Abstract

We present evidence of strong coupling between the gain material and the metallic metamaterials. It is of vital importance to understand the mechanism of the coupling of metamaterials with the gain medium. Using a four-level gain system, the numerical pump-probe experiments are performed in several configurations (split–ring resonators (SRRs), inverse SRRs and fishnets) of metamaterials, demonstrating reduction of the resonator damping in all cases and hence the possibility for loss compensation. We find that the differential transmittance ΔT/T can be negative in different SRR configurations, such as SRRs on the top of the gain substrate, gain in the SRR gap and gain covering the SRR structure, while in the fishnet metamaterial with gain ΔT/T is positive.

© 2014 Optical Society of America

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References

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  1. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
    [Crossref] [PubMed]
  2. C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials-More bulky and less lossy,” Science 330(6011), 1633–1634 (2010).C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523 (2011).
    [Crossref] [PubMed]
  3. Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
    [Crossref] [PubMed]
  4. A. Fang, T. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82(12), 121102 (2010).
    [Crossref]
  5. 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(12), 127401 (2010).
    [Crossref] [PubMed]
  6. O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
    [Crossref] [PubMed]
  7. A. Fang, Z. Huang, Th. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
    [Crossref] [PubMed]
  8. Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. 108(18), 187402 (2012).
    [Crossref] [PubMed]
  9. X. L. Zhong and Z. Y. Li, “All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity,” Phys. Rev. B 88(8), 085101 (2013).
    [Crossref]
  10. 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(7307), 735–738 (2010).
    [Crossref] [PubMed]
  11. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
    [Crossref] [PubMed]
  12. 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(22), 227403 (2010).
    [Crossref] [PubMed]
  13. N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
    [Crossref] [PubMed]
  14. N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
    [Crossref]
  15. 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(2), 027402 (2003).
    [Crossref] [PubMed]
  16. M. I. Stockman, “Spasers explained,” Nat. Photonics 2(6), 327–329 (2008).
    [Crossref]
  17. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
    [Crossref] [PubMed]
  18. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
    [Crossref] [PubMed]
  19. A. E. Siegman, Lasers (University Science, Sausalito, CA, 1986), Chaps. 2, 3, 6, and 13.
  20. The pumping rate is equivalent to a pump intensity. The pump power density is equal toℏωa PgN0, and the pump intensity Ip = (pump power)/(surface area) = ℏωa PgN0 (volume)/(surface area) = ℏωa PgN0d, and d is the thickness of the gain layer. If we use the numbers of our simulations, Pg = 3 × 109 s−1, N0 = 5 × 1023 m−3, ωa = 2π × 175 THz, and d = 20 nm, then Ip = 3.5 W/mm2.
  21. A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, London, 1995), Chaps. 3, 6, and 7.
  22. A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
    [Crossref]

2013 (1)

X. L. Zhong and Z. Y. Li, “All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity,” Phys. Rev. B 88(8), 085101 (2013).
[Crossref]

2012 (2)

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. 108(18), 187402 (2012).
[Crossref] [PubMed]

2011 (3)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

A. Fang, Z. Huang, Th. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[Crossref] [PubMed]

2010 (7)

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[Crossref]

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(22), 227403 (2010).
[Crossref] [PubMed]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

A. Fang, T. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82(12), 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(12), 127401 (2010).
[Crossref] [PubMed]

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials-More bulky and less lossy,” Science 330(6011), 1633–1634 (2010).C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523 (2011).
[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(7307), 735–738 (2010).
[Crossref] [PubMed]

2009 (3)

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

2008 (1)

M. I. Stockman, “Spasers explained,” Nat. Photonics 2(6), 327–329 (2008).
[Crossref]

2007 (1)

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

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(2), 027402 (2003).
[Crossref] [PubMed]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[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(2), 027402 (2003).
[Crossref] [PubMed]

Busch, K.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[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(7307), 735–738 (2010).
[Crossref] [PubMed]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[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(7307), 735–738 (2010).
[Crossref] [PubMed]

Fang, A.

