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通过将扭曲高斯谢尔模光束入射到波前折叠干涉仪(WFI), 构建了一类镜像与反镜像扭曲高斯谢尔模光束, 并研究了光束在传输过程中的二阶统计特性. 结果表明, 变换光场仍保持扭曲效应, 其光谱密度和光谱相干度在传输过程中绕轴旋转, 但二者的旋向相反. 值得注意的是, 扭曲相位不仅能控制光场的旋转速度, 还能有效调控光斑的整体轮廓分布, 而中心区域的光斑模式则由WFI的相位差调控主导, 具体表现为镜像扭曲光场在传输过程中始终表现为中央亮斑分布, 反镜像扭曲光场则表现为中央暗核分布. 此外, 本文证明了光场的光谱相干度可由光源相干性、扭曲相位和WFI相位差等参数灵活调制. 本研究结果对于自由空间光通信以及微粒捕获等领域有重要应用价值.We introduce a class of specular and antispecular twisted Gaussian Schell-model beams, which are generated by inserting a twisted Gaussian Schell-model beam into a wavefront folding interferometer (WFI). The analytical expression for the cross-spectral density function of the beam propagating in free space is derived, and the statistical properties of the optical field are investigated in detail. The results show that the twisted effect is still maintained after the transformation, and the spectral density of the light field always rotates to 90 degrees around the axis during propagation. Furthermore, with appropriate optical field adjustment, the twist effect of the spectral degree of coherence (DOC) can be observed, but in opposite directions to the irradiance profile. We also find that the twisted phase not only controls the rotation of the field, but also effectively modulates the overall spot contour. For the far-field spectral density distribution, a larger twist effect will induce a smaller ellipticity of the beam spot. However, the intensity pattern in the central area is mainly determined by the phase difference of WFI. To be specific, the specular twisted field always has a sharp central peak during propagation, and in the antispecular case it has a central dip. Besides, the DOC distribution can be flexibly adjusted by the source coherence, the twisted phase and the phase difference of the WFI. The results of our work have important applications in the fields of free-space beam communication and particle trapping.
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Keywords:
- partially coherent beams /
- specular and antispecular /
- twisted phase /
- propagation
[1] Simon R, Sudarshan E, Mukunda N 1985 Phys. Rev. A 31 2419Google Scholar
[2] Cai Y J, Korotkova O 2009 Appl. Phys. B 96 499Google Scholar
[3] Tong Z S, Korotkova O 2012 Opt. Lett. 37 2595Google Scholar
[4] Cui Y, Wang F, Cai Y J 2014 Opt. Commun. 324 108Google Scholar
[5] Cai Y J, Lin Q, Korotkova O 2009 Opt. Express 17 2453Google Scholar
[6] Mao Y H, Mei Z R, Wang Y Y, Zhou G Q, Qiu P Z 2020 Opt. Commun. 477 126321Google Scholar
[7] Simon R, Mukunda N 1993 J. Opt. Soc. Am. A 10 95Google Scholar
[8] Friberg A T, Tervonen E, Turunen J 1994 J. Opt. Soc. Am. A 11 1818Google Scholar
[9] Borghi R, Gori F, Guattari G, Santarsiero M 2015 Opt. Lett. 40 4504Google Scholar
[10] Borghi R 2018 Opt. Lett. 43 1627Google Scholar
[11] Mei Z R, Korotkova O 2017 Opt. Lett. 42 255Google Scholar
[12] Gori F, Santarsiero M 2018 Opt. Lett. 43 595Google Scholar
[13] Peng X F, Liu L, Wang F, Popov S, Cai Y J 2018 Opt. Express 26 33956Google Scholar
[14] Santarsiero M, Gori F, Alonzo M 2019 Opt. Express 27 8554Google Scholar
[15] Mei Z, Korotkova O 2018 Opt. Lett. 43 3905Google Scholar
[16] Tian C, Zhu S J, Huang H K, Cai Y J, Li Z H 2020 Opt. Lett. 45 5880Google Scholar
[17] Wang H Y, Peng X F, Zhang H, Liu L, Chen Y H, Wang F, Cai Y J 2022 Nanophotonics-Berlin 11 689Google Scholar
