Abstract

The optimization of laser resonators represents a crucial issue for the design of tera-hertz semiconductor lasers with high gain and low absorption loss. In this paper, we put forward and optimize the surface plasmonic metal waveguide geometry for the recently proposed tera-hertz injection laser based on resonant radiative transitions between tunnel-coupled graphene layers. We find an optimal number of active graphene layer pairs corresponding to the maximum net modal gain. The maximum gain increases with frequency and can be as large as ∼ 500 cm−1 at 8 THz, while the threshold length of laser resonator can be as small as ∼ 50 μm. Our findings substantiate the possibility of ultra-compact voltage-tunable graphene-based lasers operating at room temperature.

© 2016 Optical Society of America

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References

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    [Crossref]
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2016 (1)

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
[Crossref]

2015 (8)

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, pp 151–156 (2015).
[Crossref]

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
[Crossref]

T. Hochrein, “Markets, availability, notice, and technical performance of terahertz systems: historic development, present, and trends,” J. Infrared. Milli. Terahz. Waves 36, 235–254 (2015).
[Crossref]

M. A. Belkin and F. Capasso, “New frontiers in quantum cascade lasers: high performance room temperature terahertz sources,” Phys. Scr. 90(11), 118002 (2015)
[Crossref]

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015).
[Crossref] [PubMed]

2014 (5)

P. Weis, J. L. Garcia-Pomar, and M. Rahm, “Towards loss compensated and lasing terahertz metamaterials based on optically pumped graphene,” Opt. Express 22(7), 8473–8489 (2014).
[Crossref] [PubMed]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

T. Otsuji, V. Popov, and V. Ryzhii, “Active graphene plasmonics for terahertz device applications,” J. Phys. D: Appl. Phys. 47, 094006 (2014).
[Crossref]

A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

2013 (8)

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
[Crossref]

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2, ” Phys. Rev. B 87, 155304 (2013).
[Crossref]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, N. Yoshimoto, J. Terada, and H. Takahashi, “Terahertz wireless communications based on photonics technologies,” Opt. Express 21(20), 23736–23747 (2013)
[Crossref] [PubMed]

V. Ryzhii, A. A. Dubinov, T. Otsuji, V.Ya. Aleshkin, M. Ryzhii, and M. Shur, “Double-graphene-layer terahertz laser: concept, characteristics, and comparison, ” Opt. Express 21(25), 31567–31577 (2013).
[Crossref]

2012 (2)

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

2011 (3)

S. Vitiello and A. Tredicucci, “Tunable emission in THz quantum cascade lasers,” IEEE Trans. THz Sci. Technol. 1, 76–84 (2011).
[Crossref]

A. A. Bogdanov and R. A. Suris, “Mode structure of a quantum cascade laser,” Phys. Rev. B 83, 125316 (2011).
[Crossref]

F. H. L. Koppens, D.E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

2010 (1)

V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
[Crossref]

2009 (2)

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

V.Ya. Aleshkin, A.A. Dubinov, and V. Ryzhii, “Terahertz laser based on optically pumped graphene: model and feasibility of realization,” JETP Lett. 89(2), 63–67 (2009).
[Crossref]

2007 (3)

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101, 083114 (2007).
[Crossref]

S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
[Crossref]

L.A. Falkovsky and A.A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281 (2007).
[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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

1993 (1)

L. Zheng and A. H. MacDonald, “Tunneling conductance between parallel two-dimensional electron systems,” Phys. Rev. B 47, 10619 (1993).
[Crossref]

1984 (1)

D. M. Hoffman, G. L. Doll, and P. C. Eklund, “Optical properties of pyrolytic boron nitride in the energy range 0.05–10 eV,” Phys. Rev. B 30, 6051 (1984).
[Crossref]

1983 (1)

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

1972 (1)

R. Kazarinov and R. Suris, “Theory of electrical and electromagnetic properties of semiconductors with superlattice,” Sov. Phys. Semicond. 6, 148 (1972).

Aleiner, I. L.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Aleshkin, V. Ya.

A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
[Crossref]

Aleshkin, V.Ya.

