[1] [1] Durnin J. Exact-solutions for nondiffracting beams. I. The scalar theory［J］. Journal of the Optical Society of America A, 1987, 4(4): 651-654.

[2] [2] Gutiérrez-Vega J C, Bandres M A. Helmholtz-Gauss waves［J］. Journal of the Optical Society of America A, 2005, 22(2): 289-298.

[3] [3] Gutiérrez-Vega J C, Iturbe-Castillo M D, Chávez-Cerda S. Alternative formulation for invariant optical fields: Mathieu beams［J］. Optics Letters, 2000, 25(20): 1493-1495.

[4] [4] Belafhal A, Chafiq A, Hricha Z. Scattering of Mathieu beams by a rigid sphere［J］. Optics Communications, 2011, 284(12): 3030-3035.

[5] [5] Nadgaran H, Servatkhah M, Sabaeian M. Mathieu-Gauss beams: A thermal consideration［J］. Optics Communications, 2010, 283(3): 417-426.

[6] [6] Xie Xiaoxia, Li Dong, Wu Fengtie. Ribbon quasi-non-diffracting beam obtained with elliptical aperture and axicon system［J］. Acta Optica Sinica, 2015, 35(1): 0126001.

[7] [7] Alpmann C, Bowman R, Woerdemann M, et al. Mathieu beams as versatile light moulds for 3D micro particle assemblies［J］. Optics Express, 2010, 18(25): 26084-26091.

[8] [8] Fleischer J W, Segev M, Efremidis N K, et al. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices［J］. Nature, 2003, 422(6928): 147-150.

[9] [9] Li Y J. Mathieu-Gaussian beam for optical scanners: US6719204［P］. 2004-04-13.

[10] [10] Chávez-Cerda S, Padgett M J, Allison I, et al. Holographic generation and orbital angular momentum of high-order Mathieu beams［J］. Journal of Optics B, 2002, 4(2): S52-S57.

[11] [11] Alvarez-Elizondo M B, Rodriguez-Masegosa R, Gutierrez-Vega J C. Generation of Mathieu-Gauss modes with an axicon-based laser resonator［J］. Optics Express, 2008, 16(23): 18770-18775.

[12] [12] Li Dong, Wu Fengtie, Xie Xiaoxia. A novel method of generating quasi-non-diffracting Mathieu beam based on axicon［J］. Acta Physica Sinica, 2014, 63(15): 152401.

[13] [13] Guo Chengshan, Li Chuantao, Hong Zhengping, et al. Suitability of different sampling methods for digital simulations of the optical diffraction［J］. Acta Optica Sinica, 2008, 28(3): 442-446.

[14] [14] Ruan Lifeng, Tang Zhilie, Liu Xueling. Investigation on light intensity distribution of Raman-Nath acousto-optic diffraction based on Fourier analysis［J］. Acta Optica Sinica, 2013, 33(3): 0307001.

[15] [15] Nascov V, Logoftu P C. Fast computation algorithm for the Rayleigh-Sommerfeld diffraction formula using a type of scaled convolution［J］. Applied Optics, 2009, 48(22): 4310-4319.