Abstract

The phenomenon of surface plasmon (SP) laser based on a square array of rectangular cavities cut into a metal substrate has been investigated. Both main resonant modes of the proposed structure can be used to realize SP laser while the working mechanism is different. We study the origin of these differences and propose an efficient design that exploits them. Besides, the effect of the sample size on SPP mode lasing is also discussed.

© 2010 OSA

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  1. 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]
  2. M. I. Stockman, “Spasers explained,” Nat. Photonics 2(6), 327–329 (2008).
    [CrossRef]
  3. J. A. Gordon, and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser” Opt. Expr. 15, 2622 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2622 .
  4. M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain” Opt. Expr. 16, 19785 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19785 .
  5. Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Resonance amplification of left-handed transmission at optical frequencies by stimulated emission of radiation in active metamaterials” Opt. Expr. 16, 20974 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20974 .
  6. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
    [CrossRef]
  7. Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
    [CrossRef]
  8. 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]
  9. M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
    [CrossRef] [PubMed]
  10. A. Banerjee, R. Li, and H. Grebel, “Surface plasmon lasers with quantum dots as gain media,” Appl. Phys. Lett. 95(25), 251106 (2009).
    [CrossRef]
  11. C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
    [CrossRef]
  12. C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
    [CrossRef]
  13. C. F. Klingshirn, Semiconductor Optics, (3rd edition, Springer, 2007).
  14. M. I. Stockman, “The Spaser as a nanoscale quantum generator and ultrafast amplifer,” J. Opt. 12(2), 024004 (2010).
    [CrossRef]

2010 (1)

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

2009 (3)

A. Banerjee, R. Li, and H. Grebel, “Surface plasmon lasers with quantum dots as gain media,” Appl. Phys. Lett. 95(25), 251106 (2009).
[CrossRef]

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (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. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

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

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

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

2007 (1)

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

2003 (1)

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]

Ambati, M.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[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, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Banerjee, A.

A. Banerjee, R. Li, and H. Grebel, “Surface plasmon lasers with quantum dots as gain media,” Appl. Phys. Lett. 95(25), 251106 (2009).
[CrossRef]

Bartal, G.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[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.

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]

Cao, J. X.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

Dong, Z. G.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

Fedotov, V. A.

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

Genov, D. A.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

Grebel, H.

A. Banerjee, R. Li, and H. Grebel, “Surface plasmon lasers with quantum dots as gain media,” Appl. Phys. Lett. 95(25), 251106 (2009).
[CrossRef]

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, C. P.

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Li, J. Q.

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

Li, R.

A. Banerjee, R. Li, and H. Grebel, “Surface plasmon lasers with quantum dots as gain media,” Appl. Phys. Lett. 95(25), 251106 (2009).
[CrossRef]

Li, T.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

Liu, H.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

Nam, S. H.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

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]

Papasimakis, N.

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

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]

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, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Stockman, M. I.

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

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

Ulin-Avila, E.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

Wang, Q. J.

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Wang, S. M.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

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]

Yin, X. G.

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

Zhang, X.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(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,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Zhu, S. N.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

Zhu, Y. Y.

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Zhu, Z. H.

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

A. Banerjee, R. Li, and H. Grebel, “Surface plasmon lasers with quantum dots as gain media,” Appl. Phys. Lett. 95(25), 251106 (2009).
[CrossRef]

C. P. Huang, J. Q. Li, Q. J. Wang, X. G. Yin, and Y. Y. Zhu, “Light reflection from a metal surface with subwavelength cavities,” Appl. Phys. Lett. 93(8), 081917 (2008).
[CrossRef]

J. Opt. (1)

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

Nano Lett. (1)

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

Nat. Photonics (2)

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

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

Phys. Rev. B (2)

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials,” Phys. Rev. B 80(23), 235116 (2009).
[CrossRef]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

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]

Other (4)

J. A. Gordon, and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser” Opt. Expr. 15, 2622 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2622 .

M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain” Opt. Expr. 16, 19785 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19785 .

Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Resonance amplification of left-handed transmission at optical frequencies by stimulated emission of radiation in active metamaterials” Opt. Expr. 16, 20974 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20974 .

C. F. Klingshirn, Semiconductor Optics, (3rd edition, Springer, 2007).

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Figures (4)

Fig. 1
Fig. 1

(a) the schematic of our designed structure; a square array of cuboid cavities are carved into the metal substrate with a dielectric overlay, (b) the top-view and (c) the side-view of the unit cell, where p = 1100nm, a = 250nm, b = 375nm, t = 500nm, h = 250nm.

Fig. 2
Fig. 2

The reflection spectra for normal incidence linearly polarized light on the periodic cavities for (a) the structure without gain media present and (b-d) the structure with gain media at different location as indicated in each inset. The red and blue curves represent the simulation results of gain media with different center frequencies at νg = 193.9THz and νg = 236.2THz, respectively. Inset A and B in (a) show the magnetic field (Hy ) distribution corresponding dip A and dip B, respectively.

Fig. 3
Fig. 3

(a) and (b) are calculated reflection spectra as function of αg and frequency for dip A and dip B, respectively. Data are shown with a logarithm scale.

Fig. 4
Fig. 4

Calculated E-field distribution for the SPP mode of finite array samples, (a) and (b) are corresponding to ∞ × 5 units array with and without gain medium, (c) 23 × ∞ units array with gain medium. The samples are illuminated by a line source along x-direction which are denoted by arrows.

Equations (3)

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λ c = 2 π ε Ι Ι / ( u 2 + v 2 ) ,
ε ( ω ) = ε b + χ 0 ω g 2 ω g 2 ω 2 + i γ g ω
α = ω 100 × c 0 Im ε ( ω )

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