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基于相干与偏振的统一理论, 采用傅里叶变换和卷积定理的方法, 研究了携带多个离轴涡旋相位的径向偏振矩形对称余弦-高斯关联结构光束的传输特性. 结果表明, 该光束因其独特的空间相干结构而具有自分裂特性, 可以分裂成4束完全相同的子波瓣. 更重要的是, 多离轴涡旋相位的调制可以作用在每个子波瓣上. 当相干度较大时, 通过调制光束的离轴涡旋数量N0和光束阶数可以在焦平面处产生具有三角形或正方形等多边形空心光强分布的光斑阵列, 并且每个子波瓣上对应的偏振态呈现倒三角形或斜正方形的椭圆分布. 当相干度较小时, 部分相干光束的空间相干性调控占主导作用, 多离轴涡旋相位的调制效果消失, 每个子波瓣的光强退化成高斯形式分布, 但其偏振态分布仍保持不变, 与光束阶数和相干长度无关. 此外, 当利用障碍物遮挡住其中一个离轴涡旋相位时, 光束仍具有一定的自修复能力. 然而, 若将其中一个离轴涡旋相位完全遮挡住, 此时每个子波瓣的强度分布和偏振态分布都遭到破坏, 会出现不同程度的“缺口”.In this paper, we investigate the propagation properties of radially polarized rectangular-symmetric cosine-Gaussian Schell-model (RCGSM) beam with multiple off-axis vortex phases by using Fourier transform and convolution method based on the unified theory of coherence and polarization. The results indicate that the radially polarized RCGSM beam has self-splitting properties and can be split into four identical lobes due to its unique spatial coherence structure. Furthermore, the modulation of multiple off-axis vortex phases can be acted on each lobe. For high coherence, the spot arrays with triangular or square hollow light intensity distribution can be generated in the focal plane by modulating the number of off-axis vortices (N0) and the beam order, and the corresponding state of polarization on each lobe presents an inverted triangular or oblique square elliptic distribution. However, for small coherence, the modulation effect of multiple off-axis vortex phases disappears and the light intensity of each lobe degenerates into a quasi-Gaussian distribution, whereas its state of polarization keeps invariant, which is independent of the beam order and coherence length. In addition, the beam still has a certain self-healing ability for one of the off-axis vortex phases partially blocked by an obstacle, but it will be destroyed for completely blocking, resulting in a notch on each lobe.
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Keywords:
- partially coherent beam /
- special spatial correlation structure /
- multiple off-axis vortex phases /
- propagation properties
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图 1 (a)源平面处第j个离轴涡旋中心与观察点的位置矢量关系; (b)—(d)携带3个离轴涡旋相位(拓扑荷数l = 1)的径向偏振RCGSM光束在源平面处的(b)离轴涡旋相位排列、(c)离轴涡旋相位分布和(d)光强分布
Fig. 1. (a) An illustration of the position vector relationship between the j-th off-axis vortex phase core and the observation point in the initial plane; (b) arrangement of three off-axis vortex phases, (c) phase distribution, and (d) intensity distribution of a radially polarized RCGSM beam carrying three off-axis vortices in the source plane, respectively.
图 2 当光束阶数$ m = n = 5 $时, 携带3个离轴涡旋相位的径向偏振RCGSM光束通过薄透镜后的聚焦光强演化
Fig. 2. Evolution of the focused intensity of a radially polarized RCGSM beam carrying three off-axis vortex phases through a thin lens when the beam order $ m = n = 5 $.
图 3 当光束阶数$ m = n = 5 $时, 携带4个离轴涡旋相位的径向偏振RCGSM光束的聚焦光强演化
Fig. 3. Evolution of the focused intensity of a radially polarized RCGSM beam carrying four off-axis vortex phases through a thin lens when the beam order $ m = n = 5 $.
图 4 当光束阶数$ m = n = 5 $和相干长度$ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $时, 携带4个离轴涡旋相位的径向偏振RCGSM光束通过扇形障碍物的聚焦光强演化
Fig. 4. Evolution of the focused intensity of a radially polarized RCGSM beam carrying four off-axis vortex phases after passing through a sector-shaped opaque obstacle when the beam order $ m = n = 5 $ and coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.
图 5 携带4个离轴涡旋相位的径向偏振RCGSM光束通过圆形障碍物后的聚焦光强演化($ m = n = 5 $, $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $)
Fig. 5. Evolution of the focused intensity of a radially polarized RCGSM beam carrying four off-axis vortex phases after passing through a circular obstacle when the beam order $ m = n = 5 $ and coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.
