Nonlinear conical diffraction in fractional dimensions with a PT-symmetric optical lattice. (May 2022)

• Record Type: Journal Article
• Authors: Wu, Zhenkun; Yang, Kaibo; Zhang, Yagang; Ren, Xijun; Wen, Feng; Gu, Yuzong; Guo, Lijun
• Is Part Of: Chaos, solitons and fractals. Volume 158(2022)
• Publication Date: 2022-05
• Subjects: Parity-time symmetry -- Floquet-Bloch modes -- Kerr nonlinearity -- Conical diffraction; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112010
• Languages: English
• ISSNs: 0960-0779

Abstract

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.