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

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [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). [CrossRef]
11. 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]
12. 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]
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]
14. 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]
15. 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]
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]
19. 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]
20. 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]
21. 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]
22. 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]
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]

Adv. Funct. Mater.

• 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]

IEEE J. Quantum Electron.

• 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]

IEEE J. Sel. Top. Quantum Electron.

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

J. Mod. Opt.

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

Nano Lett.

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

Nat. Photonics

• S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]
• N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing Spaser,” Nat. Photonics 2(6), 351–354 (2008). [CrossRef]

Nature

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

Opt. Express

• 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]
• 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]
• 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, 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]

Opt. Lett.

• 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]

Phys. Rev.

• 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]

Phys. Rev. B

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

Phys. Rev. Lett.

• 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]
• 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]
• 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]
• 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. 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]
• 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]
• 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]
• 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]

Science

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

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