Abstract

We performed a rigorous study to reduce threshold gain of Au-nanoparticle lasers in the deep-subwavelength scale with the consideration of strong interband transitions in Au and device dimensions. We found that the high-threshold optical gain of the nanolaser (over 105cm1, which is matched with the result estimated from a previous article [Nature 460, 1110 (2009)]) arises from the high interband transition of Au near 530nm. It can be shown that by increasing the background index, as well as optimizing the lasing wavelength and device dimensions, the threshold gain (cavity volume) can be reduced by 43% (90%).

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef] [PubMed]
  2. H. A. Atwater, Sci. Am. 296, 56 (2007).
    [CrossRef] [PubMed]
  3. N. M. Lawandy, Appl. Phys. Lett. 90, 143104 (2007).
    [CrossRef]
  4. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  5. 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, Nature 460, 1110 (2009).
    [CrossRef] [PubMed]
  6. F. J. Garcia-Vidal and E. Moreno, Nature 461, 604 (2009).
    [CrossRef] [PubMed]
  7. J. Heber, Nature 461, 720 (2009).
    [CrossRef] [PubMed]
  8. According to , 2.7×103 dye molecules are distributed mainly in a region from r=7 to 12nm, and the peak absorption cross section is estimated to be 2.55×10−16cm2. The lasing threshold is then estimated to be Gth∼1.19×105cm−1.
  9. N. M. Lawandy, Appl. Phys. Lett. 85, 5040 (2004).
    [CrossRef]
  10. J. A. Gordon and R. W. Ziolkowski, Opt. Express 15, 2622 (2007).
    [CrossRef] [PubMed]
  11. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
    [CrossRef] [PubMed]
  12. X. F. Li, S. F. Yu, and A. Kumar, Appl. Phys. Lett. 95, 141114 (2009).
    [CrossRef]
  13. J. D. Jackson, Classical Electrodynamics, 3rd ed.(Academic, 1999).
  14. L. M. Liz-Marzan, M. Giersig, and P. Mulvaney, Langmuir 12, 4329 (1996).
    [CrossRef]

2009 (4)

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, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

F. J. Garcia-Vidal and E. Moreno, Nature 461, 604 (2009).
[CrossRef] [PubMed]

J. Heber, Nature 461, 720 (2009).
[CrossRef] [PubMed]

X. F. Li, S. F. Yu, and A. Kumar, Appl. Phys. Lett. 95, 141114 (2009).
[CrossRef]

2007 (3)

H. A. Atwater, Sci. Am. 296, 56 (2007).
[CrossRef] [PubMed]

N. M. Lawandy, Appl. Phys. Lett. 90, 143104 (2007).
[CrossRef]

J. A. Gordon and R. W. Ziolkowski, Opt. Express 15, 2622 (2007).
[CrossRef] [PubMed]

2006 (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

2004 (1)

N. M. Lawandy, Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

2003 (1)

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

1996 (1)

L. M. Liz-Marzan, M. Giersig, and P. Mulvaney, Langmuir 12, 4329 (1996).
[CrossRef]

Atwater, H. A.

H. A. Atwater, Sci. Am. 296, 56 (2007).
[CrossRef] [PubMed]

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, 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, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Bergman, D. J.

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

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal and E. Moreno, Nature 461, 604 (2009).
[CrossRef] [PubMed]

Giersig, M.

L. M. Liz-Marzan, M. Giersig, and P. Mulvaney, Langmuir 12, 4329 (1996).
[CrossRef]

Gordon, J. A.

Heber, J.

J. Heber, Nature 461, 720 (2009).
[CrossRef] [PubMed]

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, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed.(Academic, 1999).

Kumar, A.

X. F. Li, S. F. Yu, and A. Kumar, Appl. Phys. Lett. 95, 141114 (2009).
[CrossRef]

Lawandy, N. M.

N. M. Lawandy, Appl. Phys. Lett. 90, 143104 (2007).
[CrossRef]

N. M. Lawandy, Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Li, X. F.

X. F. Li, S. F. Yu, and A. Kumar, Appl. Phys. Lett. 95, 141114 (2009).
[CrossRef]

Liz-Marzan, L. M.

