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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  1. V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ,” Soviet Physics USPEKHI 10509–514 (1968)
    [CrossRef]
  2. 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]
  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,  472075–2084 (1999)
    [CrossRef]
  4. 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. 844184–4187 (2000)
    [CrossRef] [PubMed]
  5. D. R. Smith and N. Kroll, “Negative Refractive Index in Left-Handed Materials,” Phys. Rev. Lett. 852933–2936 (2000)
    [CrossRef] [PubMed]
  6. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 853966–3969 (2000)
    [CrossRef] [PubMed]
  7. 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. 78489–491 (2001)
    [CrossRef]
  8. 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, 849851 (2001).
    [CrossRef] [PubMed]
  9. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 29277–79 (2001)
    [CrossRef] [PubMed]
  10. 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. 905419–5424 (2001)
    [CrossRef]
  11. R. Marqués, F. Medina, and R. Rafi-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed materials,” Phys. Rev. B 65 144440 (2002)
    [CrossRef]
  12. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys: Condens. Matter 144035–4044 (2002)
    [CrossRef]
  13. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65 195104 (2002)
    [CrossRef]
  14. 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]
  15. N. Garcia and N. Nieto-Vesperinas, “Left-Handed Materials Do Not Make a Perfect Lens,” Phys Rev. Lett. 88 207403 (2002)
    [CrossRef] [PubMed]
  16. S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys: Condens. Matter 146393–6394 (2002)
  17. D. R. Smith, D. Schurig, and J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 812713–2715 (2002)
    [CrossRef]
  18. L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66 155411 (2002)
    [CrossRef]
  19. 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]
  20. G. Shvets, “Photonic approach to making a material with a negative index of refraction,” Phys. Rev. B 67 035109, (2003)
    [CrossRef]
  21. 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]
  22. 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]
  23. 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]
  24. V. A. Podolskiy, “Plasmon modes and negative refraction in metal nanowire composites,” Optics Express 11735–745 (2003)
    [CrossRef] [PubMed]
  25. L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Optics Express 111283–1290 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-12831.
    [CrossRef] [PubMed]

2003 (6)

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

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]

V. A. Podolskiy, “Plasmon modes and negative refraction in metal nanowire composites,” Optics Express 11735–745 (2003)
[CrossRef] [PubMed]

L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Optics Express 111283–1290 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-12831.
[CrossRef] [PubMed]

2002 (9)

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

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys: Condens. Matter 144035–4044 (2002)
[CrossRef]

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

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]

S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys: Condens. Matter 146393–6394 (2002)

D. R. Smith, D. Schurig, and J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 812713–2715 (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]

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]

2001 (4)

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. 78489–491 (2001)
[CrossRef]

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, 849851 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 29277–79 (2001)
[CrossRef] [PubMed]

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. 905419–5424 (2001)
[CrossRef]

2000 (3)

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. 844184–4187 (2000)
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, “Negative Refractive Index in Left-Handed Materials,” Phys. Rev. Lett. 852933–2936 (2000)
[CrossRef] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 853966–3969 (2000)
[CrossRef] [PubMed]

1999 (1)

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,  472075–2084 (1999)
[CrossRef]

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, 4773–4776 (1996).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ,” Soviet Physics USPEKHI 10509–514 (1968)
[CrossRef]

Chen, L.

L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Optics Express 111283–1290 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-12831.
[CrossRef] [PubMed]

Economou, E. N.

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]

Foteinopoulou, S.

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]

Garcia, N.

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

Gilderdale, D. J.

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, 849851 (2001).
[CrossRef] [PubMed]

Greegor, R. B.

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]

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. 905419–5424 (2001)
[CrossRef]

Grigorenko, A. N.

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

Grzegorzyk, T. M.

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]

Hajnal, J. V.

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, 849851 (2001).
[CrossRef] [PubMed]

He, S.

L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Optics Express 111283–1290 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-12831.
[CrossRef] [PubMed]

Holden, A. J.

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,  472075–2084 (1999)
[CrossRef]

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]

Koltenbah, B. E. C.

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]

Kong, J. A.

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]

Kroll, N.

D. R. Smith and N. Kroll, “Negative Refractive Index in Left-Handed Materials,” Phys. Rev. Lett. 852933–2936 (2000)
[CrossRef] [PubMed]

Larkman, D. J.

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, 849851 (2001).
[CrossRef] [PubMed]

Li, K.

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]

Makhnovskiy, D. P.

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

Markoš, P.

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

Marqués, R.

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

Medina, F.

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

Nemat-Nasser, S. C.

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. 78489–491 (2001)
[CrossRef]

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. 844184–4187 (2000)
[CrossRef] [PubMed]

Nieto-Vesperinas, N.

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

O’Brien, S.

