Abstract

Interactions between a semiconducting gain medium and confined plasmon-polaritons are studied using a multilevel multi-thermal-electron finite-difference time-domain (MLMTE-FDTD) simulator. We investigated the amplification of wave propagating in a plasmonic metal-semiconductor-metal (MSM) waveguide filled with semiconductor gain medium and obtained the conditions required to achieve net optical gain. The MSM gain waveguide is used to form a plasmonic semiconductor nano-ring laser(PSNRL) with an effective mode volume of 0.0071μm3, which is about an order of magnitude smaller than the smallest demonstrated integrated photonic crystal based laser cavities. The simulation shows a lasing threshold current density of 1kA/cm2 for a 300nm outer diameter ring cavity with 80nm-wide ring. This current density can be realistically achieved in typical III-V semiconductor, which shows the experimental feasibility of the proposed PSNRL structure.

© 2010 OSA

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  54. Energy density at the steady state in the cavity is determined by: η=0.5⋅∫S(ε(r¯)⋅|E(r¯)|2+μ(r¯)⋅|H(r¯)|2)⋅dr¯(S is the area of the lasing cavity).
  55. The area of lasing cavity is calculated by:S=π⋅(dOD/ 2)2−(dID/2)2] = 5.48 × 10–10 cm2.

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

D. B. Li and C. Z. Ning, “Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure,” Phys. Rev. B 80(15), 153304 (2009).
[CrossRef]

L. Tang and T. Yoshie, “Monopole woodpile photonic crystal modes for light-matter interaction and optical trapping,” Opt. Express 17(3), 1346–1351 (2009).
[CrossRef] [PubMed]

2008 (6)

2007 (7)

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

R. M. Bakker, A. Boltasseva, Z. Liu, R. H. Pedersen, S. Gresillon, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Near-field excitation of nanoantenna resonance,” Opt. Express 15(21), 13682–13688 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

F. M. Kong, K. Li, B. I. Wu, H. Huang, H. S. Chen, and J. A. Kong, “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromag. Res. PIER 76, 449–466 (2007).
[CrossRef]

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Y. Kurokawa and H. T. Miyazaki, “Metal-Insulator-Metal plasmon nanocavities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007).
[CrossRef]

2006 (5)

M. Okoniewski and E. Pkoniewska, “Drude dispersion in ADE revisited,” IEE Electron. Lett. 42 (2006).

Y. Huang and S. T. Ho, “Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multi-electron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics,” Opt. Express 14(8), 3569–3587 (2006).
[CrossRef] [PubMed]

S. A. Maier, “Gain assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
[CrossRef] [PubMed]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

2005 (3)

D. O. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[CrossRef]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

2004 (5)

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, “Optically pumped ultraviolet microdisk laser on silicon substrate,” Appl. Phys. Lett. 84(14), 2488 (2004).
[CrossRef]

X. Luo and T. Ishihara, “Subwavelength photolithography based on surface-plasmon polariton resonance,” Opt. Express 12(14), 3055–3065 (2004).
[CrossRef] [PubMed]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[CrossRef] [PubMed]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323 (2004).
[CrossRef]

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

2003 (7)

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28(6), 423–425 (2003).
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

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]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668 (2003).
[CrossRef]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal micro-cavity,” Appl. Phys. Lett. 83(10), 1915 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef] [PubMed]

2002 (1)

M. M. Lončar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81(15), 2680 (2002).
[CrossRef]

2001 (1)

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[CrossRef]

2000 (2)

A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76(16), 2164 (2000).
[CrossRef]

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance non-linearities in metal nanoparticles,” Chem. Phys. 251(1-3), 215–226 (2000).
[CrossRef]

1999 (2)

H. M. Ng, D. Doppalapudi, E. Iliopoulos, and T. D. Moustakas, “Distributed Bragg reflectors based on AlN/GaN multilayers,” Appl. Phys. Lett. 74(7), 1036 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

1997 (2)

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guide Wave Lett. 7, 121 (1997).
[CrossRef]

S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
[CrossRef] [PubMed]

1983 (1)

Adegoke, J.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

Alexander, R. W.

