Abstract

We propose an exactly solvable electrodynamical model for surface plasmon amplification by stimulated emission of radiation (spaser). The gain medium is described in terms of the nonlinear permittivity with negative losses. The model demonstrates the main feature of a spaser: a self-oscillating state (spasing) arising without an external driving field if the pumping exceeds some threshold value. In addition, it properly describes synchronization of a spaser by an external field within the Arnold tongue and the possibility of compensating for Joule losses when the pumping is below threshold. The model also gives correct qualitative dependencies of spaser characteristics on pumping.

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2012 (8)

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,” Science337(6093), 450–453 (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. B85(3), 035405 (2012).
[CrossRef]

A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B85(11), 115429 (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]

A. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
[CrossRef]

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]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett.108(9), 093901 (2012).
[CrossRef] [PubMed]

J. B. Khurgin and G. Sun, “Injection pumped single mode surface plasmon generators: threshold, linewidth, and coherence,” Opt. Express20(14), 15309–15325 (2012).
[CrossRef] [PubMed]

2011 (7)

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19(22), 22029–22106 (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]

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. Express19(25), 24849–24857 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Spaser action, loss compensation, and stability in plasmonic systems with gain,” Phys. Rev. Lett.106(15), 156802 (2011).
[CrossRef] [PubMed]

A. A. Zyablovsky, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Lasing in a gain slab as a consequence of the causality principle,” J. Commun. Technol. Electron.56(9), 1139–1145 (2011).
[CrossRef]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (2011).
[CrossRef] [PubMed]

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

2010 (6)

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt.12(2), 024004 (2010).
[CrossRef]

I. R. Gabitov, B. Kennedy, and A. I. Maimistov, “Coherent amplification of optical pulses in metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 401–409 (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]

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

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,” Nature466(7307), 735–738 (2010).
[CrossRef] [PubMed]

X. F. Li and S. F. Yu, “Design of low-threshold compact Au-nanoparticle lasers,” Opt. Lett.35(15), 2535–2537 (2010).
[CrossRef] [PubMed]

2009 (5)

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys.106(7), 073104 (2009).
[CrossRef]

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A79(4), 043824 (2009).
[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]

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,” Nature460(7259), 1110–1112 (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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

2008 (5)

V. V. Klimov, Y. N. Istomin, and Y. A. Kosevich, “Plasma phenomena in nanostructures and neutron stars,” Phys. Usp.51(8), 839–859 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

M. I. Stockman, “Spasers explained,” Nat. Photonics2(6), 327–329 (2008).
[CrossRef]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett.33(11), 1261–1263 (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. Express16(24), 19785–19798 (2008).
[CrossRef] [PubMed]

2007 (2)

J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express15(5), 2622–2653 (2007).
[CrossRef] [PubMed]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B75(8), 085436 (2007).
[CrossRef]

2006 (2)

2005 (2)

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A71(6), 063812 (2005).
[CrossRef]

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B71(11), 115409 (2005).
[CrossRef]

2004 (1)

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett.85(21), 5040–5042 (2004).
[CrossRef]

2003 (3)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003).
[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]

S. A. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B67(20), 201101 (2003).
[CrossRef]

1988 (1)

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum Electron.20(5), 395–431 (1988).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Adegoke, J.

Ahn, H.

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

Andrianov, E. S.

A. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
[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. B85(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. Express19(25), 24849–24857 (2011).
[CrossRef] [PubMed]

Aradian, A.

A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B85(11), 115429 (2012).
[CrossRef]

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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Bartal, G.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (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,” Nature461(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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Belov, P. A.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett.108(9), 093901 (2012).
[CrossRef] [PubMed]

Bergman, D. J.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B71(11), 115409 (2005).
[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]

Chang, W.-H.

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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

Chen, H.-Y.

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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

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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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

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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,” Nature466(7307), 735–738 (2010).
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P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

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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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

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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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

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A. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
[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. B85(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. Express19(25), 24849–24857 (2011).
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A. A. Zyablovsky, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Lasing in a gain slab as a consequence of the causality principle,” J. Commun. Technol. Electron.56(9), 1139–1145 (2011).
[CrossRef]

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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,” Nature466(7307), 735–738 (2010).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett.31(20), 3022–3024 (2006).
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A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt.12(2), 024013 (2010).
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N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

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Gabitov, I. R.

I. R. Gabitov, B. Kennedy, and A. I. Maimistov, “Coherent amplification of optical pulses in metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 401–409 (2010).
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A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A79(4), 043824 (2009).
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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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

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Gwo, S.