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, T. Otsuji, V.Ya. Aleshkin, M. Ryzhii, and M. Shur, “Double-graphene-layer terahertz laser: concept, characteristics, and comparison, ” Opt. Express 21(25), 31567–31577 (2013).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

V.Ya. Aleshkin, A.A. Dubinov, and V. Ryzhii, “Terahertz laser based on optically pumped graphene: model and feasibility of realization,” JETP Lett. 89(2), 63–67 (2009).
[Crossref]

Antonov, A. V.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Arnold, S.

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
[Crossref]

Avouris, P.

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

Belkin, M. A.

M. A. Belkin and F. Capasso, “New frontiers in quantum cascade lasers: high performance room temperature terahertz sources,” Phys. Scr. 90(11), 118002 (2015)
[Crossref]

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

Bellee, B. D.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Blake, P.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
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A. A. Bogdanov and R. A. Suris, “Mode structure of a quantum cascade laser,” Phys. Rev. B 83, 125316 (2011).
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Borngraber, J.

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
[Crossref]

Boubanga Tombet, S.

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
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Boubanga Tombet, S.A.

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
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Boubanga-Tombet, S.

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
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Bovkun, L. S.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
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Brida, D.

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
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Britnell, L.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Britov, A. D.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Capasso, F.

M. A. Belkin and F. Capasso, “New frontiers in quantum cascade lasers: high performance room temperature terahertz sources,” Phys. Scr. 90(11), 118002 (2015)
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Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
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Cerullo, G.

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
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Chan, S.

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

Chandrashekhar, M.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

Chang, D.E.

F. H. L. Koppens, D.E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Chassagneux, Y.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

Chizhevskiy, E. G.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Cho, A. Y.

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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Cholinia, A.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Colombelli, R.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Coudevylle, J.-R.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

Davies, A. G.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

Dawlaty, J.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

De Natale, P.

Del Pozo-Zamudio, O.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Doll, G. L.

D. M. Hoffman, G. L. Doll, and P. C. Eklund, “Optical properties of pyrolytic boron nitride in the energy range 0.05–10 eV,” Phys. Rev. B 30, 6051 (1984).
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Dubinov, A. A.

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
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V. Ryzhii, A. A. Dubinov, T. Otsuji, V.Ya. Aleshkin, M. Ryzhii, and M. Shur, “Double-graphene-layer terahertz laser: concept, characteristics, and comparison, ” Opt. Express 21(25), 31567–31577 (2013).
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A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
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T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
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V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
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V.Ya. Aleshkin, A.A. Dubinov, and V. Ryzhii, “Terahertz laser based on optically pumped graphene: model and feasibility of realization,” JETP Lett. 89(2), 63–67 (2009).
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G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Dufferwiel, S.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Eaves, L.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Eklund, P. C.

D. M. Hoffman, G. L. Doll, and P. C. Eklund, “Optical properties of pyrolytic boron nitride in the energy range 0.05–10 eV,” Phys. Rev. B 30, 6051 (1984).
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Fal’ko, V. I.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
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L.A. Falkovsky and A.A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281 (2007).
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Fan, Y.

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, pp 151–156 (2015).
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Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Ferrari, A.C.

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
[Crossref]

Fu, Q.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Fukidome, H.

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Fukushima, T.

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

Garcia de Abajo, F. J.

F. H. L. Koppens, D.E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Garcia-Pomar, J. L.

Gavrilenko, V. I.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Geim, A. K.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

George, P.A.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

Georgiou, T.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Gholinia, A.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Gmachl, 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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Godde, T.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Gorbachev, R. V.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Gu, C.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Haigh, S. J.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Haigh, S.J.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Hisatake, S.

Hochrein, T.

T. Hochrein, “Markets, availability, notice, and technical performance of terahertz systems: historic development, present, and trends,” J. Infrared. Milli. Terahz. Waves 36, 235–254 (2015).
[Crossref]

Hoffman, D. M.

D. M. Hoffman, G. L. Doll, and P. C. Eklund, “Optical properties of pyrolytic boron nitride in the energy range 0.05–10 eV,” Phys. Rev. B 30, 6051 (1984).
[Crossref]

Horiguchi, S.

Hubers, H.-W.

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
[Crossref]

Hutchinson, A. 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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Ikonnikov, A. V.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Jalil, R.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Karavaev, S. M.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Kazarinov, R.

