Second-harmonic generation in the system with fractional diffraction
arXiv:2306.06555 · doi:10.1016/j.chaos.2023.113701
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 α, 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 α, 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.
arXiv comment27 pages, 8 figures, to be published in Chaos, Solitons & Fractals
References in corpus (15)
- Fractional Quantum Mechanics and Levy Path Integrals
- Fractional Schrodinger equation
- Fractional Quantum Mechanics
- Fractional Schrödinger equation in optics
- Some properties of the one-dimensional Lévy crystal
- Spatiotemporal accessible solitons in fractional dimensions
- Soliton dynamics in a fractional complex Ginzburg-Landau model
- One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice
- Fractional quantum mechanics in polariton condensates with velocity dependent mass
- Symmetry breaking of spatial Kerr solitons in fractional dimension
- The Two-Dimensional Fractional Discrete Nonlinear Schrodinger Equation
- Embedded solitons in second-harmonic-generating lattices
- Stable and oscillating solitons of -symmetric couplers with gain and loss in fractional dimension
- Domain walls in fractional media
- Vortical light bullets in second-harmonic-generating media supported by a trapping potential