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基于强度二阶矩定义, 导出了高斯涡旋光束光束传输因子即M2 因子的解析表达式, 高斯涡旋光束的M2 因子唯一取决于拓扑电荷数n. 数值计算表明, 高斯涡旋光束的M2 因子随着拓扑电荷数n的增大而增大. 基于强度高阶矩, 还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式, 高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D. 在自由空间传输时, 高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ. 自由空间传输时, 高斯涡旋光束峭度参数的变化规律为: 峭度参数随参数δ的增大先减小而后趋向于一最小值, 随拓扑电荷数n的增大而减小. 这一研究有助于高斯涡旋光束的实际应用.Based on the definition of the second-order moment of intensity, the analytical expression for the beam propagation factor, namely the M2 factor, of a Gaussian vortex beam is derived, which is uniquely determined by the topological charge n. The numerical result indicates that the M2 factor of a Gaussian vortex beam increases with the increase of topological charge n. By means of the higher-order moment of intensity, the analytical expression for the kurtosis parameter of a Gaussian vortex beam passing through a paraxial ABCD optical system is also presented, which depends on topological charge n, parameter δ, transfer matrix elements A and D. When propagating in free space, the kurtosis parameter of a Gaussian vortex beam is determined by topological charge n and parameter δ. With the increase of parameter δ, the kurtosis parameter of a Gaussian vortex beam in free space first decreases and finally tends to a minimal value. Moreover, the kurtosis parameter of a Gaussian vortex beam in free space decreases with the increase of topological charge n. This research is helpful for the practical application of the Gaussian vortex beam.
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Keywords:
- Gaussian vortex beam /
- M2 factor /
- kurtosis parameter
[1] Simpson N, Dholakia N, Allen L, Padgett M 1997 Opt. Lett. 22 52
[2] Gahagan K T, Swartzlander Jr G A 1998 J. Opt. Soc. Am. B 15 524
[3] Molina-Terriza G, Torres J P, Torner L 2002 Phys. Rev. Lett. 88 013601
[4] Lu X H, Huang H Q, Zhao C L, Wang J F, Chen H 2008 Laser & Optoelectronics Progress 45 50 (in Chinese) [陆璇辉, 黄慧琴, 赵承良, 王将峰, 陈和 2008 激光与光电子学进展 45 50]
[5] Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1743 (in Chinese) [李阳月, 陈子阳, 刘辉, 蒲继雄 2010 59 1734]
[6] Zhu Y Y, Lü W, Zhang J C, Jing M J, Li J, Guan X W 2009 Proc. SPIE 7507 750705
[7] Cui X C, Lian X X, Lü B D 2011 High Power Laser and Particle Beams 23 20 (in Chinese) [崔学才, 连校许, 吕百达 2011 强激光与粒子束 23 20]
[8] Li J, Xin Y, Chen Y R, Xu S X, Wang Y Q, Zhou M C, Zhao Q, Chen F N 2011 Eur. Phys. J. Appl. Phys. 53 20701
[9] Wu H Y, Huang Z H, Wu W M, Xu X J, Chen J B, Zhao Y J 2011 Acta Opt. Sin. 31 0414002 (in Chinese) [吴慧云, 黄值河, 吴武明, 许晓军, 陈金宝, 赵伊君 2011 光学学报 31 0414002]
[10] Li J L 2010 Chin. Phys. B 19 124001
[11] Siegman A 1990 Proc. SPIE 1224 2
[12] Gradshteyn I S, Ryzhik I M 1980 Table of integrals, series, and products (New York: Academic Press)
[13] Goodman J W 1996 Introduction to Fourier Optics, 2nd ed. (New York: McGraw-Hill)
[14] Bock B D 1975 Multivariate statistical method in behavioral research (New York: McGraw-Hill)
[15] Erdelyi A, Magnus W, Oberhettinger F 1954 Tables of Integrals Transforms (New York: McGraw-Hill)
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[1] Simpson N, Dholakia N, Allen L, Padgett M 1997 Opt. Lett. 22 52
[2] Gahagan K T, Swartzlander Jr G A 1998 J. Opt. Soc. Am. B 15 524
[3] Molina-Terriza G, Torres J P, Torner L 2002 Phys. Rev. Lett. 88 013601
[4] Lu X H, Huang H Q, Zhao C L, Wang J F, Chen H 2008 Laser & Optoelectronics Progress 45 50 (in Chinese) [陆璇辉, 黄慧琴, 赵承良, 王将峰, 陈和 2008 激光与光电子学进展 45 50]
[5] Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1743 (in Chinese) [李阳月, 陈子阳, 刘辉, 蒲继雄 2010 59 1734]
[6] Zhu Y Y, Lü W, Zhang J C, Jing M J, Li J, Guan X W 2009 Proc. SPIE 7507 750705
[7] Cui X C, Lian X X, Lü B D 2011 High Power Laser and Particle Beams 23 20 (in Chinese) [崔学才, 连校许, 吕百达 2011 强激光与粒子束 23 20]
[8] Li J, Xin Y, Chen Y R, Xu S X, Wang Y Q, Zhou M C, Zhao Q, Chen F N 2011 Eur. Phys. J. Appl. Phys. 53 20701
[9] Wu H Y, Huang Z H, Wu W M, Xu X J, Chen J B, Zhao Y J 2011 Acta Opt. Sin. 31 0414002 (in Chinese) [吴慧云, 黄值河, 吴武明, 许晓军, 陈金宝, 赵伊君 2011 光学学报 31 0414002]
[10] Li J L 2010 Chin. Phys. B 19 124001
[11] Siegman A 1990 Proc. SPIE 1224 2
[12] Gradshteyn I S, Ryzhik I M 1980 Table of integrals, series, and products (New York: Academic Press)
[13] Goodman J W 1996 Introduction to Fourier Optics, 2nd ed. (New York: McGraw-Hill)
[14] Bock B D 1975 Multivariate statistical method in behavioral research (New York: McGraw-Hill)
[15] Erdelyi A, Magnus W, Oberhettinger F 1954 Tables of Integrals Transforms (New York: McGraw-Hill)
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