Vol. 38

Latest Volume
All Volumes
All Issues

Orbital Angular Momentum Density of a Hollow Vortex Gaussian Beam

By Yimin Zhou and Guoquan Zhou
Progress In Electromagnetics Research M, Vol. 38, 15-24, 2014


Here the hollow vortex Gaussian beam is described by the exact solution of the Maxwell equations. By means of the method of the vectorial angular spectrum, analytical expressions of the electromagnetic fields of a hollow vortex Gaussian beam propagating in free space are derived. By using the electromagnetic fields of a hollow vortex Gaussian beam beyond the paraxial approximation, one can calculate the orbital angular momentum density distribution of a hollow vortex Gaussian beam in free space. The overall transverse components of the orbital angular momentum of a hollow vortex Gaussian beam are equal to zero. Therefore, the influences of the topological charge, beam order, Gaussian waist size, and linearly polarized angle on the distribution of longitudinal component of the orbital angular momentum density of a hollow vortex Gaussian beam are numerically demonstrated in the reference plane. The outcome is useful to optical trapping, optical guiding, and optical manipulation using the hollow vortex Gaussian beams.


Yimin Zhou and Guoquan Zhou, "Orbital Angular Momentum Density of a Hollow Vortex Gaussian Beam," Progress In Electromagnetics Research M, Vol. 38, 15-24, 2014.


    1. Yin, J., Y. Zhu, W. Jhe, and Y. Wang, "Atom guiding and cooling in a dark hollow laser beam," Phys. Rev. A, Vol. 58, 509-513, 1998.

    2. Powell, P. N., "Blue-detuned dark-hollow laser guides atomic beam," Laser Focus World, Vol. 37, 58, 2001.

    3. Wang, Z., Y. Dong, and Q. Lin, "Atomic trapping and guiding by quasi-dark hollow beams," J. Opt. A: Pure Appl. Opt., Vol. 7, 147-153, 2005.

    4. Yin, J., Y. Zhu, W. Wang, Y. Wang, and W. Jhe, "Optical potential for atom guidance in a dark hollow laser beam," J. Opt. Soc. Am. B, Vol. 15, 25-33, 1998.

    5. Zhu, K., H. Tang, X. Sun, X. Wang, and T. Liu, "Flattened multi-Gaussian light beams with an axial shadow generated through superposing Gaussian beams," Opt. Commun., Vol. 207, 29-34, 2002.

    6. Cai, Y., X. Lu, and Q. Lin, "Hollow Gaussian beam and its propagation," Opt. Lett., Vol. 28, 1084-1086, 2003.

    7. Mei, Z. and D. Zhao, "Controllable dark-hollow beams and their propagation characteristics," J. Opt. Soc. Am. A, Vol. 22, 1898-1902, 2005.

    8. Liu, Z., H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, "Generation of hollow Gaussian beams by spatial filtering," Opt. Lett., Vol. 32, 2076-2078, 2007.

    9. Zheng, Y., X.Wang, F. Shen, and X. Li, "Generation of dark hollow beam via coherent combination based on adaptive optics," Opt. Express, Vol. 18, 26946-26958, 2010.

    10. Schweiger, G., R. Nett, B. Ozel, and T. Weigel, "Generation of hollow beams by spiral rays in multimode light guides," Opt. Express, Vol. 18, 4510-4517, 2010.

    11. Ma, H., Z. Liu, F. Xi, and X. Xu, "Near-diffraction-limited dark hollow beam generated by using a hybrid control way," Appl. Phys. B, Vol. 105, 883-891, 2011.

    12. Zhou, G., X. Chu, and J. Zheng, "Investigation in hollow Gaussian beam from vectorial structure," Opt. Commun., Vol. 281, 5653-5658, 2008.

    13. Chen, Y., Y. Cai, H. T. Eyyuboˇglu, and Y. Baykal, "Scintillation properties of dark hollow beams in a weak turbulent atmosphere," Appl. Phys. B, Vol. 90, 87-92, 2008.

    14. Deng, D. and Q. Guo, "Exact nonparaxial propagation of a hollow Gaussian beam," J. Opt. Soc. Am. B, Vol. 26, 2044-2049, 2009.

    15. Gao, X., Q. Zhan, M. Yun, H. Guo, X. Dong, and S. Zhuang, "Focusing properties of spirally polarized hollow Gaussian beam," Opt. Quant. Electron., Vol. 42, 827-840, 2011.

    16. Sharma, A., M. S. Sodha, S. Misra, and S. K. Mishra, "Thermal defocusing of intense hollow Gaussian laser beams in atmosphere," Laser and Particle Beams, Vol. 31, 403-410, 2013.

    17. MIshra, S. and S. K. Mishra, "Focusing of dark hollow Gaussian electromagnetic beams in a plasma with relativistic — Ponderomotive regime," Progress In Electromagnetics Research B, Vol. 16, 291-309, 2009.

    18. Zhou, G., Y. Cai, and C. Dai, "Hollow vortex Gaussian beams," Sci. China — Phys. Mech. Astron., Vol. 56, 896-903, 2013.

    1. 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.

    20. 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.

    21. Paterson, C., "Atmospheric turbulence and orbital angular momentum of single photons for optical communication," Phys. Rev. Lett., Vol. 94, 153901, 2005.

    22. Yao, A. M. and M. J. Padgett, "Orbital angular momentum: Origins behavior and applications," Adv. Opt. Photon., Vol. 3, 161-204, 2011.

    23. Cao, T. and M. J. Cryan, "Modeling of optical trapping using double negative index fishnet metamaterials," Progress In Electromagnetics Research, Vol. 129, 33-49, 2012.

    24. Zhou, X., "On independence, completeness of Maxwell’s equations and uniqueness theorems in electromagnetics," Progress In Electromagnetics Research, Vol. 64, 117-134, 2006.

    25. Sha, W., X.-L. Wu, Z.-X. Huang, and M.-S. Chen, "Maxwell’s equations, symplectic matrix, and grid," Progress In Electromagnetics Research B, Vol. 8, 115-127, 2008.

    26. Gradshteyn, I. S. and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980.

    27. Deng, D., S. Du, and Q. Guo, "Energy flow and angular momentum density of nonparaxial airy beams," Opt Commun., Vol. 289, 6-9, 2013.

    28. Zhou, G. and G. Ru, "Orbital angular momentum density of an elegant Laguerre-Gaussian beam," Progress In Electromagnetics Research, Vol. 141, 751-768, 2013.