Abstract

We present a very efficient recursive method to calculate the effective optical response of metamaterials made up of arbitrarily shaped inclusions arranged in periodic 3D arrays. We apply it to dielectric particles embedded in a metal matrix with a lattice constant much smaller than the wavelength of the incident field, so that we may neglect retardation and factor the geometrical properties from the properties of the materials. If the conducting phase is continuous the low frequency behavior is metallic, and if the conducting paths are thin, the high frequency behavior is dielectric. Thus, extraordinary-transparency bands may develop at intermediate frequencies, whose properties may be tuned by geometrical manipulation.

© 2010 OSA

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  3. L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express 17, 3903 (2009).
  4. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
  5. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystal: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
  6. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).
  7. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 2668021 (2007).
  8. W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).
  9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).
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  19. S. Darmanyan and A. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
  20. J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).
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  28. R. Haydock, “The recursive solution of the Schrödinger equation,” Solid State Phys. 35, 215 (1980).
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  38. J. B. Keller, “Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders,” J. Appl. Phys. 34, 991 (1963).
  39. J. B. Keller, “A theorem on the conductivity of a composite medium,” J. Math. Phys. 5, 548 (1964).
  40. J. Nevard and J. B. Keller, “Reciprocal relations for effective conductivities of anisotropic media,” J. Math. Phys. 26, 2761 (1985).
  41. R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732 (1975).
  42. P. Johnson and R. Christy, “Optical constant of noble metals,” Phys. Rev. B 6, 4370 (1972).
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2010 (1)

E. Cortés, W. L. Mochán, B. S. Mendoza, and G. P. Ortiz, “Optical properties of nano-structured metamaterials,” Phys. Status Solidi B 247, 2102 (2010).

2009 (3)

G. P. Ortiz, B. E. Martínez-Zérega, B. S. Mendoza, and W. Mochán, “Effective dielectric response of metamaterials,” Phys. Rev. B 79, 245132 (2009).

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72, 0644011 (2009).

L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express 17, 3903 (2009).

2008 (1)

2007 (6)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 2668021 (2007).

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

B. Hou, H. Wen, Y. Leng, and W. Wen, “Enhanced transmission of electromagnetic waves through metamaterials,” Appl. Phys. A 87, 217 (2007).

Q.-H. Park, J. H. Kang, J. W. Lee, and D. S. Kim, “Effective medium description of plasmonic metamaterials,” Opt. Express 15, 6994 (2007).

2006 (1)

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystal: theory and simulations,” Phys. Rev. B 74, 075103 (2006).

2005 (1)

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 2439051 (2005).

2004 (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004).

2003 (1)

S. Darmanyan and A. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

2002 (1)

Q. Cao and P. Lalanne, “Negative role of surface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 0574031 (2002).

2001 (1)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

2000 (2)

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

E. Popov, M. Neviére, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

1999 (2)

M. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75, 606 (1999).

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).

1998 (1)

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

1994 (1)

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795 (1994).

1993 (1)

1985 (3)

W. L. Mochán and R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. i. general formalism,” Phys. Rev. B 32, 4984 (1985).

J. Nevard and J. B. Keller, “Reciprocal relations for effective conductivities of anisotropic media,” J. Math. Phys. 26, 2761 (1985).

W. L. Mochán and R. G. Barrera, “Intrinsic surface-induced optical anisotropies of cubic crystals: local-field effect,” Phys. Rev. Lett. 55, 1192 (1985).

1982 (1)

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to difraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907 (1982).

1980 (1)

R. Haydock, “The recursive solution of the Schrödinger equation,” Solid State Phys. 35, 215 (1980).

1975 (1)

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732 (1975).

1972 (1)

P. Johnson and R. Christy, “Optical constant of noble metals,” Phys. Rev. B 6, 4370 (1972).

1964 (1)

J. B. Keller, “A theorem on the conductivity of a composite medium,” J. Math. Phys. 5, 548 (1964).

1963 (2)

J. B. Keller, “Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders,” J. Appl. Phys. 34, 991 (1963).

N. Wiser, “Dielectric constant with local field effects included,” Phys. Rev. 129, 62 (1963).

1962 (1)

S. L. Alder, “Quantum theory of the dielectric constant in real solids,” Phys. Rev. 126, 413 (1962).

1951 (1)

M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 1951051 (2002).

1842 (1)

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).

Agrawal, A.

Alder, S. L.

S. L. Alder, “Quantum theory of the dielectric constant in real solids,” Phys. Rev. 126, 413 (1962).

Atkinson, R.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Barrera, R. G.

