Abstract

We show that in plasmonic systems, exact loss compensation can be achieved with the help of spasers pumped over a wide range of pumping values both below and above the spasing threshold. We demonstrate that the difference between spaser operation below and above the spasing threshold vanishes, when the spaser is synchronized by an external field. As the spasing threshold loses its significance, a new pumping threshold, the threshold of loss compensation, arises. Below this threshold, which is smaller than the spasing threshold, compensation is impossible at any frequency of the external field.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  36. J. B. Pendry and S. A. Maier, “Comment on ‘Spaser action, loss compensation, and stability in plasmonic systems with gain’,” Phys. Rev. Lett.107(25), 259703, discussion 259704 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2013 (1)

2012 (6)

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]

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,” Physics-Uspekhi55(10), 1046–1053 (2012).
[CrossRef]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative 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, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (2012).
[CrossRef]

2011 (6)

J. B. Pendry and S. A. Maier, “Comment on ‘Spaser action, loss compensation, and stability in plasmonic systems with gain’,” Phys. Rev. Lett.107(25), 259703, discussion 259704 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Stockman Replies,” Phys. Rev. Lett.107(25), 259702 (2011).
[CrossRef]

M. I. Stockman, “Loss compensation by gain and spasing,” Philos Trans A Math Phys Eng Sci369(1950), 3510–3524 (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]

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]

2010 (5)

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

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[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, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt.12(2), 024004 (2010).
[CrossRef]

2009 (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]

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]

2008 (2)

2007 (2)

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[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]

2006 (3)

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

I. E. Protsenko and E. P. O’Reilly, “Dipole lasing phase transitions in media with singularities in polarizabilities,” Phys. Rev. A74(3), 033815 (2006).
[CrossRef]

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]

2005 (1)

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]

2003 (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]

S. Anantha 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]

1936 (1)

U. Fano, “Some theoretical considerations on anomalous diffraction gratings,” Phys. Rev.50(6), 573 (1936).
[CrossRef]

Adegoke, J.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

Adegoke, J. A.

Anantha Ramakrishna, S.

S. Anantha 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]

Andrianov, E. S.

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. Express21(9), 10779–10791 (2013).
[CrossRef] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative 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,” Physics-Uspekhi55(10), 1046–1053 (2012).
[CrossRef]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (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]

Bahoura, M.

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. Express16(2), 1385–1392 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

Baranov, D. G.

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]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Dorofeenko, A. V.

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative 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,” Physics-Uspekhi55(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. Express19(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]

Drachev, V. P.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

Fang, A.

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

Fano, U.

U. Fano, “Some theoretical considerations on anomalous diffraction gratings,” Phys. Rev.50(6), 573 (1936).
[CrossRef]

García-Pomar, J. L.

Ghannam, T.

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

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[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]

Hess, O.

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]

Khurgin, J. B.

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]

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]

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]

Koschny, T.

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

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]

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]

Linden, S.

Lisyansky, A. A.

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. Express21(9), 10779–10791 (2013).
[CrossRef] [PubMed]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Physics-Uspekhi55(10), 1046–1053 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative 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, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (2012).
[CrossRef]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (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]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Maier, S. A.

J. B. Pendry and S. A. Maier, “Comment on ‘Spaser action, loss compensation, and stability in plasmonic systems with gain’,” Phys. Rev. Lett.107(25), 259703, discussion 259704 (2011).
[CrossRef] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Mayy, M.

Meinzer, N.

Noginov, M. A.

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. Express16(2), 1385–1392 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

O’Reilly, E. P.

I. E. Protsenko and E. P. O’Reilly, “Dipole lasing phase transitions in media with singularities in polarizabilities,” Phys. Rev. A74(3), 033815 (2006).
[CrossRef]

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]

Pendry, J.

S. Anantha 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]

Pendry, J. B.

J. B. Pendry and S. A. Maier, “Comment on ‘Spaser action, loss compensation, and stability in plasmonic systems with gain’,” Phys. Rev. Lett.107(25), 259703, discussion 259704 (2011).
[CrossRef] [PubMed]

Podolskiy, V. A.

Popov, A. K.

Protsenko, I. E.

I. E. Protsenko and E. P. O’Reilly, “Dipole lasing phase transitions in media with singularities in polarizabilities,” Phys. Rev. A74(3), 033815 (2006).
[CrossRef]

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. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (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,” Physics-Uspekhi55(10), 1046–1053 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative 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, “Forced synchronization of spaser by an external optical wave,” Opt. Express19(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]

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]

Reynolds, K.

Ritzo, B. A.

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. Express16(2), 1385–1392 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

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]

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. 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.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

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]

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]

Small, C.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

Soukoulis, C. M.

Stockman, M. I.

M. I. Stockman, “Loss compensation by gain and spasing,” Philos Trans A Math Phys Eng Sci369(1950), 3510–3524 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Stockman Replies,” Phys. Rev. Lett.107(25), 259702 (2011).
[CrossRef]

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

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

Sun, G.

