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The spin-orbit interaction (SOI) of light refers to the mutual conversion and coupling between the spin angular momentum and orbital angular momentum. It is a fundamental effect in optics, and has been widely found in many basic optical processes, such as reflection, refraction, scattering, focusing, and imaging. So it plays an important role in the fields of optics, nanophotonics, and plasmonics, and has great potential applications in precision measurement and detection, information storage and processing, particle manipulation, and various functional photonic devices. Recently, it has been found that a circularly polarized light beam normally passing through an isotropic sharp interface can undergo an SOI process, that is, part of the incident beam experiences a spin-flip and acquires a spin-dependent vortex phase with a topological charge of
$ \pm2 $ . However, the physical origin of this phase and the role of the interface played in the SOI process are still unclear at present. In this work, a Fresnel Jones matrix is first established to describe the relationship between the incident beam and the transmitted beam, based on which we unveil that the vortex phase is in fact a spin-redirection Berry geometric phase, originating from the topological structure of the beam itself. The properties of the interface affect the conversion efficiency of the SOI. This kind of SOI is very similar to that in the azimuthal Pancharatnam-Berry phase elements. The difference lies in the fact that the Pancharatnam-Berry phase originates from the external anisotropy of the composite material. Generally, the efficiency of this SOI is extremely low, which limits its applications. The existing method of enhancing this SOI employs an isotropic epsilon-near-zero slab, whose maximum efficiency can reach only about 20%. Since the anisotropic medium (such as birefringent uniaxial crystals) has more degrees of freedom, we further point out that the weak SOI can be greatly enhanced by an optically thin uniaxial slab whose optical axis is parallel to the normal direction of the interface. And under certain conditions, the conversion efficiency can reach 100%. Our study not only establishes a simple and convenient full-wave theory for this SOI, but also reveals the relevant underlying physics, and further provides a possible scheme to significantly enhance the SOI.-
Keywords:
- spin-orbit interaction of light /
- vortex phase /
- geometric phase /
- angular momentum of light
[1] Bliokh K Y, Rodríguez F F J, Nori F, Zayats A V 2015 Nat. Photon. 9 796
Google Scholar
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Google Scholar
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[35] Goodman J W 2005 Introduction to Fourier Optics (Green-woood Village: Roberts and Company Publishers) p55
[36] Bliokh K Y, Gorodetski Y, Kleiner V, Hasman E 2008 Phys. Rev. Lett. 101 030404
Google Scholar
[37] Berry M V 1984 Proc. R. Soc. A 392 45
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Google Scholar
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Google Scholar
[42] Ferrari L, Wu C, Lepage D, Zhang X, Liu Z 2015 Prog. Quantum Electron. 40 1
Google Scholar
-
图 1 光束正入射至各向同性的突变界面时SOI的示意图 (a) 左旋圆偏振光束正入射至界面后, 部分光束发生自旋反转变成右旋光, 并获得拓扑荷数为2的涡旋相位(两个小图分别表示一种典型的涡旋光束的强度和相位分布); 注意, 未发生SOI的那部分光束并没有在图中画出;
$\left| + \right\rangle $ 和$\left| - \right\rangle $ 分别表示左、右旋圆偏振; (b) 光束中各平面波分量的自旋与局部坐标的旋转耦合的示意图, 其中圆锥代表光束的角谱, 绿色的箭头线代表任意的两支平面波的波矢, 橙色带箭头的小圆圈表示各平面的偏振矢量在实验室坐标上的投影(均为圆偏振),${\varOmega _\xi }$ 为坐标旋转的空间旋转Figure 1. Schematic illustration of the SOI for a light beam normally impinging onto a sharp isotropic interface. (a) When a left-circularly polarized beam normally passes through the interface, part of the incident beam converts into a right-circularly polarized beam, and carries a vortex phase with a topological charge of 2. Note that the spin-maintained portion is not shown in the picture.
$\left| + \right\rangle $ and$\left| - \right\rangle $ denotes the left- and right-handed polarization, respectively. (b) Schematic illustration of rotational coupling between the local coordinates and the spin of the plane wave components within the beam spectra. The cone represents the angular spectrum of the beam. The two green arrows represent the wave vectors of arbitrary two plane waves. The orange circles with arrows indicate the projection of polarization vectors of each plane wave on the laboratory coordinates (all circularly polarized).${\varOmega _\xi }$ is the spatial coordinate rotation.
