Abstract

Interest in negative refractive index, or left-handed (LH) materials, has escalated rapidly over the last few years and it now appears that useful LH materials may be realizable in the microwave region. However there is also considerable interest in LH materials for infrared and visible applications. The purpose of this paper is to explore the limitations of LH materials at short wavelengths due to inherent losses. Our conclusions are that it may be quite difficult to achieve useful LH materials at wavelengths less than about 10 microns using current approaches.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from Conductors and Enhanced Nonlinear Phenomena,�?? IEE Transactions on Microwave Theory and Techniques, 47 2075-2084 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. J. B. Pendry, �??Negative Refraction Makes a Perfect Lens,�?? Phys. Rev. Lett. 85 3966-3969 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

Appl. Phys. Lett.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, �??Microwave transmission through a two dimensional, isotropic, left-handed metamaterial,�?? Appl. Phys. Lett. 78 489-491 (2001).
[CrossRef]

D. R. Smith, D. Schurig and J. B. Pendry, �??Negative refraction of modulated electromagnetic waves,�?? Appl. Phys. Lett. 81 2713-2715 (2002).
[CrossRef]

IEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from Conductors and Enhanced Nonlinear Phenomena,�?? IEE Transactions on Microwave Theory and Techniques, 47 2075-2084 (1999).
[CrossRef]

J. Appl. Phys.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, �??Ab initio numerical simulation of left-handed metamaterials: Comparison of calculations and experiments,�?? J. Appl. Phys. 90 5419-5424 (2001).
[CrossRef]

J. Phys. Condens. Matter

S. O�??Brien and J. B. Pendry, �??Photonic band-gap effects and magnetic activity in dielectric composites,�?? J. Phys: Condens. Matter 14, 4035-4044 (2002).
[CrossRef]

S. O�??Brien and J. B. Pendry, �??Magnetic activity at infrared frequencies in structured metallic photonic crystals,�?? J. Phys: Condens. Matter 14 6393-6394 (2002).

Opt. Express

L. Wu, S. He, and L. Chen, �??On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,�?? Optics Express 11 1283-1290 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1283">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1283 </a>
[CrossRef] [PubMed]

V. A. Podolskiy, �??Plasmon modes and negative refraction in metal nanowire composites,�?? Optics Express 11, 735-745 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-735">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-735</a>
[CrossRef] [PubMed]

Phys. Rev. B

G. Shvets, �??Photonic approach to making a material with a negative index of refraction,�?? Phys. Rev. B 67 035109, (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, �??Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,�?? Phys. Rev. B 65 195104 (2002).
[CrossRef]

R. Marqués, F. Medina, and R. Rafi-El-Idrissi, �??Role of bianisotropy in negative permeability and lefthanded materials,�?? Phys. Rev. B 65 144440 (2002).
[CrossRef]

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, �??Optomagnetic composite medium with conducting nanoelements,�?? Phys. Rev. B 66 155411 (2002).
[CrossRef]

Phys. Rev. Lett.

J. Pacheco, T. M. Grzegorzyk, B.-I. Wu, Y. Zhang, and J. A. Kong, �??Power Propagation in Homogeneous Isotropic Frequency-Dispersive Left-Handed Media,�?? Phys. Rev. Lett. 89 257401 (2002).
[CrossRef] [PubMed]

P. M. Valanju, R. M. Walser, and A. P. Valanju. �??Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous,�?? Phys. Rev. Lett. 88 187401 (2002).
[CrossRef] [PubMed]

N. Garcia and N. Nieto-Vesperinas, �??Left-Handed Materials Do Not Make a Perfect Lens,�?? Phys Rev. Lett. 88 207403 (2002).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, 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]

D. R. Smith and N. Kroll, �??Negative Refractive Index in Left-Handed Materials,�?? Phys. Rev. Lett. 85 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, �??Negative Refraction Makes a Perfect Lens,�?? Phys. Rev. Lett. 85 3966-3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, �??Extremely Low Frequency Plasmons in Metallic Mesostructures,�?? Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

J. B. Pendry and D. R. Smith, �??Comment on �??Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous,�?? Phys. Rev. Lett. 90 029703 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielan, �??Experimental Verification and Simulation of Negative Index of Refraction Using Snell�??s Law,�?? Phys. Rev. Lett. 90 107401 (2003).
[CrossRef] [PubMed]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, �??Refraction in Media with a Negative Refractive Index,�?? Phys. Rev. Lett. 90 107402 (2003).
[CrossRef] [PubMed]

Science

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, �??Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging,�?? Science 291, 849-851 (2001).
[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]

Sov. Phys. USPEKHI

V. G. Veselago, �??The Electrodynamics of Substances with Simultaneously Negative Values of ε �?�and µ,�?? Soviet Physics USPEKHI 10 509-514 (1968).
[CrossRef]

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Figures (1)

Fig. 1.
Fig. 1.

Calculated loss factors in the modified structure are shown for the minimum loss per wavelength in the material, L m, and the minimum loss per free-space wavelength, L a, along with the model with L=4.8/λ where λ is the corresponding wavelength in free space in microns.

Tables (1)

Tables Icon

Table 1 Loss parameters calculated for the second split ring structure considered in reference [16] using their parameters and analysis and the above equations. Rows are labeled by the unit cell dimensions (in nm) for the three structures considered.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

n 2 = ε μ
k 2 = ω 2 c 2 n 2
n 2 = + { 1 2 ( ε 2 μ 2 ε 1 μ 1 ) + 1 2 ( ( ε 1 2 + ε 2 2 ) · ( μ 1 2 + μ 2 2 ) ) 1 2 } 1 2
n 1 = 1 2 n 2 ( ε 1 μ 2 + μ 1 ε 2 ) .
Λ m = 2 k 2 = 2 ω c n 2 .
λ m = 2 π n 1 · c ω ,
L m = Λ m · λ m = 4 π n 2 n 1 = 4 π ε 1 μ 2 + μ 1 ε 2 ( ε 1 μ 1 ε 2 μ 2 ) + ( ( ε 1 2 + ε 2 2 ) · ( μ 1 2 + μ 2 2 ) ) 1 2 .
L a = 4 π n 2
L m 4 π x a + ( 1 + x 2 ) 1 2
ω 2 ω ' o 2 = 1 4 Γ 2 + 1 2 f ' ω ' o 2
ω 2 ω ' o 2 ( 1 + 1 4 f ' )
L m = 4 π y = 8 π Γ f ' ω ' o .
δ = ( 2 ρ μ o ω ) 1 2
L m = 8 π δ 2 fdR
L m = 8 ρ λ π R o · a 2 R 3 d
L m = 8 π 4 4 3 3 ρ R o · ( a b ) 4 · λ a 2
L m 4.8 λ

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