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With the rapid development of metasurface and metamaterials, the image edge detection based on the optical spatial differential calculation becomes an interesting topic in recent years. There have been a certain number of studies in this region, but most of them are applicable only to one-dimensional optical spatial differential calculation. In this work, a two-dimensional optical differentiator using Pancharatnam-Berry (P-B) phase metasurface is proposed and implemented in optical image two-dimensional edge detection. Based on the principle of the spin-dependent splitting from P-B phase devices, this metasurface is capable of separating the left-handed circularly polarized light from the right-handed circularly polarized light at a certain spatial distance. After filtering out the overlapped linear polarization, the left optical information is the result of the two-dimensional optical spatial differential. Meanwhile, the resolution of the image edge information is adjustable by changing the optic axis distribution of this two-dimensional optical differentiator. These results indicate that our P-B phase metasurface can be applied to the extraction of the optical image two-dimensional edge information, and the extracted edge information is more complete than the previous one-dimensional grating metasurface. For these advantages, this two-dimensional optical differentiator shows great potential applications in ultrafast optical calculation and image processing.
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Keywords:
- metasurface /
- Pancharatnam-Berry phase /
- photonic spin Hall effect
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图 1 (a)单元结构示意图; (b)与(c) x与y方向线偏振入射光相位响应与介质柱长(l)、宽(w)之间的关系; (d) x和y方向上的相位差随l和w变化关系; (e)介质柱的旋转角与附加相位关系图.
Figure 1. (a) Schematic for basic unit structure; (b) and (c) phase response of different length (l) and width (w) of the dielectric column under x- and y- LP incident beams; (d) phase difference between the x- and y-polarized light for different length (l) and width (w) of the dielectric column; (e) relationship between the rotation angle of the dielectric column and the additional phase.
图 2 (a)光学二维边缘检测原理图; (b) LHCP与RHCP通过PB相位超表面后获得的相位梯度变化; (c) P-B相位超表面示意图; (d)和(e) RHCP与LHCP平面波通过超表面后波前变化图
Figure 2. (a) Schematic diagram of the 2D optical edge detection; (b) phase gradient of the LHCP and RHCP component after the P-B phase matesurface; (c) diagram of the metasurface; (d) and (e) wavefront changes of RHCP and LHCP plane waves through the metasurface.
图 3 (a) 深圳大学校徽掩模板; (b)−(d)周期T = 4 mm, 2 mm, 1 mm时, 一维边缘检测效果; (e)−(g)周期T = 4 mm, 2 mm, 1 mm时二维边缘检测效果
Figure 3. (a) The mask used in the simulation; (b)−(d) the result of 1D edge extraction when the period T = 4 mm, 2 mm, 1 mm; (e)−(g) the result of 2D edge extraction when the period T = 4 mm, 2 mm, 1 mm.
图 4 (a)形状不同的正方形掩膜板; (b)−(d)超表面的快轴分布以及LHCP通过超表面后的相位分布; (e)−(g)不同光轴分布的超表面实现边缘提取效果; (h)−(j)经过传输距离为0.1 m后LHCP和RHCP的相位差分布
Figure 4. (a) Mask patterns of different squre; (b)−(d) metasurface fast-axis distributions and phase distributions of LHCP after metasurface; (e)−(g) results of the edge extraction with different Metasurface fast-axis distributions; (h)−(j) phase difference distributions of LHCP and RHCP at 0.1 m transmission distance.
图 5 幂指数不同的光轴分布函数分别在x与y方向上的空间传递函数
Figure 5. Spatial spectral transfer function of the optical axis distribution functions with different power exponent in the x- and y- direction respectively.
