Surface plasmon polariton amplification in a single-walled carbon nanotube

A. S. Kadochkin; S. G. Moiseev; Y. S. Dadoenkova; V. V. Svetukhin; I. O. Zolotovskii

doi:10.1364/OE.25.027165

Optics Express
Vol. 25,
Issue 22,
pp. 27165-27171
(2017)
•https://doi.org/10.1364/OE.25.027165

Surface plasmon polariton amplification in a single-walled carbon nanotube

A. S. Kadochkin, S. G. Moiseev, Y. S. Dadoenkova, V. V. Svetukhin, and I. O. Zolotovskii

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A. S. Kadochkin, S. G. Moiseev, Y. S. Dadoenkova, V. V. Svetukhin, and I. O. Zolotovskii, "Surface plasmon polariton amplification in a single-walled carbon nanotube," Opt. Express 25, 27165-27171 (2017)

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Table of Contents Category
- Plasmonics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Free-electron lasers (FELs) (140.2600)
- Traveling-wave devices (230.7020)
- Surface plasmons (240.6680)

About this Article
History
- Original Manuscript: August 1, 2017
- Revised Manuscript: September 15, 2017
- Manuscript Accepted: September 19, 2017
- Published: October 20, 2017

Abstract

The interaction of a surface plasmon polariton wave of the far-infrared regime propagating in a single-walled carbon nanotube with a drift current is theoretically investigated. It is shown that under the synchronism condition a surface plasmon polariton amplification mechanism is implemented due to the transfer of electromagnetic energy from a drift current wave into a terahertz surface wave propagating along the surface of a single-walled carbon nanotube. Numerical calculations show that for a typical carbon nanotube surface plasmon polariton amplification coefficient reaches huge values of the order of 10⁶ сm⁻¹, which makes it possible to create a carbon-nanotube-based spaser.

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References

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Year
Author
Publication

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]
M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]
J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[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]
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]
D. A. Svintsov, A. V. Arsenin, and D. Yu. Fedyanin, “Full loss compensation in hybrid plasmonic waveguides under electrical pumping,” Opt. Express 23(15), 19358–19375 (2015).
[Crossref] [PubMed]
D. Yu. Fedyanin, “Toward an electrically pumped spaser,” Opt. Lett. 37(3), 404–406 (2012).
[Crossref] [PubMed]
D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]
R. F. Wallis, V. Lozovskii, S. Schrader, and A. Tsykhonya, “Possibility of surface plasmon-polaritons amplification by direct current in two-interface systems with 2D Bragg structure on the surface,” Opt. Commun. 282(16), 3257–3265 (2009).
[Crossref]
Y. S. Dadoenkova, S. G. Moiseev, A. S. Abramov, A. S. Kadochkin, A. A. Fotiadi, and I. O. Zolotovskii, “Surface plasmon polariton amplification in semiconductor–graphene–dielectric structure,” Ann. Phys. 529(5), 1700037 (2017).
[Crossref]
A. Moradi, “Surface plasmon–polariton modes of metallic single-walled carbon nanotubes,” Photon. Nanostructures 11(1), 85–88 (2013).
[Crossref]
F. J. García de Abajo, “Graphene plasmonics: Challenges and opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]
C. Kane, L. Balents, and M. P. A. Fisher, “Coulomb interactions and mesoscopic effects in carbon nanotubes,” Phys. Rev. Lett. 79(25), 5086–5089 (1997).
[Crossref]
M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]
G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: Dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60(24), 17136–17149 (1999).
[Crossref]
Z. Shi, X. Hong, H. A. Bechtel, B. Zeng, M. C. Martin, K. Watanabe, T. Taniguchi, Y. R. Shen, and F. Wang, “Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes,” Nat. Photonics 9(8), 515–519 (2015).
[Crossref]
L. Martín-Moreno, F. J. de Abajo, and F. J. García-Vidal, “Ultraefficient coupling of a quantum emitter to the tunable guided plasmons of a carbon nanotube,” Phys. Rev. Lett. 115(17), 173601 (2015).
[Crossref] [PubMed]
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]
S. G. Lemay, J. W. Janssen, M. van den Hout, M. Mooij, M. J. Bronikowski, P. A. Willis, R. E. Smalley, L. P. Kouwenhoven, and C. Dekker, “Two-dimensional imaging of electronic wavefunctions in carbon nanotubes,” Nature 412(6847), 617–620 (2001).
[Crossref] [PubMed]
V. Perebeinos, J. Tersoff, and P. Avouris, “Electron-phonon interaction and transport in semiconducting carbon nanotubes,” Phys. Rev. Lett. 94(8), 086802 (2005).
[Crossref] [PubMed]
W. K. Chen, The Electrical Engineering Handbook, (Elsevier, 2005).
D. I. Trubetskov and A. E. Khramov, Lectures on Microwave Electronics for Physicists, Vol. 1 (Fizmatlit, Moscow, 2003), [in Russian]
S. E. Tsimring, Electron Beams and Microwave Vacuum Electronics (Wiley, 2006).
K. G. Batrakov, S. A. Maksimenko, P. P. Kuzhir, and C. Thomsen, “Carbon nanotube as a Cherenkov-type light emitter and free electron laser,” Phys. Rev. B 79(12), 125408 (2009).
[Crossref]
S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]
A. M. Nemilentsau, G. Ya. Slepyan, and S. A. Maksimenko, “Thermal radiation from carbon nanotubes in the terahertz range,” Phys. Rev. Lett. 99(14), 147403 (2007).
[Crossref] [PubMed]

