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Families of gap solitons and their complexes in media with saturable nonlinearity and fractional diffraction

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Abstract

We demonstrate the existence of various types of gap localized modes, including one- and two-dimensional (1D and 2D) single solitons and soliton clusters, as well as the corresponding vortex modes in optical media with saturable Kerr nonlinearity and fractional diffraction. We find that soliton clusters with different number of peaks can be stable in these media. The 1D and 2D localized modes existing at the center of the first and second band gaps are stable, whereas the ones in the peripheries are unstable. In addition, the vortex modes with different number of peaks and vorticity number \(m=1\) are found to be stable, while the ones with \(m\ge 2\) are unstable. The stability of these localized modes is investigated by using the linear stability analysis and is confirmed by the numerical simulation of their dynamical propagation. The obtained results may enrich the understanding of gap solitons and their complexes in media with saturable nonlinearity and fractional diffraction, and may find potential applications in optical information processing and other related fields.

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Funding

National Major Instruments and Equipment Development Project of National Natural Science Foundation of China (61827815); National Natural Science Foundation of China (12174264, 62075138); Natural Science Foundation of Guangdong Province (2021A1515011909); Science and Technology Project of Shenzhen (JCYJ20190808121817100, JCYJ20190808164007485, JSGG20191231144201722); Natural Science Foundation of Shenzhen University (2019007); Qatar National Research Fund (NPRP-S11-1126-170033).

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Authors and Affiliations

  1. Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronics Engineering, Shenzhen University, Shenzhen, 518060, China

    Liangwei Zeng, Xiaowei Lu, Yi Cai & Jingzhen Li

  2. Texas A & M University at Qatar, 23874, Doha, Qatar

    Milivoj R. Belić

  3. Horia Hulubei National Institute of Physics and Nuclear Engineering, 077125, Magurele, Bucharest, Romania

    Dumitru Mihalache

  4. 54th Research Institute of CETC, Shijiazhuang, 050011, China

    Jincheng Shi

  5. State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi’an, 710119, China

    Jiawei Li & Siqi Li

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  1. Liangwei Zeng
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  2. Milivoj R. Belić
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  3. Dumitru Mihalache
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  4. Jincheng Shi
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Zeng, L., Belić, M.R., Mihalache, D. et al. Families of gap solitons and their complexes in media with saturable nonlinearity and fractional diffraction. Nonlinear Dyn 108, 1671–1680 (2022). https://doi.org/10.1007/s11071-022-07291-z

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