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[1] Hubel D H, Wiesel T N 1962 J. Physiol 160 106
Google Scholar
[2] Farmahini-Farahani M, Cheng J, Mosallaei H 2013 J. Opt. Soc. Am. B 30 2365
Google Scholar
[3] 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
[4] Silva A, Monticone F, Castaldi G, Galdi V, Alù A, Engheta N 2014 Science 343 160
Google Scholar
[5] Ruan Z C 2015 Opt. Lett. 40 601
Google Scholar
[6] Solli D R, Jalali B 2015 Nat. Photonics 9 704
Google Scholar
[7] Liu F F, Wang T, Qiang L, Ye T, Zhang Z Y, Qiu M, Su Y K 2008 Opt. Express 16 15800
[8] Slavík R, Park Y, Ayotte N, Doucet S, Ahn T, LaRochelle S, Azaña J 2008 Opt. Express 16 18202
Google Scholar
[9] Yang T, Dong J, Lu L, Zhou L, Zheng A, Zhang X, Chen J 2014 Sci. Rep. 4 5581
[10] Ruan Z C, Wu H, Qiu M, Fan S H 2014 Opt. Lett. 39 3587
Google Scholar
[11] Saba A, Tavakol M R, Karimi-Khoozani P, Khavasi A 2018 IEEE Photonics Technol. Lett. 30 853
Google Scholar
[12] Pors A, Nielsen M G, Bozhevolnyi S I 2015 Nano Lett. 15 791
Google Scholar
[13] Doskolovich L L, Bykov D A, Bezus E A, Soifer V A 2014 Opt. Lett. 39 1278
Google Scholar
[14] Zhu T F, Zhou Y H, Lou Y J, Ye H, Qiu M, Ruan Z C, Fan S H 2017 Nat. Commun. 8 15391
Google Scholar
[15] 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 P. Natl. Acad. Sci. USA 116 11137
Google Scholar
[16] Bykov D A, Doskolovich L L, Bezus E A, Soifer V A 2014 Opt. Express 22 25084
Google Scholar
[17] 程杨, 姚佰承, 吴宇, 王泽高, 龚元, 饶云江 2013 62 237805
Google Scholar
Cheng Y, Yao B C, Wu Y, Wang Z G, Gong Y, Rao Y J 2013 Acta Phys. Sin. 62 237805
Google Scholar
[18] 李鑫, 吴立祥, 杨元杰 2019 68 187103
Google Scholar
Li X, Wu L X, Yang Y J 2019 Acta Phys. Sin. 68 187103
Google Scholar
[19] 郭文龙, 王光明, 李海鹏, 侯海生 2016 65 074101
Google Scholar
Guo W L, Wang G M, Li H P, Hou H S 2016 Acta Phys. Sin. 65 074101
Google Scholar
[20] 余观夏, 付晶晶, 杜文文, 吕一航, 骆敏 2019 中国物理B 28 024101
Yu G X, Fu J J, Du W W, Lü Y H, Luo M 2019 Chinese Phys. B 28 024101
[21] Marrucci L, Manzo C, Paparo, D 2006 Phys. Rev. Lett. 96 163905
Google Scholar
[22] Biener G, Niv A, Kleiner V, Hasman E 2002 Opt. Lett. 27 1875
Google Scholar
[23] Luo W, Xiao S, He Q, Sun S, Zhou L 2015 Adv. Opt. Mater. 3 1102
Google Scholar
[24] Shitrit N, Bretner I, Gorodetski Y, Kleiner V, Hasman E 2011 Nano Lett. 11 2038
Google Scholar
[25] Yin X B, Ye Z L, 1 Rho J, Wang Y, Zhang X 2013 Science 339 1405
Google Scholar
[26] Luo X G, Pu M B, Li X, Ma X L 2017 Light Sci. Appl. 6 e16276
Google Scholar
[27] Declin R C, Khorasaninejad M, Chen W T, Oh J, Capasso F 2016 P. Natl. Acad. Sci. USA 113 10473
Google Scholar
[28] Declin R C, Ambrosio A, Rubin N A, Mueller J P B, Capasso F 2017 Science 358 896
Google Scholar
[29] Bomzon Z, Biener G, Kleiner V, Hasman E 2002 Opt. Lett. 27 1141
Google Scholar
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