Abstract

The literature regarding the influence of the hole shape on the performance, especially on the losses, of negative-index metamaterials on the basis of the so-called double-fishnet structure is unclear. We investigate this aspect in a systematic theoretical study showing that the figure of merit can differ by as much as a factor of 2.5 between rectangular and circular holes, respectively.

© 2007 Optical Society of America

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References

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  1. V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2006).
    [CrossRef]
  2. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
    [CrossRef] [PubMed]
  3. K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
    [CrossRef]
  4. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
    [CrossRef] [PubMed]
  5. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
    [CrossRef] [PubMed]
  6. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  7. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-Band Negative Index Metamaterial: Double-Negative at 813 nm and Single-Negative at 772 nm," Opt. Lett, in press (2007).
    [CrossRef] [PubMed]
  8. Z. Ku and S. R. J. Brueck, "Comparison of negative refractive index materials with circular, elliptical and rectangular holes," Opt. Express 15, 4515-4522 (2007).
    [CrossRef] [PubMed]
  9. G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
    [CrossRef] [PubMed]
  10. S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4930 (2005).
    [CrossRef] [PubMed]
  11. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
  12. G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, "Observation of magnetization waves in negativeindex photonic metamaterials," Appl. Phys. Lett. 89, 231118 (2006).
    [CrossRef]

2007 (6)

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-Band Negative Index Metamaterial: Double-Negative at 813 nm and Single-Negative at 772 nm," Opt. Lett, in press (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
[CrossRef] [PubMed]

Z. Ku and S. R. J. Brueck, "Comparison of negative refractive index materials with circular, elliptical and rectangular holes," Opt. Express 15, 4515-4522 (2007).
[CrossRef] [PubMed]

2006 (4)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, "Observation of magnetization waves in negativeindex photonic metamaterials," Appl. Phys. Lett. 89, 231118 (2006).
[CrossRef]

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

2005 (1)

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

G. Dolling, M. Wegener, A. Schadle, S. Burger, and S. Linden, "Observation of magnetization waves in negativeindex photonic metamaterials," Appl. Phys. Lett. 89, 231118 (2006).
[CrossRef]

Nature Photon. (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photon. 1, 41-48 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett (1)

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-Band Negative Index Metamaterial: Double-Negative at 813 nm and Single-Negative at 772 nm," Opt. Lett, in press (2007).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rep. (1)

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Science (2)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1.
Fig. 1.

Comparison of rectangular, square, and circular-shaped holes in double-layer fishnet structures. The three columns represent the three hole shapes, which are indicated on the top. The polarization configuration is also shown on the top. The rows below show the real and imaginary parts of the retrieved effective electric permittivity ε, the magnetic permeability µ, the refractive index n, and the resulting figure of merit FOM=-Re(n)/Im(n). The parameters for rectangular holes wx =316nm, wy =100nm, and a=600nm correspond to those of Ref. [4]. The best parameters that we have found here for square-shaped holes are wx =wy =w=319nm and a=625nm; for circular holes r=192nm and a=625nm. The vertical layer thicknesses are kept fixed for all three hole shapes: 45nm Ag (gray), 30nm MgF2 (blue), and 45nm Ag (gray).

Tables (1)

Tables Icon

Table 1. FOM of circular-hole double-fishnet negative-index photonic metamaterials obtained by embedding the structure in an effective homogeneous medium with refractive index n= 1.1 (i.e., no glass substrate). The FOMvalues in brackets refer the corresponding calculations for structures in air (n=1) on a glass substrate with refractive index n=1.5. The thickness of the spacer layer increases from s=30nm in the top to s=100nm in the bottom row. The metal thickness t=45nm is fixed. To keep a fixed vacuum wavelength λ=1.4µm, the lattice constant a, and the hole radius r have to be adjusted. The column labeled λ/a refers to the ratio of vacuum wavelength and lattice constant. The column to the right refers to the corresponding ratio for the material wavelength λ/n) in the embedding medium with refractive index n= 1.1 (glass substrate with refractive index n=1.5).

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