Abstract

The stimulated amplifications of surface plasmons (SPs) propagating along a single silver nanoring is theoretically investigated by considering the interactions between SPs and activated semiconductor quantum dots (SQDs). Threshold condition for the stimulated amplifications, the SP density as a function of propagation length and the maximum SP density are obtained. The SPs can be nonlinearly amplified when the pumping rate of SQDs is larger than the threshold, and the maximum value of SP density increases linearly with the pumping rate of SQDs.

© 2010 OSA

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    [CrossRef] [PubMed]
  2. E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311(5758), 189–193 (2006).
    [CrossRef] [PubMed]
  3. S. A. Maier, “Plasmonics: The Promise of Highly Integrated Optical Devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006).
    [CrossRef]
  4. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
    [CrossRef]
  5. S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007).
    [CrossRef]
  6. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
    [CrossRef]
  7. I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
    [CrossRef] [PubMed]
  8. Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
    [CrossRef] [PubMed]
  9. 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]
  10. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing Spaser,” Nat. Photonics 2(6), 351–354 (2008).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
    [CrossRef] [PubMed]
  17. 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]
  18. M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, “Active Plasmonics: Surface Plasmon Interaction With Optical Emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
    [CrossRef]
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  23. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
    [CrossRef] [PubMed]
  24. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007).
    [CrossRef]
  25. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007).
    [CrossRef] [PubMed]
  26. H. M. Gong, L. Zhou, X. R. Su, S. Xiao, S. D. Liu, and Q. Q. Wang, “Illuminating Dark Plasmons of Silver Nanoantenna Rings to Enhance Exciton–Plasmon Interactions,” Adv. Funct. Mater. 19(2), 298–303 (2009).
    [CrossRef]
  27. S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009).
    [CrossRef] [PubMed]
  28. T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87(13), 133603 (2001).
    [CrossRef] [PubMed]
  29. A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002).
    [CrossRef] [PubMed]
  30. Q. Q. Wang, A. Muller, M. T. Cheng, H. J. Zhou, P. Bianucci, and C. K. Shih, “Coherent control of a V-type three-level system in a single quantum dot,” Phys. Rev. Lett. 95(18), 187404 (2005).
    [CrossRef] [PubMed]
  31. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
    [CrossRef] [PubMed]
  32. P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42(10), 1991–2004 (1995).
    [CrossRef]
  33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]

2009

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

H. M. Gong, L. Zhou, X. R. Su, S. Xiao, S. D. Liu, and Q. Q. Wang, “Illuminating Dark Plasmons of Silver Nanoantenna Rings to Enhance Exciton–Plasmon Interactions,” Adv. Funct. Mater. 19(2), 298–303 (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]

S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009).
[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).
[CrossRef] [PubMed]

2008

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. Express 16(2), 1385–1392 (2008).
[CrossRef] [PubMed]

A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[CrossRef] [PubMed]

I. D. Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. 78, 161401 (2008).
[CrossRef]

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

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, “Active Plasmonics: Surface Plasmon Interaction With Optical Emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
[CrossRef]

2007

D. A. Genov, M. Ambati, and X. Zhang, “Surface Plasmon Amplification in Planar Metal Films,” IEEE J. Quantum Electron. 43(11), 1104–1108 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007).
[CrossRef]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007).
[CrossRef] [PubMed]

S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007).
[CrossRef]

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

2006

E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

S. A. Maier, “Plasmonics: The Promise of Highly Integrated Optical Devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[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]

2005

Q. Q. Wang, A. Muller, M. T. Cheng, H. J. Zhou, P. Bianucci, and C. K. Shih, “Coherent control of a V-type three-level system in a single quantum dot,” Phys. Rev. Lett. 95(18), 187404 (2005).
[CrossRef] [PubMed]

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

2004

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

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]

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
[CrossRef] [PubMed]

2002

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002).
[CrossRef] [PubMed]

2001

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87(13), 133603 (2001).
[CrossRef] [PubMed]

1997

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

1995

P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42(10), 1991–2004 (1995).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Abstreiter, G.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002).
[CrossRef] [PubMed]

Adegoke, J.