Atwater, H. A.

S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
[CrossRef]

Bahoura, M.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

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]

Bakker, R. M.

Barclay, P. E.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal micro-cavity,” Appl. Phys. Lett. 83(10), 1915 (2003).
[CrossRef]

Barnes, W. L.

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

Bell, R. J.

Bell, R. R.

Bell, S. E.

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]

Biswas, R.

M. M. Sigalas and R. Biswas, “Slot defect in three-dimensional photonic crystals,” Phys. Rev. B 78(3), 033101 (2008).
[CrossRef]

Blaikie, R. J.

Boltasseva, A.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16(4), 2676–2684 (2008).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668 (2003).
[CrossRef]

Cao, H.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, “Optically pumped ultraviolet microdisk laser on silicon substrate,” Appl. Phys. Lett. 84(14), 2488 (2004).
[CrossRef]

Capasso, F.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[CrossRef]

A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76(16), 2164 (2000).
[CrossRef]

Catchpole, K. R.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Chang, R. P. H.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, “Optically pumped ultraviolet microdisk laser on silicon substrate,” Appl. Phys. Lett. 84(14), 2488 (2004).
[CrossRef]

Chang, S. W.

Chen, H. S.

F. M. Kong, K. Li, B. I. Wu, H. Huang, H. S. Chen, and J. A. Kong, “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromag. Res. PIER 76, 449–466 (2007).
[CrossRef]

Chen, J.

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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]

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[CrossRef]

A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76(16), 2164 (2000).
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H. M. Ng, D. Doppalapudi, E. Iliopoulos, and T. D. Moustakas, “Distributed Bragg reflectors based on AlN/GaN multilayers,” Appl. Phys. Lett. 74(7), 1036 (1999).
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H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
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M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
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O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
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M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
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T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668 (2003).
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D. B. Li and C. Z. Ning, “Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure,” Phys. Rev. B 80(15), 153304 (2009).
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F. M. Kong, K. Li, B. I. Wu, H. Huang, H. S. Chen, and J. A. Kong, “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromag. Res. PIER 76, 449–466 (2007).
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Lipson, M.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

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X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, “Optically pumped ultraviolet microdisk laser on silicon substrate,” Appl. Phys. Lett. 84(14), 2488 (2004).
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Lomakin, V.

Loncar, M. M.

M. M. Lončar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81(15), 2680 (2002).
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S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B 67(20), 205402 (2003).
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J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
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Miyazaki, H. T.

Y. Kurokawa and H. T. Miyazaki, “Metal-Insulator-Metal plasmon nanocavities: Analysis of optical properties,” Phys. Rev. B 75(3), 035411 (2007).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006).
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Moustakas, T. D.

H. M. Ng, D. Doppalapudi, E. Iliopoulos, and T. D. Moustakas, “Distributed Bragg reflectors based on AlN/GaN multilayers,” Appl. Phys. Lett. 74(7), 1036 (1999).
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M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guide Wave Lett. 7, 121 (1997).
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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
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Nakamura, A.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance non-linearities in metal nanoparticles,” Chem. Phys. 251(1-3), 215–226 (2000).
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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).
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H. M. Ng, D. Doppalapudi, E. Iliopoulos, and T. D. Moustakas, “Distributed Bragg reflectors based on AlN/GaN multilayers,” Appl. Phys. Lett. 74(7), 1036 (1999).
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S. M. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275(5303), 1102–1106 (1997).
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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
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T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668 (2003).
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D. B. Li and C. Z. Ning, “Giant modal gain, amplified surface plasmon-polariton propagation, and slowing down of energy velocity in a metal-semiconductor-metal structure,” Phys. Rev. B 80(15), 153304 (2009).
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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).
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M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
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M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
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O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
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I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
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M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
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Okamoto, K.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
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M. Okoniewski and E. Pkoniewska, “Drude dispersion in ADE revisited,” IEE Electron. Lett. 42 (2006).

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guide Wave Lett. 7, 121 (1997).
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K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal micro-cavity,” Appl. Phys. Lett. 83(10), 1915 (2003).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[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]

Pedersen, R. H.

