[1] Chen Z G, Xu J J, Hu Y et al. Control and novel applications of self-accelerating beams[J]. Acta Optica Sinica, 36, 1026009(2016).

[2] Kartashov Y V, Malomed B A, Konotop V V et al. Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling[J]. Optics Letters, 40, 1045-1048(2015).

[3] Deng D M, Zhao X, Guo Q et al. Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media[J]. Journal of the Optical Society of America B, 24, 2537-2544(2007).

[4] Durnin J. Exact solutions for nondiffracting beams. I. The scalar theory[J]. Journal of the Optical Society of America A, 4, 651-654(1987).

[5] Gutiérrez-Vega J C, Iturbe-Castillo M D, Chávez-Cerda S. Alternative formulation for invariant optical fields: Mathieu beams[J]. Optics Letters, 25, 1493-1495(2000).

[6] Bandres M A, Gutiérrez-Vega J C, Chávez-Cerda S. Parabolic nondiffracting optical wave fields[J]. Optics Letters, 29, 44-46(2004).

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

[8] Kovalev А А, Kotlyar V V. Lommel modes[J]. Optics Communications, 338, 117-122(2015).

[9] Belafhal A, Ez-zariy L, Hricha Z. A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 184, 1-7(2016).

[10] Hui Y F, Cui Z W, Song P. Propagation characteristics of non-diffracting Lommel beams in a gradient-index medium[J]. Waves in Random and Complex Media, 31, 2514-2524(2021).

[11] Thakur V, Kumar S, Kant N. Self-focusing of a Bessel-Gaussian laser beam in plasma under density transition[J]. Journal of Nonlinear Optical Physics & Materials, 388(2022).

[12] 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).

[13] Jiang Q C, Su Y L, Ma Z W et al. Propagation properties of Airy-Gaussian beams in centrosymmetric photorefractive media[J]. Journal of Modern Optics, 65, 2243-2249(2018).

[14] Kovalev A A, Kotlyar V V. Family of three-dimensional asymmetric nonparaxial Lommel modes[J]. Proceedings of SPIE, 9448, 944828(2015).

[15] Li Y, Chu X C, Tang H L et al. Propagation and evolution properties of finite energy airy beams[J]. Laser & Optoelectronics Progress, 59, 1326001(2022).

[16] Zhang J N, Chen W J, Zhao P. Propagation and interaction of Airy-Gaussian beams in saturable nonlinear medium based on fractional effect[J]. Acta Optica Sinica, 42, 1519001(2022).

[17] Adriazola J, Goodman R H. Optimal control approach to gradient-index design for beam reshaping[J]. Journal of the Optical Society of America A, 39, 907-915(2022).

[18] Pei S X, Xu S S, Cui F P et al. Propagation of a Bessel-Gaussian beam in a gradient-index medium[J]. Applied Optics, 58, 920-926(2019).

[19] Deng D M. Propagation of Airy-Gaussian beams in a quadratic-index medium[J]. The European Physical Journal D, 65, 553-556(2011).

[20] Tu J L, Wang X Y, Yu X et al. Free space realization of the symmetrical tunable auto-focusing Lommel Gaussian vortex beam[J]. Annalen der Physik, 534, 2100419(2022).

[21] Li Y, Zhang Y X, Zhu Y. Lommel-Gaussian pulsed beams carrying orbital angular momentum propagation in asymmetric oceanic turbulence[J]. IEEE Photonics Journal, 12, 7900915(2020).

[22] Suo Q B, Han Y P, Cui Z W. The spectral properties of a partially coherent Lommel-Gaussian beam in turbulent atmosphere[J]. Optics & Laser Technology, 123, 105940(2020).