[18] Dong S J, Yang Y Z, Zhou Y J, Li X Z, Tang M M 2024 J. Opt. 26 065608Google Scholar
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[22] Zhang C Y, Fu W Y 2024 Opt. Appl. 54 15Google Scholar
[23] Wan L P, Zhao D M 2019 Opt. Lett. 44 735Google Scholar
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[26] Partanen H, Sharmin N, Tervo J, Turunen J 2015 Opt. Express 23 28718Google Scholar
[27] Guo M W, Zhao D M 2016 Opt. Express 24 6115Google Scholar
[28] Zhou Z T, Guo M W, Zhao D M 2016 Appl. Opt. 55 6757Google Scholar
[29] Zhou Z T, Guo M W, Zhao D M 2017 Opt. Commun. 383 287Google Scholar
[30] Das D, Halder A, Partanen H, Koivurova M, Turunen J 2022 Opt. Express 30 5709Google Scholar
[31] Tang M M, Dong S J, Yang Y Z, Zhou Y J, Guo M W, Li X Z 2024 J. Opt. 26 065601Google Scholar
[32] Guo M W, Zhao D M 2018 Opt. Express 26 8581Google Scholar
[33] Tang M M, Feng X X, Liu S Y, Li H H, Li X Z 2021 J. Opt. 23 045605Google Scholar
[34] Li C Q, Zhang H Y, Wang T F, Liu L S, Guo J 2013 Acta Phys. Sin. 62 224203Google Scholar
[35] 徐华锋, 张兴宇, 王仁杰 2024 物理学报 73 034201Google Scholar
Xu H F, Zhang X Y, Wang R J 2024 Acta Phys. Sin. 73 034201Google Scholar
[36] 王飞, 余佳益, 刘显龙, 蔡阳健 2018 物理学报 67 184203Google Scholar
Wang F, Yu J Y, Liu X L, Cai Y J 2018 Acta Phys. Sin. 67 184203Google Scholar
[37] Liu Y L, Dong Z, Zhu Y M, Wang H Y, Wang F, Chen Y H, Cai Y J 2024 PhotoniX 5 8Google Scholar
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[39] Chen Y H, Wang F, Cai Y J 2022 Adv. Phys-X 7 2009742Google Scholar
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图 2 WFI输出平面上的归一化光谱密度$ {{S\left( {x', y'} \right)} {/ } {{S_{\max }}}} $ (a) $\phi = 0$; (b) $ \phi = {{\text{π}} {/ } {2}} $; (c): $\phi = {\text{π}}$
Fig. 2. Normalized spectral density $ {{S\left( {x', y'} \right)} {/ } {{S_{\max }}}} $ in the WFI output plane: (a) $\phi = 0$; (b) $ \phi = {{\text{π}} {/ } {2}} $; (c) $\phi = {\text{π}}$.
图 5 扭曲因子对镜像扭曲光场的归一化光谱密度$S\left( {x, y, z} \right)/{S_{\max }}$的影响 (a) z = 0 mm; (b) z = 200 mm; (c) z = 4000 mm
Fig. 5. Influence of the twist factor on the normalized spectral density $S\left( {x, y, z} \right)/{S_{\max }}$ of the specular twisted field: (a) z = 0 mm; (b) z = 200 mm; (c) z = 4000 mm.
图 6 两个对称点之间的光谱相干度$\mu \left( {x/2, y/2, - x/2, - y/2, z} \right)$在传输距离z = 400 mm处沿$ x $轴的二维分布 (a) wx = 0.5 mm, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $; (b) $\phi = {{\text{π}} {/ } {4}}$, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $; (c) $\phi = {{\text{π}} {/ } {4}}$, wx = 0.5 mm
Fig. 6. Spectral degree of coherence $\mu \left( {x/2, y/2, - x/2, - y/2, z} \right)$ between two symmetrical points at the propagation distance z = 400 mm along $ x $ axis: (a) wx = 0.5 mm, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $; (b) $\phi = {{\text{π}} {/ } {4}}$, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $; (c) $\phi = {{\text{π}} {/ } {4}}$, wx = 0.5 mm.
图 7 两个对称点之间的光谱相干度$\mu \left( {x/2, y/2, - x/2, - y/2, z} \right)$随干涉仪两光路相位差$ \phi $的分布情况 (a) wx = 0.5 mm, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $; (b) z = 400 mm, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $
Fig. 7. Spectral degree of coherence $\mu \left( {x/2, y/2, - x/2, - y/2, z} \right)$ along $ \phi $: (a) wx = 0.5 mm, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $; (b) z = 400 mm, $ {\delta _x} = {\delta _y} = 0.2 {\text{ mm}} $.
