Abstract

At the plasmon resonance, high Joule losses in a metal nanoparticle of a spaser result in its low Q-factor. Due to the latter, to achieve the spasing regime, in which the number of coherent plasmons exceeds the number of incoherent plasmons, unsustainably high pump rates may be required. We show that under the condition of loss compensation by a spaser driven by an external optical wave, the number of coherent plasmons increases dramatically, and the quantum noise is suppressed. Since the compensation of losses of the driving wave may occur even near the spasing threshold, the number of coherent plasmons may exceed the number of spontaneously excited plasmons at achievable pump rates.

© 2015 Optical Society of America

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    [Crossref] [PubMed]

2015 (1)

J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nanotechnol. 10(1), 2–6 (2015).
[Crossref] [PubMed]

2014 (3)

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light Sci. Appl. 3(7), e191 (2014).
[Crossref]

Y. E. Lozovik, I. A. Nechepurenko, A. V. Dorofeenko, E. S. Andrianov, and A. A. Pukhov, “Spaser spectroscopy with subwavelength spatial resolution,” Phys. Lett. A 378(9), 723–727 (2014).
[Crossref]

2013 (8)

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Graphene nanoribbon based spaser,” Phys. Rev. B 88(23), 235424 (2013).
[Crossref]

D. Li and M. I. Stockman, “Electric Spaser in the Extreme Quantum Limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface Plasmon Lasing Observed in Metal Hole Arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. P. Vinogradov, A. V. Dorofeenko, and A. A. Lisyansky, “Modification of the resonance fluorescence spectrum of a two-level atom in the near field of a plasmonic nanoparticle,” JETP Lett. 97(8), 452–458 (2013).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Spectrum of surface plasmons excited by spontaneous quantum dot transitions,” Sov. Phys. JETP 117(2), 205–213 (2013).
[Crossref]

D. G. Baranov, E. S. Andrianov, A. P. Vinogradov, and A. A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21(9), 10779–10791 (2013).
[Crossref] [PubMed]

E. S. Andrianov, D. G. Baranov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Loss compensation by spasers in plasmonic systems,” Opt. Express 21(11), 13467–13478 (2013).
[Crossref] [PubMed]

2012 (8)

J. B. Khurgin and G. Sun, “Injection pumped single mode surface plasmon generators: threshold, linewidth, and coherence,” Opt. Express 20(14), 15309–15325 (2012).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during nonradiative plasmon excitation,” Phys. Rev. B 85(3), 035405 (2012).
[Crossref]

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]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

J. B. Khurgin and G. Sun, “Practicality of compensating the loss in the plasmonic waveguides using semiconductor gain medium,” Appl. Phys. Lett. 100(1), 011105 (2012).
[Crossref]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Phys. Usp. 55(10), 1046–1053 (2012).
[Crossref]

V. M. Parfenyev and S. S. Vergeles, “Intensity-dependent frequency shift in surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 86(4), 043824 (2012).
[Crossref]

2011 (4)

2010 (1)

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]

2009 (3)

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]

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Phys. Usp. 52(9), 959–967 (2009).
[Crossref]

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]

2008 (1)

2006 (1)

2005 (1)

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[Crossref]

2003 (2)

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(20), 201101 (2003).
[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]

1992 (1)

A. A. Kolokolov and G. V. Skrotskii, “Interference of reactive components of an electromagnetic field,” Sov. Phys. Usp. 35(12), 1089–1093 (1992).
[Crossref]

1984 (1)

S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29(5), 2627–2633 (1984).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1946 (1)

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev. 69(1-2), 37–38 (1946).
[Crossref]

’t Hooft, G. W.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface Plasmon Lasing Observed in Metal Hole Arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Adegoke, J. A.

Andrianov, E. S.