A. Fang, Z. Huang, Th. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[Crossref] [PubMed]

A. Fang, T. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82(12), 121102 (2010).
[Crossref]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[Crossref]

Fedotov, V. A.

Gibbs, H. M.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Hamm, J. M.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[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(12), 127401 (2010).
[Crossref] [PubMed]

Hendrickson, J.

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Hess, O.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[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(12), 127401 (2010).
[Crossref] [PubMed]

Huang, Z.

Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. 108(18), 187402 (2012).
[Crossref] [PubMed]

A. Fang, Z. Huang, Th. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[Crossref] [PubMed]

Khitrova, G.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

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(7307), 735–738 (2010).
[Crossref] [PubMed]

König, M.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

Koschny, T.

Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. 108(18), 187402 (2012).
[Crossref] [PubMed]

A. Fang, T. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82(12), 121102 (2010).
[Crossref]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[Crossref]

Koschny, Th.

Kuo, P.

Li, Z. Y.

X. L. Zhong and Z. Y. Li, “All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity,” Phys. Rev. B 88(8), 085101 (2013).
[Crossref]

Linden, S.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

Liu, Y.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

Ma, R.-M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Maier, S. A.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Meinzer, N.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

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(7307), 735–738 (2010).
[Crossref] [PubMed]

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Olitzky, 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(22), 227403 (2010).
[Crossref] [PubMed]

Oulton, R. F.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Pendry, J. B.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[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(22), 227403 (2010).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
[Crossref] [PubMed]

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(12), 127401 (2010).
[Crossref] [PubMed]

Ruther, M.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

Shalaev, V. M.

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(7307), 735–738 (2010).
[Crossref] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Soukoulis, C. M.

Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. 108(18), 187402 (2012).
[Crossref] [PubMed]

A. Fang, Z. Huang, Th. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[Crossref] [PubMed]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials-More bulky and less lossy,” Science 330(6011), 1633–1634 (2010).C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523 (2011).
[Crossref] [PubMed]

A. Fang, T. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82(12), 121102 (2010).
[Crossref]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[Crossref]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

Stockman, M. I.

M. I. Stockman, “Spasers explained,” Nat. Photonics 2(6), 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(2), 027402 (2003).
[Crossref] [PubMed]

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Suteewong, T.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

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(22), 227403 (2010).
[Crossref] [PubMed]

Tsai, D. P.

Tsakmakidis, K. L.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[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(12), 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(22), 227403 (2010).
[Crossref] [PubMed]

Wegener, M.

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials-More bulky and less lossy,” Science 330(6011), 1633–1634 (2010).C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523 (2011).
[Crossref] [PubMed]

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010).
[Crossref] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[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(12), 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(7307), 735–738 (2010).
[Crossref] [PubMed]

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(7307), 735–738 (2010).
[Crossref] [PubMed]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

Zhang, X.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[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(22), 227403 (2010).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
[Crossref] [PubMed]

Zhong, X. L.

X. L. Zhong and Z. Y. Li, “All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity,” Phys. Rev. B 88(8), 085101 (2013).
[Crossref]

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

N. Meinzer, M. König, M. Ruther, S. Linden, G. Khitrova, H. M. Gibbs, K. Busch, and M. Wegener, “Distance-dependence of the coupling between split-ring resonators and single-quantum-well gain,” Appl. Phys. Lett. 99(11), 111104 (2011).
[Crossref]

Chem. Soc. Rev. (1)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

J. Opt. (1)

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12(2), 024013 (2010).
[Crossref]

Nat. Mater. (1)

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

M. I. Stockman, “Spasers explained,” Nat. Photonics 2(6), 327–329 (2008).
[Crossref]

Nature (3)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[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(7307), 735–738 (2010).
[Crossref] [PubMed]