R. Kazarinov and R. Suris, “Theory of electrical and electromagnetic properties of semiconductors with superlattice,” Sov. Phys. Semicond. 6, 148 (1972).

Khanna, S. P.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

Kim, Y.-J.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Koppens, F. H. L.

F. H. L. Koppens, D.E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Koschny, T.

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, pp 151–156 (2015).
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L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

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Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
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Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
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T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Maksimovskii, S. N.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Maremyanin, K.V.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
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Mishchenko, A.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Mitin, V.

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
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V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
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Mitsushio, J.

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Morozov, S. V.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
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T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Nagatsuma, T.

Neumaier, P. F.-X.

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
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Nonoselov, K. S.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Novoselov, K. S.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
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Otsuji, T.

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
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A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
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T. Otsuji, V. Popov, and V. Ryzhii, “Active graphene plasmonics for terahertz device applications,” J. Phys. D: Appl. Phys. 47, 094006 (2014).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, T. Otsuji, V.Ya. Aleshkin, M. Ryzhii, and M. Shur, “Double-graphene-layer terahertz laser: concept, characteristics, and comparison, ” Opt. Express 21(25), 31567–31577 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101, 083114 (2007).
[Crossref]

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Ovchinnikov, I. I.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Pan, H.

H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2, ” Phys. Rev. B 87, 155304 (2013).
[Crossref]

Polini, M.

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
[Crossref]

Ponomarenko, L. A.

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

Popov, V.

T. Otsuji, V. Popov, and V. Ryzhii, “Active graphene plasmonics for terahertz device applications,” J. Phys. D: Appl. Phys. 47, 094006 (2014).
[Crossref]

Rahm, M.

Rana, F.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

Rooney, A.P.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Rumyantsev, V. V.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Ryzhii, M.

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, T. Otsuji, V.Ya. Aleshkin, M. Ryzhii, and M. Shur, “Double-graphene-layer terahertz laser: concept, characteristics, and comparison, ” Opt. Express 21(25), 31567–31577 (2013).
[Crossref]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101, 083114 (2007).
[Crossref]

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Ryzhii, V.

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
[Crossref]

T. Otsuji, V. Popov, and V. Ryzhii, “Active graphene plasmonics for terahertz device applications,” J. Phys. D: Appl. Phys. 47, 094006 (2014).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, T. Otsuji, V.Ya. Aleshkin, M. Ryzhii, and M. Shur, “Double-graphene-layer terahertz laser: concept, characteristics, and comparison, ” Opt. Express 21(25), 31567–31577 (2013).
[Crossref]

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
[Crossref]

V.Ya. Aleshkin, A.A. Dubinov, and V. Ryzhii, “Terahertz laser based on optically pumped graphene: model and feasibility of realization,” JETP Lett. 89(2), 63–67 (2009).
[Crossref]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101, 083114 (2007).
[Crossref]

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Rzaev, M. M.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Satou, A.

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Scalari, G.

Schmalz, K.

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
[Crossref]

Schwarz, S.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Semenikhin, I.

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Shen, N.-H.

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, pp 151–156 (2015).
[Crossref]

Shi, H.

H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2, ” Phys. Rev. B 87, 155304 (2013).
[Crossref]

Shivaraman, S.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

Shur, M.

Shur, M. S.

A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
[Crossref]

V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
[Crossref]

Sivachenko, S. D.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Soukoulis, C. M.

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, pp 151–156 (2015).
[Crossref]

Spencer, M.G.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

Starik, P. M.

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Strait, J.H.

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

Strupiechonski, E.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

Suemitsu, M.

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Suemitsu, T.

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Suris, R.

R. Kazarinov and R. Suris, “Theory of electrical and electromagnetic properties of semiconductors with superlattice,” Sov. Phys. Semicond. 6, 148 (1972).

Suris, R. A.

A. A. Bogdanov and R. A. Suris, “Mode structure of a quantum cascade laser,” Phys. Rev. B 83, 125316 (2011).
[Crossref]

Svintsov, D.

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

Takahashi, H.

Tamamushi, G.

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Taniguchi, T.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Tartakovskii, A. I.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Terada, J.

Tomadin, A.

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
[Crossref]

Tredicucci, A.

