[1] [1] BLOCH F. ber die Quantenmechanik der Elektronen in Kristallgittern[J]. Zeitschrift Fur Physik, 1929, 52: 555-600. DOI: 10.1007/BF01339455.

[2] [2] FELDMANN J, LEO K, SHAH J, et al. Optical investigation of Bloch oscillations in a semiconductor superlattice[J]. Physical Review B, 1992, 46: 7252-7255. DOI:10.1103/PhysRevB.46.7252.

[3] [3] LONGHI S. Quantum-optical analogies using photonic structures[J]. Laser and Photonics Reviews, 2009, 3: 243-261. DOI: 10.1002/lpor.200810055.

[4] [4] LEDERER F, STEGEMAN G I, CHRISTODOULIDES D N, et al. Discrete solitons in optics[J]. Physics Reports, 2008, 463: 1-126. DOI: 10.1016/j.physrep.2008.04.004.

[5] [5] KARTASHOV Y V, MALOMED B A, TORNER L. Solitons in nonlinear lattices[J]. Reviews of Modern Physics, 2011, 83: 247-305. DOI: 10.1103/RevModPhys.83.247.

[6] [6] GARANOVICH I L, LONGHI S, SUKHORUKOV A A, et al. Light propagation and localization in modulated photonic lattices and waveguides[J]. Physics Reports, 2012, 518: 1-79. DOI: 10.1016/j.physrep.2012.03.005.

[7] [7] PESCHEL U, PERTSCH T, LEDERER F. Optical Bloch oscillations in waveguide arrays[J]. Optics Letters, 1998, 23: 1701-1703. DOI: 10.1364/OL.23.001701.

[8] [8] PERTSCH T, DANNBERG P, ELFLEIN W, et al. Optical Bloch oscillations in temperature tuned waveguide arrays[J]. Physical Review Letters, 1999, 83: 4752-4755. DOI: 10.1103/PhysRevLett.83.4752.

[9] [9] MORANDOTTI R, PESCHEL U, AITCHISON S J, et al. Experimental observation of linear and nonlinear optical Bloch oscillations[J]. Physical Review Letters, 1999, 83: 4756-4759. DOI: 10.1103/PhysRevLett.83.4756.

[10] [10] TROMPETER H, PERTSCH T, LEDERER F, et al. Visual observation of Zener tunneling[J]. Physical Review Letters, 2006, 96: 023901. DOI: 10.1103/PhysRevLett.96.023901.

[11] [11] BROMBERG Y, LAHINI Y, SILBERBERG Y. Bloch oscillations of path-entangled photons[J]. Physical Review Letters, 2010, 105: 263604. DOI: 10.1103/PhysRevLett.105.263604.

[12] [12] LEBUGLE M, GRFE M, HEILMANN R, et al. Experimental observation of N00N state Bloch oscillations[J]. Nature Communication, 2015, 6: 8273. DOI:10.1038/ncomms9273.

[13] [13] LONGHI S. Bloch oscillations in complex crystals with PT symmetry[J]. Physical Review Letters, 2009, 103: 123601. DOI: 10.1103/PhysRevLett.103.123601.

[14] [14] XU Y L, FEGADOLLI W S, GAN L, et al. Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice[J]. Nature Communication, 2016, 7: 11319. DOI: 10.1038/ncomms11319.

[15] [15] ZHANG Y Q, WANG R, ZHONG H, et al. Optical Bloch oscillation and Zener tunneling in the fractional Schrdinger equation[J]. Scientific Reports, 2017, 7: 17872. DOI: 10.1038/s41598-017-17995-7.

[16] [16] LASKIN N. Fractional quantum mechanics and Lévy path integrals[J]. Physics Letters A, 2000, 268(4-6): 298-305. DOI: 10.1016/S0375-9601(00)00201-2.

[17] [17] LASKIN N. Fractional quantum mechanics[J]. Physics Letters E, 2000, 62(3): 3135-3145. DOI: 10.1103/physreve.62.3135.

[18] [18] LASKIN N. Fractional Schrdinger equation[J]. Physics Letters E, 2002, 66(5 Pt 2): 056108. DOI: 10.1103/ PhyRevE. 66. 056108.

[19] [19] LRINCZI J, MAECKI J. Spectral properties of the massless relativistic harmonic oscillator[J]. Journal of Differential Equations, 2012, 253: 2846-2871. DOI: 10.1016/j.jde.2012.07.010.

