Abstract

We demonstrate that when the frequency of the external field differs from the lasing frequency of an autonomous spaser, the spaser exhibits stochastic oscillations at low field intensity. The plasmon oscillations lock to the frequency of the external field only when the field amplitude exceeds a threshold value. We find a region of values of the external field amplitude and the frequency detuning (the Arnold tongue) for which the spaser synchronizes with the external wave.

© 2011 OSA

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  12. 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).
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    [CrossRef]
  30. A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A 79(4), 043824 (2009).
    [CrossRef]
  31. 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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2011 (1)

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

2010 (4)

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]

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

N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18(23), 24140–24151 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-23-24140 .
[CrossRef] [PubMed]

2009 (5)

Y.-Y. Yu, D.-Z. Lin, L.-S. Huang, and C.-K. Lee, “Effect of subwavelength annular aperture diameter on the nondiffracting region of generated Bessel beams,” Opt. Express 17(4), 2707–2713 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-4-2707 .
[CrossRef] [PubMed]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8548 .
[CrossRef] [PubMed]

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A 79(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,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

2008 (4)

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

M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10(2), 025031 (2008).
[CrossRef]

V. V. Klimov, “Nanoplasmonics,” Phys. Usp. 51(8), 839–844 (2008).
[CrossRef]

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

2007 (3)

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

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75(8), 085436 (2007).
[CrossRef]

A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, “Creating stable gain in active metamaterials,” J. Opt. Soc. Am. B 24(10), A53–A61 (2007).
[CrossRef]

2006 (3)

2005 (2)

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]

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B 71(11), 115409 (2005).
[CrossRef]

2004 (1)

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[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]

Adegoke, J.

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]

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.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B 71(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]

Bianucci, P.

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[CrossRef]

Boardman, A. D.

Chang, K.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Chen, T.-C.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Drachev, V. P.

Fang, A.

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

Fedotov, V. A.

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).
[CrossRef]

Ghannam, T.

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A 79(4), 043824 (2009).
[CrossRef]

Gibbs, H. M.

Govyadinov, A.

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

Hendrickson, J.

Herz, E.

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

Huang, L.-S.

Jiang, T.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Kennedy, B.

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]

Khitrova, G.

King, N.

Kissel, V. N.

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]

Klimov, V. V.

V. V. Klimov, “Nanoplasmonics,” Phys. Usp. 51(8), 839–844 (2008).
[CrossRef]

Koschny, T.

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

Kuo, P.

Lagarkov, A. N.

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]

Lee, C.-K.

Li, K.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B 71(11), 115409 (2005).
[CrossRef]

Li, X.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B 71(11), 115409 (2005).
[CrossRef]

Lin, D.-Z.

Linden, S.

Lv, X.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

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]

Malnev, V. N.

Meinzer, N.

Muller, A.

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[CrossRef]

Narimanov, E. E.

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

Noginov, M. A.

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

A. Govyadinov, V. 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. 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]

O’Reilly, E. P.

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]

Olitzky, J. D.

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.

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]

Plum, E.

Podolskiy, V.

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

Popov, A. K.

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]

Protsenko, I. E.

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]

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67(20), 201101 (2003).
[CrossRef]

Ran, L.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Rapoport, Y. G.

Ritzo, B. A.

Rosenthal, A. S.

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A 79(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. A 71(6), 063812 (2005).
[CrossRef]

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. B 75(8), 085436 (2007).
[CrossRef]

Shalaev, V. M.

Shen, Y. R.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006).
[CrossRef] [PubMed]

Shih, C. K.

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[CrossRef]

Si, L.-M.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Small, C. E.

Soukoulis, C. M.

Stockman, M. I.

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

M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10(2), 025031 (2008).
[CrossRef]

M. I. Stockman, “Spasers explained,” Nat. Photonics 2(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. B 71(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,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Suteewong, T.

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

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. B 75(8), 085436 (2007).
[CrossRef]

Tsai, D. P.

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]

Wang, F.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006).
[CrossRef] [PubMed]

Wang, Q. Q.

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[CrossRef]

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,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Xin, H.

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Xue, Q. K.

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[CrossRef]

Yu, Y.-Y.

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]

Zheludev, N. I.

