Abstract

We propose a theoretical study of the optimization of one dimensional metal-dielectric metamaterials in order to approach -1 effective optical index. Taking into account actual values of dielectric constants of metal (silver) and dielectrics (HfO2, GaP), and taking advantage of the dispersion relation of Bloch modes, we get a silver/HfO2 metamaterial with suitable parameters that possesses a near −1 effective optical index for all angles of incidence at a visible wavelength for H-polarized light (i.e. the magnetic field is parallel to the interfaces). The absorption losses of materials appear to be a crucial factor that affects the effective properties of the metamaterial. We show that the losses not only decrease the transmission of the stack, but also change the negative refraction effect. Then, we propose another silver/GaP structure design that is less sensitive to losses. When considering finite thickness structures, and with adequate thickness for the terminating layers, it is possible to achieve a high transmittance of the structure. A near −1 effective index and high transmittance metal-dielectric metamaterial may pave the way to the realization of negative refraction in the visible or ultraviolet wavelength range.

© 2007 Optical Society of America

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References

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  1. V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
    [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  4. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
  5. B. Gralak, S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
    [CrossRef]
  6. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  7. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
    [CrossRef]
  8. D. O. Melville, R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005).
    [CrossRef] [PubMed]
  9. N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
    [CrossRef] [PubMed]
  10. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
    [CrossRef] [PubMed]
  11. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).
  12. P. A. Belov and H. Yang, "Subwavelength imaging at optical frequencies using a transmission device formed by a period layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73,113110 (2006).
    [CrossRef]
  13. H. Shin and S. H. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102 (2006).
    [CrossRef]
  14. M. Scalora, G. D'Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, "Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks," Opt. Express,  15, 508-523 (2007).
    [CrossRef] [PubMed]
  15. P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media. I. General theory," J. Opt. Soc. Am. 67, 423-438 (1977).
    [CrossRef]
  16. J. A. Kong, B. L. Wu, Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33,136-139 (2002).
    [CrossRef]
  17. P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  18. R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
    [CrossRef]
  19. V. Kuzmiak, A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427-7444 (1996).
    [CrossRef]
  20. A. Tip, A. Moroz and J. M. Combes, "Band structure of absorptive photonic crystals," J. Phys. A: Math. Gen. 33, 6223-6252 (2000).
    [CrossRef]
  21. J.-M. Combes B. Gralak and A. Tip, "Spectral properties of absorptive photonic crystals,' in Contemporary Mathematics 339, Ed. P. Kuchment, 1-13 (2003).
    [CrossRef]
  22. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

2007 (1)

2006 (3)

P. A. Belov and H. Yang, "Subwavelength imaging at optical frequencies using a transmission device formed by a period layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73,113110 (2006).
[CrossRef]

H. Shin and S. H. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

D. O. Melville, R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

2003 (2)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

2002 (2)

R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
[CrossRef]

J. A. Kong, B. L. Wu, Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33,136-139 (2002).
[CrossRef]

2001 (1)

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

2000 (4)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
[CrossRef]

A. Tip, A. Moroz and J. M. Combes, "Band structure of absorptive photonic crystals," J. Phys. A: Math. Gen. 33, 6223-6252 (2000).
[CrossRef]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696 (2000).
[CrossRef]

1996 (1)

V. Kuzmiak, A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427-7444 (1996).
[CrossRef]

1977 (1)

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1968 (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
[CrossRef]

Akozbek, N.

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

Belov, P. A.

P. A. Belov and H. Yang, "Subwavelength imaging at optical frequencies using a transmission device formed by a period layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73,113110 (2006).
[CrossRef]

Blaikie, R. J.

Bloemer, M. J.

Cappeddu, M. G.

Centini, M.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Combes, J. M.

A. Tip, A. Moroz and J. M. Combes, "Band structure of absorptive photonic crystals," J. Phys. A: Math. Gen. 33, 6223-6252 (2000).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

D'Aguanno, G.

de Ceglia, D.

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Enoch, S.

Fan, S. H.

H. Shin and S. H. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

Fowler, M.

Gatto, A.

R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
[CrossRef]

Gralak, B.

Haus, J. W.

Heber, J.

R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
[CrossRef]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Hong, C. S.

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kaiser, N.

R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
[CrossRef]

Kong, J. A.

J. A. Kong, B. L. Wu, Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33,136-139 (2002).
[CrossRef]

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427-7444 (1996).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Mandatori, A.

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427-7444 (1996).
[CrossRef]

Mattiucci, N.

Melville, D. O.

Moroz, A.

A. Tip, A. Moroz and J. M. Combes, "Band structure of absorptive photonic crystals," J. Phys. A: Math. Gen. 33, 6223-6252 (2000).
[CrossRef]

Notomi, M.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Scalora, M.

