volume | PIER Journals

Abstract

Based on the Collins integral, an analytical expression of a general Lorentz-Gauss vortex beam propagating in free space is derived, which allows one to calculate the linear momentum density of a general Lorentz-Gauss vortex beam in free space. The linear momentum density distribution of a general Lorentz-Gauss vortex beam propagating in free space is graphically demonstrated. The x- and y-components of the linear momentum density are composed of two lobes with the equivalent area and the opposite sign. Therefore, the overall x- and y-components of the linear momentum in an arbitrary reference plane are equal to zero. The longitudinal component of the linear momentum density is proportional to the intensity distribution. The influences of the Gaussian waist, the width parameters of the Lorentzian part, the axial propagation distance, and the topological charge on the linear momentum density distribution of a general Lorentz-Gauss vortex beam in free space are examined in detail.

1. Naqwi, A. and F. Durst, "Focus of diode laser beams: A simple mathematical model," Appl. Opt., Vol. 29, 1780-1785, 1990.
doi:10.1364/AO.29.001780

2. Yang, J., T. Chen, G. Ding, and X. Yuan, "Focusing of diode laser beams: A partially coherent Lorentz model," Proc. SPIE, Vol. 6824, 68240A, 2008.
doi:10.1117/12.757962

3. Gawhary, O. E. and S. Severini, "Lorentz beams and symmetry properties in paraxial optics," J. Opt. A: Pure Appl. Opt., Vol. 8, 409-414, 2006.
doi:10.1088/1464-4258/8/5/007

4. Zhou, G., "Focal shift of focused truncated Lorentz-Gauss beam," J. Opt. Soc. Am. A, Vol. 25, 2594-2599, 2008.
doi:10.1364/JOSAA.25.002594

5. Zhou, G., "Beam propagation factors of a Lorentz-Gauss beam," Appl. Phys. B, Vol. 96, 149-153, 2009.
doi:10.1007/s00340-009-3460-9

6. Zhou, G. and R. Chen, "Wigner distribution function of Lorentz and Lorentz-Gauss beams through a paraxial ABCD optical system," Appl. Phys. B, Vol. 107, 183-193, 2012.
doi:10.1007/s00340-012-4889-9

7. Torre, A., "Wigner distribution function of Lorentz-Gauss beams: A note," Appl. Phys. B, Vol. 109, 671-681, 2012.
doi:10.1007/s00340-012-5236-x

8. Zhao, C. and Y. Cai, "Paraxial propagation of Lorentz and Lorentz-Gauss beams in uniaxial crystals orthogonal to the optical axis," J. Mod. Opt., Vol. 57, 375-384, 2010.
doi:10.1080/09500341003640079

9. Du, W., C. Zhao, and Y. Cai, "Propagation of Lorentz and Lorentz-Gauss beams through an apertured fractional Fourier transform optical system," Opt. Lasers in Eng., Vol. 49, 25-31, 2011.
doi:10.1016/j.optlaseng.2010.09.004

10. Zhou, G. and X. Chu, "Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere," Opt. Express, Vol. 18, 726-731, 2010.
doi:10.1364/OE.18.000726

11. Chen, R. and C. H. R. Ooi, "Evolution and collapse of a Lorentz beam in Kerr medium," Progress In Electromagnetics Research, Vol. 121, 39-52, 2011.
doi:10.2528/PIER11081712

12. Sun, Q., A. Li, K. Zhou, Z. Liu, G. Fang, and S. Liu, "Virtual source for rotational symmetric Lorentz-Gaussian beam," Chin. Opt. Lett., Vol. 10, 062601, 2012.
doi:10.3788/COL201210.062601

13. Jiang, Y., K. Huang, and X. Lu, "Radiation force of highly focused Lorentz-Gauss beams on a Rayleigh particle," Opt. Express, Vol. 19, 9708-9713, 2011.
doi:10.1364/OE.19.009708

14. Zhou, G., "Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system," Opt. Express, Vol. 18, 4637-4643, 2010.
doi:10.1364/OE.18.004637

15. Eyyubo·glu, H. T., "Partially coherent Lorentz-Gaussian beam and its scintillations," Appl. Phys. B, Vol. 103, 755-762, 2011.
doi:10.1007/s00340-011-4414-6

16. Zhao, C. and Y. Cai, "Propagation of partially coherent Lorentz and Lorentz-Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere," J. Mod. Opt., Vol. 58, 810-818, 2011.
doi:10.1080/09500340.2011.573591

17. Ni, Y. and G. Zhou, "Propagation of a Lorentz-Gauss vortex beam through a paraxial ABCD optical system," Opt. Commun., Vol. 291, 19-25, 2013.
doi:10.1016/j.optcom.2012.11.016

18. Zhou, G., X. Wang, and X. Chu, "Fractional Fourier transform of Lorentz-Gauss vortex beams," Science China-Physics, Mechanics & Astronomy, Vol. 56, 1487-1494, 2013.
doi:10.1007/s11433-013-5153-y

19. Rui, F., D. Zhang, M. Ting, X. Gao, and S. Zhuang, "Focusing of linearly polarized Lorentz-Gauss beam with one optical vortex," Optik, Vol. 124, 2969-2973, 2013.
doi:10.1016/j.ijleo.2012.09.011

20. Ni, Y. and G. Zhou, "Nonparaxial propagation of Lorentz-Gauss vortex beams in uniaxial crystals orthogonal to the optical axis," Appl. Phys. B, Vol. 108, 883-890, 2012.
doi:10.1007/s00340-012-5118-2

21. Zhou, G. and G. Ru, "Propagation of a Lorentz-Gauss vortex beam in a turbulent atmosphere," Progress In Electromagnetics Research, Vol. 143, 143-163, 2013.
doi:10.2528/PIER13082703

22. Charrier, D. S. H., "Loss of linear momentum in an electrodynamics system: From an analytical approach to simulations," Progress In Electromagnetics Research M, Vol. 13, 69-82, 2010.
doi:10.2528/PIERM10041307

23. He, Y., J. Shen, and S. He, "Consistent formalism for the momentum of electromagnetic waves in lossless dispersive metamaterials and the conservation of momentum," Progress In Electromagnetics Research, Vol. 116, 81-106, 2011.

24. Aguirregabiria, J. M., A. Hernandez, and M. Rivas, "Linear momentum density in quasistatic electromagnetic systems," Eur. J. Phys., Vol. 25, 555-567, 2004.
doi:10.1088/0143-0807/25/4/010

25. Mansuripur, M., "Radiation pressure and the linear momentum of the electromagnetic field in magnetic media," Opt. Express, Vol. 15, 13502-13517, 2007.
doi:10.1364/OE.15.013502

26. Schmidt, P. P., "A method for the convolution of lineshapes which involve the Lorentz distribution," J. Phys. B: Atom. Molec. Phys., Vol. 9, 2331-2339, 1976.
doi:10.1088/0022-3700/9/13/018

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

28. 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

Dr. Yiqing Xu

Dr. Guoquan Zhou