Abstract

We perform an experimental study of the phase and amplitude of microwaves interacting with and scattered by two-dimensional negative index metamaterials. The measurements are performed in a parallel plate waveguide apparatus at X-band frequencies (8–12 GHz), thus constraining the electromagnetic fields to two dimensions. A detection antenna is fixed to one of the plates, while a second plate with a fixed source antenna or waveguide is translated relative to the first plate. The detection antenna is inserted into, but not protruding below, the stationary plate so that fields internal to the metamaterial samples can be mapped. From the measured mappings of the electric field, the interplay between the microstructure of the metamaterial lattice and the macroscopic averaged response is revealed. For example, the mapped phase fronts within a metamaterial having a negative refractive index are consistent with a macroscopic phase—in accordance with the effective medium predictions—which travels in a direction opposite to the direction of propagation. The field maps are in excellent agreement with finite element numerical simulations performed assuming homogeneous metamaterial structures.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  6. D. R. Smith and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B 23, 391-403 (2006).
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  7. T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  14. R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
    [CrossRef]
  17. T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
    [CrossRef]
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    [CrossRef]
  19. B. I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).
    [CrossRef]
  20. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  21. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  22. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
    [CrossRef]
  23. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
    [CrossRef] [PubMed]
  24. P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
    [CrossRef]
  25. D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
    [CrossRef]
  26. C. P. Parazzoli and K. Li, Phantom Works, The Boeing Company (personal communication, 2005).
  27. V. G. Veselago "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. USPEKI 10, 509-514 (1968).
    [CrossRef]
  28. J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
    [CrossRef]
  29. P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, 640-648 (2003).
    [CrossRef] [PubMed]
  30. D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
    [CrossRef] [PubMed]

2006

D. R. Smith and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B 23, 391-403 (2006).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

B. I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

2005

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

B. I. Popa and S. A. Cummer, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

2003

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, 640-648 (2003).
[CrossRef] [PubMed]

A. A. Houck, J. B. Brock and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
[CrossRef] [PubMed]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

2002

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]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

2001

R. 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, WillieJ. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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

1968

V. G. Veselago "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. USPEKI 10, 509-514 (1968).
[CrossRef]

Basov, D. N.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Brock, J. B.

A. A. Houck, J. B. Brock and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Cao, W.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

Chen, X. D.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Chuang, I. L.

A. A. Houck, J. B. Brock and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Cummer, S. A.

B. I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).
[CrossRef]

B. I. Popa and S. A. Cummer, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Dong, Z. G.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

Driscoll, T.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Economou, E. N.

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Gollub, J. N.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

Greegor, R. B.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

Grzegorczyk, T. M.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Houck, A. A.

A. A. Houck, J. B. Brock and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Kolinko, P.

Koltenbah, B. E. C.

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

Kong, J. A.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Koschny, T.

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

Liu, H.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

Lu, W. T.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Markoš, P.

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[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]

Mock, J. J.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Nielsen, J. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Pacheco, J.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Parazzoli, C. G.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B 23, 391-403 (2006).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Perram, T.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

Popa, B. I.

B. I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).
[CrossRef]

B. I. Popa and S. A. Cummer, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

Rye, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

Rye, P. M.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

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]

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

Schurig, D.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

Shelby, R.

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

Smith, D. R.

D. R. Smith and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B 23, 391-403 (2006).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, 640-648 (2003).
[CrossRef] [PubMed]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[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. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M

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]

Soukoulis, C. M.

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

Sridhar, S.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Starr, A. F.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

Tanielian, M.

R. B. Greegor, C. G. Parazzoli, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction metamaterials," Opt. Express 11, 688-695 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

Tanielian, M. H.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Thompson, M. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Veselago, V. G.

V. G. Veselago "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. USPEKI 10, 509-514 (1968).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Vier, D. C.

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Willie, D. R.

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

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Wu, B. I.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Zhu, J.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

Zhu, S. N.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
[CrossRef]

Appl. Phys. Lett.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a graded negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

B. I. Popa and S. A. Cummer, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

IEEE Trans. Antennas Propag.

