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The far-field super-resolution focusing devices possess characteristics such as super-resolution focusing, achromatic, small size and easy machining, which make them highly promising in optical imaging, optical microscopy and lithography. In this work, we propose a binary-amplitude modulation-based method for generating far-field super-resolution achromatic focusing. By using the principles of optical super-oscillation, combined with angular spectral diffraction theory and binary particle swarm optimization (BPSO), we optimize the binary amplitude-type far-field super-resolution focusing devices, which have an identical radius of 100λ but different focal lengths: λ1 = 405 nm, λ2 = 532 nm and λ3 = 632.8 nm, respectively. Additionally, an achromatic metalens is integrated by using Boolean AND operation. To assess the feasibility of our proposed approach, numerical simulations are conducted via COMSOL Multiphysics employing FEM analysis. The simulation results demonstrate that the generated spots are located at 25.105λ, 25.106λ, and 25.105λ, respectively. The corresponding full width at half maximum (FWHM) values are 0.441λ1 (0.179 μm), 0.469λ2 (0.249 μm) and 0.427λ3 (0.270 μm), which are smaller than the Abbe diffraction limit, and the far-field super-resolution achromatic focusing is realized. The sidelobe ratios are at low levels, i.e. 12.5%, 12.6%, and 14.2%. The binary amplitude-type far-field super-resolution achromatic devices have the advantages of easy machining, achromatism and super-resolution, and are suitable for miniaturization and integration of optical systems.
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Keywords:
- optical superoscillation /
- achromatic /
- far-field super-resolution /
- angular spectral diffraction
[1] Abbe E 1873 SPIE Milestone Series 178 413
Google Scholar
[2] Brabec T, Krausz F 2000 Rev. Mod. Phys. 72 545
Google Scholar
[3] Gruner-Nielsen L, Wandel M, Kristensen P, Jorgensen C, Jorgensen L V, Edvold B, Palsdottir B, Jakobsen D 2005 J. Lightwave Technol. 23 3566
Google Scholar
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Google Scholar
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[9] Sales T R M, Morris G M 1997 J. Opt. Soc. Am. A 14 1637
Google Scholar
[10] Xu Y S, Singh J, Sheppard C J R, Chen N G 2007 Opt. Express 15 6409
Google Scholar
[11] Huang T J, Liu J Y, Yin L Z, Han F Y, Liu P K 2018 Opt. Express 26 22722
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[12] Yang C, Shen Y, Xie Y Q, Zhou Q, Deng X H, Cao J C 2019 Phys. Lett. A 383 789
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[13] Wang S M, Xu J, Zhong Y, Ren R, Lu Y Q, Wan H D, Wang J, Ding J P 2016 Opt. Commun. 372 245
Google Scholar
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[15] Berry M V 2016 J. Phys. A Math. Theor. 50 025003
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
[26] Tang D L, Chen L, Liu J J 2019 Opt. Express 27 12308
Google Scholar
[27] Wu Z X, Deng H, Li X X, Liu Q C, Shang L P 2020 Appl. Opt. 59 7841
Google Scholar
[28] Goodman J 1996 Introduction to Fourier Optics (2nd Ed.) (McGrw-Hill Compnaies, Inc
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 二值振幅型远场超分辨消色差聚焦示意图
Figure 1. Schematic diagram of the binary-amplitude achromatic super-oscillatory lens (A-SOL).
图 2 径向偏振光光场强度、相位分布 (a)—(c) 405, 532和632.8 nm的光场强度分布; (d)—(f)沿半径方向上的光场强度和相位分布
Figure 2. Intensity and phase distribution of radially polarized beam: (a)–(c) Optical field intensity distributions of 405, 532 and 632.8 nm, respectively; (d)–(f) the corresponding optical field intensity and phase distributions along the radial direction through the center of the optical field.
图 3 二值振幅型远场超分辨消色差聚焦器件设计方法
Figure 3. Design method of binary-amplitude achromatic super-oscillatory lens (BP-ASOL).
