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基于Wolf近轴传输理论, 导出离轴径向偏振光束光强的解析表达式, 并研究离轴量对离轴径向偏振光束传输中光强分布的影响, 同时根据一阶矩质心位置的定义推导出离轴径向偏振光束的质心坐标, 研究其质心位置的变化规律. 结果表明, 与径向偏振光束不同, 离轴径向偏振光束在近场处传输时光强分布不均匀, 随着传输距离的增加, 光强分布均匀性逐渐得到改善, 而径向偏振光束在传输中始终保持空心对称光斑. 离轴量较小时, 近场处光强分布呈非对称空心面包圈形, 随着传输距离增达到一定程度, 光强分布演化为对称空心面包圈形, 离轴量越小, 演变距离越短; 离轴量较大时, 随着光束的传输离轴径向偏振光束的空心部分消失, 逐渐由空心面包圈形向高斯型演变, 径向偏振光束特性消失. 另一方面, 离轴径向偏振光束的质心不随传输距离的改变而改变. 质心纵坐标恒为零, 质心横坐标与光斑尺寸及离轴量相关. 随着光斑尺寸增大, 质心横坐标成线性增长. 当离轴量较小时, 质心横坐标随离轴量的增大呈非线性增长, 增长量不明显; 离轴量较大时, 质心横坐标随离轴量的增大呈线性增长, 且变化明显.Based on the theory of paraxial approximation of beam propagation, the analytical expression of the intensity of the off axial radially polarized beam (OARPB) is derived and the effect of the off axial magnitude on the distribution of intensity of the OARPB is studied. Meanwhile, according to the definition of the first-order moment of centroid, the coordinate of centroid of the OARPB is derived and the variation of cenreoid of the OARPB is studied. Simulation result shows that the intensity distribution of the OARPB is different from that of the radially polarized beam. The intensity distribution of the OARPB is not uniform in the near-field. With increasing propagation distance, the beam spreads and the uniformity of intensity of the OARPB is improved gradually. However, the intensity distribution of the radially polarized beam keeps the form of symmetric doughnut spot during propagation all the time. When the off axial magnitude is small, the intensity distribution of the OARBP is obviously asymmetric in the near-field, and it becomes nearly symmetric while the beam propagates a certain distance. The smaller the off axial magnitude, the shorter the required propagation distance to become symmetric for the OARPB. When the off axial magnitude is larger, the hollow part of intensity distribution disappears, and the doughnut beam of the OARPB changes into a Gaussian beam spot gradually during propagation. On the other hand, the centroid of the OARPB does not change with increasing propagation distance. The value of the ordinate of centroid is equal to zero all the time. And the value of the abscissa of centroid is related to the beam size and the off axial magnitude. While the beam size increases, the abscissa of centroid increases linearly at the same time. When the off axial magnitude is small, the abscissa of the centroid of the OARPB increases with the increase of the off axial magnitude, nonlinearly and slightly; however, when the off axial magnitude is larger, the abscissa of centroid of the OARPB increases with the increase of the off axial magnitude, linearly and significantly.
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[2] Tidwell S C, Kim G H, Kimura W D 1993 Appl. Opt. 32 5222
[3] Niziev V G, Nesterov A V 1999 J. Phys. D: Appl. Phys. 32 1455
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[10] Deng D M, Guo Q 2007 Opt. Lett. 32 2711
[11] Cheng K, Tan Q F, Zhou Z H, Jin G F 2010 Acta Opt. Sin. 11 3295 (in Chinese) [程侃, 谭峭峰, 周哲海, 金国藩 2010 光学学报 11 3295]
[12] Li Z W, Chen M, Li G 2014 Chin. J. Lasers 41 0102006 (in Chinese) [李政委, 陈檬, 李港 2014 中国激光 41 0102006]
[13] Ghadyani Z, Vartiainen I, Harder I, Iff W, Berger A, Lindlein N, Kuittinen M 2011 Appl. Opt. 50 2451
[14] Ahmed M A, Haefner M, Vogel M, Pruss C, Voss A, Osten W, Graf T 2011 Opt. Express 19 5093
[15] Martínez-Herrero R, Prado F 2015 Opt. Express 23 5043
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[1] Mushiake Y, Matsumura K, Nakajima N 1972 Proc. IEEE 60 1107
[2] Tidwell S C, Kim G H, Kimura W D 1993 Appl. Opt. 32 5222
[3] Niziev V G, Nesterov A V 1999 J. Phys. D: Appl. Phys. 32 1455
[4] Novotny L, Beversluis M R, Youngworth K S, Brow T G 2001 Phys. Rev. Lett. 86 5251
[5] Dom R, Quabis S, Leuchs G 2003 Phys. Rev. Lett. 91 233901
[6] Bokor N, Davidson N 2007 Opt. Commun. 279 229
[7] Grosjean T, Courjon D 2007 Opt. Commun. 272 314
[8] Deng D M 2006 J. Opt. Soc. Am. B 23 1228
[9] Deng D M, Guo Q, Wu L, Yang X B 2007 J. Opt. Soc. Am. B 24 636
[10] Deng D M, Guo Q 2007 Opt. Lett. 32 2711
[11] Cheng K, Tan Q F, Zhou Z H, Jin G F 2010 Acta Opt. Sin. 11 3295 (in Chinese) [程侃, 谭峭峰, 周哲海, 金国藩 2010 光学学报 11 3295]
[12] Li Z W, Chen M, Li G 2014 Chin. J. Lasers 41 0102006 (in Chinese) [李政委, 陈檬, 李港 2014 中国激光 41 0102006]
[13] Ghadyani Z, Vartiainen I, Harder I, Iff W, Berger A, Lindlein N, Kuittinen M 2011 Appl. Opt. 50 2451
[14] Ahmed M A, Haefner M, Vogel M, Pruss C, Voss A, Osten W, Graf T 2011 Opt. Express 19 5093
[15] Martínez-Herrero R, Prado F 2015 Opt. Express 23 5043
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