Zhang Yiqi, Belić Milivoj R, Zheng Huaibin, Chen Haixia, Li Changbiao, Song Jianping, Zhang Yanpeng
Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China.
Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032902. doi: 10.1103/PhysRevE.89.032902. Epub 2014 Mar 5.
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