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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Hamm, J. M.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett.105(12), 127401 (2010).
[CrossRef] [PubMed]

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C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

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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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

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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).
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V. V. Klimov, Y. N. Istomin, and Y. A. Kosevich, “Plasma phenomena in nanostructures and neutron stars,” Phys. Usp.51(8), 839–859 (2008).
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P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
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I. R. Gabitov, B. Kennedy, and A. I. Maimistov, “Coherent amplification of optical pulses in metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 401–409 (2010).
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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,” Nature466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Kim, J.

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,” Science337(6093), 450–453 (2012).
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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]

Kivshar, Y. S.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett.108(9), 093901 (2012).
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V. V. Klimov, Y. N. Istomin, and Y. A. Kosevich, “Plasma phenomena in nanostructures and neutron stars,” Phys. Usp.51(8), 839–859 (2008).
[CrossRef]

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

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V. V. Klimov, Y. N. Istomin, and Y. A. Kosevich, “Plasma phenomena in nanostructures and neutron stars,” Phys. Usp.51(8), 839–859 (2008).
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C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

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A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Phys. Usp.52(9), 959–967 (2009).
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K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B71(11), 115409 (2005).
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K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B71(11), 115409 (2005).
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Li, X. F.

Lin, M.-H.

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

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Lisyansky, A. A.

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. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
[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. B85(3), 035405 (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. Express19(25), 24849–24857 (2011).
[CrossRef] [PubMed]

Lomakin, V.

Lu, M.-Y.

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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

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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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

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R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Maimistov, A. I.

I. R. Gabitov, B. Kennedy, and A. I. Maimistov, “Coherent amplification of optical pulses in metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 401–409 (2010).
[CrossRef]

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P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum Electron.20(5), 395–431 (1988).
[CrossRef]

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Mizrahi, A.

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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Nezhad, M. P.

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,” Nature466(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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett.31(20), 3022–3024 (2006).
[CrossRef] [PubMed]

Nordlander, P.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Noskov, R. E.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett.108(9), 093901 (2012).
[CrossRef] [PubMed]

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys.106(7), 073104 (2009).
[CrossRef]

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I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A71(6), 063812 (2005).
[CrossRef]

Oulton, R. F.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

Pendry, J.

S. A. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B67(20), 201101 (2003).
[CrossRef]

Penzkofer, A.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum Electron.20(5), 395–431 (1988).
[CrossRef]

Popov, A. K.

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

Protsenko, I. E.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A71(6), 063812 (2005).
[CrossRef]

Pukhov, A. A.

A. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
[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. B85(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. Express19(25), 24849–24857 (2011).
[CrossRef] [PubMed]

A. A. Zyablovsky, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Lasing in a gain slab as a consequence of the causality principle,” J. Commun. Technol. Electron.56(9), 1139–1145 (2011).
[CrossRef]

Pusch, A.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett.105(12), 127401 (2010).
[CrossRef] [PubMed]

Qiu, X.

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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. A. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B67(20), 201101 (2003).
[CrossRef]

Ritzo, B. A.

Rosenthal, A. S.

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A79(4), 043824 (2009).
[CrossRef]

Ruther, M.

Samoilov, V. N.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A71(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,” Science337(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]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B75(8), 085436 (2007).
[CrossRef]

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,” Nature466(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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett.31(20), 3022–3024 (2006).
[CrossRef] [PubMed]

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

Shih, C.-K.

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,” Science337(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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

Slutsky, B. A.

Small, C. E.

Sorger, V. J.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Soukoulis, C. M.

Spangler, W.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum Electron.20(5), 395–431 (1988).
[CrossRef]

Sperber, P.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum Electron.20(5), 395–431 (1988).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Spaser action, loss compensation, and stability in plasmonic systems with gain,” Phys. Rev. Lett.106(15), 156802 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19(22), 22029–22106 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt.12(2), 024004 (2010).
[CrossRef]

M. I. Stockman, “Spasers explained,” Nat. Photonics2(6), 327–329 (2008).
[CrossRef]

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B71(11), 115409 (2005).
[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,” Nature460(7259), 1110–1112 (2009).
[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. Express20(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,” Nature460(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]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B75(8), 085436 (2007).
[CrossRef]

Tsakmakidis, K. L.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett.105(12), 127401 (2010).
[CrossRef] [PubMed]

Tsarev, M. V.

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys.106(7), 073104 (2009).
[CrossRef]

Uskov, A. V.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A71(6), 063812 (2005).
[CrossRef]

Veltri, A.

A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B85(11), 115429 (2012).
[CrossRef]

Vinogradov, A. P.

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. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
[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. B85(3), 035405 (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]

A. A. Zyablovsky, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Lasing in a gain slab as a consequence of the causality principle,” J. Commun. Technol. Electron.56(9), 1139–1145 (2011).
[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. Express19(25), 24849–24857 (2011).
[CrossRef] [PubMed]

Wang, C.-Y.

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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

Wegener, M.

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,” Nature460(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,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

Wu, C.-Y.