图 4 二值振幅型远场超分辨消色差聚焦器件振幅分布 (a)—(c) 单波长超振荡透镜振幅分布; (d) 消色差超振荡透镜振幅分布
Figure 4. Optimized amplitude distributions of super-oscillatory lens (SOLs): (a)–(c) Amplitude distributions of S-SOL1, S-SOL2和S-SOL3; (d) amplitude distribution of A-SOL.
图 5 (a) λ1 = 405 nm, λ2 = 532 nm和λ3 = 632.8 nm入射条件下传播平面上的光场强度分布; (b)—(d) 沿传播方向上峰值强度、半高全宽和旁瓣比率分布
Figure 5. (a) Distribution of optical field intensity on the propagation plane at λ1 = 405 nm, λ2 = 532 nm and λ3 = 632.8 nm incidence; (b)–(d) distribution of peak intensity, FWHM and sidelobe ratio along the propagation direction.
图 6 (a) λ1 = 405 nm, λ2 = 532 nm和λ3 = 632.8 nm入射条件下传播平面上和焦平面上的归一化光场强度分布仿真结果; (b) 通过焦斑中心沿半径方向上的光场强度分布
Figure 6. (a) Normalized distributions of optical field intensity on the propagation plane and the focal plane at λ1 = 405 nm, λ2 = 532 nm and λ3 = 632.8 nm incidence; (b) intensity profiles along the radial direction across the center of the focal spot.
图 7 (a)—(c) λ1 = 405 nm, λ2 = 532 nm和λ3 = 632.8 nm入射条件下焦平面上的光场强度分布仿真结果; (d)—(f)沿半径方向上不同分量的光场强度分布和相位分布
Figure 7. (a)–(c) Distributions of optical field intensity on the propagation plane and the focal plane at λ1 = 405 nm, λ2 = 532 nm and λ3 = 632.8 nm incidence; (d)–(f) intensity profiles and phase profiles along the radial direction.
表 1 二值振幅型远场超分辨消色差聚焦器件理论计算和数值仿真对比结果
Table 1. Comparison of theoretical calculation and numerical simulation results of binary amplitude-type achromatic SOLs.
关键参数 λ1 = 405 nm λ2 = 532 nm λ3 = 632.8 nm 理论 仿真 理论 仿真 理论 仿真 焦距/λ 24.894 25.105 24.948 25.106 25.211 25.105 数值孔径 0.970 0.970 0.970 0.970 0.970 0.970 峰值半高全宽 0.462λ1 0.441λ1 0.468λ2 0.469λ2 0.429λ3 0.427λ3 旁瓣比率 10.3% 12.5% 11.6% 12.6% 13.4% 14.2% 阿贝衍射极限 0.515λ1 0.516λ1 0.515λ2 0.516λ2 0.516λ3 0.516λ3 
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[1] Abbe E 1873 SPIE Milestone Series 178 413
Google Scholar
[2] Brabec T, Krausz F 2000 Rev. Mod. Phys. 72 545
Google Scholar
[3] Gruner-Nielsen L, Wandel M, Kristensen P, Jorgensen C, Jorgensen L V, Edvold B, Palsdottir B, Jakobsen D 2005 J. Lightwave Technol. 23 3566
Google Scholar
[4] Gu M, Zheng P L, Hu Z W, Ma S D, Xu F, Pu D L, Wang Q H 2022 Chin. Phys. B 31 74210
Google Scholar
[5] Chen W T, Zhu A Y, Capasso F 2020 Nat. Rev. Mater. 5 604
Google Scholar
[6] Chen W T, Zhu A Y, Sanjeev V, Khorasaninejad M, Shi Z, Lee E, Capasso F 2018 Nat. Nanotechnol. 13 220
Google Scholar
[7] Arbabi E, Arbabi A, Kamali S M, Horie Y, Faraon A 2017 Optica 4 625
Google Scholar