图 6 当光束阶数$ {m_0} = {n_0} = 5 $和相干长度$ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $时, 携带多个离轴涡旋相位的径向偏振RCGSM光束通过薄透镜后的偏振态演化情况
Fig. 6. Evolution of the state of polarization of radially polarized RCGSM beams carrying multiple off-axis vortex phases through a thin lens when the beam order $ {m_0} = {n_0} = 5 $ and coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.
图 7 当相干长度$ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $时, 光束阶数$ {m_0}, {n_0} $对携带多个离轴涡旋相位的径向偏振RCGSM光束在焦平面处偏振态分布的影响
Fig. 7. Influences of beam order $ {m_0}, {n_0} $ on the distribution of the state of polarization of radially polarized RCGSM beams carrying multiple off-axis vortex phases in the focal plane when the coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.
图 8 当光束阶数$ {m_0} = {n_0} = 2 $时, 相干长度$ {\delta _0} $对携带多个离轴涡旋相位的径向偏振RCGSM光束在焦平面处偏振态分布的影响
Fig. 8. Influence of coherent length $ {\delta _0} $ on the distribution of the state of polarization of radially polarized RCGSM beams carrying multiple off-axis vortex phases in the focal plane when the beam order $ {m_0} = {n_0} = 2 $.
图 9 当光束阶数$ m = n = 2 $和相干长度$ {\delta _0} = 0.5{\text{mm}} $时, 携带多个离轴涡旋相位的径向偏振RCGSM光束通过扇形障碍物后在焦平面处的偏振态分布
Fig. 9. Distribution of the state of polarization in the focal plane for the radially polarized RCGSM beams carrying multiple off-axis vortex phases through a sector-shaped opaque when the beam order $ m = n = 2 $ and the coherent length $ {\delta _0} = 0.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.
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[1] Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
Google Scholar
[2] Cai Y J 2011 Proc. SPIE 7924 792402
Google Scholar
[3] 王飞, 余佳益, 刘显龙, 蔡阳健 2018 物理学报 67 184203
Google Scholar
Wang F, Yu J Y, Liu X L, Cai Y J 2018 Acta Phys. Sin. 67 184203
Google Scholar
[4] Peng D M, Huang Z F, Liu Y L, Chen Y H, Wang F, Ponomarenko S A, Cai Y J 2021 PhotoniX 2 6
Google Scholar
[5] Chen Y H, Wang F, Cai Y J 2022 Adv. Phys. X 7 2009742
Google Scholar
[6] 许文慧, 宁守琮, 张福才 2021 物理学报 70 214201
Google Scholar
Xu W H, Ning S C, Zhang F C 2021 Acta Phys. Sin. 70 214201
Google Scholar
[7] Gori F, Santarsiero M 2007 Opt. Lett. 32 3531
Google Scholar
[8] Gori F, Ramírez-Sánchez V, Santarsiero M, Shirai T 2009 J. Opt. A: Pure Appl. Opt. 11 085706
Google Scholar
[9] Chen Y H, Gu J X, Wang F, Cai Y J 2015 Phys. Rev. A 91 013823
Google Scholar
[10] Mei Z R 2014 Opt. Lett. 39 347
Google Scholar
[11] Chen Y H, Cai Y J 2014 Opt. Lett. 39 2549
Google Scholar
[12] Mei Z R 2014 Opt. Express 22 13029
Google Scholar
[13] Liang C H, Wang F, Liu X L, Cai Y J, Korotkova O 2014 Opt. Lett. 39 769
Google Scholar
[14] Chen Y H, Wang F, Cai Y J 2015 物理学进展 35 51
Google Scholar
陈亚红, 王飞, 蔡阳健 2015 Prog. Phys. 35 51
Google Scholar
[15] 陈亚红, 蔡阳健 2016 光学学报 36 1026002
Google Scholar
Chen Y H, Cai Y J 2016 Acta Opt. Sin. 36 1026002
Google Scholar
[16] 曾军, 陈亚红, 刘显龙, 蔡阳健 2019 光学学报 39 1026004
Google Scholar
Zeng J, Chen Y H, Liu X L, Cai Y J 2019 Acta Opt. Sin. 39 1026004
Google Scholar
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Google Scholar
Cheng K, Ma Z Y, Zhang M M, Dou J T, Hu Y Y 2022 Acta Phys. Sin. 71 014203
Google Scholar
[21] Zhang H, Zeng J, Lu X Y, Wang Z Y, Zhao C L, Cai Y J 2021 Nanophoto. 11 241
Google Scholar
[22] Ostrovsky A S, Rickenstorffparrao C, Arrizon V 2013 Opt. Lett. 38 534
Google Scholar
[23] 李阳月, 陈子阳, 刘辉, 蒲继雄 2010 物理学报 59 1740
Google Scholar
Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1740
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[37] Korotkova O, Wolf E 2005 Opt. Commun. 246 35
Google Scholar
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