Schultz, S.

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

Shelby, R. A.

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

Shin, H.

H. Shin and S. H. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Sibilia, C.

Smith, D.

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

Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Tayeb, G.

Thielsch, R.

R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
[CrossRef]

Tip, A.

A. Tip, A. Moroz and J. M. Combes, "Band structure of absorptive photonic crystals," J. Phys. A: Math. Gen. 33, 6223-6252 (2000).
[CrossRef]

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
[CrossRef]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

Wu, B. L.

J. A. Kong, B. L. Wu, Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33,136-139 (2002).
[CrossRef]

Yang, H.

P. A. Belov and H. Yang, "Subwavelength imaging at optical frequencies using a transmission device formed by a period layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73,113110 (2006).
[CrossRef]

Yariv, A.

Yeh, P.

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Zhang, Y.

J. A. Kong, B. L. Wu, Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33,136-139 (2002).
[CrossRef]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

H. Shin and S. H. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near field," J. Mod. Opt. 50, 1419-1430 (2003).

J. Opt. Soc. Am. (1)

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

J. Phys. A: Math. Gen. (1)

A. Tip, A. Moroz and J. M. Combes, "Band structure of absorptive photonic crystals," J. Phys. A: Math. Gen. 33, 6223-6252 (2000).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. A. Kong, B. L. Wu, Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33,136-139 (2002).
[CrossRef]

Nature (London) (1)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (4)

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696 (2000).
[CrossRef]

P. A. Belov and H. Yang, "Subwavelength imaging at optical frequencies using a transmission device formed by a period layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73,113110 (2006).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, "Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation," Phys. Rev. B 55, 7427-7444 (1996).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (4)

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-Diffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
[CrossRef]

Thin. Solid. Films (1)

R. Thielsch, A. Gatto, J. Heber, N. Kaiser, "A comparative study of the UV optical and structural properties of SiO2, Al2O3, and HfO2 single layers deposited by reactive evaporation, ion-assisted deposition and plasma ion-assisted deposition," Thin. Solid. Films 410, 86-93 (2002).
[CrossRef]

Other (2)

J.-M. Combes B. Gralak and A. Tip, "Spectral properties of absorptive photonic crystals,' in Contemporary Mathematics 339, Ed. P. Kuchment, 1-13 (2003).
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

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Figures (8)

Fig. 1.
Fig. 1.

1DMD metamaterial with a symmetric arrangement. The dashed line shows the unit cell.

Fig. 2.
Fig. 2.

(a). Band structure of 1DMD metamaterial. The purple zones represent the pass bands. The green dashed line represents the light line in free space. The black solid line indicates the frequency at which neff = -1 . (b) EFCs for the second band, the labels indicate the frequencies in unit of 2πc/d . Black curve: EFC of free space for ω = 0.375×2πc /d .

Fig. 3.
Fig. 3.

Time-averaged power density distribution for negative refraction of a Gaussian beam by a 5-periods stack (H polarization). (a) incident angle 30° (b) incident angle 45°. The arrow line in the map shows the locus of the maximum incident, refracted and transmitted fields. We use arbitrary units for the power density in all the maps.

Fig. 4.
Fig. 4.

(a). The red dashed curve is the real component of the Bloch vector of 1DMD stack with losses. The black and blue curves are the same as Fig.2 (b), i.e. for lossless materials. The dot line illustrates the conservation of the parallel component of the wave vector. (b) Imaginary component of the Bloch vector. The red dashed curve represents the case with losses and the black case with lossless materials.

Fig. 5.
Fig. 5.

Identical to Fig. 3(b) but with losses in the metallic and dielectric layers.

Fig. 6.
Fig. 6.

Identical to Fig. 4, but for the silver/GaP metamaterial.

Fig. 7.
Fig. 7.

Time-averaged power density distribution of negative refraction with the 4-periods silver/Gap metamaterial without or with losses as the angle of incidence is 45°.

Fig. 8.
Fig. 8.

Transmittance of silver/HfO2 and silver/GaP metamaterials. The solid curves are for 5-periods silver/HfO2 metamaterial, the dashed curves are for 4-periods silver/GaP metamaterial. The black two are the results without loss, the red are with losses.

Equations (3)

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cos ( K z d ) = cos ( α 1 d 1 ) cos ( α 2 d 2 ) α 1 2 ε 2 2 + α 2 2 ε 1 2 2 α 1 α 2 ε 1 ε 2 sin ( α 1 d 1 ) sin ( α 2 d 2 )
H iy = d k x exp [ i ( k x x + k iz z ) ] ϕ ( k x )
ϕ ( k x ) = g 2 π exp [ g 2 ( k x k ix ) 2 4 ]

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