S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys: Condens. Matter 146393–6394 (2002)

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys: Condens. Matter 144035–4044 (2002)
[CrossRef]

Pacheco, J.

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]

Padilla, W. J.

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. 844184–4187 (2000)
[CrossRef] [PubMed]

Panina, L. V.

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

Parazzoli, C. G.

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]

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. 905419–5424 (2001)
[CrossRef]

Pendry, J. B.

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]

D. R. Smith, D. Schurig, and J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 812713–2715 (2002)
[CrossRef]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys: Condens. Matter 144035–4044 (2002)
[CrossRef]

S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys: Condens. Matter 146393–6394 (2002)

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, 849851 (2001).
[CrossRef] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 853966–3969 (2000)
[CrossRef] [PubMed]

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,  472075–2084 (1999)
[CrossRef]

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]

Podolskiy, V. A.

V. A. Podolskiy, “Plasmon modes and negative refraction in metal nanowire composites,” Optics Express 11735–745 (2003)
[CrossRef] [PubMed]

Rafi-El-Idrissi, R.

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

Robbins, D. J.

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,  472075–2084 (1999)
[CrossRef]

Schuhmann, R.

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. 905419–5424 (2001)
[CrossRef]

Schultz, S.

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

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. 905419–5424 (2001)
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 29277–79 (2001)
[CrossRef] [PubMed]

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. 78489–491 (2001)
[CrossRef]

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. 844184–4187 (2000)
[CrossRef] [PubMed]

Schurig, D.

D. R. Smith, D. Schurig, and J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 812713–2715 (2002)
[CrossRef]

Shelby, R. A.

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. 78489–491 (2001)
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 29277–79 (2001)
[CrossRef] [PubMed]

Shvets, G.

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

Smith, D. R.

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]

D. R. Smith, D. Schurig, and J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 812713–2715 (2002)
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, 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. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 29277–79 (2001)
[CrossRef] [PubMed]

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. 905419–5424 (2001)
[CrossRef]

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. 78489–491 (2001)
[CrossRef]

D. R. Smith and N. Kroll, “Negative Refractive Index in Left-Handed Materials,” Phys. Rev. Lett. 852933–2936 (2000)
[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. 844184–4187 (2000)
[CrossRef] [PubMed]

Soukoulis, C. M.

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]

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

Stewart, W. J.

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,  472075–2084 (1999)
[CrossRef]

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]

Tanielan, M.

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]

Valanju, A. P.

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]

Valanju, P. M.

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]

Veselago, V. G.

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ,” Soviet Physics USPEKHI 10509–514 (1968)
[CrossRef]

Vetter, A. M.

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. 905419–5424 (2001)
[CrossRef]

Vier, D. C.

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. 905419–5424 (2001)
[CrossRef]

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. 844184–4187 (2000)
[CrossRef] [PubMed]

Walser, R. M.

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]

Weiland, T.

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. 905419–5424 (2001)
[CrossRef]

Wiltshire, M. C. K.

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, 849851 (2001).
[CrossRef] [PubMed]

Wu, B.-I.

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]

Wu, L.

L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Optics Express 111283–1290 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-12831.
[CrossRef] [PubMed]

Young, I. R.

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, 849851 (2001).
[CrossRef] [PubMed]

Youngs, I.

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]

Zhang, Y.

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]

Appl. Phys. Lett. (2)

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. 78489–491 (2001)
[CrossRef]

D. R. Smith, D. Schurig, and J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 812713–2715 (2002)
[CrossRef]

IEE Transactions on Microwave Theory and Techniques (1)

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,  472075–2084 (1999)
[CrossRef]

J. Appl. Phys. (1)

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. 905419–5424 (2001)
[CrossRef]

J. Phys: Condens. Matter (2)

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys: Condens. Matter 144035–4044 (2002)
[CrossRef]

S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys: Condens. Matter 146393–6394 (2002)

Optics Express (2)

V. A. Podolskiy, “Plasmon modes and negative refraction in metal nanowire composites,” Optics Express 11735–745 (2003)
[CrossRef] [PubMed]

L. Wu, S. He, and L. Chen, “On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,” Optics Express 111283–1290 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-12831.
[CrossRef] [PubMed]

Phys Rev. Lett. (1)

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

Phys. Rev. B (4)

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

D. R. Smith, S. Schultz, P. Markoš, 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 left-handed materials,” Phys. Rev. B 65 144440 (2002)
[CrossRef]

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

Phys. Rev. Lett. (9)

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]

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]

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]

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. 844184–4187 (2000)
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, “Negative Refractive Index in Left-Handed Materials,” Phys. Rev. Lett. 852933–2936 (2000)
[CrossRef] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 853966–3969 (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]

Science (2)

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, 849851 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 29277–79 (2001)
[CrossRef] [PubMed]

Soviet Physics USPEKHI (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ,” Soviet Physics USPEKHI 10509–514 (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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