Pile, D. F. P.

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323 (2004).
[CrossRef]

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S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
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M. Okoniewski and E. Pkoniewska, “Drude dispersion in ADE revisited,” IEE Electron. Lett. 42 (2006).

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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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I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
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M. M. Lončar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81(15), 2680 (2002).
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M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
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J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

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T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668 (2003).
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I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
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K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
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M. M. Lončar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81(15), 2680 (2002).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Sergent, A. M.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[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]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

R. M. Bakker, A. Boltasseva, Z. Liu, R. H. Pedersen, S. Gresillon, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Near-field excitation of nanoantenna resonance,” Opt. Express 15(21), 13682–13688 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Shvartser, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Sigalas, M. M.

M. M. Sigalas and R. Biswas, “Slot defect in three-dimensional photonic crystals,” Phys. Rev. B 78(3), 033101 (2008).
[CrossRef]

Sivco, D. L.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[CrossRef]

A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76(16), 2164 (2000).
[CrossRef]

Slutsky, B. A.

Smalbrugge, B.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Small, C.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

Smit, M. K.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Srinivasan, K.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal micro-cavity,” Appl. Phys. Lett. 83(10), 1915 (2003).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[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]

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]

Stuchly, M. A.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guide Wave Lett. 7, 121 (1997).
[CrossRef]

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]

Tang, L.

Tredicucci, A.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[CrossRef]

A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76(16), 2164 (2000).
[CrossRef]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Turkiewicz, J. P.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Uskov, A.

I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[CrossRef]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef] [PubMed]

Vallee, F.

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance non-linearities in metal nanoparticles,” Chem. Phys. 251(1-3), 215–226 (2000).
[CrossRef]

van Otten, F. W. M.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

van Veldhoven, P. J.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Wanke, M. C.

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[CrossRef]

Ward, C. A.

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]

Wu, B. I.

F. M. Kong, K. Li, B. I. Wu, H. Huang, H. S. Chen, and J. A. Kong, “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromag. Res. PIER 76, 449–466 (2007).
[CrossRef]

Wu, X. H.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, “Optically pumped ultraviolet microdisk laser on silicon substrate,” Appl. Phys. Lett. 84(14), 2488 (2004).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999).
[CrossRef] [PubMed]

Yoshie, T.

L. Tang and T. Yoshie, “Monopole woodpile photonic crystal modes for light-matter interaction and optical trapping,” Opt. Express 17(3), 1346–1351 (2009).
[CrossRef] [PubMed]

M. M. Lončar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81(15), 2680 (2002).
[CrossRef]

Zaimidoroga, O.

I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[CrossRef]

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]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

Zhu, Y.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

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A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, and A. Y. Cho, “Single-mode surface-plasmon laser,” Appl. Phys. Lett. 76(16), 2164 (2000).
[CrossRef]

R. Colombelli, F. Capasso, C. Gmachl, A. L. Hutchinson, D. L. Sivco, A. Tredicucci, M. C. Wanke, A. M. Sergent, and A. Y. Cho, “Far-infrared surface-plasmon quantum-cascade lasers at 21.5μm and 24μm wavelengths,” Appl. Phys. Lett. 78(18), 2620 (2001).
[CrossRef]

M. M. Lončar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. 81(15), 2680 (2002).
[CrossRef]

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[CrossRef]

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, “Optically pumped ultraviolet microdisk laser on silicon substrate,” Appl. Phys. Lett. 84(14), 2488 (2004).
[CrossRef]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal micro-cavity,” Appl. Phys. Lett. 83(10), 1915 (2003).
[CrossRef]

Chem. Phys. (1)

N. Del Fatti, F. Vallee, C. Flytzanis, Y. Hamanaka, and A. Nakamura, “Electron dynamics and surface plasmon resonance non-linearities in metal nanoparticles,” Chem. Phys. 251(1-3), 215–226 (2000).
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M. Okoniewski and E. Pkoniewska, “Drude dispersion in ADE revisited,” IEE Electron. Lett. 42 (2006).

