Abstract

We present a computational approach, allowing for a self-consistent treatment of a split ring resonator (SRR) array with a gain layer underneath. We apply three different pumping schemes on the gain layer: (1) homogeneously pumped isotropic gain, (2) homogeneously pumped isotropic gain with a shadow cast by the SRR and (3) anisotropic gain pumped in a selected direction only. We show numerically the magnetic losses of the SRR can be compensated by the gain. The difference on loss compensations among the three pumping schemes is analyzed by the electric field distribution. Studies also show the dielectric background of gain does not affect the loss compensation much for the gain only pumped in the direction parallel to the SRR plane.

© 2011 OSA

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  4. V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41–48 (2007).
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  7. F. Capolino, Theory and Phenomena of Metamaterials (CRC Press, Taylor and Francis Group, 2009).
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  9. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
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  10. J. Zhou, Th. Koschny, and C. M. Soukoulis, “An efficient way to reduce losses of left-handed metamaterials,” Opt. Express 16, 11147–11152 (2008).
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  36. Th. Koschny, P. Markoŝ, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
    [CrossRef]
  37. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
    [CrossRef]
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2011 (1)

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).

2010 (8)

C. M. Soukoulis and M. Wegener, “Optical metamaterials–more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

A. N. Lagarkov, V. N. Kisel, and A. K. Sarychev, “Loss and gain in metamaterials,” J. Opt. Soc. Am. B 27, 648–659 (2010).
[CrossRef]

A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

A. Fang, Th. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82, 121102 (2010).
[CrossRef]

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

2009 (4)

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Y. Sivan, S. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17, 24060–24074 (2009).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).
[CrossRef]

D. O. Guney, Th. Koschny, and C. M. Soukoulis, “Reducing ohmic losses in metamaterials by geometric tailoring,” Phys. Rev. B 80, 125129 (2009).
[CrossRef]

2008 (5)

J. Zhou, Th. Koschny, and C. M. Soukoulis, “An efficient way to reduce losses of left-handed metamaterials,” Opt. Express 16, 11147–11152 (2008).
[CrossRef] [PubMed]

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, 376–379 (2008).
[CrossRef] [PubMed]

M. Wegener, J. Luis Garca-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008).
[CrossRef] [PubMed]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[CrossRef]

2007 (4)

A. D. Boardman, Yu. G. Rapoport, N. King, and V. N. Malnev, “Creating stable gain in active metamaterials,” J. Opt. Soc. Am. B 24, A53–A61 (2007).
[CrossRef]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41–48 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[CrossRef] [PubMed]

2006 (5)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. 31, 3022–3024 (2006).
[CrossRef] [PubMed]

T. A. Klar, “Negative-index metamaterials: Going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

2005 (2)

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[CrossRef]

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

2004 (3)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

J. B. Pendry, “Negative refraction,” Contemp. Phys. 45, 191–202 (2004).
[CrossRef]

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

2003 (1)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

2000 (1)

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

1951 (1)

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

Adegoke, J.

Bahoura, M.

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, 376–379 (2008).
[CrossRef] [PubMed]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Boardman, A. D.

Capolino, F.

F. Capolino, Theory and Phenomena of Metamaterials (CRC Press, Taylor and Francis Group, 2009).
[CrossRef]

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Y. Sivan, S. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17, 24060–24074 (2009).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. 31, 3022–3024 (2006).
[CrossRef] [PubMed]

Economou, E. N.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

Fang, A.

A. Fang, Th. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82, 121102 (2010).
[CrossRef]

A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

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, 376–379 (2008).
[CrossRef] [PubMed]

Gibbs, H. M.

Guney, D. O.

D. O. Guney, Th. Koschny, and C. M. Soukoulis, “Reducing ohmic losses in metamaterials by geometric tailoring,” Phys. Rev. B 80, 125129 (2009).
[CrossRef]

Hamm, J. M.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Hendrickson, J.

Hess, O.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).
[CrossRef]

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

Khitrova, G.

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Y. Sivan, S. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17, 24060–24074 (2009).
[CrossRef]

King, N.

Kisel, V. N.

Klar, T. A.

T. A. Klar, “Negative-index metamaterials: Going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

Koschny, Th.

