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.

(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).

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

[1] Siviloglou G A and Christodoulides D N 2007 Opt. Lett.32 979 [2] Siviloglou G A, Broky J, Dogariu A and Christodoulides D N 2007 Phys. Rev. Lett.99 213901 [3] Broky J, Siviloglou G A, Dogariu A and Christodoulides D N 2008 Opt. Express16 12880 [4] Ellenbogen T, Voloch-Bloch N, GananyPadowicz A and Arie A 2009 Nat. Photon.3 395 [5] Chong A, Renninger W H, Christodoulides D N and Wise F W 2010 Nat. Photon.4 103 [6] Zhou J X, Liu Y H, Ke Y G, Luo H L and Wen S C 2015 Opt. Lett.40 3193 [7] Wu W J, Zhang W S, Chen S Z, Ling X H, Shu W X, Luo H L, Wen S C and Yin X B 2018 Opt. Express26 23705 [8] Xu D Y, He S S, Zhou J X, Chen S Z, Wen S C and Luo H L 2020 Opt. Lett.45 6867 [9] Berry M V and Balazs N L 1979 Am. J. Phys.47 264 [10] Lin C L, Hsiung T C and Huang M J 2008 Europhys. Lett.83 30002 [11] Durnin J 1987 J. Opt. Soc. Am. A4 651 [12] Bouchal Z 2003 Czech. J. Phys.53 537 [13] Wu Z K and Gu Y Z 2019 Commun. Theor. Phys.71 741 [14] Chen Y H, Wu L X, Mo Z X, Wu L C and Deng D M 2021 Chin. Phys. B30 014204 [15] He S L, Malomed B A, Mihalache D, Peng X, Yu X, He Y J and Deng D M 2021 Chaos, Solitons and Fractals142 110470 [16] Liu X Y, Sun C and Deng D M 2021 Chin. Phys. B30 024202 [17] Chen B, Chen C D, Peng X, Peng Y L, Zhou M L, Deng D M and Guo H 2016 J. Opt.18 055504 [18] Zhang X H, Wang F L, Bai L Y, Lou C B and Liang Y 2020 Chin. Phys. B29 064204 [19] Zhu Y F and Geng T 2020 Acta Phys. Sin.69 014205 (in Chinese) [20] Chen X P, Xu C J, Yang Q, Luo Z M, Li X X and Deng D M 2020 Chin. Phys. B29 064202 [21] Zhang P, Hu Y, Li T, Cannan D, Yin X, Morandotti R, Chen Z and Zhang X 2012 Phys. Rev. Lett.109 193901 [22] Kaminer I, Segev M and Christodoulides D N 2011 Phys. Rev. Lett.106 213903 [23] Lotti A, Faccio D, Couairon A, Papazoglou D G, Panagiotopoulos P, Abdollahpour D and Tzortzakis S 2011 Phys. Rev. A84 021807 [24] Panagiotopoulos P, Abdollahpour D, Lotti A, Couairon A, Faccio D, Papazoglou D G and Tzortzakis S 2012 Phys. Rev. A86 013842 [25] Efremidis N K, Paltoglou V and von Klitzing W 2013 Phys. Rev. A87 043637 [26] Zhuang F, Shen J, Du X and Zhao D 2012 Opt. Lett.37 3054 [27] Ru J M, Wu Z K, Zhang Y G, Wen F and Gu Y Z 2020 Front. Phys.15 52503 [28] Zhuang F, Du X, Ye Y and Zhao D 2012 Opt. Lett.37 1871 [29] Kaminer I, Nemirovsky J, Makris K G and Segev M 2013 Opt. Express21 8886 [30] Kong Q, Wang Q, Bang O and Krolikowski W 2010 Phys. Rev. A82 013826 [31] Hu W, Zhang T and Guo Q 2006 Appl. Phys. Lett.89 071111 [32] Bekenstein R and Segev M 2011 Opt. Express19 23706 [33] Wu Z K, Wang Z P, Guo H and Gu Y Z 2017 Opt. Express25 30468 [34] Zhou G Q, Chen R P and Ru G Y 2014 Laser Phys. Lett.11 105001 [35] Bekenstein R, Schley R, Mutzafi M, Rotschild C and Segev M 2015 Nat. Phys.11 872 [36] Peccianti M, Conti C, Assanto G, De Luca A and Umeton C 2004 Nature432 733 [37] Rotschild C, Alfassi B, Cohen O and Segev M 2006 Nat. Phys.2 769 [38] Wu Z K, Li P, Zhang Y B, Guo H and Gu Y Z 2019 J. Opt.21 105602 [39] Xu X M and Taha T 2003 J. Math. Model. Algorithms2 185 [40] Muslu G M and Erbay H A 2005 Math. Comput. Simulat.67 581 [41] Zhang Y Q, Belić M R, Zheng H B, Wu Z K, Li Y Y, Lu K Q and Zhang Y P 2013 Europhys. Lett.104 34007 [42] Zhang Y Q, Belić M R, Zheng H B, Chen H X, Li C B, Li Y Y and Zhang Y P 2014 Opt. Express22 7160 [43] Zhang Y Q, Belić M R, Wu Z K, Zheng H B, Lu K Q, Li Y Y and Zhang Y P 2013 Opt. Lett.38 4585 [44] Zhang Y Q, Liu X, Belić M R, Zhong W P, Zhang Y P and Xiao M 2015 Phys. Rev. Lett.115 180403 [45] Wu Z K, Zhang Y G, Ru J M and Gu Y Z 2020 Results Phys.16 103008 [46] Zhang Y G, Wu Z K, Ru J M, Wen F and Gu Y Z 2020 J. Opt. Soc. A B37 3414 [47] Eichelkraut T J, Siviloglou G A, Besieris I M and Christodoulides D N 2010 Opt. Lett.35 3655 [48] Wu Z K, Li P and Gu Y Z 2016 Front. Phys.12 124203

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