[8] Wang S M, Wu P C, Su V C, Lai Y C, Chu C H, Chen J W, Lu S H, Chen J, Xu B B, Kuan C H, Li T, Zhu S N, Tsai D P 2017 Nat. Commun. 8 187
Google Scholar
[9] Sales T R M, Morris G M 1997 J. Opt. Soc. Am. A 14 1637
Google Scholar
[10] Xu Y S, Singh J, Sheppard C J R, Chen N G 2007 Opt. Express 15 6409
Google Scholar
[11] Huang T J, Liu J Y, Yin L Z, Han F Y, Liu P K 2018 Opt. Express 26 22722
Google Scholar
[12] Yang C, Shen Y, Xie Y Q, Zhou Q, Deng X H, Cao J C 2019 Phys. Lett. A 383 789
Google Scholar
[13] Wang S M, Xu J, Zhong Y, Ren R, Lu Y Q, Wan H D, Wang J, Ding J P 2016 Opt. Commun. 372 245
Google Scholar
[14] Davis B J, Karl W C, Swan A K, Ünlü M S, Goldberg B B 2004 Opt. Express 12 4150
Google Scholar
[15] Berry M V 2016 J. Phys. A Math. Theor. 50 025003
Google Scholar
[16] Berry C W, Wang N, Hashemi M R, Unlu M, Jarrahi M 2013 Nat. Commun. 4 1622
Google Scholar
[17] Berry M V, Dennis M R 2009 J. Phys. A 42 022003
Google Scholar
[18] Berry M V, Popescu S 2006 J. Phys. A 39 6965
Google Scholar
[19] Qian Z H, Tian S N, Zhou W, Wang J W, Guo H M 2022 Opt. Express 30 11203
Google Scholar
[20] Zhuang Z P, Chen R, Fan Z B, Pang X N, Dong J W 2019 Nanophotonics 8 1279
Google Scholar
[21] Kim H, Rogers E T F 2020 Sci. Rep. 10 1328
Google Scholar
[22] Wu Z X, Zhu J X, Zou Y Y, Deng H, Xiong L, Liu Q C, Shang L P 2022 Opt. Mater. 123 111924
Google Scholar
[23] Tang D L, Wang C, Zhao Z, Wang Y, Pu M, Li X, Gao P, Luo X 2015 Laser Photonics Rev. 9 713
Google Scholar
[24] Chen L, Liu J, Zhang X H, Tang D L 2020 Opt. Lett. 45 5772
Google Scholar
[25] Yuan G, Rogers E T F, Zheludev N I 2017 Light-Sci. Appl. 6 e17036
Google Scholar
[26] Tang D L, Chen L, Liu J J 2019 Opt. Express 27 12308
Google Scholar
[27] Wu Z X, Deng H, Li X X, Liu Q C, Shang L P 2020 Appl. Opt. 59 7841
Google Scholar
[28] Goodman J 1996 Introduction to Fourier Optics (2nd Ed.) (McGrw-Hill Compnaies, Inc
[29] Huang K, Ye H, Teng J, Yeo S P, Lukyanchuk B, Qiu C 2014 Laser Photonics Rev. 8 152
Google Scholar
[30] Malitson I H 1965 J. Opt. Soc. Am 55 1205
Google Scholar
[31] Rakić A D, Djurišić A B, Elazar J M, Majewski M L 1998 Appl. Opt. 37 5271
Google Scholar
[32] Liang Y Y, Liu H Z, Wang F Q, Meng H Y, Guo J P, Li J F, Wei Z C 2018 Nanomaterials 8 288
Google Scholar
[33] Arbabi A, Horie Y, Ball A J, Bagheri M, Faraon A 2015 Nat. Commun. 6 7069
Google Scholar
[34] Dorn R, Quabis S, Leuchs G 2003 Phys. Rev. Lett. 91 233901
Google Scholar
[35] Rogers E T F, Zheludev N I 2013 J. Opt. 15 094008
Google Scholar
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