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Nonlinear conical diffraction in fractional dimensions with a PT-symmetric optical lattice

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

Abstract

Space-fractional parity-time symmetry, featuring the fractional Laplacian operator rather than the standard operator, continues to be a challenge. This report analytically and numerically assesses the dynamics of wave packets in a space-fractional parity-time symmetric lattice by invoking Kerr nonlinearity. By adjusting the Lévy index, the basic properties of Floquet-Bloch modes in parity-time symmetric optical lattices are examined. It is demonstrated that the width of the first three Floquet-Bloch modes increases as the Lévy index decreases and that the corresponding band structure becomes symmetrically linear. These features result in peculiar properties during propagation, including splitting or diffraction-free propagation, preferential propagation, unidirectional propagation, and phase dislocations. In the two-dimensional fractional case, when the band structure is cone-like, it causes conical diffraction, and non-diffracting propagation occurs when the Floquet-Bloch mode of the upper band is excited by the input beam. Kerr nonlinearity modulates the energy in a certain nonlinear region toward the middle and suppresses the formation of conical diffraction.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s096007792200220x
    DOI: 10.1016/j.chaos.2022.112010
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    References listed on IDEAS

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    1. 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).

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