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2013-08-12
Orbital Angular Momentum Density of an Elegant Laguerre-Gaussian Beam
By
Progress In Electromagnetics Research, Vol. 141, 751-768, 2013
Abstract
Based on the method of the vectorial angular spectrum, an analytical expression of the electric field of an elegant Laguerre-Gaussian beam in free space is derived beyond the paraxial approximation, and the corresponding magnetic field is obtained by taking the curl of the electric field. By using the expressions for the electromagnetic fields, the expression of the orbital angular momentum density of the elegant Laguerre.Gaussian beam is derived, which is applicable to both the near and far fields. The effects of the three beam parameters on the distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam are studied. The distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is also compared with that of the standard Laguerre-Gaussian beam. The result shows that the distribution of the orbital angular momentum density of the elegant Laguerre-Gaussian beam is more simple and centralized than that of the standard Laguerre-Gaussian beam.
Citation
Guoquan Zhou, and Guoyun Ru, "Orbital Angular Momentum Density of an Elegant Laguerre-Gaussian Beam," Progress In Electromagnetics Research, Vol. 141, 751-768, 2013.
doi:10.2528/PIER13051608
References

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