Abstract

The phase matching condition relating the real transverse wave vectors across a periodic boundary has been generalized to the case of complex transverse wave vectors. Based on this generalization, we describe diffraction of a complex Bloch wave propagating within a composite prism, and show that the resulting light in free space is an inhomogeneous plane wave in the presence of losses within the prism.

© 2010 OSA

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  1. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
    [CrossRef]
  2. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
    [CrossRef]
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton and Oxford, 2008), pp. 221–222.
  4. A. Damascelli, Z. Hussain, and Z. X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75(2), 473–541 (2003).
    [CrossRef]
  5. J. B. Pendry, “Photonic Band Structures,” J. Mod. Opt. 41(2), 209–229 (1994).
    [CrossRef]
  6. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [CrossRef] [PubMed]
  7. 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(10), 107401 (2003).
    [CrossRef] [PubMed]
  8. 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 materials,” Opt. Express 11(7), 688–695 (2003).
    [CrossRef] [PubMed]
  9. X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
    [CrossRef] [PubMed]
  10. N. Garcia and M. Nieto-Vesperinas, “Is there an experimental verification of a negative index of refraction yet?” Opt. Lett. 27(11), 885–887 (2002).
    [CrossRef]
  11. 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(19), 195104 (2002).
    [CrossRef]
  12. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
    [CrossRef]
  13. D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
    [CrossRef]
  14. D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
    [CrossRef]
  15. C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
    [CrossRef]
  16. 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(4), 489–491 (2001).
    [CrossRef]
  17. K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001), pp. 30–32.
  18. 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(13), 137405 (2004).
    [CrossRef] [PubMed]
  19. N. W. Ashcroft, and N. D. Mermin, Solid State Physics, Solid State Physics (Holt, Rinehart and Winston, New York, 1976), pp. 368–369.
  20. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon Press, Oxford and New York, 1966), pp. 13–14.
  21. N. F. Declercq, J. Degrieck, and O. Leroy, “The Laplace transform to describe bounded inhomogeneous waves,” J. Acoust. Soc. Am. 116(1), 51–60 (2004).
    [CrossRef]
  22. W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
    [CrossRef]
  23. R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
    [CrossRef]
  24. N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
    [CrossRef] [PubMed]
  25. 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(13), 137401 (2003).
    [CrossRef] [PubMed]
  26. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
    [CrossRef] [PubMed]
  27. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
    [CrossRef] [PubMed]
  28. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  29. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
    [CrossRef]
  30. X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
    [CrossRef]
  31. I. Tsukerman, “Negative refraction and the minimum lattice cell size,” J. Opt. Soc. Am. B 25(6), 927–936 (2008).
    [CrossRef]

2009 (1)

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

2008 (5)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[CrossRef]

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

I. Tsukerman, “Negative refraction and the minimum lattice cell size,” J. Opt. Soc. Am. B 25(6), 927–936 (2008).
[CrossRef]

2005 (2)

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
[CrossRef]

N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
[CrossRef] [PubMed]

2004 (2)

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(13), 137405 (2004).
[CrossRef] [PubMed]

N. F. Declercq, J. Degrieck, and O. Leroy, “The Laplace transform to describe bounded inhomogeneous waves,” J. Acoust. Soc. Am. 116(1), 51–60 (2004).
[CrossRef]

2003 (6)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[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(13), 137401 (2003).
[CrossRef] [PubMed]

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 materials,” Opt. Express 11(7), 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(10), 107401 (2003).
[CrossRef] [PubMed]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

A. Damascelli, Z. Hussain, and Z. X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75(2), 473–541 (2003).
[CrossRef]

2002 (3)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, “Is there an experimental verification of a negative index of refraction yet?” Opt. Lett. 27(11), 885–887 (2002).
[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(19), 195104 (2002).
[CrossRef]

2001 (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. 78(4), 489–491 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[CrossRef]

1999 (2)

R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (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(25), 4773–4776 (1996).
[CrossRef] [PubMed]

1994 (2)

W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
[CrossRef]

J. B. Pendry, “Photonic Band Structures,” J. Mod. Opt. 41(2), 209–229 (1994).
[CrossRef]

Akozbek, N.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Bloemer, M. J.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Briers, R.

N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
[CrossRef] [PubMed]

R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
[CrossRef]

W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
[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(13), 137401 (2003).
[CrossRef] [PubMed]

Cappeddu, M. G.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Centini, M.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[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(13), 137401 (2003).
[CrossRef] [PubMed]

Damascelli, A.

A. Damascelli, Z. Hussain, and Z. X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75(2), 473–541 (2003).
[CrossRef]

Davanco, M.

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

Davanço, M.

