Abstract

We study arrays of silver split-ring resonators operating at around 1.5-µm wavelength coupled to an MBE-grown single 12.7-nm thin InGaAs quantum well separated only 4.8 nm from the wafer surface. The samples are held at liquid-helium temperature and are pumped by intense femtosecond optical pulses at 0.81-µm center wavelength in a pump-probe geometry. We observe much larger relative transmittance changes (up to about 8%) on the split-ring-resonator arrays as compared to the bare quantum well (not more than 1-2%). We also observe a much more rapid temporal decay component of the differential transmittance signal of 15 ps for the case of split-ring resonators coupled to the quantum well compared to the case of the bare quantum well, where we find about 0.7 ns. These observations are ascribed to the evanescent coupling of the split-ring resonators to the quantum-well gain. All experimental results are compared with a recently introduced analytical toy model that accounts for this evanescent coupling, leading to excellent overall qualitative agreement.

© 2010 OSA

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  1. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  2. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
    [CrossRef] [PubMed]
  3. K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
    [CrossRef]
  4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  5. 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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  6. 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]
  7. T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
    [CrossRef]
  8. J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15(5), 2622–2653 (2007).
    [CrossRef] [PubMed]
  9. A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: Sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
    [CrossRef]
  10. M. I. Stockman, “Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality,” Phys. Rev. Lett. 98(177404), 1–4 (2007).
    [CrossRef]
  11. P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
    [CrossRef] [PubMed]
  12. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
    [CrossRef]
  13. J. A. Gordon and R. W. Ziolkowski, “CNP optical metamaterials,” Opt. Express 16(9), 6692–6716 (2008).
    [CrossRef] [PubMed]
  14. M. Wegener, J. L. García-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(24), 19785–19798 (2008).
    [CrossRef] [PubMed]
  15. A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(241104), 1–4 (2009).
    [CrossRef]
  16. 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]
  17. 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]
  18. K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multi-fold Enhancement of Quantum Dot Luminescence in a Plasmonic Metamaterial”, arXiv:1008.4770 (2010).

2010

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

2008

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

J. A. Gordon and R. W. Ziolkowski, “CNP optical metamaterials,” Opt. Express 16(9), 6692–6716 (2008).
[CrossRef] [PubMed]

M. Wegener, J. L. García-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(24), 19785–19798 (2008).
[CrossRef] [PubMed]

2007

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

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

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15(5), 2622–2653 (2007).
[CrossRef] [PubMed]

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: Sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

M. I. Stockman, “Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality,” Phys. Rev. Lett. 98(177404), 1–4 (2007).
[CrossRef]

2006

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

2003

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]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[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.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[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]

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(5801), 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(7307), 735–738 (2010).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

Fang, A.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(241104), 1–4 (2009).
[CrossRef]

Fedotov, V. A.

García-Pomar, J. L.

Gordon, J. A.

Govyadinov, A. A.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: Sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

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(5801), 977–980 (2006).
[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]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

Kinsler, P.

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

Klar, T. A.

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

Koschny, Th.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(241104), 1–4 (2009).
[CrossRef]

Kuo, P.

Linden, S.

M. Wegener, J. L. García-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(24), 19785–19798 (2008).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

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

McCall, M. W.

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

Meinzer, N.

Mingaleev, S. F.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

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(5801), 977–980 (2006).
[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.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: Sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Pendry, J. B.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Plum, E.

Podolskiy, V. A.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: Sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Ruther, M.

Schurig, D.

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(5801), 977–980 (2006).
[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]

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

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(241104), 1–4 (2009).
[CrossRef]

M. Wegener, J. L. García-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(24), 19785–19798 (2008).
[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]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, “Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality,” Phys. Rev. Lett. 98(177404), 1–4 (2007).
[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]

Tkeshelashvili, L.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

Tsai, D. P.

von Freymann, G.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

Wegener, M.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(241104), 1–4 (2009).
[CrossRef]

M. Wegener, J. L. García-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(24), 19785–19798 (2008).
[CrossRef] [PubMed]

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

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

Zheludev, N. I.

Ziolkowski, R. W.

