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Solitons in the fractional Schr?dinger equation with parity-time-symmetric lattice potential

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Abstract

We investigate the properties of spatial solitons in the fractional Schr?dinger equation (FSE) with parity-time (PT)-symmetric lattice potential supported by the focusing of Kerr nonlinearity. Both one- and two-dimensional solitons can stably propagate in PT-symmetric lattices under noise perturbations. The domains of stability for both one- and two-dimensional solitons strongly depend on the gain/loss strength of the lattice. In the spatial domain, the solitons are rigidly modulated by the lattice potential for the weak diffraction in FSE systems. In the inverse space, due to the periodicity of lattices, the spectra of solitons experience sharp peaks when the values of wavenumbers are even. The transverse power flows induced by the imaginary part of the lattice are also investigated, which can preserve the internal energy balances within the solitons.

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DOI:10.1364/prj.6.000875

基金项目:National Natural Science Foundation of China (NSFC)10.13039/501100001809 (61525505, 11774310); Natural Science Foundation of Shaanxi Province10.13039/501100007128 (2015KCT-06).

收稿日期:2018-06-11

录用日期:2018-07-05

网络出版日期:2018-07-08

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Xiankun Yao:State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China
Xueming Liu:State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China

联系人作者:Xueming Liu(liuxm1972@163.com)

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引用该论文

Xiankun Yao and Xueming Liu, "Solitons in the fractional Schr?dinger equation with parity-time-symmetric lattice potential," Photonics Research 6(9), 875-879 (2018)

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