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S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Nat. Mater. (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Nat. Photonics (3)

V. M. Shalaev, “Optical negative index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

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

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Nature (3)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[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).
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[CrossRef] [PubMed]

S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express 16(14), 10580–10595 (2008).
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D. O. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
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X. Luo and T. Ishihara, “Subwavelength photolithography based on surface-plasmon polariton resonance,” Opt. Express 12(14), 3055–3065 (2004).
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S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express 16(14), 10580–10595 (2008).
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S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16(4), 2676–2684 (2008).
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Phys. Rev. A (1)

I. Protsenko, A. Uskov, O. Zaimidoroga, V. Samoilov, and E. O’Reilly, “Dipole nanolaser,” Phys. Rev. A 71(6), 063812 (2005).
[CrossRef]

Phys. Rev. B (4)

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F. M. Kong, K. Li, B. I. Wu, H. Huang, H. S. Chen, and J. A. Kong, “Propagation properties of the SPP modes in nanoscale narrow metallic gap, channel, and hole geometries,” Prog. Electromag. Res. PIER 76, 449–466 (2007).
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[CrossRef] [PubMed]

Other (10)

Energy density at the steady state in the cavity is determined by: η=0.5⋅∫S(ε(r¯)⋅|E(r¯)|2+μ(r¯)⋅|H(r¯)|2)⋅dr¯(S is the area of the lasing cavity).

The area of lasing cavity is calculated by:S=π⋅(dOD/ 2)2−(dID/2)2] = 5.48 × 10–10 cm2.

www.Lumerical.com , Lumerical Solutions Inc., Vancouver, British Columbia, Canada.

L. A. Coldren, and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley Interscience, New York, NY, 1995).

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One may question the validity of the effective refractive index approximation since the effect of the lateral plasmonic waveguiding is stronger than the “planar dielectric waveguiding”. Exact waveguide mode calculation is expected to give some correction but it is not the focus of this paper and can be addressed separately.

The effective refractive index of the semiconductor structure will obviously be a function of the thickness of the semiconductor layer. Appropriate value shall be used in practice depending on the thickness. Here, for simulation illustration purpose, we take it to be n = 3.4.

The simulation takes approximately 96 hours on single Dell server with 2 AMD® Opteron 2350 Quad-core 2.0 GHz and 8GB memory.

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Figures (16)

Fig. 1
Fig. 1

Energy band diagram for the MLMTE model showing the intraband and interband transitions used in the FDTD simulation.

Fig. 2
Fig. 2

Schematic of the MSM plasmonic waveguiding structure. The InGaAs semiconducting core is sandwiched laterally by gold and vertically by lower refractive index InP cladding.

Fig. 3
Fig. 3

Propagation loss (a) and propagating index (b) for a straight waveguide as a function of width of the semiconductor core. The refractive index of the core and cladding of the MSM waveguide are 3.4 and 0.38 + 10.75i respectively at 1550nm.

Fig. 4
Fig. 4

Plasmonic propagation loss as a function of refractive index of the dielectric or semiconductor.

Fig. 5
Fig. 5

Bulk absorption coefficient of InGaAs simulated using the MLMTE-FDTD model with total valence band volume density of states N0 = 8.16 x 1016 cm-3.

Fig. 6
Fig. 6

Effective propagating gain coefficient as a function of bulk gain coefficient of the semiconducting gain medium (4 um). This enhancement effect can be attributed to a reduction in group velocity of the surface plasmonic wave.

Fig. 7
Fig. 7

Straight waveguide loss and enhanced gain from an MSM waveguide with a gain coefficient of 0.25μm-1. The total number density is set at 8.16 x 1016 cm-3. The optimum plasmon-polariton waveguide width for loss-less propagation is 75nm.

Fig. 8
Fig. 8

Field profiles for the MSM waveguides a) without any SiO2 buffer b) with 5nm SiO2buffer layers on each side between metal and semiconductor.