Opt. Express (3)

Phys. Rev. B (2)

X. L. Zhong and Z. Y. Li, “All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity,” Phys. Rev. B 88(8), 085101 (2013).
[Crossref]

A. Fang, T. Koschny, and C. M. Soukoulis, “Self-consistent calculations of loss-compensated fishnet metamaterials,” Phys. Rev. B 82(12), 121102 (2010).
[Crossref]

Phys. Rev. Lett. (4)

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(12), 127401 (2010).
[Crossref] [PubMed]

Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. 108(18), 187402 (2012).
[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(22), 227403 (2010).
[Crossref] [PubMed]

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(2), 027402 (2003).
[Crossref] [PubMed]

Science (2)

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

C. M. Soukoulis and M. Wegener, “Materials science. Optical metamaterials-More bulky and less lossy,” Science 330(6011), 1633–1634 (2010).C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523 (2011).
[Crossref] [PubMed]

Other (3)

A. E. Siegman, Lasers (University Science, Sausalito, CA, 1986), Chaps. 2, 3, 6, and 13.

The pumping rate is equivalent to a pump intensity. The pump power density is equal toℏωa PgN0, and the pump intensity Ip = (pump power)/(surface area) = ℏωa PgN0 (volume)/(surface area) = ℏωa PgN0d, and d is the thickness of the gain layer. If we use the numbers of our simulations, Pg = 3 × 109 s−1, N0 = 5 × 1023 m−3, ωa = 2π × 175 THz, and d = 20 nm, then Ip = 3.5 W/mm2.

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

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Figures (12)

Fig. 1
Fig. 1

Schematic illustration of pump-probe experiments.

Fig. 2
Fig. 2

(a) Schematic of the unit cell for the silver-based SRRs structure (yellow) with the electric field polarization parallel to the gap. The dielectric constants ε for gain (red) and GaAs (light blue) are 9.0 and 11.0, respectively. (b) Calculated spectra for transmittance T (black), reflectance R (red), and absorptance A (blue) for the structure shown in Fig. 2(a). The inset shows the profile of the probe pulse with a center frequency of 175 THz (FWHM = 2 THz).

Fig. 3
Fig. 3

The structure and the corresponding parameters. The gain material, which is denoted by the areas with ε = 1 is located (a) in the gap, and (b) above the structure. In these configurations, we have changed the permittivity of the gain material in order to fix the resonance frequency at 175 THz, and here we only consider the perpendicular incidence case.

Fig. 4
Fig. 4

Schematic of the numerical pump-probe experiments [12,13 ] for the case on resonance. The results correspond to the geometry of Fig. 2(a) with ε = 9, accounting for quantum wells as the gain medium, as in [12]. From the top to the bottom, each row corresponds to the pump pulse, population inversion, incident signal (with time delays 5, 45, and 135 ps), transmitted signal, and differential transmittance ΔT/T. It should be mentioned here that the incident frequency of the probe pulse is 175 THz with a FWHM of 2 THz and is equal to the SRR resonance frequency.

Fig. 5
Fig. 5

Results of spectrum difference for three different designs with pumping rate 3 × 109 1/s (solid black, multiplied by 6) and 29 × 109 1/s (dotted black). (a) gain underneath, (b) gain in gap, and (c) gain above the structure. The shaded area corresponds to the spectral range examined in Fig. 6.

Fig. 6
Fig. 6

The transmittance T (without pump, solid line) and the on-resonance differential transmittance ΔT/T results (vector arrow) for the SRRs with (a) gain in gap and (b) gain above the structure. The direction and the length of the arrow stand for the sign and the amplitude of ΔT/T, respectively. The squares from (P)1 to (P)6 correspond to the frequency of probe pulse ranging from 169 to 179 THz with uniform step of 2 THz.