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

de Ceglia, D.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Declercq, N. F.

N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
[CrossRef] [PubMed]

N. F. Declercq, J. Degrieck, and O. Leroy, “The Laplace transform to describe bounded inhomogeneous waves,” J. Acoust. Soc. Am. 116(1), 51–60 (2004).
[CrossRef]

Degrieck, J.

N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
[CrossRef] [PubMed]

N. F. Declercq, J. Degrieck, and O. Leroy, “The Laplace transform to describe bounded inhomogeneous waves,” J. Acoust. Soc. Am. 116(1), 51–60 (2004).
[CrossRef]

Deschamps, M.

R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
[CrossRef]

D'Orazio, A.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Forrest, S. R.

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

Garcia, N.

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Greegor, R. B.

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 materials,” Opt. Express 11(7), 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(10), 107401 (2003).
[CrossRef] [PubMed]

Haus, J. W.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (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(25), 4773–4776 (1996).
[CrossRef] [PubMed]

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(13), 137401 (2003).
[CrossRef] [PubMed]

Huang, W.

W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
[CrossRef]

Hussain, Z.

A. Damascelli, Z. Hussain, and Z. X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75(2), 473–541 (2003).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Koltenbah, B. E. C.

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(10), 107401 (2003).
[CrossRef] [PubMed]

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 materials,” Opt. Express 11(7), 688–695 (2003).
[CrossRef] [PubMed]

Koschny, T.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

Lederer, F.

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[CrossRef]

Leroy, O.

N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
[CrossRef] [PubMed]

N. F. Declercq, J. Degrieck, and O. Leroy, “The Laplace transform to describe bounded inhomogeneous waves,” J. Acoust. Soc. Am. 116(1), 51–60 (2004).
[CrossRef]

R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
[CrossRef]

W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
[CrossRef]

Li, K.

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 materials,” Opt. Express 11(7), 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(10), 107401 (2003).
[CrossRef] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

Mahdjoubi, K.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
[CrossRef]

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (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(19), 195104 (2002).
[CrossRef]

Menzel, C.

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[CrossRef]

Mock, J. J.

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(13), 137405 (2004).
[CrossRef] [PubMed]

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. 78(4), 489–491 (2001).
[CrossRef]

Nieto-Vesperinas, M.

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[CrossRef]

Parazzoli, C. G.

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 materials,” Opt. Express 11(7), 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(10), 107401 (2003).
[CrossRef] [PubMed]

Paul, T.

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (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(25), 4773–4776 (1996).
[CrossRef] [PubMed]

J. B. Pendry, “Photonic Band Structures,” J. Mod. Opt. 41(2), 209–229 (1994).
[CrossRef]

Pertsch, T.

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[CrossRef]

Poncelet, O.

R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Rockstuhl, C.

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[CrossRef]

Rokhlin, S. I.

W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
[CrossRef]

Rye, P. M.

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(13), 137405 (2004).
[CrossRef] [PubMed]

Sauleau, R.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
[CrossRef]

Scalora, M.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Schultz, S.

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(19), 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (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. 78(4), 489–491 (2001).
[CrossRef]

Seetharamdoo, D.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
[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. 78(4), 489–491 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Shen, Z. X.

A. Damascelli, Z. Hussain, and Z. X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75(2), 473–541 (2003).
[CrossRef]

Shvets, G.

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

Smith, D. R.

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(13), 137405 (2004).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (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(19), 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (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. 78(4), 489–491 (2001).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (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(19), 195104 (2002).
[CrossRef]

Starr, A. F.

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(13), 137405 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (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(25), 4773–4776 (1996).
[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 materials,” Opt. Express 11(7), 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(10), 107401 (2003).
[CrossRef] [PubMed]

Tarot, A. C.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
[CrossRef]

Tsukerman, I.

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Urzhumov, Y.

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Vier, D. C.

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(13), 137405 (2004).
[CrossRef] [PubMed]

Vincenti, M. A.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

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(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, X. H.