Y. E. Lozovik, I. A. Nechepurenko, A. V. Dorofeenko, E. S. Andrianov, and A. A. Pukhov, “Spaser spectroscopy with subwavelength spatial resolution,” Phys. Lett. A 378(9), 723–727 (2014).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. P. Vinogradov, A. V. Dorofeenko, and A. A. Lisyansky, “Modification of the resonance fluorescence spectrum of a two-level atom in the near field of a plasmonic nanoparticle,” JETP Lett. 97(8), 452–458 (2013).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Spectrum of surface plasmons excited by spontaneous quantum dot transitions,” Sov. Phys. JETP 117(2), 205–213 (2013).
[Crossref]

D. G. Baranov, E. S. Andrianov, A. P. Vinogradov, and A. A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21(9), 10779–10791 (2013).
[Crossref] [PubMed]

E. S. Andrianov, D. G. Baranov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Loss compensation by spasers in plasmonic systems,” Opt. Express 21(11), 13467–13478 (2013).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during nonradiative plasmon excitation,” Phys. Rev. B 85(3), 035405 (2012).
[Crossref]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Phys. Usp. 55(10), 1046–1053 (2012).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Dipole Response of Spaser on an External Optical Wave,” Opt. Lett. 36(21), 4302–4304 (2011).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Forced synchronization of spaser by an external optical wave,” Opt. Express 19(25), 24849–24857 (2011).
[Crossref] [PubMed]

Apalkov, V.

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light Sci. Appl. 3(7), e191 (2014).
[Crossref]

Atwater, H. A.

A. Boltasseva and H. A. Atwater, “Materials science. Low-Loss Plasmonic Metamaterials,” Science 331(6015), 290–291 (2011).
[Crossref] [PubMed]

Bahoura, M.

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]

Baranov, D. G.

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]

Berman, O. L.

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Graphene nanoribbon based spaser,” Phys. Rev. B 88(23), 235424 (2013).
[Crossref]

Boltasseva, A.

A. Boltasseva and H. A. Atwater, “Materials science. Low-Loss Plasmonic Metamaterials,” Science 331(6015), 290–291 (2011).
[Crossref] [PubMed]

Chang, W.-H.

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

Chen, H.-Y.

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

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Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
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W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
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Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
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E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during nonradiative plasmon excitation,” Phys. Rev. B 85(3), 035405 (2012).
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A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Phys. Usp. 55(10), 1046–1053 (2012).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Forced synchronization of spaser by an external optical wave,” Opt. Express 19(25), 24849–24857 (2011).
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E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Dipole Response of Spaser on an External Optical Wave,” Opt. Lett. 36(21), 4302–4304 (2011).
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W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
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Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
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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).
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J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
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[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
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Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

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[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Spectrum of surface plasmons excited by spontaneous quantum dot transitions,” Sov. Phys. JETP 117(2), 205–213 (2013).
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[Crossref] [PubMed]

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[Crossref]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Phys. Usp. 55(10), 1046–1053 (2012).
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E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Forced synchronization of spaser by an external optical wave,” Opt. Express 19(25), 24849–24857 (2011).
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Y. E. Lozovik, I. A. Nechepurenko, A. V. Dorofeenko, E. S. Andrianov, and A. A. Pukhov, “Spaser spectroscopy with subwavelength spatial resolution,” Phys. Lett. A 378(9), 723–727 (2014).
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Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
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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).
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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).
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[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
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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).
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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).
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Y. E. Lozovik, I. A. Nechepurenko, A. V. Dorofeenko, E. S. Andrianov, and A. A. Pukhov, “Spaser spectroscopy with subwavelength spatial resolution,” Phys. Lett. A 378(9), 723–727 (2014).
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E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Spectrum of surface plasmons excited by spontaneous quantum dot transitions,” Sov. Phys. JETP 117(2), 205–213 (2013).
[Crossref]

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[Crossref]

E. S. Andrianov, D. G. Baranov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Loss compensation by spasers in plasmonic systems,” Opt. Express 21(11), 13467–13478 (2013).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during nonradiative plasmon excitation,” Phys. Rev. B 85(3), 035405 (2012).
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[Crossref]

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[Crossref] [PubMed]

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S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29(5), 2627–2633 (1984).
[Crossref]

Samoilov, V. N.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[Crossref]

Sanders, C. E.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

Sarychev, A. K.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Phys. Usp. 52(9), 959–967 (2009).
[Crossref]

Schatz, G. C.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

Shalaev, V. 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]

A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. 31(14), 2169–2171 (2006).
[Crossref] [PubMed]

Shih, C.-K.