Fig. 7
Fig. 7

(a) Schematic of a plasmonic metamaterial functionalized with gain material (εg = 2.2). Feature sizes: unit cell D = 545 nm, horizontal slit a = 470 nm, unit length h = 230 nm, hs = 180 nm, top vertical slit and gap t = g = 170 nm, and slit width w = 65 nm. Also, there is an additional 400 nm glass substrate on the top of the structure with εsub = 2.56. The metamaterial is made of gold with its permittivity modeled by a Drude response. (b) Calculated spectra for transmittance T (black), reflectance R (red), and absorptance A (blue) for the structure shown in Fig. 7(a). The inset shows the profile of the probe pulse with a center frequency of 214 THz (FWHM = 3 THz).

Fig. 8
Fig. 8

(a) Calculated time domain results of ΔT/T for the inverse SRR structure with pumping rate 3 × 109 1/s. (i) to (vii) correspond to the probe frequency ranging from 205 THz to 223 THz with uniform step of 3 THz. (b) Results of spectrum difference with pumping rate 1 × 109 1/s (solid black) and 4 × 109 1/s (dotted black) for pump-probe delay of 0.6ps. The small ripples around 300THz are numerical artifacts due to the limited bandwidth of the probe pulse (54THz). The shaded area corresponds to the spectral range examined in Fig. 9.

Fig. 9
Fig. 9

The transmittance T (without pump, solid line) and the on-resonance differential transmittance ΔT/T results (vector arrow) for the inverse SRR structure with pumping rate 1 × 109 1/s. The direction and the length of the arrow stand for the sign and the amplitude of ΔT/T, respectively. The squares from (P)1 to (P)7 correspond to the frequency of probe pulse ranging from 205 to 223 THz with uniform step of 3 THz.

Fig. 10
Fig. 10

Unit cell (px = py = 280 nm) of the perforated fishnet structure with gain embedded in-between two metal (silver) layers. The geometric parameters are wx = 75 nm, wy = 115 nm, h = 170 nm, hm = hs = 50 nm, hd = 10 nm and hg = 20 nm. The thicknesses of the silver (yellow) and gain (magenta) layer are hm and hg , respectively. The dielectric layer (blue) and the gain have a refractive index n = 1.65. (b) Calculated spectra for transmittance T (black), reflectance R (red), and absorptance A (blue) for the structure shown in Fig. 10(a). The inset shows the profile of the probe pulse with a center frequency of 495 THz (FWHM = 2 THz).

Fig. 11
Fig. 11

Frequency domain numerical pump-probe experiments results for the fishnet structure. Simulations results for the differences in transmittance (ΔT), reflectance (ΔR), and absorptance (ΔA) versus frequency with pumping rate 1.7 × 109 1/s. The shaded area corresponds to the spectral range examined in Fig. 12.

Fig. 12
Fig. 12

The transmittance T (without pump, solid line) and the on-resonance differential transmittance ΔT/T results (vector arrow) for the fishnet structure with pumping rate 1.7 × 109 1/s. The direction and the length of the arrow stand for the sign and the amplitude of ΔT/T, respectively. The squares from (P)1 to (P)3 correspond to the frequency of probe pulse ranging from 493 to 497 THz with uniform step of 2 THz.

Equations (5)

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2 P ( r , t ) t 2 + Γ a P ( r , t ) t + ω a 2 P ( r , t ) = σ a Δ N ( r , t ) E ( r , t )
N 3 ( r , t ) t = P g ( t ) N 0 ( r , t ) N 3 ( r , t ) τ 32
N 2 ( r , t ) t = N 3 ( r , t ) τ 32 + 1 ω a E ( r , t ) P a ( r , t ) t N 2 ( r , t ) τ 21
N 1 ( r , t ) t = N 2 ( r , t ) τ 21 1 ω a E ( r , t ) P a ( r , t ) t N 1 ( r , t ) τ 10
N 0 ( r , t ) t = N 1 ( r , t ) τ 10 P g ( t ) N 0 ( r , t )

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