1. Takenaka, T., M. Yokota, and O. Fukumitsu, "Propagation of light beams beyond the paraxial approximate," J. Opt. Soc. Am. A, Vol. 2, 826-829, 1985.
doi:10.1364/JOSAA.2.000826
2. Zauderer, E., "Complex argument Hermite-Gaussian and Laguerre-Gaussian beams," J. Opt. Soc. Am. A, Vol. 3, 465-469, 1986.
doi:10.1364/JOSAA.3.000465
3. Saghafi, S. and C. J. R. Sheppard, "Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes," J. Mod. Opt., Vol. 45, 1999-2009, 1998.
doi:10.1080/09500349808231738
4. Deng, D., Q. Guo, L. Wu, and X. Yang, "Propagation of radially polarized elegant light beams," J. Opt. Soc. Am. B, Vol. 24, 636-643, 2007.
doi:10.1364/JOSAB.24.000636
5. Luo, S. and B. Lu, "Propagation of the kurtosis parameter of elegant Hermite-Gaussian and Laguerre-Gaussian beams passing through ABCD systems," Optik, Vol. 113, 227-231, 2002.
doi:10.1078/0030-4026-00150
6. Mei, Z. and D. Zhao, "Propagation of Laguerre-Gaussian and elegant Laguerre-Gaussian beams in apertured fractional Hankel transform systems," J. Opt. Soc. Am. A, Vol. 21, 2375-2381, 2004.
doi:10.1364/JOSAA.21.002375
7. Mei, Z., "The elliptical elegant Laguerre-Gaussian beam and its propagation through aligned and misaligned paraxial optical systems," Optik, Vol. 118, 361-366, 2007.
doi:10.1016/j.ijleo.2006.04.009
8. Nasalski, W., "Elegant Hermite and Laguerre-Gaussian beams at a dielectric interface," Opt. Appl., Vol. XL, 615-622, 2010.
9. Qu, J., Y. Zhong, Z. Cui, and Y. Cai, "Elegant Laguerre-Gaussian beam in a turbulent atmosphere," Opt. Commun., Vol. 283, No. 14, 2772-2781, 2010.
doi:10.1016/j.optcom.2010.03.022
10. Xu, H., Z. Cui, and J. Qu, "Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence," Opt. Express, Vol. 19, 21163-21173, 2011.
doi:10.1364/OE.19.021163
11. Chu, X., "Evolution of elegant Laguerre-Gaussian beam disturbed by an opaque obstacle," Journal of Electromagnetic Waves and Applications, Vol. 26, No. 13, 1749-1755, 2012.
doi:10.1080/09205071.2012.711518
12. Ni, Y. and G. Zhou, "Nonparaxial propagation of an elegant Laguerre-Gaussian beam orthogonal to the optical axis of a uniaxial crystal," Opt. Express, Vol. 20, 17160-17173, 2012.
doi:10.1364/OE.20.017160
13. Zhao, D., Z. Mei, J. Gu, H. Mao, L. Chen, and S. Wang, "Propagation characteristics of truncated standard and elegant Laguerre-Gaussian beams," Proc. SPIE, Vol. 5639, 149-158, 2004.
doi:10.1117/12.574891
14. Mei, Z. and D. Zhao, "The generalized beam propagation factor of truncated standard and elegant Laguerre-Gaussian beams," J. Opt. A: Pure and Appl. Opt., Vol. 6, 1005-1011, 2004.
doi:10.1088/1464-4258/6/11/002
15. Zhou, G., "Vectorial structure of an elegant Laguerre-Gaussian beam in the far-field regime," Lasers in Eng., Vol. 24, 127-146, 2012.
16. Bandres, M. A. and J. C. Gutierrez-Vega, "Higher-order complex source for elegant Laguerre-Gaussian waves," Opt. Lett., Vol. 29, 2213-2215, 2004.
doi:10.1364/OL.29.002213
17. Porras, M. A., R. Borghi, and M. Santarsiero, "Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams," J. Opt. Soc. Am. A, Vol. 18, 177-184, 2001.
doi:10.1364/JOSAA.18.000177
18. Pagani, Y. and W. Nasalski, "Diagonal relations between elegant Hermite-Gaussian and Laguerre-Gaussian beam fields," Opto-Electron. Rev., Vol. 13, 51-60, 2005.
