[1] Durnin J. Exact solutions for nondiffracting beams. I. The scalar theory[J]. Journal of the Optical Society of America A, 4, 651-654(1987). http://www.opticsinfobase.org/abstract.cfm?uri=josaa-4-4-651

[2] Durnin J, Miceli J J, Eberly J H. Diffraction-free beams[J]. Physical Review Letters, 58, 1499-1501(1987).

[3] Clerici M, Hu Y, Lassonde P et al. Laser-assisted guiding of electric discharges around objects[J]. Science Advances, 1, e1400111(2015).

[4] Liang Y, Hu Y, Song D et al. Image signal transmission with Airy beams[J]. Optics Letters, 40, 5686-5689(2015).

[5] Berry M V, Balazs N L. Nonspreading wave packets[J]. American Journal of Physics, 47, 264-267(1979).

[6] Siviloglou G A, Broky J, Dogariu A et al. Observation of accelerating Airy beams[J]. Physical Review Letters, 99, 213901(2007).

[7] Siviloglou G A, Christodoulides D N. Accelerating finite energy Airy beams[J]. Optics Letters, 32, 979-981(2007).

[8] Broky J, Siviloglou G A, Dogariu A et al. Self-healing properties of optical Airy beams[J]. Optics Express, 16, 12880-12891(2008).

[9] Siviloglou G A, Broky J, Dogariu A et al. Ballistic dynamics of Airy beams[J]. Optics Letters, 33, 207-209(2008).

[10] Bandres M A. Rodríguez-Lara B M. Nondiffracting accelerating waves: Weber waves and parabolic momentum[J]. New Journal of Physics, 15, 013054(2013).

[11] Rose P, Diebel F, Boguslawski M et al. Airy beam induced optical routing[J]. Applied Physics Letters, 102, 101101(2013).

[12] Chen R P, Yin C F, Chu X X et al. Effect of Kerr nonlinearity on an Airy beam[J]. Physical Review A, 82, 043832(2010).

[13] Zhang Y Q, Belić M R, Zhang H B et al. Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media[J]. Optics Express, 22, 7160-7171(2014).

[14] Zhang L, Zhang J, Xiao Y. Propagation of chirped Airy pulse and soliton in inhomogeneous optical fiber[J]. Chinese Journal of Lasers, 44, 0906005(2017).

[15] Chen W J, Yang J K, Liu C Y et al. Generation and propagation regulation of Airy solitons in saturable nonlinear medium[J]. Acta Optica Sinica, 38, 0119001(2018).

[16] Zhang L, Bai X Q, Wang Y H et al. Interaction of Airy beams in a medium with parabolic potential[J]. Optik, 161, 106-110(2018).

[17] Dai C Y, Han H M, Fan Y P et al. Generation of tunable Airy beams using deformable lens[J]. Chinese Journal of Lasers, 47, 0805002(2020).

[18] Baumgartl J, Mazilu M, Dholakia K. Optically mediated particle clearing using Airy wavepackets[J]. Nature Photonics, 2, 675-678(2008).

[19] Abdollahpour D, Suntsov S, Papazoglou D G et al. Spatiotemporal Airy light bullets in the linear and nonlinear regimes[J]. Physical Review Letters, 105, 253901(2010).

[20] Voloch-Bloch N, Lereah Y, Lilach Y et al. Generation of electron Airy beams[J]. Nature, 494, 331-335(2013).

[21] Chen C D, Chen B, Peng X et al. Propagation of Airy-Gaussian beam in Kerr medium[J]. Journal of Optics, 17, 035504(2015).

[22] Zhou M L, Peng Y L, Chen C D et al. Interaction of Airy-Gaussian beams in saturable media[J]. Chinese Physics B, 25, 084102(2016).

[23] Chen W J, Song D, Li Y et al. Control on interaction of Airy-Gaussian beams in competing nonlinear medium[J]. Acta Physica Sinica, 68, 094206(2019).

[24] Bai X Q, Wang Y H, Zhang J et al. Soliton shedding from Airy-Gaussian beams in photorefractive media[J]. Chinese Journal of Lasers, 46, 0805001(2019).

[25] Bai X Q, Wang Y H, Zhang J et al. Bound states of chirped Airy-Gaussian beams in a medium with a parabolic potential[J]. Applied Physics B, 125, 188(2019).

[26] Wang Y H, Xiao Y, Bai X Q et al. Optical field rotation of finite energy Airy-Hermite-Gaussian beams in medium with potential well[J]. Laser & Optoelectronics Progress, 56, 240602(2019).

[27] Laskin N. Fractional quantum mechanics[J]. Physical Review E, 62, 3135-3145(2000).

[28] Laskin N. Fractional quantum mechanics and Lévy path integrals[J]. Physics Letters A, 268, 298-305(2000).

[29] Laskin N. Fractional Schrödinger equation[J]. Physical Review E, 66, 056108(2002).

[30] Longhi S. Fractional Schrödinger equation in optics[J]. Optics Letters, 40, 1117-1120(2015).

[31] Zhang Y Q, Zhong H, Belić M R et al. Diffraction-free beams in fractional Schrödinger equation[J]. Scientific Reports, 6, 23645(2016).

[32] Zhang Y Q, Liu X, Belić M R et al. Propagation dynamics of a light beam in a fractional Schrödinger equation[J]. Physical Review Letters, 115, 180403(2015).

[33] Huang X W, Shi X H, Deng Z X et al. Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation[J]. Optics Express, 25, 32560-32569(2017).