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The resolution of traditional far-field imaging system is generally restricted by half of the wavelength of incident light due to the diffraction limit. The more specific reason is that evanescent waves carrying sub-wavelength information cannot propagate in the far field and make no contribution to the imaging. However, higher imaging resolution is required in practical applications. To realize the far-field super-resolution imaging, the imaging system should be able to collect both propagating waves and evanescent waves. Many designs have been proposed to solve this issue. In 2007, a far-field superlens was proposed by Liu et al. (Liu Z W, Durant S, Lee H, Pikus Y, Fang N, Xiong Y, Sun C, Zhang X 2007 Nano Lett. 7 403) to realize far-field super-resolution in optical range, which consisted of a silver film and a nanoscale grating coupler. The silver film was used to amplify the evanescent waves, which were then converted into propagating waves by the sub-wavelength gratings. However, the special material properties limit the freedom of design. In microwave band, the incident components can be converted into Bloch modes by the resonant metalens, which consists of subwavelength resonators, and then be radiated to far field. Nevertheless, Green function between antenna and target is necessary, which is difficult to obtain due to the complex and even time-dependent imaging environment in practical applications, especially for super-resolution imaging system. It has been demonstrated in recent research that frequency information can be associated with spatial information of imaging target by localization resonant modes. Therefore, super-resolution imaging can be realized based on frequency information, without using Green function. Thus, a novel microstructure array is proposed to realize the far-field super-resolution scanning imaging based on a fractal resonator. The fractal resonator can work at several frequencies because of the self-similarity, which provides higher selectivity according to practical conditions. Several working statuses can be obtained for the resonator by adding photoconductive semiconductor switches, which are controlled by laser. On account of localization mode resonance, the array can realize the conversion between evanescent waves and propagating waves. Then with the help of antennas in the far-field to receive the frequency information, the location of imaging source can be confirmed according to the spectrum. Then by using the magnitude of resonant peak, sub-wavelength image can be reconstructed without using Green function. To verify the super-resolution scanning imaging characteristics of the array, an imaging simulation of “laugh face”-shaped target is performed. The image is reconstructed very well and the resolution determined by the period of the array is 20 mm, corresponding to λ/10. In view of the particularity of proposed fractal resonator, a novel scanning method is proposed. By combining the first and the third resonance, the imaging efficiency can be well improved compared with by the traditional point-by-point scanning method.
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图 1 (a)分形谐振器单元的物理尺寸; (b)开关设置模型
Fig. 1. (a) Physical dimensions of fractal resonator cell; (b) switch setup model.
图 2 分形谐振器单元远场频谱仿真模型及两种工作状态下的远场频谱 (a)远场频谱仿真模型; (b)两种工作状态下的远场频谱
Fig. 2. Far-field spectrum simulation setup of fractal resonator cell and simulated far-field spectra of two working status: (a) Far-field spectrum simulation setup; (b) far-field spectra of two working status.
图 4 一阶谐振两种工作状态的远场频谱
Fig. 4. Far-field spectra of the first resonance at two working status.
图 5 三阶谐振的两种工作状态设置及远场频谱 (a)工作状态设置; (b)远场频谱
Fig. 5. Two working status and far-field spectra of the third resonance: (a) Working status setup; (b) far-field spectra.
图 6 分形微结构阵列编号及成像模型设置 (a)编号模型; (b)成像模型
Fig. 6. Number of fractal microstructure array and imaging model: (a) Number model; (b) imaging model.