R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Phys. Rev. B

T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[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]

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic surface plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402 (2005).
[CrossRef]

Phys. Rev. E

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped samples," Phys. Rev. E 72, 016607 (2005).
[CrossRef]

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
[CrossRef]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective medium parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

B. I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).
[CrossRef]

Phys. Rev. Lett.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2002).
[CrossRef]

A. A. Houck, J. B. Brock and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

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

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, "Enhanced diffraction from a grating on the surface of a negative-index metamaterial," Phys. Rev. Lett. 93, 137405 (2004).
[CrossRef] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Science

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

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Sov. Phys. USPEKI

V. G. Veselago "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. USPEKI 10, 509-514 (1968).
[CrossRef]

Other

C. P. Parazzoli and K. Li, Phantom Works, The Boeing Company (personal communication, 2005).

R. M. Walser, "Electromagnetic metamaterials," in Complex Mediums II: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, W. S. Weiglhofer, I. J. Hodgkinson, eds., Proc. SPIE 4467, 1-15 (2001).
[CrossRef]

Supplementary Material (9)

» Media 1: AVI (1694 KB)     
» Media 2: AVI (1679 KB)     
» Media 3: AVI (1698 KB)     
» Media 4: AVI (1740 KB)     
» Media 5: AVI (835 KB)     
» Media 6: AVI (1572 KB)     
» Media 7: AVI (766 KB)     
» Media 8: AVI (1673 KB)     
» Media 9: AVI (874 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Photograph of the field mapping planar waveguide chamber in the open position. The upper plate (including the detector antenna) is lowered parallel to the lower plate prior to the scan and after the sample is positioned relative to the source on the lower plate. The lower plate is mounted to two computer controlled linear translation stages, enabling an area of 20 cm by 20 cm to be scanned in steps of 1 mm (or less if desired). The detector probe mounted in the stationary upper plate can detect the amplitude and phase of the electric field within the chamber.

Fig. 2.
Fig. 2.

(a). Field map of the real part of the lowest order outgoing Hankel function (scale in mm). (b) (1.65 MB) The measured real part of the electric field radiated by a coaxial antenna introduced into the lower plate of the planar waveguide apparatus (scale in mm). (c) A comparison of the line scans corresponding to the measured field (solid line) and the lowest order outgoing Hankel function (dashed line).

Fig. 3.
Fig. 3.

(a). Measured spatial map of the intensity of the electric field corresponding to a planar beam generated within the planar waveguide. (b) (1.63 MB) Measured spatial map of the real part of the electric field field. The channel, made using absorbing material, is indicated by the lighter portions on the figures.

Fig. 4.
Fig. 4.

A microwave beam refracting from a positive index (polycarbonate, ε=2.6) wedge at 10.5 GHz. (a) Measured spatial map of the electric field intensity with an arrow indicating expected angle of refraction. (b) (1.65 MB) Measured spatial map of the real part of the electric field. (c) (1.69 MB) Measured spatial map of the real part of the electric field, with a larger input aperture. (d) (0.84 MB) Numerical simulation of a positive index wedge with the same parameters as in (c).

Fig. 5.
Fig. 5.

Design of the negative index metamaterial. (a) Extracted parameter set from the simulation of a single unit cell at 10.5 GHz. (b) A photograph of the fabricated wedge, showing the elements and construction near the angled surface. (c) A planar view of the unit cell, with dimensions indicated. The gap in the rings is 0.6 mm, while the line width is 0.2 mm. The wire, patterned on the reverse side of the circuit board, has a length of 9.8 mm (including the cross pieces), with a line width of 0.4 mm. The cross pieces extend a length of 3.0 mm. The circuit board material (FR4) has a thickness of 0.20 mm, with a dielectric constant of 3.71. The copper thickness for all structures is 17 µm.

Fig. 6.
Fig. 6.

(a). Measured spatial map of the intensity of a beam refracting from the negative index metamaterial sample at 10.5 GHz. The arrow indicates the expected angle of refraction as extracted from the unit cell simulations. (b) (1.53 MB) Measured spatial map of the real part of the electric field for the same configuration. (c) (0.77 MB) Numerical simulation of a negative index wedge at the same frequency.

Fig. 7.
Fig. 7.

(a). Measured spatial map of the intensity of the beam refracting from the negative index metamaterial sample with a small local structural defect introduced, causing corruption of the refracted beam at 10.5 GHz. (b) (1.63 MB) Measured spatial map of the real part of the electric field for the same configuration, with defect. Note that the phase fronts within the negative index wedge are no longer uniform. (c) (0.87 MB) Numerical simulation of a homogeneous negative index wedge with defect.

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