Abstract

We find the conditions upon the amplitude and frequency of an external electromagnetic field at which the dipole moment of a Bergman–Stockman spaser oscillates in antiphase with the field. For these values of the amplitude and frequency the loss in metal nanoparticles is exactly compensated by the gain. This shows that spasers may be used as inclusions in designing lossless metamaterials.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Marques, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2008).
  2. W. Cai and V. Shalaev, Optical Metamaterials (Springer, 2010).
    [CrossRef]
  3. M. Premaratne and G. P. Agrawal, Light Propagation in Gain Medium (Cambridge University, 2011).
  4. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  5. D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef] [PubMed]
  6. I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
    [CrossRef]
  7. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  8. U. Leonhardt, IEEE J. Sel. Top. Quantum Electron. 9, 102 (2003).
    [CrossRef]
  9. K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
    [CrossRef]
  10. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
    [CrossRef] [PubMed]
  11. M. I. Stockman, J. Opt. 12, 024004 (2010).
    [CrossRef]
  12. 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,” arXiv:1105.5656v2 (2011).
  13. M. O. Scully and M. S. Zubairy, Quantum Optics(Cambridge University, 1997).
  14. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  15. R. H. Pantell and H. E. Puthoff, Fundamentals of Quantum Electronics (Wiley, 1969).
  16. I. E. Protsenko, Phys. Rev. A 71, 063812 (2005).
    [CrossRef]
  17. A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
    [CrossRef]
  18. A. S. Rosenthal and T. Ghannam, Phys. Rev. A 79, 043824(2009).
    [CrossRef]

2010

M. I. Stockman, J. Opt. 12, 024004 (2010).
[CrossRef]

2009

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
[CrossRef]

A. S. Rosenthal and T. Ghannam, Phys. Rev. A 79, 043824(2009).
[CrossRef]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

2008

I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
[CrossRef]

2005

I. E. Protsenko, Phys. Rev. A 71, 063812 (2005).
[CrossRef]

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
[CrossRef]

2003

U. Leonhardt, IEEE J. Sel. Top. Quantum Electron. 9, 102 (2003).
[CrossRef]

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

2000

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1968

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Agrawal, G. P.

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Medium (Cambridge University, 2011).

Andrianov, E. S.

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,” arXiv:1105.5656v2 (2011).

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Bergman, D. J.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
[CrossRef]

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Cai, W.

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

Dorofeenko, A. V.

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,” arXiv:1105.5656v2 (2011).

Ghannam, T.

A. S. Rosenthal and T. Ghannam, Phys. Rev. A 79, 043824(2009).
[CrossRef]

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Kissel, V. N.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
[CrossRef]

Krotova, K. E.

I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
[CrossRef]

Lagarkov, A. N.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
[CrossRef]

Leonhardt, U.

U. Leonhardt, IEEE J. Sel. Top. Quantum Electron. 9, 102 (2003).
[CrossRef]

Li, K.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
[CrossRef]

Li, X.

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
[CrossRef]

Lisyansky, A. A.

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,” arXiv:1105.5656v2 (2011).

Marques, R.

R. Marques, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2008).

Martin, F.

R. Marques, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2008).

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

O’Reilly, E. P.

I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
[CrossRef]

Palik, E. D.

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

Pantell, R. H.

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

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Premaratne, M.

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Medium (Cambridge University, 2011).

Protsenko, I. E.

I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
[CrossRef]

I. E. Protsenko, Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Pukhov, A. A.

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,” arXiv:1105.5656v2 (2011).

Puthoff, H. E.

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

Rosenthal, A. S.

A. S. Rosenthal and T. Ghannam, Phys. Rev. A 79, 043824(2009).
[CrossRef]

Sarychev, A. K.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
[CrossRef]

Scully, M. O.

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

Shalaev, V.

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

Shalaev, V. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Sorolla, M.

R. Marques, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2008).

Stockman, M. I.

M. I. Stockman, J. Opt. 12, 024004 (2010).
[CrossRef]

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
[CrossRef]

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Tartakovsky, G.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
[CrossRef]

Uskov, A. V.

I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vinogradov, A. P.

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,” arXiv:1105.5656v2 (2011).

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Zubairy, M. S.

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

IEEE J. Sel. Top. Quantum Electron.

U. Leonhardt, IEEE J. Sel. Top. Quantum Electron. 9, 102 (2003).
[CrossRef]

J. Opt.

M. I. Stockman, J. Opt. 12, 024004 (2010).
[CrossRef]

J. Phys.: Conf. Ser.

I. E. Protsenko, A. V. Uskov, K. E. Krotova, and E. P. O’Reilly, J. Phys.: Conf. Ser. 107, 012010 (2008).
[CrossRef]

Nature

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, and E. Herz, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Phys. Rev. A

A. S. Rosenthal and T. Ghannam, Phys. Rev. A 79, 043824(2009).
[CrossRef]

I. E. Protsenko, Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Phys. Rev. B

K. Li, X. Li, M. I. Stockman, and D. J. Bergman, Phys. Rev. B 71, 115409 (2005).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Phys. Usp.

A. N. Lagarkov, A. K. Sarychev, V. N. Kissel, and G. Tartakovsky, Phys. Usp. 52, 959 (2009).
[CrossRef]

Sov. Phys. Usp.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other

R. Marques, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications (Wiley, 2008).

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

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Medium (Cambridge University, 2011).

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,” arXiv:1105.5656v2 (2011).

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

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Dependences of the real (solid line) and imaginary (dashed line) parts of the NP dipole moment on the frequency detuning Δ for a value of the amplitude of the external field greater than the synchronization threshold, E > E Synch ( Δ ) .

Fig. 2
Fig. 2

Dependence of ϕ = tan 1 ( Im d NP / Re d NP ) on the amplitude of the external field E and the detuning Δ. The smooth part of the surface corresponds to the Arnold tongue where the spaser is synchronized by the external field. At the discontinuity line, on which ϕ = π , the loss is exactly compensated.

Fig. 3
Fig. 3

Dependence of the plasmon dipole moment on the amplitude of the external field for zero frequency detuning ( Δ = 0 ).

Equations (10)

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

H ^ auto = ω TLS σ ˜ ^ σ ˜ ^ + ω SP a ˜ ^ a ˜ ^ + Ω R ( a ˜ ^ σ ˜ ^ + σ ˜ ^ a ˜ ^ ) ,
D ^ ˙ = 2 i 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 ^ .
H ^ ef = H ^ auto + d ^ NP E ( t ) + d ^ TLS E ( t ) .
D ^ ˙ = 2 i Ω R ( a ^ σ ^ σ ^ a ^ ) + 2 i Ω 2 ( σ ^ σ ^ ) ( D ^ D ^ 0 ) / τ D ,
σ ^ ˙ = ( i δ 1 / τ σ ) σ ^ + i Ω R a ^ D ^ + i Ω 2 D ^ ,
a ^ ˙ = ( i Δ 1 / τ a ) a ^ i Ω R σ ^ i Ω 1 ,
α / r NP 3 = 3 2 ( ε / ω ) ( Δ + i / τ a ) .
( μ NP E / ) 2 = { ( τ σ 3 / τ a ) Δ 4 + [ D 0 Ω τ σ 3 ( μ TLS / μ NP ) / τ D ] Δ 3 [ ( τ σ / τ D ) Ω 2 D 0 τ a τ σ 2 / τ D ] Δ 2 } [ 4 ( τ σ Δ μ TLS / μ NP + τ a Ω ) 2 ] 1 .

Metrics