图 7 分形微结构阵列远场超分辨率扫描成像结果 (a) 8 × 8像素点成像结果; (b) 16 × 16像素点成像结果
Fig. 7. Far-field super-resolution scanning imaging results of microstructure array: (a) 8 × 8 pixel imaging result; (b) 16 × 16 pixel imaging result
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[1] Merlin R 2007 Science 317 927
Google Scholar
[2] Grbic A, Jiang L, Merlin R 2008 Science 320 511
Google Scholar
[3] Grbic A, Merlin R 2008 IEEE Trans. Antennas Propag. 56 3159
Google Scholar
[4] 祝生祥 2000 光学仪器 22 34
Google Scholar
Zhu S X 2000 Opt. Instrum. 22 34
Google Scholar
[5] 波恩M, 沃尔夫E 著 (杨葭荪 译) 1999 光学原理 (北京: 电子工业出版社) 第342−427页
Born M, Wolf E (translated by Yang J S) 1999 Principles of Optics (Beijing: Electronic Industry Press) pp342−427 (in Chinese)
[6] Pohl D W, Denk W, Lanz M 1984 Appl. Phys. Lett. 44 651
Google Scholar
[7] Pendry J B 2000 Phys. Rev. Lett. 85 3966
Google Scholar
[8] Pendry J B, Ramakrishna S A 2003 J. Phys.: Condens. Matter 15 6345
Google Scholar
[9] Nicholas F, Lee H, Sun C, Zhang X 2005 Science 308 534
Google Scholar
[10] 杨晨, 张洪欣, 王海侠, 徐楠, 许媛媛, 黄丽玉, 张可欣 2012 61 164101
Google Scholar
Yang C, Zhang H X, Wang H X, Xu N, Xu Y Y, Huang L Y, Zhang K X 2012 Acta Phys. Sin. 61 164101
Google Scholar
[11] Liu Z W, Durant S, Lee H, Pikus Y, Fang N, Xiong Y, Sun C, Zhang X 2007 Nano Lett. 7 403
Google Scholar
[12] Zhang Z Y, Du J L, Guo Y K, Niu X J, Li M, Luo X G, Du C L 2009 Chin. Phys. Lett. 26 014211
Google Scholar
[13] Lemoult F, Lerosey G, de Rosny J, Fink M 2010 Phys. Rev. Lett. 104 203901
Google Scholar
[14] Lemoult F, Fink M, Lerosey G 2011 Waves Random and Complex Media 21 614
Google Scholar
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Google Scholar
[16] Gao Q, Wang B Z, Wang X H 2015 IEEE Trans. Antennas Propag. 63 5586
Google Scholar
[17] Jouvaud C, Ourir A, de Rosny J 2014 Appl. Phys. Lett. 104 243507
Google Scholar
[18] 高强 2018 博士学位论文 (成都: 电子科技大学)
Gao Q 2018 Ph. D. Dessertation (Chengdu: University of Electronics Science and Technology of China) (in Chinese)
[19] 龚志双, 王秉中, 王任 2018 67 084101
Google Scholar
Gong Z S, Wang B Z, Wang R 2018 Acta Phys. Sin. 67 084101
Google Scholar
[20] 周洪澄, 王秉中, 丁帅, 欧海燕 2013 62 114101
Google Scholar
Zhou H C, Wang B Z, Ding S, Ou H Y 2013 Acta Phys. Sin. 62 114101
Google Scholar
[21] Yao J, Ye Y H 2012 Chin. Phys. Lett. 29 047802
Google Scholar
[22] Wang P W, Li W, Wang C L, Bo Z W, Gong W L 2018 Chin. Phys. B 27 074202
Google Scholar
[23] Duan J H, Chen R K, Chen J N 2017 Chin. Phys. B 26 117802
Google Scholar
[24] Wang H, Brandl D W, Le F, Nordlander P, Halas N J 2006 Nano Lett. 6 827
Google Scholar
[25] Wang R, Wang B Z, Gong Z S, Ding X 2015 Sci. Rep. 5 11131
Google Scholar
[26] Prodan E, Radloff C, Halas N J, Nordlander P 2003 Science 302 419
Google Scholar
[27] Nordlander P, Oubre C, Prodan E, Li K, Stockman M I 2004 Nano Lett. 4 899
Google Scholar
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