A. Fang, Th. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82, 121102 (2010).
[CrossRef]

A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

D. O. Guney, Th. Koschny, and C. M. Soukoulis, “Reducing ohmic losses in metamaterials by geometric tailoring,” Phys. Rev. B 80, 125129 (2009).
[CrossRef]

J. Zhou, Th. Koschny, and C. M. Soukoulis, “An efficient way to reduce losses of left-handed metamaterials,” Opt. Express 16, 11147–11152 (2008).
[CrossRef] [PubMed]

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

Lagarkov, A. N.

Lawandy, N. M.

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

Linden, S.

Luis Garca-Pomar, J.

Malnev, V. N.

Markos, P.

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

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

Meinzer, N.

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Noginov, M. A.

Olitsky, J. D.

Ou, J. Y.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction,” Contemp. Phys. 45, 191–202 (2004).
[CrossRef]

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

Plum, E.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Pusch, A.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[CrossRef]

Rapoport, Yu. G.

Ritzo, B. A.

Ruther, M.

Sarychev, A. K.

A. N. Lagarkov, V. N. Kisel, and A. K. Sarychev, “Loss and gain in metamaterials,” J. Opt. Soc. Am. B 27, 648–659 (2010).
[CrossRef]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

Schultz, S.

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

Schurig, D.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Siegman, A. E.

A. E. Siegman, Lasers (Hill Valley, 1986), Chaps. 2, 3, 6, and 13.

Sivan, Y.

Small, C. E.

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

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

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

Soukoulis, C. M.

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

A. Fang, Th. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82, 121102 (2010).
[CrossRef]

C. M. Soukoulis and M. Wegener, “Optical metamaterials–more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

D. O. Guney, Th. Koschny, and C. M. Soukoulis, “Reducing ohmic losses in metamaterials by geometric tailoring,” Phys. Rev. B 80, 125129 (2009).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).
[CrossRef]

J. Zhou, Th. Koschny, and C. M. Soukoulis, “An efficient way to reduce losses of left-handed metamaterials,” Opt. Express 16, 11147–11152 (2008).
[CrossRef] [PubMed]

M. Wegener, J. Luis Garca-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[CrossRef] [PubMed]

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

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

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, London, 1995). See Chaps. 3, 6, and 7.

Tanaka, K.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

Tartakovsky, G.

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

Tsakmakidis, K. L.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Uchino, T.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

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, 376–379 (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, 376–379 (2008).
[CrossRef] [PubMed]

Vier, D. C.

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

Wegener, M.

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitsky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Optical metamaterials–more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

M. Wegener, J. Luis Garca-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16, 19785–19798 (2008).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[CrossRef] [PubMed]

Wuestner, S.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Y. Sivan, S. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17, 24060–24074 (2009).
[CrossRef]

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[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, 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, 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, 376–379 (2008).
[CrossRef] [PubMed]

Zheludev, N. I.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).
[CrossRef]

J. Zhou, Th. Koschny, and C. M. Soukoulis, “An efficient way to reduce losses of left-handed metamaterials,” Opt. Express 16, 11147–11152 (2008).
[CrossRef] [PubMed]

Zhu, G.

Adv. Mater. (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85, 5040–5042 (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[CrossRef]

Contemp. Phys. (1)

J. B. Pendry, “Negative refraction,” Contemp. Phys. 45, 191–202 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

T. A. Klar, “Negative-index metamaterials: Going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

J. Opt. (1)

A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (2)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

M. I. Stockman, “Spasers explained,” Nat. Photonics 2, 327–329 (2008).
[CrossRef]

Nature (2)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

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, 376–379 (2008).
[CrossRef] [PubMed]

Nature Photon. (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41–48 (2007).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (8)

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).
[CrossRef]

D. O. Guney, Th. Koschny, and C. M. Soukoulis, “Reducing ohmic losses in metamaterials by geometric tailoring,” Phys. Rev. B 80, 125129 (2009).
[CrossRef]

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).

A. Fang, Th. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82, 121102 (2010).
[CrossRef]

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

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

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

Phys. Rev. Lett. (4)

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold Enhancement of Quantum Dot Luminescence in Plasmonic Metamaterials,” Phys. Rev. Lett. 105, 227403 (2010).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

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

Rep. Prog. Phys. (1)

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449–521 (2005).
[CrossRef]

Science (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Optical metamaterials–more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef] [PubMed]

Other (3)

F. Capolino, Theory and Phenomena of Metamaterials (CRC Press, Taylor and Francis Group, 2009).
[CrossRef]

A. E. Siegman, Lasers (Hill Valley, 1986), Chaps. 2, 3, 6, and 13.

A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, London, 1995). See Chaps. 3, 6, and 7.