2017 (1)

Y. S. Dadoenkova, S. G. Moiseev, A. S. Abramov, A. S. Kadochkin, A. A. Fotiadi, and I. O. Zolotovskii, “Surface plasmon polariton amplification in semiconductor–graphene–dielectric structure,” Ann. Phys. 529(5), 1700037 (2017).
[Crossref]

2015 (3)

Z. Shi, X. Hong, H. A. Bechtel, B. Zeng, M. C. Martin, K. Watanabe, T. Taniguchi, Y. R. Shen, and F. Wang, “Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes,” Nat. Photonics 9(8), 515–519 (2015).
[Crossref]

L. Martín-Moreno, F. J. de Abajo, and F. J. García-Vidal, “Ultraefficient coupling of a quantum emitter to the tunable guided plasmons of a carbon nanotube,” Phys. Rev. Lett. 115(17), 173601 (2015).
[Crossref] [PubMed]

D. A. Svintsov, A. V. Arsenin, and D. Yu. Fedyanin, “Full loss compensation in hybrid plasmonic waveguides under electrical pumping,” Opt. Express 23(15), 19358–19375 (2015).
[Crossref] [PubMed]

2014 (1)

F. J. García de Abajo, “Graphene plasmonics: Challenges and opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]

2013 (2)

A. Moradi, “Surface plasmon–polariton modes of metallic single-walled carbon nanotubes,” Photon. Nanostructures 11(1), 85–88 (2013).
[Crossref]

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]

2012 (3)

D. Yu. Fedyanin, “Toward an electrically pumped spaser,” Opt. Lett. 37(3), 404–406 (2012).
[Crossref] [PubMed]

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]

2010 (2)

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

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]

R. F. Wallis, V. Lozovskii, S. Schrader, and A. Tsykhonya, “Possibility of surface plasmon-polaritons amplification by direct current in two-interface systems with 2D Bragg structure on the surface,” Opt. Commun. 282(16), 3257–3265 (2009).
[Crossref]

K. G. Batrakov, S. A. Maksimenko, P. P. Kuzhir, and C. Thomsen, “Carbon nanotube as a Cherenkov-type light emitter and free electron laser,” Phys. Rev. B 79(12), 125408 (2009).
[Crossref]

2007 (1)

A. M. Nemilentsau, G. Ya. Slepyan, and S. A. Maksimenko, “Thermal radiation from carbon nanotubes in the terahertz range,” Phys. Rev. Lett. 99(14), 147403 (2007).
[Crossref] [PubMed]

2005 (3)

V. Perebeinos, J. Tersoff, and P. Avouris, “Electron-phonon interaction and transport in semiconducting carbon nanotubes,” Phys. Rev. Lett. 94(8), 086802 (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]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

2001 (1)

S. G. Lemay, J. W. Janssen, M. van den Hout, M. Mooij, M. J. Bronikowski, P. A. Willis, R. E. Smalley, L. P. Kouwenhoven, and C. Dekker, “Two-dimensional imaging of electronic wavefunctions in carbon nanotubes,” Nature 412(6847), 617–620 (2001).
[Crossref] [PubMed]

1999 (2)

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

G. Ya. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. Yevtushenko, and A. V. Gusakov, “Electrodynamics of carbon nanotubes: Dynamic conductivity, impedance boundary conditions, and surface wave propagation,” Phys. Rev. B 60(24), 17136–17149 (1999).
[Crossref]

1997 (1)

C. Kane, L. Balents, and M. P. A. Fisher, “Coulomb interactions and mesoscopic effects in carbon nanotubes,” Phys. Rev. Lett. 79(25), 5086–5089 (1997).
[Crossref]

Abramov, A. S.