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, 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]

Appl. Phys. Lett. (2)

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

A. Muller, Q. Q. Wang, P. Bianucci, C. K. Shih, and Q. K. Xue, “Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations,” Appl. Phys. Lett. 84(6), 981–983 (2004).
[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. Opt. (2)

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

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

J. Opt. Soc. Am. B (1)

Materials (1)

L.-M. Si, T. Jiang, K. Chang, T.-C. Chen, X. Lv, L. Ran, and H. Xin, “Active microwave metamaterials incorporating ideal gain devices,” Materials 4(1), 73–83 (2011).
[CrossRef]

Nat. Photonics (2)

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

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

Nature (1)

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]

New J. Phys. (1)

M. I. Stockman, “Ultrafast nanoplasmonics under coherent control,” New J. Phys. 10(2), 025031 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (2)

A. S. Rosenthal and T. Ghannam, “Dipole nanolasers: A study of their quantum properties,” Phys. Rev. A 79(4), 043824 (2009).
[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 (3)

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, “Surface plasmon amplification by stimulated emission in nanolenses,” Phys. Rev. B 71(11), 115409 (2005).
[CrossRef]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75(8), 085436 (2007).
[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]

Phys. Rev. Lett. (2)

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. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006).
[CrossRef] [PubMed]

Phys. Usp. (2)

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, “Nanoplasmonics,” Phys. Usp. 51(8), 839–844 (2008).
[CrossRef]

Other (7)

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

R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, 1969).

P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press, 1994).

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

M. A. Noginov, G. Zhu, V. P. Drachev, and V. M. Shalaev, “Surface plasmons and gain media,” in Nanophotonics with Surface Plasmons, V. M. Shalaev and S. Kawata, eds. (Elsevier, 2007).

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization. A Universal Concept in Nonlinear Sciences (Cambridge University Press, 2001).

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

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Figures (4)

Fig. 1
Fig. 1

Stationary amplitudes a and σ are shown by dash-double dotted and dash-dotted lines, respectively. The stable solution for D is shown by the solid line. The unstable solution appearing for D> D th is shown by the dashed line. For D 0 = D 0 (also shown in Fig. 2) the stable and unstable solutions of D are marked by red dots.

Fig. 2
Fig. 2

The stationary values of D as a function of the amplitude of the external field for (a) zero ( Δ=0 ) and (b) non-zero ( Δ= 10 11 s 1 ) detuning. For both graphs τ a = 10 14 s , τ σ = 10 11 s , τ D =0.5 10 14 s , Ω R = 10 13 s 1 , D 0 = D 0 =0.55 .

Fig. 3
Fig. 3

The dependence of the plasmon dipole moment on the amplitude of the external field and the frequency detuning Δ. The speckle structure at low values of E corresponds to the chaotic behavior of the dipole moment.

Fig. 4
Fig. 4

The potential U(φ) for | ξ/Δ |<1 (dashed blue line) and | ξ/Δ |>1 (solid red line).

Equations (19)

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H ^ = H ^ SP + H ^ TLS + V ^ + Г ^ ,
H ^ SP = ω SP a ˜ ^ (t) a ˜ ^ (t),
H ^ TLS = ω TLS σ ˜ ^ (t) σ ˜ ^ (t)
E ^ NP = q ω q 2 W q [ a ^ q E q ( r )exp( i ω q t )+ a ^ q + E q ( r )exp( i ω q t ) ] ,
W q = 1 4π ( Reε ω 2 ) ω 2 | ω q E q E q dV= 1 8π ( 2Reε+ω Reε ω ) | ω SP E 1 E 1 dV
W 1 = 1 8π volume ofNP ω Reε ω | ω SP E 1 E 1 dV = | μ 1 | 2 6 r NP 3 ω Reε ω | ω SP ,
V ^ = Ω R ( a ^ σ ^ + σ ^ a ^ ),
D ^ · =2i Ω R ( a ^ σ ^ σ ^ a ^ ) D ^ D ^ 0 τ D ,
σ ^ · =(i δ TLS 1 τ σ ) σ ^ +i Ω R a ^ D ^ ,
a ^ · =(i δ SP 1 τ a ) a ^ i Ω R σ ^ ,
a= e iφ 2 ( D 0 D th ) τ a τ D ,σ= e iψ 2 ( D 0 D th )( δ SP 2 +1/ τ a 2 ) τ a Ω R 2 τ D , D= D th ,ω= ω SP τ a + ω TLS τ σ τ a + τ σ ,
H ^ ef = H ^ + Ω 1 ( a ˜ ^ + a ˜ ^ )( exp( i ω f t )+exp( i ω f t ) ) + Ω 2 ( σ ˜ ^ + σ ˜ ^ )( exp( i ω f t )+exp( i ω f t ) ),
D ^ · =2i Ω R ( a ^ σ ^ σ ^ a ^ )+2i Ω 2 ( σ ^ σ ^ ) D ^ D ^ 0 τ D ,
σ ^ · =(i Δ TLS 1 τ σ ) σ ^ +i Ω R a ^ D ^ +i Ω 2 D ^ ,
a ^ · =(i Δ SP 1 τ a ) a ^ i Ω R σ ^ i Ω 1 .
α r NP 3 = 3 2( Δ SP +i/ τ a ) ( ε NP (ω) ω ) 1 ,
φ · =Δ Ω R | σ | | a | cos( ψφ ) Ω | a | cosφ.
φ · =Δξcosφ,
φ · = U( φ ) φ .

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