W. L. Mochán and R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. i. general formalism,” Phys. Rev. B 32, 4984 (1985).

W. L. Mochán and R. G. Barrera, “Intrinsic surface-induced optical anisotropies of cubic crystals: local-field effect,” Phys. Rev. Lett. 55, 1192 (1985).

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), 7th ed.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).

Cao, Q.

Q. Cao and P. Lalanne, “Negative role of surface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 0574031 (2002).

Chan, C. T.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 2439051 (2005).

Chen, L.

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).

Christy, R.

P. Johnson and R. Christy, “Optical constant of noble metals,” Phys. Rev. B 6, 4370 (1972).

Cortés, E.

E. Cortés, W. L. Mochán, B. S. Mendoza, and G. P. Ortiz, “Optical properties of nano-structured metamaterials,” Phys. Status Solidi B 247, 2102 (2010).

Darmanyan, S.

S. Darmanyan and A. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Depine, R.

Dickson, W.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

Ebbesen, T.

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

Engheta, N.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystal: theory and simulations,” Phys. Rev. B 74, 075103 (2006).

Enoch, S.

E. Popov, M. Neviére, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Evans, P.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

Fuchs, R.

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732 (1975).

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

García-Valenzuela, A.

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).

Garcia-Vidal, F. J.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004).

García-Vidal, F.

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

Ghaemi, H.

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

Grupp, D.

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

Haydock, R.

R. Haydock, “The recursive solution of the Schrödinger equation,” Solid State Phys. 35, 215 (1980).

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, New York, 2006).

Hou, B.

B. Hou, H. Wen, Y. Leng, and W. Wen, “Enhanced transmission of electromagnetic waves through metamaterials,” Appl. Phys. A 87, 217 (2007).

Johnson, P.

P. Johnson and R. Christy, “Optical constant of noble metals,” Phys. Rev. B 6, 4370 (1972).

Kang, J. H.

Keller, J. B.

J. Nevard and J. B. Keller, “Reciprocal relations for effective conductivities of anisotropic media,” J. Math. Phys. 26, 2761 (1985).

J. B. Keller, “A theorem on the conductivity of a composite medium,” J. Math. Phys. 5, 548 (1964).

J. B. Keller, “Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders,” J. Appl. Phys. 34, 991 (1963).

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).

Kim, D. S.

Lalanne, P.

Q. Cao and P. Lalanne, “Negative role of surface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 0574031 (2002).

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

Lee, J. W.

Leng, Y.

B. Hou, H. Wen, Y. Leng, and W. Wen, “Enhanced transmission of electromagnetic waves through metamaterials,” Appl. Phys. A 87, 217 (2007).

Lezec, H.

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

Lochbihler, H.

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795 (1994).

H. Lochbihler and R. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32, 3459 (1993).

Martínez-Zérega, B. E.

G. P. Ortiz, B. E. Martínez-Zérega, B. S. Mendoza, and W. Mochán, “Effective dielectric response of metamaterials,” Phys. Rev. B 79, 245132 (2009).

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004).

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

Mendoza, B. S.

E. Cortés, W. L. Mochán, B. S. Mendoza, and G. P. Ortiz, “Optical properties of nano-structured metamaterials,” Phys. Status Solidi B 247, 2102 (2010).

G. P. Ortiz, B. E. Martínez-Zérega, B. S. Mendoza, and W. Mochán, “Effective dielectric response of metamaterials,” Phys. Rev. B 79, 245132 (2009).

Mochán, W.

G. P. Ortiz, B. E. Martínez-Zérega, B. S. Mendoza, and W. Mochán, “Effective dielectric response of metamaterials,” Phys. Rev. B 79, 245132 (2009).

Mochán, W. L.

E. Cortés, W. L. Mochán, B. S. Mendoza, and G. P. Ortiz, “Optical properties of nano-structured metamaterials,” Phys. Status Solidi B 247, 2102 (2010).

W. L. Mochán and R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. i. general formalism,” Phys. Rev. B 32, 4984 (1985).

W. L. Mochán and R. G. Barrera, “Intrinsic surface-induced optical anisotropies of cubic crystals: local-field effect,” Phys. Rev. Lett. 55, 1192 (1985).

Nahata, A.

Nevard, J.

J. Nevard and J. B. Keller, “Reciprocal relations for effective conductivities of anisotropic media,” J. Math. Phys. 26, 2761 (1985).

Neviére, M.

E. Popov, M. Neviére, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Novotny, L.

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 2668021 (2007).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, New York, 2006).

O’Connor, D.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

Ortiz, G. P.