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Figures (9)

Fig. 1
Fig. 1

(Color online) (a) One unit cell for the silver-based SRR structure (light blue) with the gain layer underneath. The dielectric constants ε for GaAs (yellow) and gain (red) are 11 and 2, respectively. The whole structure is in vacuum background (light gray). The dimensions are a = 250nm, l = 160nm, h = 80nm, h 1 = 15nm, h 2 = h 3 = 10nm, h 4 = 45nm, hs = 25nm, w = 40nm and d = 20nm. (b) same as (a) except the gain is embedded in the SRR gap with ε = 1 and the gain layer in (a) is replaced by a dielectric layer (ε = 2) (blue).

Fig. 2
Fig. 2

(Color online) The retrieved results for the real and imaginary parts of the effective permeability μ, without and with gain, for two different gain configurations. (a) the gain is underneath the SRR as shown in Fig. 1(a). The pumping rate is Γpump = 1.0 × 109 s−1. (b) the gain is in the SRR gap as shown in Fig. 1(b). The pumping rate is Γpump = 7.0×108 s−1.

Fig. 3
Fig. 3

(Color online) The real (solid) and imaginary (dashed) parts of I/(ηω 2 E) as a function of frequency for different pumping rates. (a) For the structure with a gain layer below the SRR, shown in Fig. 1(a). (b) For the structure with the gain in the SRR gap as shown in Fig. 1(b). Notice that the resonance is getting stronger and narrower as the pumping rate increases.

Fig. 4
Fig. 4

(Color online) (a) Schematic of the excitation of the magnetic resonance by the incident electric field E parallel to the gap bearing side of the SRR. A circular current appears due to the different configuration of surface charges on both sides of the SRR. (b) The retrieved results for the real (solid) and imaginary (dashed) parts of the effective permittivity ε, with and without gain, for the normal incidence in Fig. 1(a). For the case with gain, the pumping rate Γpump = 1.0 × 109 s−1.

Fig. 5
Fig. 5

Top view of the gain layer in Fig. 1(a) when a shadow (blue) is cast by the SRR structure. The gain does not exist in the shadow, while in other area (red) it is homogeneously pumped.

Fig. 6
Fig. 6

(Color online) The real (solid) and imaginary (dashed) parts of I/(ηω 2 E) as a function of frequency for different pumping rates. (a) For the structure with a shadow on the gain layer cast by the SRR. (b) For the structure where the gain is pumped in y direction only.

Fig. 7
Fig. 7

(Color online) The electric field amplitude distribution at the resonance frequency in the cross-section of the gain layer (z = 20nm from the bottom of the structure) for different components: (a) Ex , (b) Ey and (c) Ez . The area enclosed by the white line is the projection of the SRR on the gain layer. The electric fields are calculated without gain.

Fig. 8
Fig. 8

(Color online) The imaginary parts of I/(ηω 2 E) as a function of frequency for different background dielectric constants of the gain material, which is only pumped in y direction. For the case with gain, the pumping rate is Γpump = 1.5 × 109 s−1. Note the resonance enhancements by the gain are almost the same.

Fig. 9
Fig. 9

(Color online) The electric field amplitude distributions for different background dielectric constants of the gain material (εg = 2, 5 and 11) at their corresponding resonance frequencies, in a yz plane crossing the middle of the gap bearing side of the SRR. (a) Ey and (b) Ez . The area enclosed by the dashed green line indicates the position of the gain layer. The electric fields are calculated without gain.

Equations (7)

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

2 P ( t ) t 2 + Γ a P ( t ) t + ω a 2 P ( t ) = σ a Δ N ( t ) E ( t ) ,
N 3 t = Γ pump N 0 N 3 τ 32 ,
N 2 t = N 3 τ 32 + 1 h ¯ ω a E P t N 2 τ 21 ,
N 1 t = N 2 τ 21 1 h ¯ ω a E P t N 1 τ 10 ,
N 0 t = N 1 τ 10 Γ pump N 0 ,
L dI dt + Idt C + IR = ε emf ,
I η ω 2 E = 1 ω 2 ω 0 2 + i γ ω ,

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