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

Shvets, G.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

Skrotskii, G. V.

A. A. Kolokolov and G. V. Skrotskii, “Interference of reactive components of an electromagnetic field,” Sov. Phys. Usp. 35(12), 1089–1093 (1992).
[Crossref]

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]

Stockman, M. I.

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light Sci. Appl. 3(7), e191 (2014).
[Crossref]

D. Li and M. I. Stockman, “Electric Spaser in the Extreme Quantum Limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[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]

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]

Suh, J. Y.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Sun, G.

J. B. Khurgin and G. Sun, “Practicality of compensating the loss in the plasmonic waveguides using semiconductor gain medium,” Appl. Phys. Lett. 100(1), 011105 (2012).
[Crossref]

J. B. Khurgin and G. Sun, “Injection pumped single mode surface plasmon generators: threshold, linewidth, and coherence,” Opt. Express 20(14), 15309–15325 (2012).
[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]

Tartakovsky, G.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Phys. Usp. 52(9), 959–967 (2009).
[Crossref]

Torrey, H. C.

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev. 69(1-2), 37–38 (1946).
[Crossref]

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]

Uskov, A. V.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[Crossref]

van Beijnum, F.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface Plasmon Lasing Observed in Metal Hole Arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

van Exter, M. P.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface Plasmon Lasing Observed in Metal Hole Arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

van Veldhoven, P. J.

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface Plasmon Lasing Observed in Metal Hole Arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

Vergeles, S. S.

V. M. Parfenyev and S. S. Vergeles, “Intensity-dependent frequency shift in surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 86(4), 043824 (2012).
[Crossref]

Vinogradov, A. P.

E. S. Andrianov, A. A. Pukhov, A. P. Vinogradov, A. V. Dorofeenko, and A. A. Lisyansky, “Modification of the resonance fluorescence spectrum of a two-level atom in the near field of a plasmonic nanoparticle,” JETP Lett. 97(8), 452–458 (2013).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Spectrum of surface plasmons excited by spontaneous quantum dot transitions,” Sov. Phys. JETP 117(2), 205–213 (2013).
[Crossref]

D. G. Baranov, E. S. Andrianov, A. P. Vinogradov, and A. A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21(9), 10779–10791 (2013).
[Crossref] [PubMed]

E. S. Andrianov, D. G. Baranov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Loss compensation by spasers in plasmonic systems,” Opt. Express 21(11), 13467–13478 (2013).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during nonradiative plasmon excitation,” Phys. Rev. B 85(3), 035405 (2012).
[Crossref]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Phys. Usp. 55(10), 1046–1053 (2012).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Forced synchronization of spaser by an external optical wave,” Opt. Express 19(25), 24849–24857 (2011).
[Crossref] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Dipole Response of Spaser on an External Optical Wave,” Opt. Lett. 36(21), 4302–4304 (2011).
[Crossref] [PubMed]

Wang, C.-Y.

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

Wasielewski, M. R.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[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]

Wu, C.

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[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]

Zaimidoroga, O. A.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[Crossref]

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.

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]

Zhou, W.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

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]

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

J. B. Khurgin and G. Sun, “Practicality of compensating the loss in the plasmonic waveguides using semiconductor gain medium,” Appl. Phys. Lett. 100(1), 011105 (2012).
[Crossref]

JETP Lett. (1)

E. S. Andrianov, A. A. Pukhov, A. P. Vinogradov, A. V. Dorofeenko, and A. A. Lisyansky, “Modification of the resonance fluorescence spectrum of a two-level atom in the near field of a plasmonic nanoparticle,” JETP Lett. 97(8), 452–458 (2013).
[Crossref]

Light Sci. Appl. (1)

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light Sci. Appl. 3(7), e191 (2014).
[Crossref]

Nano Lett. (2)

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic Bowtie Nanolaser Arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Y.-J. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M. I. Stockman, C.-K. Shih, and S. Gwo, “All-Color Plasmonic Nanolasers with Ultralow Thresholds: Autotuning Mechanism for Single-Mode Lasing,” Nano Lett. 14(8), 4381–4388 (2014).
[Crossref] [PubMed]

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. Nanotechnol. (2)

