Dual-band left-handed metamaterials fabricated by using tree-shaped fractal

doi:10.1088/1674-1056/21/12/124101

Abstract A method of fabricating dual-band left-handed metematerials (LHMs) is investigated numerically and experimentally by single-sided tree-like fractals. The resulting structure features multiband magnetic resonances and two electric resonances. By appropriately adjusting the dimensions, two left-handed (LH) bands with simultaneous negative permittivity and permeability are engineered and are validated by full-wave eigenmode analysis and measurement as well in the microwave frequency range. To study the multi-resonant mechanism in depth, the LHM is analysed from three different perspectives of field distribution analysis, circuit model analysis, and geometrical parameters evaluation. The derived formulae are consistent with all simulated results and resulting electromagnetic phenomena, indicating the effectiveness of the established theory. The method provides an alternative to the design of multi-band LHM and has the advantage of not requiring two individual resonant particles and electrically continuous wires, which in turn facilitates planar design and considerably simplifies the fabrication.

Keywords: planar left-handed metamaterial multi-band metamaterial fractal eigenmode

Received: 06 April 2012
Revised: 11 June 2012
Accepted manuscript online:

PACS:	41.20.Jb	(Electromagnetic wave propagation; radiowave propagation)
	42.25.Bs	(Wave propagation, transmission and absorption)
	73.20.Mf	(Collective excitations (including excitons, polarons, plasmons and other charge-density excitations))
	78.67.Pt	(Multilayers; superlattices; photonic structures; metamaterials)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60971118) and the Innovation Foundation for Postgraduate's Dissertation of Air Force Engineering University, China (Grant No. DY12101).

Corresponding Authors: Xu He-Xiu
E-mail: hxxu20008@yahoo.cn

Cite this article:

Xu He-Xiu (许河秀), Wang Guang-Ming (王光明), Wang Jia-Fu (王甲富), Yang Zi-Mu (杨自牧) Dual-band left-handed metamaterials fabricated by using tree-shaped fractal 2012 Chin. Phys. B 21 124101