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[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,” Nature466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Yu, S. F.

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,” Nature466(7307), 735–738 (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. A71(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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zhang, X.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (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,” Nature461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zharov, A. A.

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys.106(7), 073104 (2009).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[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,” Nature460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett.31(20), 3022–3024 (2006).
[CrossRef] [PubMed]

Ziolkowski, R. W.

Zyablovsky, A. A.

A. A. Zyablovsky, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Lasing in a gain slab as a consequence of the causality principle,” J. Commun. Technol. Electron.56(9), 1139–1145 (2011).
[CrossRef]

Appl. Phys. Lett. (2)

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett.85(21), 5040–5042 (2004).
[CrossRef]

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]

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

I. R. Gabitov, B. Kennedy, and A. I. Maimistov, “Coherent amplification of optical pulses in metamaterials,” IEEE J. Sel. Top. Quantum Electron.16(2), 401–409 (2010).
[CrossRef]

J. Appl. Phys. (1)

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, “Plasmon-induced terahertz radiation generation due to symmetry breaking in a nonlinear metallic nanodimer,” J. Appl. Phys.106(7), 073104 (2009).
[CrossRef]

J. Commun. Technol. Electron. (1)

A. A. Zyablovsky, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Lasing in a gain slab as a consequence of the causality principle,” J. Commun. Technol. Electron.56(9), 1139–1145 (2011).
[CrossRef]

J. Opt. (2)

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

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt.12(2), 024004 (2010).
[CrossRef]

Nano Lett. (1)

C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett.11(10), 4256–4260 (2011).
[CrossRef] [PubMed]

Nat. Mater. (1)

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater.10(2), 110–113 (2011).
[CrossRef] [PubMed]

Nat. Photonics (2)

M. I. Stockman, “Spasers explained,” Nat. Photonics2(6), 327–329 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics2(6), 351–354 (2008).
[CrossRef]

Nature (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,” Nature460(7259), 1110–1112 (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,” Nature461(7264), 629–632 (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,” Nature466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum Electron.20(5), 395–431 (1988).
[CrossRef]

Phys. Rev. A (2)

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, “Dipole nanolaser,” Phys. Rev. A71(6), 063812 (2005).
[CrossRef]

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A79(4), 043824 (2009).
[CrossRef]

Phys. Rev. B (6)

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. B85(3), 035405 (2012).
[CrossRef]

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B71(11), 115409 (2005).
[CrossRef]

S. A. Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B67(20), 201101 (2003).
[CrossRef]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B75(8), 085436 (2007).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B85(11), 115429 (2012).
[CrossRef]

Phys. Rev. Lett. (4)

M. I. Stockman, “Spaser action, loss compensation, and stability in plasmonic systems with gain,” Phys. Rev. Lett.106(15), 156802 (2011).
[CrossRef] [PubMed]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett.108(9), 093901 (2012).
[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]

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]

Phys. Usp. (3)

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]

V. V. Klimov, Y. N. Istomin, and Y. A. Kosevich, “Plasma phenomena in nanostructures and neutron stars,” Phys. Usp.51(8), 839–859 (2008).
[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]

Proc. SPIE (1)

A. A. Lisyansky, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Forced spaser oscillations,” Proc. SPIE8457, 84570X (2012).
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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,” Science337(6093), 450–453 (2012).
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Figures (4)

Fig. 1
Fig. 1

A schematic drawing of a core-shell spaser.

Fig. 2
Fig. 2

Spaser response on external harmonic field in (top panels) below- and (bottom panels) above-threshold regimes. Solid and dashed lines show real and imaginary parts of the dipole moment, respectively. Frequencies of incident field are (a), (c) ω< = 1.98 eV < ωsp and (b), (d) ω> = 1.99 eV < ωsp. The red and green circles in the bottom panels show the exact loss compensation when the imaginary part of the dipole moment turns to zero.

Fig. 3
Fig. 3

Real parts of the instability growth rate Λ for below- (solid line) and above-threshold (dashed line) regimes of a driven spaser at the frequency of incident field ω< = 1.98 eV. For below-threshold spaser the instability growth rate is always negative so that spaser oscillations in external field are always stable. Above threshold, spaser is synchronized by strong external field, while its oscillations in weak external field are unstable and may show stochastic dynamics [16].

Fig. 4
Fig. 4

Stable (filled) and unstable regions of a driven above-threshold spaser for D0 = 0.25. The region of stability corresponds to steady-state solutions with ReΛ<0 . The two vertical lines correspond to the frequencies ω > and ω < , which are also used in Fig. 2. The red and green circles correspond to those in Fig. 2 (c) and 2(d). The red circle, in which Im[d]=0 , lies in the instability region, so loss compensation does not occur, while the green circle lies in the stable region and compensation does take place. The red and green curves show the compensation curves lying in unstable and stable regions, respectively, along which the imaginary part of dipole moment turns to zero.