Appl. Phys. Lett.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: Sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-Index Metamaterials: Going Optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

Nat. Photonics

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

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Nature

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

Phys. Rep.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444(3-6), 101–202 (2007).
[CrossRef]

Phys. Rev. B

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(241104), 1–4 (2009).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[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]

M. I. Stockman, “Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality,” Phys. Rev. Lett. 98(177404), 1–4 (2007).
[CrossRef]

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

Science

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(5801), 977–980 (2006).
[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]

Other

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multi-fold Enhancement of Quantum Dot Luminescence in a Plasmonic Metamaterial”, arXiv:1008.4770 (2010).

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Figures (5)

Fig. 1
Fig. 1

(a) Layer sequence (not to scale) and composition of the semiconductor crystal structure grown by molecular-beam epitaxy (MBE), lattice-matched to the InP substrate. After MBE growth, arrays of 30-nm thin Ag split-ring resonators (SRR) are fabricated on top of this wafer using a standard electron-beam-lithography process. (b) Low-temperature quantum well photoluminescence (PL) spectra for increasing power, P, of the exciting femtosecond Ti:sapphire laser at 0.81-µm center wavelength as indicated. In the pump-probe experiments depicted in Figs. 2-4, we have used the identical laser with P = 200 mW under identical focusing conditions. (c) Electron micrograph of SRR array “D”. (d) Optical normal-incidence linear intensity transmittance spectra of some of the SRR arrays used in this work (horizontal linear incident polarization of light) taken at room-temperature. The gray area corresponds to the low-temperature PL spectrum of the bare QW for an excitation power of P = 200 mW.

Fig. 2
Fig. 2

Femtosecond pump-probe experiments for an array of SRR that is nearly resonant with the QW gain (sample “D” in Figs. 1 and 4). The left column corresponds to horizontal probe polarization with respect to the SRR, the right column to vertical probe polarization. The differential transmittance signals for the case of QW and SRR are shown by the red curves, the case of QW alone by the blue curves. Zero differential signal, i.e., ΔT/T = 0, is indicated by the dashed horizontal lines. One tick on the vertical axis corresponds to ΔT/T = 1%. The curves are unequally vertically displaced for clarity. The OPO probe wavelength increases from top to bottom as indicated on the right-hand side. Sample temperature is 5-10 K, the 150-fs pump pulses are centered at around 0.81-µm wavelength.

Fig. 3
Fig. 3

Same as Fig. 2, but for an off-resonant array of split-ring resonators (sample “A” in Figs. 1 and 4).

Fig. 4
Fig. 4

Summary of femtosecond pump-probe experiments (like exemplified in Figs. 2 and 3) for various SRR arrays. The OPO probe polarization is horizontal. For reference, the measured linear optical spectra of the corresponding SRR arrays are shown in Fig. 1(d). The color coding is the same as in Figs. 2 and 3. Spectra of the differential transmittance signal are shown versus OPO probe wavelength for a fixed time delay of Δt = + 5 ps. Dots connected by dashed straight lines correspond to the experiment, the solid curves are derived from the toy model (parameters are given in the main text). The plasmonic resonance frequencies of the toy model quoted in Table 1 are illustrated by the black arrow in sub-panels B to F; for the other panels the resonances lie outside the wavelength range shown here.

Fig. 5
Fig. 5

Illustration of the loss = gain condition for the case that the quantum-well and the split-ring-resonator resonances are degenerate [see Eq. (1)]. Complete loss compensation is possible within the white triangle, but is not possible in the gray triangle. The two triangles are separated by the straight line with γ = V [see Eq. (1)]. The red dot inside the gray triangle corresponds to the experimental conditions of sample “D” and is obtained from exactly the same model parameters that we have used to fit to these experimental results (compare Fig. 4).

Tables (1)

Tables Icon

Table 1 Model parameters Ω pl and L that are individually adjusted for samples “A” to “I” (compare Fig. 4).

Equations (3)

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

f = 1 2 ( 1 + γ pl γ 2LS V pl V 2LS ) = : 1 2 ( 1 + γ 2 V 2 ) [ 0 , 1 ] .
V 2LS = 1 d 2LS L N pl d pl ,
V pl = 1 d pl L N 2LS d 2LS .

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