[1]	Shelby R A, Smith D R and Schultz S 2001 Science 292 77
[2]	Chen H S, Ran L X, Huangfu J T, Zhang X M, Chen K S, Grzegorczyk T M and Kong J A 2004 J. Appl. Phys. 96 5338
[3]	Tretyakov S A 1998 J. Electrom. Waves and Appl. 12 821
[4]	Huangfu J T, Ran L X, Chen H S, Zhang X M, Chen K S, Grzegorczyk T M and Kong J A 2004 Appl. Phys. Lett. 84 1537
[5]	Lheurette É, Houzet G, Carbonell J, Zhang F L, Vanbésien O and Lippens D 2008 IEEE Trans. Antennas Propag. 56 3462
[6]	Bulu I, Caglayan H and Ozbay E 2005 Opt. Express 13 10238
[7]	Zhou J, Koschny T, Zhang L, Tuttle G and Soukoulis C M 2006 Appl. Phys. Lett. 88 221103
[8]	Zhou J, Zhang L, Tuttle G, Koschny T and Soukoulis C M 2006 Phys. Rev. B 73 041101(R)
[9]	Chen C H, Qu S B, Wang J F, Ma H, Wang X H and Xu Z 2011 Chin. Phys. B 20 034101
[10]	Yao Y and Zhao X P 2007 J. Appl. Phys. 101 124904
[11]	Kafesaki M, Tsiapa I, Katsarakis N, Koschny T, Soukoulis C M and Economou E N 2007 Phys. Rev. B 75 235114
[12]	Liu Y H, Luo C R and Zhao X P 2007 Acta Phys. Sin. 56 5883 (in Chinese)
[13]	Liu R, Degiron A, Mock J J and Smith D R 2007 Appl. Phys. Lett. 90 263504
[14]	Wang J F, Qu S B, Yang Y M, Ma H, Wu X and Xu Z 2009 Appl. Phys. Lett. 95 014105
[15]	Zhu W R, Zhao X P and Ji N 2007 Appl. Phys. Lett. 90 011911
[16]	Huang Y J, Wen G J, Yang Y J and Xie K 2012 Appl. Phys. A 106 79
[17]	Guo Y and Xu R 2006 Progress in Electromagnetics Research 66 239
[18]	Kwon D H, Werner D H, Kildishev A V and Shalaev V M 2007 Opt. Express 15 1647
[19]	He X J, Wang Y, Mei J S, Gui T L and Yin J H 2012 Chin. Phys. B 21 044101
[20]	Xu H X, Wang G M, Liu Q, Wang J F and Gong J Q 2012 Appl. Phys. A 107 261
[21]	Gu C, Qu S B, Pei Z B, Xu Z, Liu J and Gu W 2011 Chin. Phys. B 20 017801
[22]	Xu H X, Wang G M and Liang J G 2011 Radio Sci. 46 RS5008
[23]	Xu H X, Wang G M and Wang X 2011 Electron. Lett. 47 1081
[24]	Wen W, Zhou L, Hou B, Chan C T and Sheng P 2005 Phys. Rev. B 72 153406
[25]	Hao J M, Zhou L and Chan C T 2007 Appl. Phys. A 87 281
[26]	Zhao G Z, Tian Y, Sun H Q, Zhang C L and Yang G Z 2006 Chin. Phys. Lett. 23 1456
[27]	Du Q J, Liu J S, Yang H W and Yi X N 2011 Appl. Opt. 50 4798
[28]	Soukoulis C M, Linden S and Wegener M 2007 Science 315 47
[29]	Xu L and Michael Y W C 1999 Microwave Opt. Technol. Lett. 23 242
[30]	Pendry J B, Holden A J, Stewart W J and Youngs I 1996 Phys. Rev. Lett. 76 4773
[31]	Chen X D, Grzegorczyk T M, Wu B I, Pacheco J and Kong J A 2004 Phys. Rev. E 70 016608
[32]	Smith D R, Vier D C, Koschny Th and Soukoulis C M 2005 Phys. Rev. E 71 036617
[33]	Urbani F 2010 IEEE Antennas Wireless Propag. Lett. 9 720
[34]	Simovski C R 2011 J. Opt. 13 013001
[35]	Alu A 2011 Phys. Rev. B 83 081102(R)
[36]	Smith D R 2010 Phys. Rev. E 81 036605
[37]	Koschny T, Markoš P, Economou E N, Smith D R, Vier D C and Soukoulis C M 2005 Phys. Rev. B 71 245105
[38]	Markoš P, Rousochatzakis I and Soukoulis C M 2002 Phys. Rev. E 66 045601(R)
[39]	Wang J F, Qu S B, Xu Z, Zhang J Q, Ma H, Yang Y M and Gu C 2009 Chin. Phys. Lett. 26 084103
[40]	Zhou J F, Koschny T, Kafesaki M and Soukoulis C M 2008 Photonics and Nanostructures-Fundamentals and Applications 6 96
[41]	Wang J F, Qu S B, Xu Z, Ma H, Yang Y M and Gu C 2008 IEEE Trans. Antennas Propag. 56 2018
[42]	Bahl I and Bhartia P 2003 Microwave Solid State Circuit Design (New Jersey: John Wiley & Sons) pp. 58-60
[43]	Simovski C R, Belov P A and He S L 2003 IEEE Trans. Antennas Propag. 51 2582

