Abstract
In this work we establish an equivalent circuit model to analyze the resonace of the metamaterial considering the loss of the unit cell and coupling effect between them. From this model, we find that metamaterial can be divided into three categories: weak, critical and strong couplings, depending on the values of the loss and coupling strength, where the different resonant properties are presented. The physical reason of the division is whether the loss in each unit cell can be offset by energy coupling from the adjunct unit cells. Full-wave electromagnetic simulations have also been carried out to verify the equivalent circuit analysis. Our circuit analysis provides a simple and effective way to understand the coupling of the metamaterial and gives guidance for the analysis and design of the metamaterial.
概要
创新点
人工电磁材料的结构之间存在电磁耦合, 特别是结构距离很近的时候. 这种电磁耦合以及结构的损耗对其谐振特性起很重要的影响. 本文建立了人工电磁材料的等效电路模型, 在模型中分别考虑了电场耦合和磁场耦合以及结构损耗, 并根据耦合强度和损耗值的关系, 把人工电磁材料中的谐振特性分成三类: 强耦合, 临界耦合和弱耦合. 通过对等效电路模型的分析, 得出了人工电磁材料的谐振频率的劈裂和这三类耦合之间的关系, 并从能量的角度解释了其物理机理.
Similar content being viewed by others
References
Tao H, Padilla WJ, Zhang X, et al. Recent progress in electromagnetic metamaterial devices for terahertz applications. IEEE J Sel Top Quantum Electron, 2010, 99: 1–10
Liu Y, Zhang X. Metamaterials: A new frontier of science and technology. Chem Soc Rev, 2011, 40: 2494–2507
Veselago V G. The electrodynamics of substances with simultaneously negative values of ɛ and µ. Sov Phys Usp, 1968, 10: 509–514
Christos A, Nasim M E, Francesco M, et al. Negative refraction, gain and nonlinear effects in hyperbolic metamaterials, Opt Express, 2013, 21: 15037–15047
Xu T, Amit A, Maxim A, et al. All-angle negative refraction and active flat lensing of ultraviolet light. Nature, 2013, 497: 470–474
Alexander P, Ivan I, Pavel B, et al. Hyperbolic metamaterials. Nat Photon, 2013, 7: 948–957
Wang Z B, Feng Y J, Zhao J M, et al. Analog study of near-field focusing and subwavelength imaging with nonlinear transmission-line metamaterial. Sci China Inf Sci, 2013, 56: 120407(8)
Xu S, Wang Y, Zhang B L, et al. Invisibility cloaks from forward design to inverse design. Sci China Inf Sci, 2013, 56: 120408(11)
Schurig D, Mock J J, Justice B J, et al. Metamaterial electromagnetic cloak at microwave frequencies. Science, 2006, 314: 977–980
Shao J, Chen P, Wu R X, et al. Analogue of electromagnetically induced transparency by doubly degenerate modes in a U-shaped metamaterial. Appl Phys Lett, 2013, 102: 034106
Jin B B, Wu J B, Zhang C H, et al. Enhanced slow light in superconducting electromagnetically induced transparency metamaterials. Supercond Sci Technol, 2013, 26: 074004
Meng C, Peng R W, Fan R H, et al. Making structured metals transparent for broadband electromagnetic waves. Sci China Inf Sci, 2013, 56: 120409(9)
Yanchuk B L, Zheludev N I, Halas N J, et al. The Fano resonance in plasmonic nanostructures and metamaterials. Nat Mater, 2010, 9: 707–715
Cao W, Singh R, Naib I A I A, et al. Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials. Opt Lett, 2012, 37: 3366–3368
Husu H, Canfield B K, Laukkanen J, et al. Chiral coupling in gold nanodimers. Appl Phys Lett, 2008, 93: 183115
Li Z F, Caglayan H, Colak E, et al. Coupling effect between two adjacent chiral structure layers. Opt Express, 2010, 9: 5375–5377
Huang C, Feng Y J, Zhao J M, et al. Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures. Phys Rev B, 2012, 85: 195131
Liu H, Cao J X, Zhu S N, et al. Lagrange model for the chiral optical properties of stereometamaterials. Phy Rev B, 2010, 81: 241403
Liu N, Liu H, Zhu S N, et al. Stereometamaterials. Nat Photon, 2009, 3: 157–162
Liu H, Genov D A, Wu D M, et al. Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures. Phys Rev B, 2007, 76: 073101
Liu M, Chen P. Study on resonance modes separation of metallic split ring resonator pair at microwave frequencies (in Chinese). J Microwaves, 2010, 27: 1, 71–74
Xiong X, Sun W H, Bao Y J, et al. Switching the electric and magnetic responses in a metamaterial. Phys Rev B, 2009, 80: 201105
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Zhang, Y., Wu, J., Liang, L. et al. Effect of loss and coupling on the resonance of metamaterial: An equivalent circuit approach. Sci. China Inf. Sci. 57, 1–8 (2014). https://doi.org/10.1007/s11432-014-5184-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-014-5184-7