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Conical diffraction modulation in fractional dimensions with a PT-symmetric potential

Author

Listed:
  • Wu, Zhenkun
  • Yang, Kaibo
  • Ren, Xijun
  • Li, Peng
  • Wen, Feng
  • Gu, Yuzong
  • Guo, Lijun

Abstract

This study analyzes conical diffraction in space-fractional parity-time (PT) symmetry, which arises in a fractional Schrödinger equation with a periodic PT-symmetric potential. The peculiar characteristics of the corresponding Floquet Bloch modes are also examined in detail. We find that the band structure in such a model is different from that in regular PT symmetry, especially the critical point, which becomes symmetric linear for the one-dimensional case, and cone-like for the two-dimensional case. During propagation, the linear band structure has peculiar properties, including splitting or diffraction-free propagation, preferential propagation, and unidirectional propagation. Whether the cone-like band structure leads to cone diffraction or nondiffracting propagation depends on which Floquet Bloch modes are excited by the input. Our results may have potential application in light modulation in PT symmetry and provide a new platform to study other exciting topics related to conical diffraction.

Suggested Citation

  • Wu, Zhenkun & Yang, Kaibo & Ren, Xijun & Li, Peng & Wen, Feng & Gu, Yuzong & Guo, Lijun, 2022. "Conical diffraction modulation in fractional dimensions with a PT-symmetric potential," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008128
    DOI: 10.1016/j.chaos.2022.112631
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    References listed on IDEAS

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    1. He, Shangling & Malomed, Boris A. & Mihalache, Dumitru & Peng, Xi & Yu, Xing & He, Yingji & Deng, Dongmei, 2021. "Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Martin Wimmer & Alois Regensburger & Mohammad-Ali Miri & Christoph Bersch & Demetrios N. Christodoulides & Ulf Peschel, 2015. "Observation of optical solitons in PT-symmetric lattices," Nature Communications, Nature, vol. 6(1), pages 1-9, November.
    3. Mikael C. Rechtsman & Julia M. Zeuner & Yonatan Plotnik & Yaakov Lumer & Daniel Podolsky & Felix Dreisow & Stefan Nolte & Mordechai Segev & Alexander Szameit, 2013. "Photonic Floquet topological insulators," Nature, Nature, vol. 496(7444), pages 196-200, April.
    4. Zeng, Liangwei & Zhu, Yongle & Malomed, Boris A. & Mihalache, Dumitru & Wang, Qing & Long, Hu & Cai, Yi & Lu, Xiaowei & Li, Jingzhen, 2022. "Quadratic fractional solitons," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Zhaoyang Zhang & Rong Wang & Yiqi Zhang & Yaroslav V. Kartashov & Feng Li & Hua Zhong & Hua Guan & Kelin Gao & Fuli Li & Yanpeng Zhang & Min Xiao, 2020. "Observation of edge solitons in photonic graphene," Nature Communications, Nature, vol. 11(1), pages 1-7, December.
    6. Daohong Song & Vassilis Paltoglou & Sheng Liu & Yi Zhu & Daniel Gallardo & Liqin Tang & Jingjun Xu & Mark Ablowitz & Nikolaos K. Efremidis & Zhigang Chen, 2015. "Unveiling pseudospin and angular momentum in photonic graphene," Nature Communications, Nature, vol. 6(1), pages 1-7, May.
    7. Zeng, Liangwei & Mihalache, Dumitru & Malomed, Boris A. & Lu, Xiaowei & Cai, Yi & Zhu, Qifan & Li, Jingzhen, 2021. "Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Wu, Zhenkun & Yang, Kaibo & Zhang, Yagang & Ren, Xijun & Wen, Feng & Gu, Yuzong & Guo, Lijun, 2022. "Nonlinear conical diffraction in fractional dimensions with a PT-symmetric optical lattice," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    9. Alois Regensburger & Christoph Bersch & Mohammad-Ali Miri & Georgy Onishchukov & Demetrios N. Christodoulides & Ulf Peschel, 2012. "Parity–time synthetic photonic lattices," Nature, Nature, vol. 488(7410), pages 167-171, August.
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