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Chin. Phys. B, 2021, Vol. 30(11): 114209    DOI: 10.1088/1674-1056/ac068e

Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity

Yagang Zhang(张亚港)1, Yuheng Pei(裴宇恒)2, Yibo Yuan(袁一博)2, Feng Wen(问峰)3, Yuzong Gu(顾玉宗)1, and Zhenkun Wu(吴振坤)1,†
1 Institute of Nano/Photon Materials and Application & International Joint Research Laboratory of New Energy Materials and Devices of Henan Province, School of Physics and Electronics, Henan University, Kaifeng 475004, China;
2 College of Miami, Henan University, Kaifeng 475004, China;
3 Key Laboratory for Physical Electronics and Devices of the Ministry of Education & School of Science & Shaanxi Key Laboratory of Information Photonic Technique & Institute of Wide Bandgap Semiconductors, Xi'an Jiaotong University, Xi'an 710049, China
Abstract  Accelerating beams have been the subject of extensive research in the last few decades because of their self-acceleration and diffraction-free propagation over several Rayleigh lengths. Here, we investigate the propagation dynamics of a Fresnel diffraction beam using the nonlocal nonlinear Schrödinger equation (NNLSE). When a nonlocal nonlinearity is introduced into the linear Schrödinger equation without invoking an external potential, the evolution behaviors of incident Fresnel diffraction beams are modulated regularly, and certain novel phenomena are observed. We show through numerical calculations, under varying degrees of nonlocality, that nonlocality significantly affects the evolution of Fresnel diffraction beams. Further, we briefly discuss the two-dimensional case as the equivalent of the product of two one-dimensional cases. At a critical point, the Airy-like intensity profile oscillates between the first and third quadrants, and the process repeats during propagation to yield an unusual oscillation. Our results are expected to contribute to the understanding of NNLSE and nonlinear optics.
Keywords:  Fresnel diffraction beams, nonlocal nonlinearity, real space, momentum space, three-dimensional (3D) Schrö      dinger equation  
Received:  06 May 2021      Revised:  26 May 2021      Accepted manuscript online:  29 May 2021
PACS:  42.25.Fx (Diffraction and scattering)  
  42.25.Bs (Wave propagation, transmission and absorption)  
  42.25.Gy (Edge and boundary effects; reflection and refraction)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61805068, 61875053, and 62074127), China Postdoctoral Science Foundation (Grant No. 2017M620300), and the Fund from the Science and Technology Department of Henan Province, China (Grant No. 202102210111).
Corresponding Authors:  Zhenkun Wu     E-mail:

Cite this article: 

Yagang Zhang(张亚港), Yuheng Pei(裴宇恒), Yibo Yuan(袁一博), Feng Wen(问峰), Yuzong Gu(顾玉宗), and Zhenkun Wu(吴振坤) Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity 2021 Chin. Phys. B 30 114209

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