Abstract

We introduce a plasmon hybridization picture to understand the optical properties of double split-ring resonator metamaterials. The analysis is based on the calculated reflectance spectra from a finite-integration time-domain algorithm. Field distributions of the double split-ring resonators at the resonant frequencies confirm the results from the plasmon hybridization analysis. We demonstrate that the plasmon hybridization is a simple and powerful tool for understanding and designing metamaterials in the near infrared and visible regime.

© 2007 Optical Society of America

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  1. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  3. D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  4. R. Marques, F. Medina, and R. Raffi-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
    [CrossRef]
  5. P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
    [CrossRef]
  6. K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peak in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
    [CrossRef] [PubMed]
  7. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
    [CrossRef] [PubMed]
  8. N. Katsarakis, T. Koschny, and M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. H. C. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Thickness dependence of the optical properties of split-ring resonator metamaterials," Phys. Status Solidi B 244, 1256 (2007).
    [CrossRef]
  19. E. Prodan, C. Radloff, N. J. Halas, P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
    [CrossRef] [PubMed]
  20. H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, "Nanorice: a hybrid plasmonic nanostructure," Nano Lett. 6, 827-832 (2006).
    [CrossRef] [PubMed]
  21. N. Liu, H. C. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mat., in press (2007).
  22. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1120 (1983).
    [CrossRef] [PubMed]
  23. <other>. We have used ∑∞ = 1, ωp = 2ω × 2175 THz, and ωτ = 2π × 19.5 THz in the Drude model dielectric function of [22].</other>

2007

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for metamaterials: optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

N. Liu, H. C. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 244, 1251 (2007).
[CrossRef]

H. C. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Thickness dependence of the optical properties of split-ring resonator metamaterials," Phys. Status Solidi B 244, 1256 (2007).
[CrossRef]

N. Liu, H. C. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mat., in press (2007).

W. J. Padilla, "Group theoretical description of artificial electromagnetic metamaterials," Opt. Express 15, 1639- 1646 (2007).
[CrossRef] [PubMed]

2006

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, "Nanorice: a hybrid plasmonic nanostructure," Nano Lett. 6, 827-832 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Single-slit split-ring resonators at optical frequencies: limits of size scaling," Opt. Lett. 31, 1259-1261 (2006).
[CrossRef] [PubMed]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827 (2006).
[CrossRef] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

2005

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
[CrossRef] [PubMed]

2004

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peak in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, and M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

2003

E. Prodan, C. Radloff, N. J. Halas, P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

2002

R. Marques, F. Medina, and R. Raffi-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1999

B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1983

Adv. Mat.

N. Liu, H. C. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mat., in press (2007).

Appl. Opt.

Appl. Phys. B

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Appl. Phys. Lett.

N. Katsarakis, T. Koschny, and M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

Nano Lett.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, "Nanorice: a hybrid plasmonic nanostructure," Nano Lett. 6, 827-832 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

R. Marques, F. Medina, and R. Raffi-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for metamaterials: optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

Phys. Rev. E

P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Phys. Status Solidi B

N. Liu, H. C. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 244, 1251 (2007).
[CrossRef]

H. C. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Thickness dependence of the optical properties of split-ring resonator metamaterials," Phys. Status Solidi B 244, 1256 (2007).
[CrossRef]

Science

E. Prodan, C. Radloff, N. J. Halas, P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Other

<other>. We have used ∑∞ = 1, ωp = 2ω × 2175 THz, and ωτ = 2π × 19.5 THz in the Drude model dielectric function of [22].</other>

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Figures (6)

Fig. 1.
Fig. 1.

The energy diagram describes the plasmon hybridization in a DSRR. The interaction between the plasmonic modes (|ω1〉 and |ω2〉) of its constitute outer ring and inner rings results in a new coupled mode pair: an anti-symmetric mode |ω-〉 and a symmetric mode |ω+〉.

Fig. 2.
Fig. 2.

Schematic diagram of a DSRR. t denotes the thickness of the SRR, w the width of the wire, lox (lix ) the length of the wire parallel to the gap bearing side in the outer (inner) ring, and loy (liy ) the length of the wire perpendicular to the gap bearing side in the outer (inner) ring.

Fig. 3.
Fig. 3.

Simulated reflectance spectra for DSRR (dotted blue curves) compared to the outer SRR alone (dashed red curves) and the inner SRR alone (solid black curves) for various inner-ring sizes. |ω1〉 and |ω2〉 present the fundamental plasmonic eigenmodes of the outer and inner rings alone, respectively. For DSRRs, the lower energy anti-symmetric mode and higher energy symmetric modes are denoted as |ω-〉 and |ω+〉, respectively. In the simulations, the outer-ring size (lox =410 nm, loy =380 nm, w=50 nm, t=20 nm) and the array periods (px =py =550 nm) are kept constant. The inner-ring geometry is varied from (a) lix =270 nm and liy =290 nm; (b) lix =210 nm and liy =230 nm; and (c) lix =150 nm and liy =170 nm. The corresponding structure and plasmon hybridization diagrams are shown adjacent to the spectra. The individual spectra are shifted vertically for clarity.

Fig. 4.
Fig. 4.

Calculated reflectance spectra of the DSRRs with two different inner-ring orientations: the gap bearing side of the outer and inner rings are in the opposite direction (configuration A) and in the same direction (configuration B). Resonances at lower and higher energies in configuration A (B) are denoted by |ω-〉 (|ω*-〉) and |ω+〉 (|ω*+〉), respectively. The insets show the dipole oscillations at the corresponding resonances by the plasmon hybridization analysis. The individual spectra are shifted upwards for clarity.

Fig. 5.
Fig. 5.

Simulated electric maximum peak field distribution of Ez in a plane 30 nm above the structure for resonant modes of: (a) |ω-〉, (b) |ω+〉, (c) |ω*-〉, (d) |ω*+〉, corresponding to the peaks shown in Fig. 4. The amplitudes are normalized to that of the incident light field.

Fig. 6.
Fig. 6.

Simulated magnetic maximum peak field distributions of Hz in a plane 30nm above the structure for the resonant modes of (a) |ω-〉 and (b) |ω*-〉 corresponding to the lower energy peaks shown in Fig. 4. The amplitudes are normalized to those of incident field.

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