Surface plasmons amplifications in single Ag nanoring

Zhong-Jian Yang; Nam-Chol Kim; Jian-Bo Li; Mu-Tian Cheng; Shao-Ding Liu; Zhong-Hua Hao; Qu-Quan Wang

doi:10.1364/OE.18.004006

Surface plasmons amplifications in single Ag nanoring

Zhong-Jian Yang, Nam-Chol Kim, Jian-Bo Li, Mu-Tian Cheng, Shao-Ding Liu, Zhong-Hua Hao, and Qu-Quan Wang

Optics Express
Vol. 18,
Issue 5,
pp. 4006-4011
(2010)
•https://doi.org/10.1364/OE.18.004006

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Zhong-Jian Yang, Nam-Chol Kim, Jian-Bo Li, Mu-Tian Cheng, Shao-Ding Liu, Zhong-Hua Hao, and Qu-Quan Wang, "Surface plasmons amplifications in single Ag nanoring," Opt. Express 18, 4006-4011 (2010)

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Related Topics
Table of Contents Category
- Optics at Surfaces
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Waveguides (230.7370)
- Optical amplifiers (230.4480)
- Surface plasmons (240.6680)
- Quantum-well, -wire and -dot devices (250.5590)

About this Article
History
- Original Manuscript: December 18, 2009
- Revised Manuscript: January 21, 2010
- Manuscript Accepted: January 26, 2010
- Published: February 16, 2010

Accessible

Open Access

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.

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References

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Year
|
Author
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Publication

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]
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]
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]
S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007).
[Crossref]
W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]
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]
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]
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]
N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing Spaser,” Nat. Photonics 2(6), 351–354 (2008).
[Crossref]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42(10), 1991–2004 (1995).
[Crossref]
P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

2009 (5)

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]

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]

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]

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]

2008 (7)

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]

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]

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]

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]

2007 (5)

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]

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]

2006 (4)

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]

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]

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]

2005 (3)

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]

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]

2004 (1)

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

2003 (3)

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 (1)

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 (1)

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 (1)

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 (1)

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

1972 (1)

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

Abstreiter, G.

Adegoke, J.

Adegoke, J. A.

Akimov, A. V.

Ambati, M.

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.

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.

Beham, E.

Belgrave, A. M.

Bergman, D. J.

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.

Bichler, M.

Chang, D. E.

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.

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.

Dasari, R.

Davis, C. C.

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.

Eng, L.

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.

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

Feld, M. S.

Findeis, F.

Gammon, D.

Genov, D. A.

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.

Gong, H. M.

Grafström, S.

Halas, N. S.

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

Hemmer, P. R.

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]

Herz, E.

Itzkan, I.

Johnson, P. B.

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

Katzer, D. S.

Kneipp, H.

Kneipp, K.

Kumar, A.

Kuo, P.

Lal, S.

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

Lau, S. P.

Lee, H.

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]

Leon, I. D.

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]

Li, X.

Li, X. F.

Link, S.

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

Liu, S. D.

Liu, Z. W.

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]

Lukin, M. D.

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]

Luo, Q.

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

Ma, R. M.

Maier, S. A.

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

Mayy, M.

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]

Milonni, P. W.

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

Mukherjee, A.

Muller, A.

Nam, S. H.

Narimanov, E. E.

Noginov, M. A.

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]

Noginova, N.

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]

Oulton, R. F.

Ozbay, E.

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

Park, D.

Park, H.

Perelman, L. T.

Piermarocchi, C.

Plum, E.

Podolskiy, V. A.

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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.

Download Full Size | PPT Slide | PDF

Fig. 2 The change of N _sp(l) within short propagating length l. (a)

W_{10} \geq W_{01}^{c}

. (b)

W_{10} \leq W_{01}^{c}

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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.

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Equations (8)

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Q_{1} (r) = [{H^{'}}_{0} (k_{1 ⊥} r) \times (i k_{/ /} k_{1 ⊥} / k_{1}^{2}) \hat{r} + H_{0} (k_{1 ⊥} r) \times (k_{1 ⊥}^{2} / k_{1}^{2}) \hat{z}],

H_{int} = - ℏ g [\hat{a} σ_{10} \exp (i k_{/ /} z - i ω_{sp} t) + {\hat{a}}^{+} σ_{01} \exp (- i k_{/ /} z + i ω_{sp} t)],

d N_{sp} (l) υ_{sp} = Γ_{sp}^{(StE)} ρ_{eff} d l,

\frac{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 [\frac{N_{sp} (l)}{N_{sp}^{0}}] = (G^{0} - α) l + \frac{G^{0}}{α} \ln \frac{G^{0} - α [1 + N_{sp} (l) / N_{}^{'}]}{G^{0} - α [1 + N_{sp}^{0} / N_{}^{'}]},

N_{sp}^{max} = N_{}^{'} (G^{0} / α - 1) .