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

Zhenkun Wu, Kaibo Yang, Yagang Zhang, Xijun Ren, Feng Wen, Yuzong Gu and Lijun Guo

Chaos, Solitons & Fractals, 2022, vol. 158, issue C

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.

Keywords: Parity-time symmetry; Floquet-Bloch modes; Kerr nonlinearity; Conical diffraction (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:158:y:2022:i:c:s096007792200220x

DOI: 10.1016/j.chaos.2022.112010

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