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8(7), 506–511 (2013).
[Crossref] [PubMed]

J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nanotechnol. 10(1), 2–6 (2015).
[Crossref] [PubMed]

Nature (2)

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]

Opt. Express (6)

Opt. Lett. (2)

Phys. Lett. A (1)

Y. E. Lozovik, I. A. Nechepurenko, A. V. Dorofeenko, E. S. Andrianov, and A. A. Pukhov, “Spaser spectroscopy with subwavelength spatial resolution,” Phys. Lett. A 378(9), 723–727 (2014).
[Crossref]

Phys. Rev. (1)

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev. 69(1-2), 37–38 (1946).
[Crossref]

Phys. Rev. A (3)

S. Sachdev, “Atom in a damped cavity,” Phys. Rev. A 29(5), 2627–2633 (1984).
[Crossref]

V. M. Parfenyev and S. S. Vergeles, “Intensity-dependent frequency shift in surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. A 86(4), 043824 (2012).
[Crossref]

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[Crossref]

Phys. Rev. B (4)

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Graphene nanoribbon based spaser,” Phys. Rev. B 88(23), 235424 (2013).
[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(20), 201101 (2003).
[Crossref]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during nonradiative plasmon excitation,” Phys. Rev. B 85(3), 035405 (2012).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[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]

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]

F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. ’t Hooft, and M. P. van Exter, “Surface Plasmon Lasing Observed in Metal Hole Arrays,” Phys. Rev. Lett. 110(20), 206802 (2013).
[Crossref] [PubMed]

D. Li and M. I. Stockman, “Electric Spaser in the Extreme Quantum Limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]

Phys. Usp. (2)

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Phys. Usp. 55(10), 1046–1053 (2012).
[Crossref]

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Phys. Usp. 52(9), 959–967 (2009).
[Crossref]

Science (2)

A. Boltasseva and H. A. Atwater, “Materials science. Low-Loss Plasmonic Metamaterials,” Science 331(6015), 290–291 (2011).
[Crossref] [PubMed]

Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic Nanolaser Using Epitaxially Grown Silver Film,” Science 337(6093), 450–453 (2012).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Spectrum of surface plasmons excited by spontaneous quantum dot transitions,” Sov. Phys. JETP 117(2), 205–213 (2013).
[Crossref]

Sov. Phys. Usp. (1)

A. A. Kolokolov and G. V. Skrotskii, “Interference of reactive components of an electromagnetic field,” Sov. Phys. Usp. 35(12), 1089–1093 (1992).
[Crossref]

Other (10)

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

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

A. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced Spaser Oscillations,” Proc. SPIE 8457, 0X1–0X16 (2012).
[Crossref]

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, 1995).

V. M. Shalaev and A. K. Sarychev, Electrodynamics of Metamaterials (World Scientific, 2007).

S. I. Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits (Pan Stanford Publishing, 2008).

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).

Y. I. Khanin, Fundamentals of laser dynamics (Cambridge international science publishing, 2006).

R. H. Pantell and H. E. Puthoff, Fundamentals of quantum electronics (Wiley, 1969).

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Figures (4)

Fig. 1
Fig. 1 The sine of the phase difference between oscillations of the spaser dipole moment and the external field as a function of the external field amplitude and the frequency detuning. The dashed line shows the compensation curve which corresponds to oscillations in antiphase with the external wave. The region bounded by this line corresponds to the amplification of the external field.
Fig. 2
Fig. 2 The same as in Fig. 1 obtained in the semiclassical approximation [27, 33]. The dashed line corresponds to oscillations in antiphase with the external wave, the solid line corresponds to in-phase oscillations.
Fig. 3
Fig. 3 The dependencies of the energy of the NP dipole moment, W coh ω SP | a ^ | 2 (the solid line), and the energy of spontaneously excited plasmons, W incoh ω SP ( a ^ + a ^ | a ^ | 2 ) (the dashed line), calculated at the compensation curve near the first spasing threshold γ p / γ p th(1) 1 , on the frequency detuning, Δ E . The parameters used in obtaining Fig. 3 are taken form Refs [9, 10]: γ a 10 14 s 1 , γ σ 10 11 s 1 , and Ω R 10 13 s 1 . These parameters correspond to a silver NP and a semiconducting active medium (e.g., InGaAs).
Fig. 4
Fig. 4 The dependencies of the energy of the NP dipole moment, W coh ω SP | a ^ | 2 (the red solid line), and the energy of spontaneously excited plasmons, W incoh ω SP ( a ^ + a ^ | a ^ | 2 ) (the blue dashed line), on the pump rate characterized by D 0 for (a) an autonomous spaser and (b) a spaser driven by an external field.

