[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).

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

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

[4] Wiersma N, Marsal N, Sciamanna M et al. All-optical interconnects using Airy beams[J]. Optics Letters, 39, 5997-6000(2014).

[5] Zhan K Y, Jiao R Y, Wang J et al. Self-imaging effect based on Airy beams with quadratic phase modulation[J]. Annalen Der Physik, 532, 1900546(2020).

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

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

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

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

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

[14] 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).

[15] Polynkin P, Kolesik M, Moloney J V et al. Curved plasma channel generation using ultraintense Airy beams[J]. Science, 324, 229-232(2009).

[16] Salandrino A, Christodoulides D N. Airy plasmon: a nondiffracting surface wave[J]. Optics Letters, 35, 2082-2084(2010).

[17] Zhang P, Wang S, Liu Y M et al. Plasmonic Airy beams with dynamically controlled trajectories[J]. Optics Letters, 36, 3191-3193(2011).

[18] Ashkin A, Dziedzic J M, Bjorkholm J E et al. Observation of a single-beam gradient force optical trap for dielectric particles[J]. Optics Letters, 11, 288-290(1986).

[19] McGloin D, Reid J P. Forty years of optical manipulation[J]. Optics and Photonics News, 21, 20-26(2010).

[20] 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).

[21] Chong A, Renninger W H, Christodoulides D N et al. Airy-Bessel wave packets as versatile linear light bullets[J]. Nature Photonics, 4, 103-106(2010).

[22] Panagiotopoulos P, Papazoglou D G, Couairon A et al. Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets[J]. Nature Communications, 4, 1-6(2013).

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

[24] Bandres M A, Gutiérrez-Vega J C. Airy-Gauss beams and their transformation by paraxial optical systems[J]. Optics Express, 15, 16719-16728(2007).

[25] Deng D, Li H. Propagation properties of Airy-Gaussian beams[J]. Applied Physics B, 106, 677-681(2012).

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

[27] 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).

[28] Zhang T, Chen W J, Mu Y N et al. Propagation properties of Airy-Gaussian beams in a biased photovoltaic-photorefractive crystal[J]. Acta Photonica Sinica, 48, 1048004(2019).

[29] Chen W J, Ju Y, Liu C Y et al. Generation of breathing solitons in the propagation and interactions of Airy-Gaussian beams in a cubic-quintic nonlinear medium[J]. Chinese Physics B, 27, 114216(2018).

[30] Chen W J, Lu K Q, Hui J L et al. Propagation and interactions of Airy-Gaussian beams in saturable nonliear medium[J]. Acta Physica Sinica, 65, 244202(2016).

[31] Zuo M W, Shi Z W, Li H G. Interaction of two Airy-Gaussian beams in nonlocal nonlinear medium with defected lattices[J]. Laser & Optoelectronics Progress, 57, 051901(2020).

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

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

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

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

[36] Zang F, Wang Y, Li L. Dynamics of Gaussian beam modeled by fractional Schrödinger equation with a variable coefficient[J]. Optics Express, 26, 23740-23750(2018).

[37] Zhang L F, Li C X, Zhong H Z et al. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes[J]. Optics Express, 24, 14406-14418(2016).

[38] Huang X W, Deng Z X, Fu X Q. Dynamics of finite energy Airy beams modeled by the fractional Schrödinger equation with a linear potential[J]. Journal of the Optical Society of America B, 34, 976-982(2017).

[39] Xiao Y, Zhang J, Wang P X. Periodic evolution of Airy-Gaussian beams under linear potential[J]. Chinese Journal of Lasers, 48, 0105002(2021).

[40] Vallée O, Soares M. Airy functions and applications to physics[M](2004).

[41] Abramowitz M, Stegun I. Handbook of mathematical functions[M](1965).