In this paper, we report the formation of sharp Fano resonance in planar metamaterial array with perturbed periodicity. Rigorous sheet impedance theory is given to analyze the electric-magnetic and magnetic-magnetic coupling effects. It is found that periodicity perturbation can provide a general approach for Fano resonance with ultra-strong local field enhancement.

© 2013 OSA

1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
2. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001). [CrossRef] [PubMed]
3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
4. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004). [CrossRef] [PubMed]
5. M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007). [CrossRef]
6. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009). [CrossRef] [PubMed]
7. Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett.37(11), 2133–2135 (2012). [CrossRef] [PubMed]
8. C. Wu and G. Shvets, “Design of metamaterial surfaces with broadband absorbance,” Opt. Lett.37(3), 308–310 (2012). [CrossRef] [PubMed]
9. Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011). [CrossRef]
10. M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express20(3), 2246–2254 (2012). [CrossRef] [PubMed]
11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010). [CrossRef] [PubMed]
12. C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011). [CrossRef] [PubMed]
13. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007). [CrossRef] [PubMed]
14. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008). [CrossRef] [PubMed]
15. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008). [CrossRef] [PubMed]
16. V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010). [CrossRef] [PubMed]
17. N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009). [CrossRef]
18. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008). [CrossRef]
19. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009). [CrossRef] [PubMed]
20. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011). [CrossRef] [PubMed]
21. Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006). [CrossRef]
22. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011). [CrossRef]
23. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005). [CrossRef] [PubMed]
24. V. D. Lam, J. B. Kim, S. J. Lee, Y. P. Lee, and J. Y. Rhee, “Dependence of the magnetic-resonance frequency on the cut-wire width ofcut-wire pair medium,” Opt. Express15(25), 16651–16656 (2007). [CrossRef] [PubMed]
25. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007). [CrossRef]
26. S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009). [CrossRef]
27. P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012). [CrossRef]

Adv. Mater. (Deerfield Beach Fla.)

• N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. (Deerfield Beach Fla.)19(21), 3628–3632 (2007). [CrossRef]

Appl. Phys. Lett.

• Y. Cui, J. Xu, K. Hung Fung, Y. Jin, A. Kumar, S. He, and N. X. Fang, “A thin film broadband absorber based on multi-sized nanoantennas,” Appl. Phys. Lett.99(25), 253101 (2011). [CrossRef]

Nano Lett.

• N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10(7), 2342–2348 (2010). [CrossRef] [PubMed]
• F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett.8(11), 3983–3988 (2008). [CrossRef] [PubMed]
• A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008). [CrossRef] [PubMed]

Nat. Mater.

• C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater.11(1), 69–75 (2011). [CrossRef] [PubMed]

Nat. Photonics

• N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008). [CrossRef]

Opt. Express

• E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009). [CrossRef] [PubMed]
• M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express20(3), 2246–2254 (2012). [CrossRef] [PubMed]
• V. D. Lam, J. B. Kim, S. J. Lee, Y. P. Lee, and J. Y. Rhee, “Dependence of the magnetic-resonance frequency on the cut-wire width ofcut-wire pair medium,” Opt. Express15(25), 16651–16656 (2007). [CrossRef] [PubMed]

Opt. Lett.

• G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005). [CrossRef] [PubMed]
• Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett.37(11), 2133–2135 (2012). [CrossRef] [PubMed]
• C. Wu and G. Shvets, “Design of metamaterial surfaces with broadband absorbance,” Opt. Lett.37(3), 308–310 (2012). [CrossRef] [PubMed]

Phys. Rev. B

• M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007). [CrossRef]
• S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B80(15), 153103 (2009). [CrossRef]
• N. Papasimakis, V. A. Fedotov, Y. H. Fu, D. P. Tsai, and N. I. Zheludev, “Coherent and incoherent metamaterials and order-disorder transitions,” Phys. Rev. B80(4), 041102 (2009). [CrossRef]
• B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83(23), 235427 (2011). [CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

• R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001). [CrossRef] [PubMed]
• R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004). [CrossRef] [PubMed]

Phys. Rev. Lett.

• C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett.106(10), 107403 (2011). [CrossRef] [PubMed]
• V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007). [CrossRef] [PubMed]
• V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010). [CrossRef] [PubMed]

Phys. Scr.

• Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr.74(2), 259–266 (2006). [CrossRef]

Physica B

• P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: Theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B407(20), 4062–4065 (2012). [CrossRef]

Science

• R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
• N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
• R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009). [CrossRef] [PubMed]

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