图 2 左旋圆偏振贝塞尔光束正入射至一个界面时, 透射光束的反常模式(a)和寻常模式(b)的归一化光强分布, 其中两个小图分别表示为对应的相位分布, 在计算中, 取入射光束的波长
$\lambda = 1$ 且${w_0} = 20\lambda $ Figure 2. Normalized intensity distribution of the abnormal mode (a) and normal mode (b) of transmitted light beam under the normal incidence of a left-handed circularly polarized Bessel beam at a sharp interface. The insets represent the phase distribution of corresponding modes. Here, we take the working wavelength as
$\lambda = 1$ and${w_0} = 20\lambda $ .
图 3 三种放置于自由空间的单层薄膜材料的透射系数, 以及SOI的转换效率
$\eta = {\left| {{t_{\rm{TM}}} - {t_{\rm{TE}}}} \right|^2}/4$ (a)$\varepsilon = 2.25$ , (b)$\varepsilon = 0.01$ , (c)${\varepsilon _x} = {\varepsilon _y} = 1$ 且${\varepsilon _z} = 0.01$ ; 计算中, 取入射光束的波长$\lambda = 1$ , 三种材料厚度$h = 2\lambda $ ; (d)和(e)分别是${\vartheta ^{\rm{i}}}$ 和${\varepsilon _z}$ ,${\vartheta ^{\rm{i}}}$ 和h同时变化时的转换效率, 在(d)中, 取${\varepsilon _x} = {\varepsilon _y} = 1$ ,$h = 1\lambda $ ; 在(e)中, 取${\varepsilon _x} = {\varepsilon _y} = 1$ ,${\varepsilon _z} = 0.01$ Figure 3. Transmission coefficients and conversion efficiency (
$\eta = {\left| {{t_{\rm{TM}}} - {t_{\rm{TE}}}} \right|^2}/4$ ) of three optically thin films placed in free space: (a)$\varepsilon = 2.25$ , (b)$\varepsilon = 0.01$ , (c)${\varepsilon _x} = {\varepsilon _y} = 1$ and${\varepsilon _z} = 0.01$ , where we take$\lambda = 1$ and$h = 2\lambda $ ; (d) conversion efficiencies versus${\vartheta ^{\rm{i}}}$ and${\varepsilon _z}$ of a uniaxial layer with${\varepsilon _x} = {\varepsilon _y} = 1$ and$h = 1\lambda $ ; (e) conversion efficiencies versus${\vartheta ^{\rm{i}}}$ and h of a uniaxial layer with${\varepsilon _x} = {\varepsilon _y} = 1$ and${\varepsilon _z} = 0.01$ . -
[1] Bliokh K Y, Rodríguez F F J, Nori F, Zayats A V 2015 Nat. Photon. 9 796
Google Scholar
[2] Bliokh K Y, Nori F 2015 Phys. Rep. 592 1
Google Scholar
[3] Shitrit N, Yulevich I, Maguid E, Ozeri D, Veksler D, Kleiner V, Hasman E 2013 Science 340 724
Google Scholar
[4] Petersen J, Volz J, Rauschenbeutel A 2014 Science 346 67
Google Scholar
[5] O’connor D, Ginzburg P, Rodríguez F F J, Wurtz G A, Zayats A V 2014 Nat. Commun. 5 5327
Google Scholar
[6] Pan D, Wei H, Gao L, Xu H X 2016 Phys. Rev. Lett. 117 166803
Google Scholar
[7] Ling X H, Zhou X X, Huang K, Liu Y C, Qiu C W, Luo H L, Wen S C 2017 Rep. Prog. Phys. 80 066401
Google Scholar
[8] Zhu T F, Lou Y J, Zhou Y H, Zhang J H, Huang J Y, Li Y, Luo H L, Wen S C, Zhu S Y, Gong Q H, Qiu M, Ruan Z C 2019 Phys. Rev. Appl. 11 034043
Google Scholar
[9] Zhou J X, Qian H L, Chen C F, Zhao J X, Li G R, Wu Q Y, Luo H L, Wen S C, Liu Z W 2019 Proc. Natl. Acad. Sci. USA 116 11137
Google Scholar
[10] Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93 083901
Google Scholar
[11] Bliokh K Y, Bliokh Y P 2006 Phys. Rev. Lett. 96 073903
Google Scholar
[12] Bliokh K Y, Bliokh Y P 2007 Phys. Rev. E 75 066609
