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

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-05, Vol.158, p.112010, Article 112010
• Main Authors: Wu, Zhenkun, Yang, Kaibo, Zhang, Yagang, Ren, Xijun, Wen, Feng, Gu, Yuzong, Guo, Lijun
• Format: Article
• Language: English
• Subjects: Conical diffraction; Floquet-Bloch modes; Kerr nonlinearity; Parity-time symmetry
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112010

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.