IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008128.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008128
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112631?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Ren, Boquan & Kartashov, Yaroslav V. & Wang, Hongguang & Li, Yongdong & Zhang, Yiqi, 2023. "Floquet topological insulators with hybrid edges," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Tang, Qian & Zhang, Yiqi & Kartashov, Yaroslav V. & Li, Yongdong & Konotop, Vladimir V., 2022. "Vector valley Hall edge solitons in superhoneycomb lattices," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Zhu, Xing & Xiang, Dan & Zeng, Liangwei, 2023. "Fundamental and multipole gap solitons in spin-orbit-coupled Bose-Einstein condensates with parity-time-symmetric Zeeman lattices," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Jie Qian & C. H. Meng & J. W. Rao & Z. J. Rao & Zhenghua An & Yongsheng Gui & C. -M. Hu, 2023. "Non-Hermitian control between absorption and transparency in perfect zero-reflection magnonics," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    6. Simone Zanotto & Giorgio Biasiol & Paulo V. Santos & Alessandro Pitanti, 2022. "Metamaterial-enabled asymmetric negative refraction of GHz mechanical waves," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    7. Zhongming Gu & He Gao & Haoran Xue & Jensen Li & Zhongqing Su & Jie Zhu, 2022. "Transient non-Hermitian skin effect," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    8. Pengtao Song & Xinhui Ruan & Haijin Ding & Shengyong Li & Ming Chen & Ran Huang & Le-Man Kuang & Qianchuan Zhao & Jaw-Shen Tsai & Hui Jing & Lan Yang & Franco Nori & Dongning Zheng & Yu-xi Liu & Jing , 2024. "Experimental realization of on-chip few-photon control around exceptional points," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    9. Kartashov, Yaroslav V. & Konotop, Vladimir V., 2024. "Topological star junctions: Linear modes and solitons," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    10. Zhongqiang Chen & Hongsong Qiu & Xinjuan Cheng & Jizhe Cui & Zuanming Jin & Da Tian & Xu Zhang & Kankan Xu & Ruxin Liu & Wei Niu & Liqi Zhou & Tianyu Qiu & Yequan Chen & Caihong Zhang & Xiaoxiang Xi &, 2024. "Defect-induced helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    11. Zhaohui Dong & Xiaoxiong Wu & Yiwen Yang & Penghong Yu & Xianfeng Chen & Luqi Yuan, 2024. "Temporal multilayer structures in discrete physical systems towards arbitrary-dimensional non-Abelian Aharonov-Bohm interferences," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    12. Triki, Houria & Sun, Yunzhou & Zhou, Qin & Biswas, Anjan & Yıldırım, Yakup & Alshehri, Hashim M., 2022. "Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    13. Meng, Hongjuan & Zhou, Yushan & Li, Xiaolin & Ren, Xueping & Wan, Xiaohuan & Zhou, Zhikun & Wang, Wenyuan & Shi, Yuren, 2021. "Gap solitons in Bose–Einstein condensate loaded in a honeycomb optical lattice: Nonlinear dynamical stability, tunneling, and self-trapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    14. Chenwei Lv & Ren Zhang & Zhengzheng Zhai & Qi Zhou, 2022. "Curving the space by non-Hermiticity," Nature Communications, Nature, vol. 13(1), pages 1-6, December.
    15. Cao, Xuefei & Wang, Kaile & Yang, Song & Gao, Yuanmei & Cai, Yangjian & Wen, Zengrun, 2024. "Localization and delocalization of light in synthetic photonic lattices with hybrid Bloch-Anderson modulations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    16. Xiao-Chen Sun & Hao Chen & Hua-Shan Lai & Chu-Hao Xia & Cheng He & Yan-Feng Chen, 2023. "Ideal acoustic quantum spin Hall phase in a multi-topology platform," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    17. Khater, Mostafa M.A., 2022. "Nonparaxial pulse propagation in a planar waveguide with Kerr–like and quintic nonlinearities; computational simulations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    18. Li, Jun-Jie & Zhang, Hui-Cong, 2024. "Interaction-produced vector vortex chaoticons in nonlocal nonlinear media," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    19. Kai Zhang & Zhesen Yang & Chen Fang, 2022. "Universal non-Hermitian skin effect in two and higher dimensions," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    20. Sihong Lei & Shiqi Xia & Daohong Song & Jingjun Xu & Hrvoje Buljan & Zhigang Chen, 2024. "Optical vortex ladder via Sisyphus pumping of Pseudospin," Nature Communications, Nature, vol. 15(1), pages 1-9, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008128. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.