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]

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]

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. 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]

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]

Vinogradov, A. P.

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. Express21(9), 10779–10791 (2013).
[CrossRef] [PubMed]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative 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,” Physics-Uspekhi55(10), 1046–1053 (2012).
[CrossRef]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (2012).
[CrossRef]

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (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]

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]

Wegener, M.

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. A71(6), 063812 (2005).
[CrossRef]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Zhu, G.

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. Express16(2), 1385–1392 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

AIP Conf. Proc. (1)

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Using spaser-effect for loss compensation in metamaterials,” AIP Conf. Proc.1475, 92–94 (2012).
[CrossRef]

Appl. Phys. B (1)

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B86(3), 455–460 (2007).
[CrossRef]

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]

J. Opt. (3)

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]

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

Nat. Mater. (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Philos Trans A Math Phys Eng Sci (1)

M. I. Stockman, “Loss compensation by gain and spasing,” Philos Trans A Math Phys Eng Sci369(1950), 3510–3524 (2011).
[CrossRef] [PubMed]

Phys. Rev. (1)

U. Fano, “Some theoretical considerations on anomalous diffraction gratings,” Phys. Rev.50(6), 573 (1936).
[CrossRef]

Phys. Rev. A (3)

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

I. E. Protsenko and E. P. O’Reilly, “Dipole lasing phase transitions in media with singularities in polarizabilities,” Phys. Rev. A74(3), 033815 (2006).
[CrossRef]

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]

Phys. Rev. B (4)

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Stationary behavior of a chain of interacting spasers,” Phys. Rev. B85(16), 165419 (2012).
[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]

E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, “Rabi oscillations in spasers during non-radiative plasmon excitation,” Phys. Rev. B85(3), 035405 (2012).
[CrossRef]

S. Anantha 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]

Phys. Rev. Lett. (6)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett.90(2), 027402 (2003).
[CrossRef] [PubMed]

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

J. B. Pendry and S. A. Maier, “Comment on ‘Spaser action, loss compensation, and stability in plasmonic systems with gain’,” Phys. Rev. Lett.107(25), 259703, discussion 259704 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Stockman Replies,” Phys. Rev. Lett.107(25), 259702 (2011).
[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]

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

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]

Physics-Uspekhi (1)

A. P. Vinogradov, E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “Quantum plasmonics of metamaterials: loss compensation using spasers,” Physics-Uspekhi55(10), 1046–1053 (2012).
[CrossRef]

Other (8)

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

A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986).

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

V. P. Bykov, Laser Electrodynamics (Cambridge Scholars, 2008).

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

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), p. 558.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, 1995), Vol. 8, p. 460.

I. E. Tamm, Fundamentals of the theory of electricity (Mir, Moscow, 1979).

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Figures (8)

Fig. 1
Fig. 1

The dependencies of spaser’s parameters (in arbitrary units) on the amplitude of the external field (a) below and (b) above the pumping threshold D th =0.1 . The NP dipole moment, the TLS dipole moment, and the inversion are shown by solid, dashed, and dot-dashed lines, respectively. The values of pumping for Figs. (a) and (b) are D 0 bt =0.07 and D 0 at =0.12 , respectively. The irregular behavior of NP and TLS dipole moments at small fields corresponds to spaser stochastic oscillations outside the Arnold tongue [12]. Note, that the ratio of E max ( D 0 ) below and above threshold ( μ TLS E max ( D 0 bt )/=0.8 10 12 s 1 and μ TLS E max ( D 0 at )/=1.1 10 12 s 1 , respectively) is of the order of the ratio of corresponding pumping values.

Fig. 2
Fig. 2

The dependence of ϕ= tan 1 (Im d spaser /Re d spaser ) on the amplitude of the external field E and the detuning Δ E for above-threshold pumping. The smooth part of the surface corresponds to the Arnold tongue where the spaser is synchronized by the external field while the speckle structure at low field corresponds to the spaser’s stochastic behavior. At the discontinuity line, on which ϕ=π , loss is exactly compensated. In this and subsequent figures, except for the value of pumping, D 0 =0.12 , the calculations are made for the following values of parameters: τ a = 10 14 s , τ σ = 10 11 s , τ D = 10 13 s , and Ω R = 10 13 s 1 .

Fig. 3
Fig. 3

The dependencies of imaginary parts of dipole moments of the whole spaser, which has D th =0.1 , on the frequency detuning (dot-dashed lines) in the external field for the level of pumping of (a) D 0 =0.9 and (b) D 0 =0.08 . Solid and dashed lines show imaginary parts of dipole moments of the NP and the TLS, respectively. The imaginary part of the dipole moment of the NP not interacting with the TLS in the external field is shown by the double dot-dashed line. This dependency is very slow and looks like a horizontal line at the scale of the figure.