E. Cortés, W. L. Mochán, B. S. Mendoza, and G. P. Ortiz, “Optical properties of nano-structured metamaterials,” Phys. Status Solidi B 247, 2102 (2010).

G. P. Ortiz, B. E. Martínez-Zérega, B. S. Mendoza, and W. Mochán, “Effective dielectric response of metamaterials,” Phys. Rev. B 79, 245132 (2009).

Park, Q.-H.

Pellerin, K.

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

Pendry, J.

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004).

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

Pollard, R.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

Popov, E.

E. Popov, M. Neviére, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Porto, J.

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).

Reinisch, R.

E. Popov, M. Neviére, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Reyes-Coronado, A.

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Salandrino, A.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystal: theory and simulations,” Phys. Rev. B 74, 075103 (2006).

Sanda, P.

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to difraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907 (1982).

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).

Sheng, P.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 2439051 (2005).

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to difraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907 (1982).

Stepleman, R.

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to difraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907 (1982).

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

Treacy, M.

M. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75, 606 (1999).

M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 1951051 (2002).

Vardeny, Z.

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Wang, G. P.

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

Weiner, J.

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72, 0644011 (2009).

Wen, H.

B. Hou, H. Wen, Y. Leng, and W. Wen, “Enhanced transmission of electromagnetic waves through metamaterials,” Appl. Phys. A 87, 217 (2007).

Wen, W.

B. Hou, H. Wen, Y. Leng, and W. Wen, “Enhanced transmission of electromagnetic waves through metamaterials,” Appl. Phys. A 87, 217 (2007).

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 2439051 (2005).

Wiser, N.

N. Wiser, “Dielectric constant with local field effects included,” Phys. Rev. 129, 62 (1963).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), 7th ed.

Wurtz, G.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

Zayats, A.

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

S. Darmanyan and A. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

Zhou, L.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 2439051 (2005).

Appl. Opt. (1)

Appl. Phys. A (1)

B. Hou, H. Wen, Y. Leng, and W. Wen, “Enhanced transmission of electromagnetic waves through metamaterials,” Appl. Phys. A 87, 217 (2007).

Appl. Phys. Lett (1)

D. Grupp, H. Lezec, T. Ebbesen, K. Pellerin, and T. Thio, “Surface plasmon enhanced optical transmission through subwavelength holes,” Appl. Phys. Lett 77, 1569 (2000).

Appl. Phys. Lett. (2)

M. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75, 606 (1999).

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 1111051 (2007).

J. Appl. Phys. (1)

J. B. Keller, “Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders,” J. Appl. Phys. 34, 991 (1963).

J. Math. Phys. (2)

J. B. Keller, “A theorem on the conductivity of a composite medium,” J. Math. Phys. 5, 548 (1964).

J. Nevard and J. B. Keller, “Reciprocal relations for effective conductivities of anisotropic media,” J. Math. Phys. 26, 2761 (1985).

Opt. Express (3)

Phys. Rev. (2)

S. L. Alder, “Quantum theory of the dielectric constant in real solids,” Phys. Rev. 126, 413 (1962).

N. Wiser, “Dielectric constant with local field effects included,” Phys. Rev. 129, 62 (1963).

Phys. Rev. B (13)

W. L. Mochán and R. G. Barrera, “Electromagnetic response of systems with spatial fluctuations. i. general formalism,” Phys. Rev. B 32, 4984 (1985).

R. G. Barrera, A. Reyes-Coronado, and A. García-Valenzuela, “Nonlocal nature of the electrodynamic response of colloidal systems,” Phys. Rev. B 75, 184202 (2007).

S. Darmanyan and A. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

M. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 1951051 (2002).

E. Popov, M. Neviére, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

G. P. Ortiz, B. E. Martínez-Zérega, B. S. Mendoza, and W. Mochán, “Effective dielectric response of metamaterials,” Phys. Rev. B 79, 245132 (2009).

W. Dickson, G. Wurtz, P. Evans, D. O’Connor, R. Atkinson, R. Pollard, and A. Zayats, “Dielectric-loaded plasmonic nanoantenna arrays: A metamaterial with tunable optical properties,” Phys. Rev. B 76, 115411 (2007).

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystal: theory and simulations,” Phys. Rev. B 74, 075103 (2006).

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to difraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907 (1982).

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795 (1994).

H. Ghaemi, T. Thio, D. Grupp, T. Ebbesen, and H. Lezec, “Surface plasmon enhanced optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779 (1998).

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732 (1975).

P. Johnson and R. Christy, “Optical constant of noble metals,” Phys. Rev. B 6, 4370 (1972).

Phys. Rev. Lett. (6)

W. L. Mochán and R. G. Barrera, “Intrinsic surface-induced optical anisotropies of cubic crystals: local-field effect,” Phys. Rev. Lett. 55, 1192 (1985).