S. Vitiello and A. Tredicucci, “Tunable emission in THz quantum cascade lasers,” IEEE Trans. THz Sci. Technol. 1, 76–84 (2011).
[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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Umbetalieva, K. R.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Varlamov, A.A.

L.A. Falkovsky and A.A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281 (2007).
[Crossref]

Vasko, F. T.

F. T. Vasko and A. V. Kuznetsov, Electronic States and Optical Transitions in Semiconductor Heterostructures (Springer, New York, 1999).
[Crossref]

Vitiello, M. S.

Vitiello, S.

S. Vitiello and A. Tredicucci, “Tunable emission in THz quantum cascade lasers,” IEEE Trans. THz Sci. Technol. 1, 76–84 (2011).
[Crossref]

Vyurkov, V.

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

Wako, H.

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Walker, P.M.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Wang, Q. J.

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

Ward, L.

L. Ward, The Optical Constants of Bulk Materials and Films (IOP Publishing, Bristol, 1994).

Watanabe, K.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Watanabe, T.

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

Wei, Z.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Weis, P.

Williams, B.

Williams, S.

S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
[Crossref]

Withers, F.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Woods, C.R.

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Wylde, R.

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
[Crossref]

Yabe, Y.

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

Yadav, D.

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
[Crossref]

Yakobson, B.

H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2, ” Phys. Rev. B 87, 155304 (2013).
[Crossref]

Yoshimizu, Y.

Yoshimoto, N.

Zasavitskiy, I. I.

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Zhang, F.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Zhang, Y.-W.

H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2, ” Phys. Rev. B 87, 155304 (2013).
[Crossref]

Zhao, Q.

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Zheng, L.

L. Zheng and A. H. MacDonald, “Tunneling conductance between parallel two-dimensional electron systems,” Phys. Rev. B 47, 10619 (1993).
[Crossref]

2D Materials (1)

D. Yadav, S. Boubanga Tombet, T. Watanabe, S. Arnold, V. Ryzhii, and T. Otsuji, “Terahertz wave generation and detection in double-graphene layered van der Waals heterostructures,” 2D Materials 3(4), 045009 (2016).
[Crossref]

ACS Nano (1)

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

ACS Photonics (1)

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, pp 151–156 (2015).
[Crossref]

Analyst (1)

P. F.-X. Neumaier, K. Schmalz, J. Borngraber, R. Wylde, and H.-W. Hubers, “Terahertz gas-phase spectroscopy: chemometrics for security and medical applications,” Analyst 140, 213–222 (2015).
[Crossref]

Appl. Phys. Lett. (2)

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 21.5 μm and 24 μm wavelengths,” Appl. Phys. Lett. 78(18), 2620–2622 (2001).
[Crossref]

V. Ryzhii, A. A. Dubinov, V.Ya. Aleshkin, M. Ryzhii, and T. Otsuji, “Injection terahertz laser using the resonant inter-layer radiative transitions in double-graphene-layer structure,” Appl. Phys. Lett. 103, 163507 (2013).
[Crossref]

Eur. Phys. J. B (1)

L.A. Falkovsky and A.A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56, 281 (2007).
[Crossref]

IEEE Trans. THz Sci. Technol. (2)

S. Vitiello and A. Tredicucci, “Tunable emission in THz quantum cascade lasers,” IEEE Trans. THz Sci. Technol. 1, 76–84 (2011).
[Crossref]

Y. Chassagneux, Q. J. Wang, S. P. Khanna, E. Strupiechonski, J.-R. Coudevylle, E. H. Linfield, A. G. Davies, F. Capasso, M. A. Belkin, and R. Colombelli, “Limiting factors to the temperature performance of THz quantum cascade lasers based on the resonant-phonon depopulation scheme,” IEEE Trans. THz Sci. Technol. 2(1), 83–92 (2012).
[Crossref]

J. Appl. Phys. (4)

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101, 083114 (2007).
[Crossref]

V. Ryzhii, A.A. Dubinov, T. Otsuji, V. Mitin, and M. S. Shur, “Terahertz lasers based on optically pumped multiple graphene structures with slot-line and dielectric waveguides,” J. Appl. Phys. 107, 054505 (2010).
[Crossref]

V. Ryzhii, I. Semenikhin, M. Ryzhii, D. Svintsov, V. Vyurkov, A. Satou, and T. Otsuji, “Double injection in graphene p-i-n structures,” J. Appl. Phys. 113, 244505 (2013).
[Crossref]