L. M. Liz-Marzan, M. Giersig, and P. Mulvaney, Langmuir 12, 4329 (1996).
[CrossRef]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Moreno, E.

F. J. Garcia-Vidal and E. Moreno, Nature 461, 604 (2009).
[CrossRef] [PubMed]

Mulvaney, P.

L. M. Liz-Marzan, M. Giersig, and P. Mulvaney, Langmuir 12, 4329 (1996).
[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, 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, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Shalaev, V. M.

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

Stockman, M. I.

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, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (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, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Wiesner, U.

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

Yu, S. F.

X. F. Li, S. F. Yu, and A. Kumar, Appl. Phys. Lett. 95, 141114 (2009).
[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, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Ziolkowski, R. W.

Appl. Phys. Lett. (3)

N. M. Lawandy, Appl. Phys. Lett. 90, 143104 (2007).
[CrossRef]

N. M. Lawandy, Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

X. F. Li, S. F. Yu, and A. Kumar, Appl. Phys. Lett. 95, 141114 (2009).
[CrossRef]

J. Chem. Phys. (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Langmuir (1)

L. M. Liz-Marzan, M. Giersig, and P. Mulvaney, Langmuir 12, 4329 (1996).
[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, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

F. J. Garcia-Vidal and E. Moreno, Nature 461, 604 (2009).
[CrossRef] [PubMed]

J. Heber, Nature 461, 720 (2009).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. Lett. (1)

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

Sci. Am. (1)

H. A. Atwater, Sci. Am. 296, 56 (2007).
[CrossRef] [PubMed]

Other (3)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

According to , 2.7×103 dye molecules are distributed mainly in a region from r=7 to 12nm, and the peak absorption cross section is estimated to be 2.55×10−16cm2. The lasing threshold is then estimated to be Gth∼1.19×105cm−1.

J. D. Jackson, Classical Electrodynamics, 3rd ed.(Academic, 1999).

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 (4)

Fig. 1
Fig. 1

(a) Schematic of an NPL composed of an Au core (with radius R M and permittivity ε M ), an active region (with radius R G and permittivity ε G ), and an infinite background dielectric (with permittivity ε B ). The static electric field has the amplitude of E 0 and wavelength of λ. Plots of (b) ( n G ) and (c) G th versus lasing wavelength λ 0 (fulfilling the singular condition) for different values of R M [i.e., 7 nm (solid curve), 10 nm (dashed curve), 20 nm (dotted curve), and 50 nm (dashed-dotted curve)]. The inset of Fig. 1c shows the lasing spectra with n G = 1.516 0.473 i as indicated by • [ λ 0 = 524 nm ) and n G = 2.884 0.223 i as indicated by ▪ ( λ 0 = 710 nm ) to obtain the lowest G th ].

Fig. 2
Fig. 2

Images of (a) ( n G ) and (b) G th in the plane of λ 0 and η. (c) Plot of G th versus η for different values of λ 0 [ 530 nm (solid curve), 560 nm (dashed curve), and 710 nm (dotted curve)]. (d) Minimal η versus λ 0 with different values of ξ [1% (solid curve), 2% (dashed curve), 5% (dotted curve), and 10% (dashed-dotted curve)]. (e) Minimal η versus ξ for different values of λ 0 [ 530 nm (solid curve), 560 nm (dashed curve), and 710 nm (dotted curve)], where the value used in [5] is also indicated.

Fig. 3
Fig. 3

Images of (a) ( n G ) and (b) G th in the plane of n B and η. Plots of (c) ( n G ) and (d) G th versus n B for several values of η (i.e., 1.10, 1.18, 1.28, 1.48, 1.88, and 4.08, as indicated by arrows). λ 0 = 710 nm is used in this calculation.

Fig. 4
Fig. 4

Images of (a) ( n G ) and (b) G th in the plane of λ 0 and η with n B = 3.25 used in the calculation. In the figure, the positions where ( n G ) 1.4 have been indicated by red dots.

Equations (2)

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

ε M = ε ω p 2 ω 2 + i γ ω + ε x 1 + ε x 2 ,
2 ( ε G ε M ) ( ε G ε A ) ( ε M + 2 ε G ) ( ε G + 2 ε A ) = η 3 ,

Metrics