Equations (19)

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H ^ = H ^ NP + H ^ TLS + V ^ TLSNP + V ^ TLSw + V ^ NPw ,
V ^ NPw =αΩ( a ^ + + a ^ ),
D ^ · =2i Ω R ( a ^ σ ^ σ ^ a ^ )+2iΩ( σ ^ σ ^ ) γ D ( D ^ D ^ 0 )+ F ^ D (t),
σ ^ · =(iδ γ σ ) σ ^ +i Ω R a ^ D ^ +iΩ D ^ + F ^ σ (t),,
a ^ · =(iΔ γ a ) a ^ i Ω R σ ^ iαΩ+ F ^ a (t),
d dt D ^ =2i Ω R ( a ^ σ ^ σ ^ a ^ )+2iΩ( σ ^ σ ^ ) γ D ( D ^ D ^ 0 )
d dt σ ^ =(iδ γ σ ) σ ^ +i Ω R a ^ D ^ +iΩ D ^
d dt a ^ =(iΔ γ a ) a ^ i Ω R σ ^ iαΩ
d dt a ^ =( iΔ γ a ) a ^ i Ω R σ ^ iαΩ, d dt σ ^ =( iδ γ σ ) σ ^ +i Ω R a ^ D ^ +iΩ D ^ , d dt ( a ^ D ^ ) = γ D D 0 a ^ +i Ω R σ ^ +( iΔ γ a γ D ) a ^ D ^ +2i Ω R a ^ + σ ^ a ^ iαΩ D ^ iΩ σ ^ + a ^ , d dt ( a ^ + σ ^ a ^ ) =iΩ a ^ /2+iΩ a ^ D ^ /2+( iδ2 γ a γ σ ) a ^ + σ ^ a ^ iαΩ a ^ + σ ^ iΩ a ^ + D ^ a ^ , d dt ( a ^ + a ^ ) =iαΩ( a ^ a ^ + )2 γ a a ^ + a ^ iΩ( a ^ + σ ^ σ ^ + a ^ ), d dt D ^ =2iΩ( σ ^ σ ^ + ) γ D D ^ +2iΩ( a ^ + σ ^ σ ^ + a ^ )+ γ D D 0 , d dt ( a ^ + σ ^ ) =iαΩ σ +iΩ a ^ + D ^ +iΩ D ^ /2 +( i( δΔ ) γ a γ σ ) a ^ + σ ^ +iΩ a ^ + D ^ a ^ +iΩ/2, d dt ( a ^ + D ^ a ^ ) =iaΩ( a ^ D ^ a ^ + D ^ )+2iΩ( a ^ + σ ^ a ^ a ^ + σ ^ + a ^ ) + γ D D 0 a ^ + a ^ +iΩ( a ^ + σ ^ σ ^ + a ^ )( 2 γ a + γ D ) a ^ + D ^ a ^ .
γ D =2 γ σ + γ p ,
D 0 =( γ p 2 γ σ )/( γ p +2 γ σ ).
γ p th(1) =2 γ σ (1+ D th (1) )/(1 D th (1) )
n c = a ^ a ^ coherent = | a | 2 =( D 0 D th (1) ) γ D /4 γ a ,
a ^ a ^ spontaneous = Ω R 2 γ a 2 (1+ D 0 )/2
a ^ a ^ spontaneous =F γ σ γ a 1 (1+ D 0 )/8
F=4 Ω R 2 / γ a γ σ =4/ D 0th (1) .
γ p th(1) 2 γ σ .
a ^ a ^ coherent ~ a ^ a ^ spontaneous .
γ p th(2) 4 γ σ D th (1) ~F γ p th(1) .

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