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[1] Simon R, Sudarshan E, Mukunda N 1985 Phys. Rev. A 31 2419Google Scholar
[2] Cai Y J, Korotkova O 2009 Appl. Phys. B 96 499Google Scholar
[3] Tong Z S, Korotkova O 2012 Opt. Lett. 37 2595Google Scholar
[4] Cui Y, Wang F, Cai Y J 2014 Opt. Commun. 324 108Google Scholar
[5] Cai Y J, Lin Q, Korotkova O 2009 Opt. Express 17 2453Google Scholar
[6] Mao Y H, Mei Z R, Wang Y Y, Zhou G Q, Qiu P Z 2020 Opt. Commun. 477 126321Google Scholar
[7] Simon R, Mukunda N 1993 J. Opt. Soc. Am. A 10 95Google Scholar
[8] Friberg A T, Tervonen E, Turunen J 1994 J. Opt. Soc. Am. A 11 1818Google Scholar
[9] Borghi R, Gori F, Guattari G, Santarsiero M 2015 Opt. Lett. 40 4504Google Scholar
[10] Borghi R 2018 Opt. Lett. 43 1627Google Scholar
[11] Mei Z R, Korotkova O 2017 Opt. Lett. 42 255Google Scholar
[12] Gori F, Santarsiero M 2018 Opt. Lett. 43 595Google Scholar
[13] Peng X F, Liu L, Wang F, Popov S, Cai Y J 2018 Opt. Express 26 33956Google Scholar
[14] Santarsiero M, Gori F, Alonzo M 2019 Opt. Express 27 8554Google Scholar
[15] Mei Z, Korotkova O 2018 Opt. Lett. 43 3905Google Scholar
[16] Tian C, Zhu S J, Huang H K, Cai Y J, Li Z H 2020 Opt. Lett. 45 5880Google Scholar
[17] Wang H Y, Peng X F, Zhang H, Liu L, Chen Y H, Wang F, Cai Y J 2022 Nanophotonics-Berlin 11 689Google Scholar
[18] Dong S J, Yang Y Z, Zhou Y J, Li X Z, Tang M M 2024 J. Opt. 26 065608Google Scholar
[19] Ponomarenko S A 2001 Phys. Rev. E. 64 036618Google Scholar
[20] Wu G F 2016 J. Opt. Soc. Am. A 33 345Google Scholar
[21] Zhang C, Zhou Z L, Xu H F, Zhou Z X, Han Y S, Yuan Y S, Qu J 2022 Opt. Express 30 4071Google Scholar
[22] Zhang C Y, Fu W Y 2024 Opt. Appl. 54 15Google Scholar
[23] Wan L P, Zhao D M 2019 Opt. Lett. 44 735Google Scholar
[24] Cai Y J, Lin Q, Ge D 2002 J. Opt. Soc. Am. A Opt. Image Sci. Vis. 19 2036Google Scholar
[25] Gori F, Guattari G, Palma C, Padovani C 1988 Opt. Commun. 68 239Google Scholar
[26] Partanen H, Sharmin N, Tervo J, Turunen J 2015 Opt. Express 23 28718Google Scholar
[27] Guo M W, Zhao D M 2016 Opt. Express 24 6115Google Scholar
[28] Zhou Z T, Guo M W, Zhao D M 2016 Appl. Opt. 55 6757Google Scholar
[29] Zhou Z T, Guo M W, Zhao D M 2017 Opt. Commun. 383 287Google Scholar
[30] Das D, Halder A, Partanen H, Koivurova M, Turunen J 2022 Opt. Express 30 5709Google Scholar
[31] Tang M M, Dong S J, Yang Y Z, Zhou Y J, Guo M W, Li X Z 2024 J. Opt. 26 065601Google Scholar
[32] Guo M W, Zhao D M 2018 Opt. Express 26 8581Google Scholar
[33] Tang M M, Feng X X, Liu S Y, Li H H, Li X Z 2021 J. Opt. 23 045605Google Scholar
[34] Li C Q, Zhang H Y, Wang T F, Liu L S, Guo J 2013 Acta Phys. Sin. 62 224203Google Scholar
[35] 徐华锋, 张兴宇, 王仁杰 2024 物理学报 73 034201Google Scholar
Xu H F, Zhang X Y, Wang R J 2024 Acta Phys. Sin. 73 034201Google Scholar
[36] 王飞, 余佳益, 刘显龙, 蔡阳健 2018 物理学报 67 184203Google Scholar
Wang F, Yu J Y, Liu X L, Cai Y J 2018 Acta Phys. Sin. 67 184203Google Scholar
[37] Liu Y L, Dong Z, Zhu Y M, Wang H Y, Wang F, Chen Y H, Cai Y J 2024 PhotoniX 5 8Google Scholar
[38] Yu J Y, Zhu X L, Wang F, Chen Y H, Cai Y J 2023 Prog. Quant. Electron. 91-92 100486Google Scholar
[39] Chen Y H, Wang F, Cai Y J 2022 Adv. Phys-X 7 2009742Google Scholar
[40] Peng D M, Huang Z F, Liu Y L, Chen Y H, Wang F, Ponomarenko S A, Cai Y J 2021 PhotoniX 2 6Google Scholar
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