A.A. Dubinov, V. Ya. Aleshkin, V. Ryzhii, M. S. Shur, and T. Otsuji, “Surface-plasmons lasing in double-graphene-layer structures,” J. Appl. Phys. 115, 044511 (2014).
[Crossref]

J. Infrared. Milli. Terahz. Waves (1)

T. Hochrein, “Markets, availability, notice, and technical performance of terahertz systems: historic development, present, and trends,” J. Infrared. Milli. Terahz. Waves 36, 235–254 (2015).
[Crossref]

J. Phys. D: Appl. Phys. (1)

T. Otsuji, V. Popov, and V. Ryzhii, “Active graphene plasmonics for terahertz device applications,” J. Phys. D: Appl. Phys. 47, 094006 (2014).
[Crossref]

JETP Lett. (2)

V.Ya. Aleshkin, A.A. Dubinov, and V. Ryzhii, “Terahertz laser based on optically pumped graphene: model and feasibility of realization,” JETP Lett. 89(2), 63–67 (2009).
[Crossref]

L.N. Kurbatov, A. D. Britov, S. M. Karavaev, S. D. Sivachenko, S. N. Maksimovskii, I. I. Ovchinnikov, M. M. Rzaev, and P. M. Starik, “Far-IR heterojunction lasers tunable to 46.2 μm,” JETP Lett. 37(9), 499–502 (1983).

Nano Lett. (2)

F. H. L. Koppens, D.E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light–matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P.M. Walker, T. Godde, A.P. Rooney, A. Gholinia, C.R. Woods, P. Blake, S.J. Haigh, K. Watanabe, T. Taniguchi, I. L. Aleiner, A. K. Geim, V. I. Fal’ko, A. I. Tartakovskii, and K. S. Novoselov, “WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature,” Nano Lett. 15, 8223–8228 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1, 517–525 (2007).
[Crossref]

Nature Nanotechnology (1)

T. Georgiou, R. Jalil, B. D. Bellee, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Cholinia, S. J. Haigh, O. Makarovsky, L. Eaves, L. A. Ponomarenko, A. K. Geim, K. S. Nonoselov, and A. Mishchenko, “Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics,” Nature Nanotechnology 7, 100–103 (2013).

New J. Phys. (1)

T. Watanabe, T. Fukushima, Y. Yabe, S.A. Boubanga Tombet, A. Satou, A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15, 075003 (2013).
[Crossref]

Opt. Express (5)

Phys. Rev. B (7)

L. Zheng and A. H. MacDonald, “Tunneling conductance between parallel two-dimensional electron systems,” Phys. Rev. B 47, 10619 (1993).
[Crossref]

D. M. Hoffman, G. L. Doll, and P. C. Eklund, “Optical properties of pyrolytic boron nitride in the energy range 0.05–10 eV,” Phys. Rev. B 30, 6051 (1984).
[Crossref]

H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2, ” Phys. Rev. B 87, 155304 (2013).
[Crossref]

A. A. Bogdanov and R. A. Suris, “Mode structure of a quantum cascade laser,” Phys. Rev. B 83, 125316 (2011).
[Crossref]

S. Boubanga-Tombet, S. Chan, T. Watanabe, A. Satou, V. Ryzhii, and T. Otsuji, “Ultrafast carrier dynamics and terahertz emission in optically pumped graphene at room temperature,” Phys. Rev. B 85, 035443 (2012).
[Crossref]

F. Rana, P.A. George, J.H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M.G. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79, 115447 (2009)
[Crossref]

A. Tomadin, D. Brida, G. Cerullo, A.C. Ferrari, and M. Polini, “Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening,” Phys. Rev. B 88, 035430 (2013).
[Crossref]

Phys. Scr. (1)

M. A. Belkin and F. Capasso, “New frontiers in quantum cascade lasers: high performance room temperature terahertz sources,” Phys. Scr. 90(11), 118002 (2015)
[Crossref]

Sci. Rep. (1)

Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Semiconductors (1)

K.V. Maremyanin, A. V. Ikonnikov, A. V. Antonov, V. V. Rumyantsev, S. V. Morozov, L. S. Bovkun, K. R. Umbetalieva, E. G. Chizhevskiy, I. I. Zasavitskiy, and V. I. Gavrilenko, “Long-wavelength injection lasers based on Pb1−xSnxSe alloys and their use in solid-state spectroscopy,” Semiconductors 49(12), 1623–1626 (2015).
[Crossref]

Sov. Phys. Semicond. (1)

R. Kazarinov and R. Suris, “Theory of electrical and electromagnetic properties of semiconductors with superlattice,” Sov. Phys. Semicond. 6, 148 (1972).