[20] [20] LONGHI S. Fractional Schrdinger equation in optics[J]. Optics Letters, 2015, 40: 1117-1120. DOI: 10. 1364/ ol. 40. 001117.

[21] [21] LIEMERT A, KIENLE A. Fractional Schrdinger equation in the presence of the linear potential[J]. Mathematics, 2016, 4: 31. DOI: 10.3390/math4020031.

[22] [22] HUANG C M, DONG L W. Beam propagation management in a fractional Schrdinger equation[J]. Scientific Reports, 2019, 7: 5442. DOI: 10.1038/s41598-017-05926-5.

[23] [23] WU G Z, YU L J, WANG Y Y. Fractional optical solitons of the space-time fractional nonlinear Schrodinger equation[J]. Optik, 2020, 207: 164405. DOI: 10.1016/j.ijleo.2020.164405.

[24] [24] SIVILOGLOU G A, CHRISTODOULIDES D N. Airy-Gauss beams and their transformation by paraxial optical systems[J]. Optics Letters, 2007, 32: 979. DOI: 10.1364/OE.15.016719.

[27] [27] HU Y, TEHRANCHI A, WABNITZ S, et al. Improved intrapulse Raman scattering control via asymmetric Airy pulses[J]. Physical Review Letters, 2015, 114: 073901. DOI: 10.1364/CLEO_QELS.2013.QM2E.2.

[28] [28] ZHONG H, ZHANG Y Q, ZHANG Z Y, et al. Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency[J]. Optics Letters, 2016, 41: 5644. DOI: 10.1364/OL.41.005644

[29] [29] HU Y, SIVILOGLOU G A, ZHANG P, et al. Nonlinear Photonics and Novel Optical Phenomena[N](Eds: Chen Z G, Morandott R), Springer Series in Optical Sciences Vol. 170, Springer, New York paper, 2012: 1-46. DOI: 10.1007/978-1-4614-3538-9.

[30] [30] BANDRES M A, KAMINER I, MILLS M, et al. Accelerating Optical Beams[J]. Optics & Photonics News, 2013, 24: 30-37. DOI: 10.1364/OPN.24.6.000030.

[31] [31] CHEN Z G, XU J J, HU Y, et al. Control and novel applications of self-accelerating beams[J]. Acta Optica Sinica, 2016, 36: 1026009. DOI:10.3788/AOS201636.1026009.

[32] [32] LIU W, NESHEV D N, SHADRIVOV I V, et al. Plasmonic Airy beam manipulation in linear optical potentials[J]. Optics Letters, 2011, 36: 1164. DOI: 10.1364/OL.36.001164.

[33] [33] EFREMIDIS N K. Airy trajectory engineering in dynamic linear index potentials[J]. Optics Letters, 2011, 36: 3006-3008. DOI: 10.1364/OL.36.003006.

[36] [36] Zhan K Y, Zhang W Q, Jiao R Y, et al. Propagations of Airy beams with quadratic phase modulation, and their interaction in paraxial optical systems[J]. Optics Communications, 2020, 474: 126156. DOI: 10.1016/j.optcom.2020.126156.

[37] [37] CHEN W J, WANG T, WANG J, et al. Dynamics of interactiong Airy beams in the fractional Schrdinger equation with a linear potential[J]. Optics Communications, 2021, 496: 127136. DOI: 10.1016/j.optcom.2021.127136.

[38] [38] HAN T W, CHEN H, LI W W, et al.Temporal Airy-Talbot effect in linear optical potentials[J]. Chinese Optics Letters, 2021, 19: 082601. DOI:10.3788/COL202119.082601.

[39] [39] XIAO F J, ZHANG P, ZHU W R, et al. Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient[J]. Optics Express, 2014, 22: 22763. DOI: 10.1364/OE.22.022763.

[40] [40] XIAO F J, ZHU W R, SHANG W S, et al. Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices[J]. Optics Express, 2016, 24: 18332. DOI: 10.1364/OE.24.018332.

[41] [41] CAO Z, LI X J, TAN Q G, et al. Trajectory variations of optical Bloch oscillations for Airy beams in transversely and longitudinally modulated photonic lattices[J]. Applied Optics, 2017, 56: 3484. DOI: 10.1364/AO.56.003484.