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[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. 78(4), 489–491 (2001).
[CrossRef]

X. H. Zhang, M. Davanco, Y. Urzhumov, G. Shvets, and S. R. Forrest, “A Subwavelength Near-Infrared Negative-Index Material,” Appl. Phys. Lett. 94(13), 131107 (2009).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

N. F. Declercq, R. Briers, J. Degrieck, and O. Leroy, “The history and properties of ultrasonic inhomogeneous waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(5), 776–791 (2005).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (3)

N. F. Declercq, J. Degrieck, and O. Leroy, “The Laplace transform to describe bounded inhomogeneous waves,” J. Acoust. Soc. Am. 116(1), 51–60 (2004).
[CrossRef]

W. Huang, R. Briers, S. I. Rokhlin, and O. Leroy, “Experimental-Study of Inhomogeneous Wave Reflection from a Solid-Air Periodically Rough Boundary Using Leaky Rayleigh-Waves,” J. Acoust. Soc. Am. 96(1), 363–369 (1994).
[CrossRef]

R. Briers, O. Leroy, O. Poncelet, and M. Deschamps, “Experimental verification of the calculated diffraction field generated by inhomogeneous waves obliquely incident on a periodically rough liquid-solid boundary,” J. Acoust. Soc. Am. 106(2), 682–687 (1999).
[CrossRef]

J. Appl. Phys. (1)

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys. 98(6), 063505 (2005).
[CrossRef]

J. Mod. Opt. (1)

J. B. Pendry, “Photonic Band Structures,” J. Mod. Opt. 41(2), 209–229 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Phys. Rev. B (5)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refraction like behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65(20), 201104 (2002).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in a fishnet metamaterial,” Phys. Rev. B 78(15), 155102 (2008).
[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(19), 195104 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

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(13), 137405 (2004).
[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(25), 4773–4776 (1996).
[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(13), 137401 (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(10), 107401 (2003).
[CrossRef] [PubMed]

X. H. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

A. Damascelli, Z. Hussain, and Z. X. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75(2), 473–541 (2003).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton and Oxford, 2008), pp. 221–222.

N. W. Ashcroft, and N. D. Mermin, Solid State Physics, Solid State Physics (Holt, Rinehart and Winston, New York, 1976), pp. 368–369.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon Press, Oxford and New York, 1966), pp. 13–14.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001), pp. 30–32.

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Figures (3)

Fig. 1
Fig. 1

A homogeneous plane wave is normally incident along x ^ ' in the x’-y’ plane on a composite prism consisting of subwavelength unit cells and excites a complex Bloch wave that is diffracted by the interface grating at the hypotenuse. The diffracted light is detected in the far field. Constant and exponentially decaying wave amplitudes of phase fronts represent the incident homogeneous and detected inhomogeneous plane waves, respectively. Here, θ and θ 0 are incidence and refraction angles, a is the unit cell size, d is the interface periodicity, k B is the first Brillouin zone wave vector of the Bloch mode, and k m and k B ( m ) are the complex wave vector of the m th transmitted diffraction order and reflected Bloch wave in the extended Brillouin zone scheme, respectively. Subscripts r and i denote real and imaginary parts, and G = 2 π / d is the magnitude of the surface reciprocal lattice vector.

Fig. 2
Fig. 2

Observed effective index nr calculated using Eqs. (5) and (6) in text. The parameters used in the calculation are: θ = 18 (Refs. [6,9,25]), 26 (Refs. [9,25]); λ/a = 6 (Refs. [6,9,25]); FOM = 100 (Ref. [7]), 3 (Refs. [9,26]). The frequency dispersion of the vacuum wave number, k 0 , is neglected due to the narrow bandwidth of the negative index band. The lossless case (Eq. (7) in text) is nearly identical to that for FOM = 100. Also, n T I R is the onset of total internal reflection in the lossless case for θ = 26 .

Fig. 3
Fig. 3

Effective indices derived via Eq. (7) in text from calculated band structures of Refs. [7,8]. Both are consistent with the experimentally measured values for these metamaterials. Solid and dashed lines are guide to the eye.

Equations (7)

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

P ( x ' ) = 1 2 Re ( S ( x ' ) ( E ( r ' ) × H * ( r ' ) ) · x ^ ' d y ' d z ' )     = 1 2 Re ( S ( x ' ) ( E 0 ( r ' ) × H 0 * ( r ' ) ) · x ^ ' e 2 k i B x ' d y ' d z ' ) ,
k t B = k t m + m G ,
{ [ k r B ] y = [ k r m ] y + m ( 2 π / d ) [ k i B ] y = [ k i m ] y ,
| k r m | 2 | k i m | 2 = k 0 2 ,
| k r 0 | 2 = 1 2 { k 0 2 + ( | k r B | 2 + | k i B | 2 ) sin 2 θ ± [ k 0 2 + ( | k r B | 2 + | k i B | 2 ) sin 2 θ ] 2 4 | k r B | 2 k 0 2 sin 2 θ } .
n r = sin θ 0 / sin θ = ( k r B / k r 0 ) sgn ( k i B ) ,
n r = { ( k r B / k 0 ) sgn ( ω / k r B ) w h e n ( k 0 > k r B sin θ ) ( 1 / sin θ ) sgn ( ω / k r B ) w h e n ( k 0 k r B sin θ ) ,

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