frequency conversion in conditions under consideration possesses multi-stability: there are many modes of SHG efficiency. We write a wave phase evolution for each of the modes. The derived formulas are verified by computer simulation based on using the corresponding Schrodinger equations.
Vyacheslav A. Trofimov, Dmitry M. Kharitonov, and Mikhail V. Fedotov, "Evolution of phase difference and absolute phase of interacting waves under SHG of high intensive femtosecond pulse," Proc. SPIE 10111, Quantum Sensing and Nano Electronics and Photonics XIV, 101110Z (Presented at SPIE OPTO: January 30, 2017; Published: 27 January 2017); https://doi.org/10.1117/12.2253650.
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