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114 (2001).

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, “Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields,” Phys. Rev. Lett. 94, 2439051 (2005).

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 2668021 (2007).

J. Porto, F. García-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with narrow slits,” Phys. Rev. Lett. 83, 2845 (1999).

Q. Cao and P. Lalanne, “Negative role of surface plasmon in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 0574031 (2002).

Phys. Status Solidi B (1)

E. Cortés, W. L. Mochán, B. S. Mendoza, and G. P. Ortiz, “Optical properties of nano-structured metamaterials,” Phys. Status Solidi B 247, 2102 (2010).

Rep. Prog. Phys. (1)

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72, 0644011 (2009).

Science (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847 (2004).

Solid State Phys. (1)

R. Haydock, “The recursive solution of the Schrödinger equation,” Solid State Phys. 35, 215 (1980).

Other (6)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), 7th ed.

K. Glazebrook, J. Brinchmann, J. Cerney, C. DeForest, D. Hunt, T. Jenness, T. Luka, R. Schwebel, and C. Soeller, “The perl data language v.2.4.4,” Available from http://pdl.perl.org .

K. Glazebrook and F. Economou, “Pdl: The perl data language,” Dr. Dobb’s Journal (1997). http://www.ddj.com/184410442 .

That the long-wavelength response ɛM is independent of the direction of q → 0 allows us to use the results of longitudinal calculations to solve optical (i.e., transverse) problems.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, New York, 2006).

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513 (2009).

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Figures (3)

Fig. 1
Fig. 1

(a) Macroscopic dielectric function ɛM for a simple cubic array of spherical inclusions with response ɛb = 4 within a host with ɛa = 1 as a function of filling fraction f calculated with our Haydock’s recursive method (H), with Maxwell-Garnett’s (MG) and with Bruggeman’s formulae (B). (b) ɛM normal to the optical axis of a square array of square prisms with diagonals along the sides of the unit cell as a function of f for the theories H, MG and B in 2D.

Fig. 2
Fig. 2

(a) Normal-incidence reflectance R of a semi-infinite metamaterial and transmittance T of a d = 200 nm film made of a model Drude conductor with low (Γ = 0.01ωp) and high (Γ = 0.1ωp) dissipation parameters with a simple cubic lattice of cubical cavities of filling fraction f = 0.6, as a function of the frequency ω, together with the corresponding transmittance Teff of an homogeneous Drude film with an effective width deff = (1 – f)d. (b) Macroscopic dielectric response of the low dissipation metamaterial. The vertical lines indicate the frequencies at which ɛM ≈ 1.

Fig. 3
Fig. 3

Normal-incidence transmittance Tα for α = x, y polarization vs. frequency ω for 200 nm Au films with faces normal to the z axis with an embedded lattice of dielectric inclusions, normalized to the transmittance Teff of a homogeneous Au film with the same amount of metal. (a) Simple cubic lattice of spheres of radius r = 0.6a with a the lattice parameter with ɛb = 4. (b) Simple orthorhombic lattice of z-oriented cylinders with radius r = 0.53ax, height h = 0.9az and dielectric response ɛb = 2 with lattice parameters ax = az and ay = 1.15ax.

Equations (14)

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

ɛ ( r ) = ɛ a B ( r ) ɛ a b
D G ( q ) = G ɛ GG E G ( q ) ,
E G E G L = G ^ G ^ E G ,
E 0 L = q ^ η 00 1 q ^ D 0 L ,
η GG G ^ . ( ɛ GG G ^ )
ɛ M L 1 q ^ ξ q ^ = q ^ η 00 1 q ^ ,
B GG B G G = ( 1 / Ω ) v d 3 r e i ( G G ) r
η GG 1 = 1 ɛ a b [ u δ GG B GG L L ] 1 = 1 ɛ a b 𝒢 GG ,
GG B GG L L = G ^ ( B GG G ^ ) ,
| n ˜ = ^ | n 1 = b n 1 | n 2 + a n 1 | n 1 + b n | n .
𝒢 n 1 = ( A n n + 1 T | n + 1 𝒢 n + 1 1 ) ,
𝒢 n = ( R n 𝒬 n | 𝒫 n 𝒮 n ) ,
R n = 1 A n n + 1 𝒢 n + 1 1 n + 1 T = 1 A n b n + 1 2 R n + 1 ,
ξ = R 0 ɛ a b = u ɛ a 1 u a 0 b 1 2 u a 1 b 2 2 u a 2 b 3 2 .

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