Arsenin, A. V.

Avouris, P.

V. Perebeinos, J. Tersoff, and P. Avouris, “Electron-phonon interaction and transport in semiconducting carbon nanotubes,” Phys. Rev. Lett. 94(8), 086802 (2005).
[Crossref] [PubMed]

Bakker, R.

Balents, L.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

C. Kane, L. Balents, and M. P. A. Fisher, “Coulomb interactions and mesoscopic effects in carbon nanotubes,” Phys. Rev. Lett. 79(25), 5086–5089 (1997).
[Crossref]

Batrakov, K. G.

K. G. Batrakov, S. A. Maksimenko, P. P. Kuzhir, and C. Thomsen, “Carbon nanotube as a Cherenkov-type light emitter and free electron laser,” Phys. Rev. B 79(12), 125408 (2009).
[Crossref]

Bechtel, H. A.

Belgrave, A. M.

Berini, P.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

Bockrath, M.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

Bronikowski, M. J.

Co, D. T.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Cobden, D. H.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

Dadoenkova, Y. S.

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

de Abajo, F. J.

De Leon, I.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

Dekker, C.

Dubonos, S. V.

Eng, L.

Fedyanin, D. Yu.

D. Yu. Fedyanin, “Toward an electrically pumped spaser,” Opt. Lett. 37(3), 404–406 (2012).
[Crossref] [PubMed]

Firsov, A. A.

Fisher, M. P. A.

C. Kane, L. Balents, and M. P. A. Fisher, “Coulomb interactions and mesoscopic effects in carbon nanotubes,” Phys. Rev. Lett. 79(25), 5086–5089 (1997).
[Crossref]

Fotiadi, A. A.

García de Abajo, F. J.

F. J. García de Abajo, “Graphene plasmonics: Challenges and opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]

García-Vidal, F. J.

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

Geim, A. K.

Gong, S.

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]

Grafström, S.

Grigorieva, I. V.

Gusakov, A. V.

Herz, E.

Hong, X.

Hu, M.

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]

Huntington, M. D.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Janssen, J. W.

Jiang, D.

Kadochkin, A. S.

Kane, C.

C. Kane, L. Balents, and M. P. A. Fisher, “Coulomb interactions and mesoscopic effects in carbon nanotubes,” Phys. Rev. Lett. 79(25), 5086–5089 (1997).
[Crossref]

Katsnelson, M. I.

Kim, C. H.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Kouwenhoven, L. P.

Kuzhir, P. P.

K. G. Batrakov, S. A. Maksimenko, P. P. Kuzhir, and C. Thomsen, “Carbon nanotube as a Cherenkov-type light emitter and free electron laser,” Phys. Rev. B 79(12), 125408 (2009).
[Crossref]

Lakhtakia, A.

Lemay, S. G.

Leosson, L.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

Li, D.

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]

Liu, S.

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]

Liu, W.

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]

Lozovskii, V.

Lu, J.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

Maksimenko, S. A.

K. G. Batrakov, S. A. Maksimenko, P. P. Kuzhir, and C. Thomsen, “Carbon nanotube as a Cherenkov-type light emitter and free electron laser,” Phys. Rev. B 79(12), 125408 (2009).
[Crossref]

A. M. Nemilentsau, G. Ya. Slepyan, and S. A. Maksimenko, “Thermal radiation from carbon nanotubes in the terahertz range,” Phys. Rev. Lett. 99(14), 147403 (2007).
[Crossref] [PubMed]

Martin, M. C.

Martín-Moreno, L.

McEuen, P. L.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and L. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[Crossref]

Moiseev, S. G.

Mooij, M.

Moradi, A.

A. Moradi, “Surface plasmon–polariton modes of metallic single-walled carbon nanotubes,” Photon. Nanostructures 11(1), 85–88 (2013).
[Crossref]

Morozov, S. V.

Narimanov, E. E.

Nemilentsau, A. M.

A. M. Nemilentsau, G. Ya. Slepyan, and S. A. Maksimenko, “Thermal radiation from carbon nanotubes in the terahertz range,” Phys. Rev. Lett. 99(14), 147403 (2007).
[Crossref] [PubMed]

Noginov, M. A.

Novoselov, K. S.

Odom, T. W.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Perebeinos, V.

V. Perebeinos, J. Tersoff, and P. Avouris, “Electron-phonon interaction and transport in semiconducting carbon nanotubes,” Phys. Rev. Lett. 94(8), 086802 (2005).
[Crossref] [PubMed]

Rinzler, A. G.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

Schrader, S.

