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arXiv · 2306.06555

Second-harmonic generation in the system with fractional diffraction

Pengfei Li·Hidetsugu Sakaguchi·Liangwei Zeng·Xing Zhu·Dumitru Mihalache·Boris A. Malomed
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Abstract

We construct a family of bright optical solitons composed of fundamental frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Levy index {\alpha}, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical collapse, respectively. The existence domain and stability boundary for the solitons are delineated in the space of {\alpha}, FF-SH mismatch parameter, and propagation constant. The stability boundary is tantamount to that predicted by the Vakhitov-Kolokolov criterion, while unstable solitons spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied to the stable solitons excite small internal vibrations in the stable solitons, without setting them in motion. A stronger kick makes the solitons' trajectories tilted, simultaneously destabilizing the solitons.

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Pengfei Li, Hidetsugu Sakaguchi, Liangwei Zeng, Xing Zhu, Dumitru Mihalache, Boris A. Malomed. 2023-06-11. Second-harmonic generation in the system with fractional diffraction. https://doi.org/10.1016/j.chaos.2023.113701

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