Fig. 9
Fig. 9

The overlap integral, (a), and propagating refractive index, (b), of the surface plasmonic waveguide as a function of width of the intermediate SiO2 layer for a total core width of 50nm (red) and 100nm (black).(c) and (d) show the variation in the total propagating gain or loss coefficient (μm-1) as a function of SiO2 intermediate layer width for the plasmon-polariton waveguide total width of w = 50nm and 100nm respectively.

Fig. 10
Fig. 10

3D schematic of the plasmonic nano-laser considered for MLTME-FDTD simulations.

Fig. 11
Fig. 11

Power spectrum plot of lasing cavity

Fig. 12
Fig. 12

Simulation results: (a) Steady state magnetic field distribution in the lasing cavity; (b)The cross-sectional plot of the Hz magnetic field strength across a diameter of the laser.

Fig. 13
Fig. 13

Lasing spectrum for the plasmonic nano-ring laser. The lasing peak is at 1548nm.

Fig. 14
Fig. 14

2D Energy density inside of lasing cavity as a function of different current density of the semiconductor medium.

Fig. 15
Fig. 15

Gain spectrum at lasing steady state for three cases corresponding to 1.3, 5.2, and 10.4kA/cm2.

Fig. 16
Fig. 16

a) The cross-sectional schematic of the plasmonic nano-waveguide; b) The fundamental mode profile of the w = 50nm wide plasmonic waveguide.

Tables (2)

Tables Icon

Table 1 Simulation parameters utilized for simulating InGaAs semiconducting medium in the MLMTE-FDTD program.

Tables Icon

Table 2 Simulation Results for w = 50 nm and w = 100 nm Surface Plasmonic Waveguides with InGaAs Gain Medium for SiO2 Thicknesses of 5 nm and 10 nm for w = 50 nm, and SiO2 Thicknesses of 10 nm and 20 nm for w = 100 nma

Equations (15)

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ε ( ω ) = ε ω p 2 ω 2 j ω τ ,
k m k d = ε m ( ω ) ε d tanh ( d 2 k d ) ,
β = k ε d + 0.5 ( β 0 k ) 2 + [ ε d ε m ( ω ) + 0.25 ( β 0 k ) 2 ] ( β 0 k ) 2 ,
β 0 = 2 ε d d ε m ( ω ) ,
n z = [ [ K 2 + L 2 ] 0.5 + K 2 ] 0.5 , α = j 2 k 0 [ [ K 2 + L 2 ] 0.5 K 2 ] 0.5 ,
K = G A + H B k 0 + ε d + 0.5 k 0 2 [ 4 ε d 2 ( ε m r 2 ε m i 2 ) d 2 ( ε m r 2 + ε m i 2 ) 2 ] , L = G B H A k 0 0.5 k 0 2 [ 8 ε d 2 ε m r ε m i d 2 ( ε m r 2 + ε m i 2 ) 2 ] ,
A = 2 ε d ε m r d ( ε m r 2 + ε m i 2 ) , B = 2 ε d ε m i d ( ε m r 2 + ε m i 2 ) , G = E 2 + F 2 + E 2 , H = E 2 + F 2 E 2 ,
E = ε d ε m r + ε d 2 ( ε m r 2 ε m i 2 ) k 0 2 d 2 ( ε m r 2 + ε m i 2 ) 2 , F = ε m i + 2 ε d 2 ε m r ε m i k 0 2 d 2 ( ε m r 2 + ε m i 2 ) 2 ,
N C , V i 0 ( r ¯ ) = Δ E C , V ( i 1 ) Δ E C , V i ρ ( Δ E ) d E = 16 2 m C 3 / 2 m V 3 / 2 [ ( E i + B E G ) 3 / 2 ( E i B E G ) 3 / 2 ] 3 π 2 3 ( m C + m V ) 3 / 2 .
g z = g b u l k n z n b u l k Γ ,
Q = 2 π 2 R n z a ( 1 a ) λ 0 ,
a = exp ( α π R ) ,
V e f f = V μ ( r ) | H ( r ) | 2 d 2 r max [ μ ( r ) | H ( r ) | 2 ] h .
ε ' ( ω ) = 1 ω p 2 ω 2 + τ 2 , ε ' ' ( ω ) = ω p 2 τ ω 3 + ω τ 2 .
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