[1]	Multifractal analysis of the software evolution in software networks Meili Liu(刘美丽), Xiaogang Qi(齐小刚), and Hao Pan(潘浩). Chin. Phys. B, 2022, 31(3): 030501.
[2]	Invariable mobility edge in a quasiperiodic lattice Tong Liu(刘通), Shujie Cheng(成书杰), Rui Zhang(张锐), Rongrong Ruan(阮榕榕), and Houxun Jiang(姜厚勋). Chin. Phys. B, 2022, 31(2): 027101.
[3]	Fractal sorting vector-based least significant bit chaotic permutation for image encryption Yong-Jin Xian(咸永锦), Xing-Yuan Wang(王兴元), Ying-Qian Zhang(张盈谦), Xiao-Yu Wang(王晓雨), and Xiao-Hui Du(杜晓慧). Chin. Phys. B, 2021, 30(6): 060508.
[4]	Fractal microstructure of Ag film via plasma discharge as SERS substrates Xue-Fen Kan(阚雪芬), Cheng Yin(殷澄), Zhuang-Qi Cao(曹庄琪), Wei Su(苏巍), Ming-Lei Shan(单鸣雷), and Xian-Ping Wang(王贤平). Chin. Phys. B, 2021, 30(12): 125201.
[5]	Analysis of secondary electron emission using the fractal method Chun-Jiang Bai(白春江), Tian-Cun Hu(胡天存), Yun He(何鋆), Guang-Hui Miao(苗光辉), Rui Wang(王瑞), Na Zhang(张娜), and Wan-Zhao Cui(崔万照). Chin. Phys. B, 2021, 30(1): 017901.
[6]	Dynamic crossover in [VIO²⁺][Tf₂N^-]₂ ionic liquid Gan Ren(任淦). Chin. Phys. B, 2021, 30(1): 016105.
[7]	Numerical study on permeability characteristics of fractal porous media Yongping Huang(黄永平), Feng Yao(姚峰), Bo Zhou(周博), Chengbin Zhang(张程宾). Chin. Phys. B, 2020, 29(5): 054701.
[8]	Dynamical response of a neuron-astrocyte coupling system under electromagnetic induction and external stimulation Zhi-Xuan Yuan(袁治轩), Pei-Hua Feng(冯沛华), Meng-Meng Du(独盟盟), Ying Wu(吴莹). Chin. Phys. B, 2020, 29(3): 030504.
[9]	Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas Xiao-Long Zhu(朱霄龙), Feng Wang(王丰), Zheng-Xiong Wang(王正汹). Chin. Phys. B, 2020, 29(2): 025201.
[10]	Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms Yanhui Zhang(张延惠), Xiulan Xu(徐秀兰), Lisha Kang(康丽莎), Xiangji Cai(蔡祥吉), Xu Tang(唐旭). Chin. Phys. B, 2018, 27(5): 053401.
[11]	Preliminary computation of the gap eigenmode of shear Alfvén waves on the LAPD Lei Chang(苌磊). Chin. Phys. B, 2018, 27(12): 125201.
[12]	Numerical simulation of the multiple reversed shear Alfvén eigenmodes associated with the triangularity Alfvén gap Wenjia Wang(王文家), Deng Zhou(周登), Youjun Hu(胡友俊), Yue Ming(明玥), Baolong Hao(郝保龙). Chin. Phys. B, 2018, 27(12): 125202.
[13]	Study on the phase transition of the fractal scale-free networks Qing-Kuan Meng(孟庆宽), Dong-Tai Feng(冯东太), Yu-Ping Sun(孙玉萍), Ai-Ping Zhou(周爱萍), Yan Sun(孙艳), Shu-Gang Tan(谭树刚), Xu-Tuan Gao(高绪团). Chin. Phys. B, 2018, 27(10): 106402.
[14]	Detection of meso-micro scale surface features based on microcanonical multifractal formalism Yuanyuan Yang(杨媛媛), Wei Chen(陈伟), Tao Xie(谢涛), William Perrie. Chin. Phys. B, 2018, 27(1): 010502.
[15]	Polaron effects in cylindrical GaAs/Al_xGa_1-xAs core-shell nanowires Hui Sun(孙慧), Bing-Can Liu(刘炳灿), Qiang Tian(田强). Chin. Phys. B, 2017, 26(9): 097302.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dual-band left-handed metamaterials fabricated by using tree-shaped fractal

Cite this article:

Online attention