19. Gutierrez-Vega, J. C., "Fractionalization of optical beams: II. Elegant Laguerre-Gaussian modes," Opt. Express, Vol. 15, 6300-6313, 2007.
doi:10.1364/OE.15.006300
20. Borghi, R., "Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams," J. Opt. Soc. Am. A, Vol. 18, 1627-1633, 2001.
doi:10.1364/JOSAA.18.001627
21. April, A., "Nonparaxial elegant Laguerre-Gaussian beams," Opt. Lett., Vol. 33, 1392-1394, 2008.
doi:10.1364/OL.33.001392
22. Mei, Z. and J. Gu, "Comparative studies of paraxial and nonparaxial vectorial elegant Laguerre-Gaussian beams," Opt. Express, Vol. 17, 14865-14871, 2009.
doi:10.1364/OE.17.014865
23. Wang, F., Y. Cai, and O. Korotkova, "Partially coherent standard and elegant Laguerre-Gaussian beams of all orders," Opt. Express, Vol. 17, 22366-22379, 2009.
doi:10.1364/OE.17.022366
24. Wang, F., Y. Cai, H. T. Eyyuboglu, and Y. K. Baykal, "Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere," Progress In Electromagnetics Research, Vol. 103, 33-56, 2010.
doi:10.2528/PIER10021901
25. Luo, H., H. Xu, Z. Cui, and J. Qu, "Beam propagation factor of partially coherent Laguerre-Gaussian beams in non-Kolmogorov turbulence," Progress In Electromagnetics Research M, Vol. 22, 205-218, 2012.
doi:10.2528/PIERM11102203
26. He, H., M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett., Vol. 75, 826-829, 1995.
doi:10.1103/PhysRevLett.75.826
27. Curtis, J. E., B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun., Vol. 207, 169-175, 2002.
doi:10.1016/S0030-4018(02)01524-9
28. Gibson, G., J. Courtial, M. Padgett, M. Vasnetsov, V. Pas'ko, S. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express, Vol. 12, 5448-5456, 2004.
doi:10.1364/OPEX.12.005448
29. Lee, W. M., X.-C. Yuan, and W. C. Cheong, "Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation," Opt. Lett., Vol. 29, 1796-1798, 2004.
doi:10.1364/OL.29.001796
30. Paterson, C., "Atmospheric turbulence and orbital angular momentum of single photons for optical communication," Phys. Rev. Lett., Vol. 94, 153901, 2005.
doi:10.1103/PhysRevLett.94.153901
31. Li, C. F., "Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization," Phys. Rev. A, Vol. 80, 063814, 2009.
doi:10.1103/PhysRevA.80.063814
32. Bliokh, K. Y., M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, "Angular momentum and spin-orbit interaction of nonparaxial light in free space," Phys. Rev. A, Vol. 82, 063825, 2010.
doi:10.1103/PhysRevA.82.063825
33. Porras, M. A., "Nonparaxial vectorial moment theory of light beam propagation," Opt. Commun., Vol. 127, 79-95, 1996.
doi:10.1016/0030-4018(96)00089-2
34. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980.
35. Agrawal, G. P. and D. N. Pattanayak, "Gaussian beam propagation beyond the paraxial approximation," J. Opt. Soc. Am., Vol. 69, 575-578, 1979.
doi:10.1364/JOSA.69.000575
36. Cicchitelli, L., H. Hora, and R. Postle, "Longitudinal field components for laser beams in vacuum," Phys. Rev. A, Vol. 41, 3727-3732, 1990.
doi:10.1103/PhysRevA.41.3727
37. Chen, C. G., P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, "Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations," J. Opt. Soc. Am. A, Vol. 19, 404-412, 2002.
doi:10.1364/JOSAA.19.000404
38. Cerjan, A. and C. Cerjan, "Analytica solution of flat-top Gaussian and Laguerre-Gaussian laser field components," Opt. Lett., Vol. 35, 3465-3467, 2010.
doi:10.1364/OL.35.003465
39. Cerjan, A. and C. Cerjan, "Orbital angular momentum of Laguerre-Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A, Vol. 28, 2253-2260, 2011.
doi:10.1364/JOSAA.28.002253
40. Gao, C., G. Wei, and H. Weber, "Orbital angular momentum of the laser beam and the second order intensity moments," Science in China (Ser. A), Vol. 43, 1306-1311, 2000.
doi:10.1007/BF02880068
41. Allen, L., M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A, Vol. 45, 8185-8189, 1992.
doi:10.1103/PhysRevA.45.8185