Seidel, J.

Shalaev, V. M.

Shen, Y. R.

Shi, Z.

Slepyan, G. Ya.

A. M. Nemilentsau, G. Ya. Slepyan, and S. A. Maksimenko, “Thermal radiation from carbon nanotubes in the terahertz range,” Phys. Rev. Lett. 99(14), 147403 (2007).
[Crossref] [PubMed]

Smalley, R. E.

M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397(6720), 598–601 (1999).
[Crossref]

Stockman, M. I.

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110(10), 106803 (2013).
[Crossref] [PubMed]

Stout, S.

Suh, J. Y.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Suteewong, T.

Svintsov, D. A.

Taniguchi, T.

Tersoff, J.

V. Perebeinos, J. Tersoff, and P. Avouris, “Electron-phonon interaction and transport in semiconducting carbon nanotubes,” Phys. Rev. Lett. 94(8), 086802 (2005).
[Crossref] [PubMed]

Thomsen, C.

K. G. Batrakov, S. A. Maksimenko, P. P. Kuzhir, and C. Thomsen, “Carbon nanotube as a Cherenkov-type light emitter and free electron laser,” Phys. Rev. B 79(12), 125408 (2009).
[Crossref]

Tsykhonya, A.

van den Hout, M.

Wallis, R. F.

Wang, F.

Wasielewski, M. R.

J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12(11), 5769–5774 (2012).
[Crossref] [PubMed]

Watanabe, K.

Wiesner, U.

Willis, P. A.

Yevtushenko, O.

Zeng, B.

Zhang, P.

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109(15), 153902 (2012).
[Crossref] [PubMed]

Zhang, Y.

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Fig. 1 (a) Single-walled CNT of the length L. The direction of the electric current is shown with red arrow, and

(ρ, φ, z)

are cylindrical coordinates. (b) Spatial distribution of the electric field component E_z of the SPP wave.

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Fig. 2 Dispersion of the SPP and drift current parameters: (a) SPP propagation constant β (solid red line), SPP phase velocity

V_{p h}

(solid blue line) and charge-drift velocity V₀ = 5·10⁷ cm/s (dashed blue line); (b) SPP amplification coefficient a.

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Equations (9)

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\begin{array}{l} E_{z} (ρ < a) = E_{0 z} \frac{I_{0} (q ρ)}{I_{0} (q a)}, H_{z} (ρ < a) = H_{0 z} \frac{I_{0} (q ρ)}{{d I_{0} (x) / d x |}_{x = q a}}, \\ E_{z} (ρ > a) = E_{0 z} \frac{K_{0} (q ρ)}{K_{0} (q a)}, H_{z} (ρ > a) = H_{0 z} \frac{K_{0} (q ρ)}{{\partial K_{0} (x) / \partial x |}_{x = q a}};, \end{array}

E_{r} = \frac{β}{ω ε_{0}} H_{φ} = - i \frac{β}{q^{2}} \frac{d E_{z}}{d r}, H_{r} = - \frac{β}{ω μ_{0}} E_{φ} = - i \frac{β}{q^{2}} \frac{d H_{z}}{d r} .

\frac{i ε_{0} ω}{a q^{2} I_{0} (q a) K_{0} (q a)} - σ_{z z}^{0} = 0,

σ_{z z}^{0} = \frac{i n_{s} e^{2}}{m_{e}} \frac{ω}{ω (ω + i γ) - η q^{2}}

\frac{d E_{z}}{d z} + i \frac{ω}{V_{p h}} E_{z} = - \frac{1}{2} {(\frac{ω}{V_{p h}})}^{2} B I_{d},

B \approx \frac{I_{0} (β a) K_{0} (β a)}{2 π ε_{0} V_{g}} .

\frac{d^{2} J}{d z^{2}} + 2 i \frac{ω}{V_{0}} \frac{d J}{d z} - \frac{1}{V_{0}^{2}} (ω^{2} - ω_{q}^{2}) J = i \frac{ω}{V_{0}} \frac{I_{d 0}}{2 U_{0}} E_{z},

(ω - G V_{p h}) [{(ω - G V_{0})}^{2} - ω_{q}^{2}] = C^{3} ω^{3},

C = {(\frac{B I_{d}}{4 U_{0}} \frac{V_{0}}{V_{p h}})}^{1 / 3} = {(\frac{π a^{2} ω_{q}^{2}}{V_{g} V_{p h}} I_{0} (β a) K_{0} (β a))}^{1 / 3} .