Other (3)

F. T. Vasko and A. V. Kuznetsov, Electronic States and Optical Transitions in Semiconductor Heterostructures (Springer, New York, 1999).
[Crossref]

L. Ward, The Optical Constants of Bulk Materials and Films (IOP Publishing, Bristol, 1994).

G. Tamamushi, T. Watanabe, A.A. Dubinov, J. Mitsushio, H. Wako, A. Satou, T. Suemitsu, H. Fukidome, M. Suemitsu, M. Ryzhii, V. Ryzhii, and T. Otsuji, “Single-mode terahertz emission from current-injection graphene-channel transistor under population inversion,” in 74th Annual Device Research Conference (IEEE, 2016), pp. 1–2.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic view of the terahertz laser with a stack of tunnel-coupled graphene layers (N pairs) with side injection embedded in a surface plasmon waveguide (b) Band diagram illustrating the process of stimulated photon-assisted resonant tunneling under application of interlayer voltage V.

Fig. 2
Fig. 2

Spatial distributions of the photon electric field components in TM mode of the surface plasmonic waveguide under consideration for two different heights of the metal contacts, corresponding to N = 30 (a,b) and N = 100 (c,d). Panels (a, c) show the z-component of electric field, panels (b, d) show the y-component. The wave frequency is ω/2π = 5 THz.

Fig. 3
Fig. 3

(a) Frequency dependence of modal gain at fixed numbers of double graphene layers N. (b) Dependence of modal gain on the number of double layers at fixed frequencies. The increase in N above the threshold value leads to increase in Drude absorption and reduction in modal gain.

Fig. 4
Fig. 4

Frequency dependence of the optimal number of double graphene layers Nopt and the corresponding maximum modal gain. Inset: frequency dependence of dimensionless ’gain factor’ 4 π σ zz ( ω max ) / c κ.

Fig. 5
Fig. 5

Frequency dependence of waveguide absorption and reflection coefficients different values of N.

Fig. 6
Fig. 6

Frequency dependence of laser threshold length for different values number of double graphene layers (DGLs) N.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

g ( ω ) = 4 π n eff ( ω , N ) c κ [ Re σ z z ( ω ) Γ z ( ω ) + Re σ y y ( ω ) Γ y ( ω ) ]
Γ z , y ( ω ) = j = 0 N 1 0 L | E z , y ( x , w + f + d ) j , ω | 2 d x + + | E z ( x , z , ω ) | 2 d x d z
Re σ z z ( ω ) 2 e 2 | z u , l | 2 Σ ω γ ( ω ω max ) 2 + γ 2 ,
Δ dep = 8 π e 2 | z u , l | 2 Σ κ d ,
Re σ z z ( ω max ) 2 e 2 | z u , l | 2 Σ ω max γ .
z u , l = ϕ u * ( z ) z ϕ l ( z ) d z ,
Re σ y y ( ω ) = e 2 { 2 γ μ π ( 2 ω 2 + γ 2 ) + 1 4 [ f ( ω / 2 ) f ( ω / 2 ) ] } ,
Δ = e ( V + V 0 V 0 2 + V t 2 + 2 V V 0 ) ,
L th ( ω ) = ln [ 1 / R ( ω ) ] g ( ω ) α ( ω )
R ( ω ) = ( n eff ( ω ) 1 n eff ( ω ) + 1 ) 2 .
γ = 2 π q | V t ( q ) V b ( q ) | 2 δ [ v W ( p | p q | ) ] ( 1 cos θ p , p q ) / 2 ,
γ = 2 π ( Σ i , t + Σ i , b ) q V 0 2 ( q ) ( 1 e q d ) 2 δ [ v W ( p | p q | ) ] ( 1 cos θ p , p q ) / 2 ,

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