Adegoke, J. A.

Akimov, A. V.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007).
[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]

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, “Active Plasmonics: Surface Plasmon Interaction With Optical Emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
[CrossRef]

D. A. Genov, M. Ambati, and X. Zhang, “Surface Plasmon Amplification in Planar Metal Films,” IEEE J. Quantum Electron. 43(11), 1104–1108 (2007).
[CrossRef]

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]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

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]

Beham, E.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002).
[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]

Berini, P.

I. D. Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. 78, 161401 (2008).
[CrossRef]

Bianucci, P.

Q. Q. Wang, A. Muller, M. T. Cheng, H. J. Zhou, P. Bianucci, and C. K. Shih, “Coherent control of a V-type three-level system in a single quantum dot,” Phys. Rev. Lett. 95(18), 187404 (2005).
[CrossRef] [PubMed]

Bichler, M.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002).
[CrossRef] [PubMed]

Chang, D. E.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[CrossRef] [PubMed]

Cheng, M. T.

Q. Q. Wang, A. Muller, M. T. Cheng, H. J. Zhou, P. Bianucci, and C. K. Shih, “Coherent control of a V-type three-level system in a single quantum dot,” Phys. Rev. Lett. 95(18), 187404 (2005).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Dasari, R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Drachev, V. P.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Elliott, J.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

Eng, L.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Fedotov, V. A.

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Findeis, F.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002).
[CrossRef] [PubMed]

Gammon, D.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
[CrossRef] [PubMed]

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87(13), 133603 (2001).
[CrossRef] [PubMed]

Genov, D. A.

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, “Active Plasmonics: Surface Plasmon Interaction With Optical Emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
[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]

D. A. Genov, M. Ambati, and X. Zhang, “Surface Plasmon Amplification in Planar Metal Films,” IEEE J. Quantum Electron. 43(11), 1104–1108 (2007).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Gong, H. M.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the cross section of an Ag nanoring surrounded by SQDs. The nanoring and SQDs are embedded in a dielectric with electric permittivity ε 1. (b) Schematic of a small part of the ring with a SQD to show the stimulated emission. (c) Energy-level diagram of a two-level SQD, | 1 and | 0 are excited and ground states of the SQD, respectively.

Fig. 2
Fig. 2

The change of N sp(l) within short propagating length l. (a) W 10 W 01 c . (b) W 10 W 01 c .

Fig. 3
Fig. 3

(a) The calculated N sp(l) as a function of l after long distance propagation when W 10 > W 01 c . (b) The maximum SPs number per unit length N sp max as a function of the pumping rate of SQDs.

Equations (8)

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Q 1 ( r ) = [ H 0 ( k 1 r ) × ( i k / / k 1 / k 1 2 ) r ^ + H 0 ( k 1 r ) × ( k 1 2 / k 1 2 ) z ^ ] ,
H int = g [ a ^ σ 10 exp ( i k / / z i ω sp t ) + a ^ + σ 01 exp ( i k / / z + i ω sp t ) ] ,
d N sp ( l ) υ sp = Γ sp ( StE ) ρ eff d l ,
d ρ eff d t = η ( W 01 Γ sp (SpE) ) ρ eff ( W 01 + Γ sp (SpE) + 2 Γ sp (StE) ) ,
ρ eff = ρ eff 0 / ( 1 + N s p ( l ) / N ' ) ,
G = G 0 / [ 1 + N sp ( l ) / N ' ] α .
ln [ N sp ( l ) N sp 0 ] = ( G 0 α ) l + G 0 α ln G 0 α [ 1 + N sp ( l ) / N ' ] G 0 α [ 1 + N sp 0 / N ' ] ,
N sp max = N ' ( G 0 / α 1 ) .

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