Equations (25)

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××E+ ε 0 c 2 2 E t 2 = 4π c 2 2 P t 2 ,
2 P t 2 + 2 τ p P t + ω 0 2 P= 2 ω 0 | μ | 2 nE,
n t + 1 τ n ( n n 0 )= 1 ω 0 Re( E * P t ),
ε gain (ω)= ε 0 + D 0 ω 0 ω i+( ω 2 ω 0 2 )/2ωΓ 1+β | E(ω) | 2 + [ ( ω 2 ω 0 2 )/2ωΓ ] 2 ,
E shell ( r )=b E in c E in / r 3 +3c( E in n)n/ r 3 ,
E out ( r )=a E in / r 3 +3a( E in n)n/ r 3 ,
D core n | r core = D shell n | r core , E core ×n | r core = E shell ×n | r core , D shell n | r shell = D out n | r shell , E shell ×n | r shell = E out ×n | r shell ,
{ ε gain ( ω, E in , D 0 )=( b+2c/ r core 3 ) ε shell , 1=bc/ r core 3 , (b+2c/ r shell 3 ) ε shell =2a/ r shell 3 , bc/ r shell 3 =a/ r shell 3 .
ε gain ( ω, E in , D 0 )= ε shell 2( ε shell (ω)1 ) r core 3 2( 2+ ε shell (ω) ) r shell 3 2( ε shell (ω)1 ) r core 3 +( 2+ ε shell (ω) ) r shell 3 .
ε 0 + D 0 ω 0 ω i+( ω 2 ω 0 2 )/2ωΓ 1+β | E in | 2 + [ ( ω 2 ω 0 2 )/2ωΓ ] 2 =F(ω),
F( ω )= ε shell 2( ε shell (ω)1 ) r core 3 2( 2+ ε shell (ω) ) r shell 3 2( ε shell (ω)1 ) r core 3 +( 2+ ε shell (ω) ) r shell 3 .
D 0 1+β | E in | 2 + [ ( ω 2 ω 0 2 )/2ωΓ ] 2 = F(ω) ε 0 i+( ω 2 ω 0 2 )/2ωΓ ω ω 0 .
Im F( ω sp ) ε 0 i+( ω sp 2 ω 0 2 )/2 ω sp Γ =0.
D 0 1+β | E in ( D 0 ) | 2 + [ ( ω sp 2 ω 0 2 )/2 ω sp Γ ] 2 = ω sp ω 0 Re F( ω sp ) ε 0 i+( ω sp 2 ω 0 2 )/2 ω sp Γ .
D 0 1+β | E in ( D 0 ) | 2 + [ ( ω sp 2 ω 0 2 )/2 ω sp Γ ] 2 = D th 1+0+ [ ( ω sp 2 ω 0 2 )/2 ω sp Γ ] 2 .
E in = ( D 0 D th )/β D th 1+ [ ( ω sp 2 ω 0 2 )/2 ω sp Γ ] 2 , d=a E in .
D th = ω sp ω 0 ( 1+ [ ( ω sp 2 ω 0 2 )/2 ω sp Γ ] 2 )Re F( ω sp ) ε 0 i+( ω sp 2 ω 0 2 )/2 ω sp Γ .
{ ε gain ( ω, E in , D 0 )=( b+2c/ r core 3 ) ε shell , 1=bc/ r core 3 , (b+2c/ r shell 3 ) ε shell =x+2a/ r shell 3 , bc/ r shell 3 =xa/ r shell 3 .
α ^ 1 ( t, E in (t) )d( t )= E ext ( t ).
α 1 ( ω, E in ( ω ) ) d ˜ ( ω )= E ˜ ext ( ω ),
E ext ( t )= α 1 ( Ω, E in ) d ˜ ( Ω ) e iΩt dΩ = e iωt α 1 ( ω+ν, E in ) d ˜ slow ( ν ) e iνt dν .
E ext ( t ) e iωt [ α 1 ( ω, E in )+ν d α 1 ( ω, E in ) dω ] d ˜ slow ( ν ) e iνt dν = = e iωt α 1 ( ω, E in ) d ˜ slow ( ν ) e iνt dν + e i ω 0 t d α 1 ( ω, E in ) dω ν d ˜ slow ( ν ) e iνt dν = e iωt [ α 1 ( ω, E in ) d slow ( t )+i d α 1 ( ω, E in ) dω d d slow ( t ) dt ],
i d α 1 dω d dt d slow ( t )+ α 1 d slow ( t )= E slow ( t ).
i d α 1 dω δdΛ+ α 1 δd=0.
Λ=i α 1 ( ω, E in ) ( d α 1 ( ω, E in )/dω ) 1 .

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