Fig. 4
Fig. 4

The dependence of ϕ= tan 1 (Im d spaser /Re d spaser ) on the amplitude of the external field E and the frequency detuning Δ E in the below-threshold pumping, D 0 =0.08 . The Arnold tongue occupies the whole half-plane, so that the spaser is always synchronized by the external field. At the discontinuity line, on which ϕ=π , loss is exactly compensated.

Fig. 5
Fig. 5

The dependence of ϕ= tan 1 (Im d spaser /Re d spaser ) on the amplitude of the external field E and the detuning Δ E in the below-threshold pumping, D 0 =0.05 . The pumping is insufficient for loss compensation, so that the compensation line doesn’t exist.

Fig. 6
Fig. 6

The maximum value of the external field at which exact compensation takes place as a function of pumping.

Fig. 7
Fig. 7

The dependencies of D comp (solid line) and D th (dashed line) on Ω R .

Fig. 8
Fig. 8

Part of the compensation curves for small frequency detuning. Solid (red), dashed (blue), and dot-dashed (green) lines correspond to the pumping above (D0 = 0.12), at (D0 = Dth = 0.10.1), and below (D0 = 0.08) the threshold, respectively.

Equations (31)

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

d ¨ NP + ω SP 2 d NP =0.
d ^ NP = μ NP ( a ˜ ^ + a ˜ ^ ).
H ^ SP = ω SP 2 ( a ˜ ^ a ˜ ^ + a ˜ ^ a ˜ ^ ).
ω SP 2 = 1 8π Re( ωε(ω) ) ω | ω SP | E NP | 2 dV = 1 8π ( Reε(ω)+ω Reε(ω) ω ) | ω SP | E NP | 2 dV ,
ω SP 2 = 1 8π volume ofNP ω Re ε NP (ω) ω | ω SP | E NP | 2 dV ,
ω SP 2 = | μ NP | 2 6 r NP 3 ω SP Reε ω | ω pl ,
μ NP = 3 r NP 3 /( Re ε NP ω ) μ 1 | μ 1 | .
μ ^ TLS = μ TLS ( σ ˜ ^ (t)+ σ ˜ ^ (t) ),
H ^ TLS = ω TLS σ ˜ ^ σ ˜ ^ ,
H ^ = H ^ SP + H ^ TLS + V ^ + Г ^ ,
V ^ = Ω R ( a ˜ ^ + a ˜ ^ )( σ ˜ ^ + σ ˜ ^ ).
V ^ = Ω R ( a ^ σ ^ + σ ^ a ^ )
D ^ · =2i Ω R ( a ^ σ ^ σ ^ a ^ )( D ^ D ^ 0 ) τ D 1 ,
σ ^ · =( iδ τ σ 1 ) σ ^ +i Ω R a ^ D ^ ,
a ^ · =( iΔ τ a 1 ) a ^ i Ω R σ ^ .
D th = [ 1+ ( ω SP ω a ) 2 τ a 2 ] / ( Ω R 2 τ a τ σ ) ,
ω a = ( ω SP τ a + ω TLS τ σ ) / ( τ a + τ σ ) .
H ^ eff = H ^ + Ω 1 ( a ˜ ^ + a ˜ ^ )( e iνt + e iνt )+ Ω 2 ( σ ˜ ^ + σ ˜ ^ )( e iνt + e iνt ),
D ^ · =2i Ω R ( a ^ σ ^ σ ^ a ^ )+2i Ω 2 ( σ ^ σ ^ ) τ D 1 ( D ^ D ^ 0 ),
σ ^ · =(i δ E τ σ 1 ) σ ^ +i Ω R a ^ D ^ +i Ω 2 D ^ ,
a ^ · =(i Δ E τ a 1 ) a ^ i Ω R σ ^ i Ω 1 .
D ^ · =2i Ω 2 ( σ ^ σ ^ )( D ^ D ^ 0 ) τ D 1 ,
σ ^ · =( i δ E τ σ 1 ) σ ^ +i Ω 2 D ^ ,
a ^ · =( i Δ E τ a 1 ) a ^ i Ω 1 .
a st = ( Δ E +i τ a 1 ) μ NP / Δ E 2 + τ a 2 E,
σ st = D 0 ( δ E i τ D 1 ) μ TLS / τ σ 2 + δ E 2 +4 ( μ TLS E/ ) 2 2 τ D τ σ 2 E,
D st = D 0 ( δ E 2 + τ σ 2 ) τ σ 2 + δ E 2 +4 ( μ TLS E/ ) 2 2 τ D τ σ 1 .
D 0 = ( μ NP μ TLS ) 2 τ σ τ a τ σ 2 + δ E 2 +4 ( μ TLS E/ ) 2 2 τ D τ σ 1 Δ E 2 + τ a 2 ,
Δ E + δ E τ σ / τ a <0.
f=( ω+q )/( ω 2 +1 ),
Im μ tot ( Δ E + Ω R | D 0 | μ TLS / μ NP ) 2 +| D 0 |/ τ a τ σ ( Δ E 2 τ a 2 ( 1/ τ a τ σ + Ω R 2 | D 0 | ) ) 2 + Δ E 2 .

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