Two-dimensional solitons in second-harmonic-generating media with fractional diffraction
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917680612638720 |
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| author | Sakaguchi, Hidetsugu Malomed, Boris A. |
| author_facet | Sakaguchi, Hidetsugu Malomed, Boris A. |
| contents | We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical solution produces families of ground-state (zero-vorticity) two-dimensional solitons in the free space, which are stable in exact agreement with the Vakhitov-Kolokolov criterion, while vortex solitons are completely unstable in that case. Mobility of the stable solitons and inelastic collisions between them are briefly considered too. In the presence of a harmonic-oscillator (HO) trapping potential, families of partially stable single- and two-color solitons (SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero vorticities. The single-and two-color solitons are linked by a bifurcation which takes place withthe increase of the soliton's power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-dimensional solitons in second-harmonic-generating media with fractional diffraction Sakaguchi, Hidetsugu Malomed, Boris A. Pattern Formation and Solitons Optics We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical solution produces families of ground-state (zero-vorticity) two-dimensional solitons in the free space, which are stable in exact agreement with the Vakhitov-Kolokolov criterion, while vortex solitons are completely unstable in that case. Mobility of the stable solitons and inelastic collisions between them are briefly considered too. In the presence of a harmonic-oscillator (HO) trapping potential, families of partially stable single- and two-color solitons (SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero vorticities. The single-and two-color solitons are linked by a bifurcation which takes place withthe increase of the soliton's power. |
| title | Two-dimensional solitons in second-harmonic-generating media with fractional diffraction |
| topic | Pattern Formation and Solitons Optics |
| url | https://arxiv.org/abs/2405.20944 |