Google Scholar
[13] Hosten O, Kwiat P 2008 Science 319 787
Google Scholar
[14] Qin Y, Li Y, He H, Gong Q H 2009 Opt. Lett. 34 2551
Google Scholar
[15] Luo H L, Zhou X X, Shu W X, Wen S C, Fan D Y 2011 Phys. Rev. A 84 043806
Google Scholar
[16] Kong L J, Wang X L, Li S M, Li Y N, Chen J, Gu B, Wang H T 2012 Appl. Phys. Lett. 100 071109
Google Scholar
[17] 刘金安, 涂佳隆, 卢志利, 吴柏威, 胡琦, 马洪华, 陈欢, 易煦农 2019 物理学报 68 064201
Google Scholar
Liu J A, Tu J L, Lu Z L, Wu B W, Hu Q, Ma H H, Chen H, Yi X N 2019 Acta Phys. Sin. 68 064201
Google Scholar
[18] Shitrit N, Bretner I, Gorodetski Y, Kleiner V, Hasman E 2011 Nano Lett. 11 2038
Google Scholar
[19] Huang L L, Chen X Z, Bai B F, Tan Q F, Jin G F, Zentgraf T, Zhang S 2013 Light: Sci. Appl. 2 e70
Google Scholar
[20] Ling X H, Zhou X X, Yi X N, Shu W X, Liu Y C, Chen S Z, Luo H L, Wen S C, Fan D Y 2015 Light: Sci. Appl. 4 e290
Google Scholar
[21] Liberman V S, Zel’dovich B Y 1992 Phys. Rev. A 46 5199
Google Scholar
[22] Bliokh K Y, Bliokh Y P 2004 Phys. Lett. A 333 181
Google Scholar
[23] Bliokh K Y 2009 J. Opt. A 11 094009
Google Scholar
[24] Bomzon Z, Kleiner V, Hasman E 2001 Opt. Lett. 26 1424
Google Scholar
[25] Marrucci L, Manzo C, Paparo D 2006 Phys. Rev. Lett. 96 163905
Google Scholar
[26] Beresna M, Gecevičius M, Kazansky P G, Gertus T 2011 Appl. Phys. Lett. 98 201101
Google Scholar
[27] Devlin R C, Ambrosio A, Rubin N A, Balthasar Mueller J P, Capasso F 2018 Science 358 896
Google Scholar
[28] Zhao Y Q, Edgar J S, Jeffries G D M, McGloin D, Chiu D T 2007 Phys. Rev. Lett. 99 073901
Google Scholar
[29] Bliokh K Y, Ostrovskaya E A, Alonso M A, Rodríguez H O G, Lara D, Dainty C 2011 Opt. Express 19 26132
Google Scholar
[30] Khilo N A, Petrova E S, Ryzhevich A A 2001 Quantum Electron. 31 85
Google Scholar
[31] Ciattoni A, Cincotti G, Palma C 2003 J. Opt. Soc. Am. A 20 163
Google Scholar
[32] Yavorsky M, Brasselet E 2012 Opt. Lett. 37 3810
Google Scholar
[33] Ciattoni A, Marini A, Rizza C 2017 Phys. Rev. Lett. 118 104301
Google Scholar
[34] Ciattoni A, Rizza C, Lee H W H, Conti C, Marini A 2018 Laser Photonics Rev. 12 1800140
Google Scholar
[35] Goodman J W 2005 Introduction to Fourier Optics (Green-woood Village: Roberts and Company Publishers) p55
[36] Bliokh K Y, Gorodetski Y, Kleiner V, Hasman E 2008 Phys. Rev. Lett. 101 030404
Google Scholar
[37] Berry M V 1984 Proc. R. Soc. A 392 45
Google Scholar
[38] Berry M V 1987 J. Mod. Opt. 34 1401
Google Scholar
[39] Born M, Wolf E 1999 Principles of Optics (Cambridge: University Press) p64
[40] Lekner J 1994 Pure Appl. Opt. 3 821
Google Scholar
[41] Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 958
Google Scholar
[42] Ferrari L, Wu C, Lepage D, Zhang X, Liu Z 2015 Prog. Quantum Electron. 40 1
Google Scholar
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