Abstract

We propose and analyze the concept of injection terahertz (THz) lasers based on double-graphene-layer (double-GL) structures utilizing the resonant radiative transitions between GLs. We calculate main characteristics of such double-GL lasers and compare them with the characteristics of the GL lasers with intra-GL interband transitions. We demonstrate that the double-GL THz lasers under consideration can operate in a wide range of THz frequencies and might exhibit advantages associated with the reduced Drude absorption, weaker temperature dependence, voltage tuning of the spectrum, and favorable injection conditions.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  4. L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  21. K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  24. F. T. Vasko, “Resonant and nondissipative tunneling in independently contacted graphene structures,” Phys. Rev. B87, 075424 (2013).
    [CrossRef]
  25. L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B56, 281–284 (2007).
    [CrossRef]
  26. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B76, 153410 (2007).
    [CrossRef]
  27. F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
    [CrossRef]
  28. F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
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  32. 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. B30, 6051–6056 (1984).
    [CrossRef]
  33. H. Shi, H. Pan, Y.-W. Zhang, and B. Yakobson, “Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2,” Phys. Rev. B87, 155304 (2013).
  34. 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]
  35. R. Rengel and M. J. Martin, “Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene,” J. Appl. Phys.114, 143702 (2013).
    [CrossRef]
  36. M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys.46, L151–L153 (2007).
    [CrossRef]
  37. M. Ryzhii and V. Ryzhii, “”Population inversion in optically and electrically pumped graphene,” Physica E40, 317–320 (2007).
    [CrossRef]

2014 (1)

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Top. Quantum Electron.20, 8500109 (2014).

2013 (11)

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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
[CrossRef]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (2013).
[CrossRef]

V. Ryzhii, M. Ryzhii, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (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. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (2013).
[CrossRef]

F. T. Vasko, “Resonant and nondissipative tunneling in independently contacted graphene structures,” Phys. Rev. B87, 075424 (2013).
[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. B87, 155304 (2013).

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]

R. Rengel and M. J. Martin, “Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene,” J. Appl. Phys.114, 143702 (2013).
[CrossRef]

2012 (9)

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
[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. B85, 035443 (2012).
[CrossRef]

R. M. Feenstra, D. Jena, and G. Gu, “Single-particle tunneling in doped graphene-insulator-graphene junctions,” J. Appl. Phys111, 043711 (2012).
[CrossRef]

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett.12, 1482–1485 (2012).
[CrossRef] [PubMed]

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, and M. S. Shur, “Double graphene-layer plasma resonances terahertz detector,” J. Phys. D Appl. Phys.45, 302001 (2012).
[CrossRef]

H. Kanaya, H. Shibayama, R. Sogabe, S. Suzuki, and M. Asada, “Fundamental oscillation up to 1.31 THz in resonant tunneling diodes with thin well and barriers”, Appl. Phys. Express5, 124101 (2012).
[CrossRef]

2011 (1)

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys.110, 094503 (2011).
[CrossRef]

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)

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[CrossRef]

2008 (1)

2007 (6)

M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys.46, L151–L153 (2007).
[CrossRef]

M. Ryzhii and V. Ryzhii, “”Population inversion in optically and electrically pumped graphene,” Physica E40, 317–320 (2007).
[CrossRef]

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B56, 281–284 (2007).
[CrossRef]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B76, 153410 (2007).
[CrossRef]

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1, 517 (2007).
[CrossRef]

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

2002 (1)

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[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. B30, 6051–6056 (1984).
[CrossRef]

Asada, M.

H. Kanaya, H. Shibayama, R. Sogabe, S. Suzuki, and M. Asada, “Fundamental oscillation up to 1.31 THz in resonant tunneling diodes with thin well and barriers”, Appl. Phys. Express5, 124101 (2012).
[CrossRef]

Bastard, G.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

Belkin, M. A.

Belle, B.D.

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

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,” Nat. Nanotechnol.7, 100–103 (2013).

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1964).

Boubanga Tombet, S. A.

T. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (2013).
[CrossRef]

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. B85, 035443 (2012).
[CrossRef]

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).
[CrossRef]

Britnell, L.

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

Capasso, F.

M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K,” Opt. Express16, 3242–3248 (2008).
[CrossRef] [PubMed]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[CrossRef]

Carosella, F.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

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. B85, 035443 (2012).
[CrossRef]

Cho, A. Y.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[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,” Nat. Nanotechnol.7, 100–103 (2013).

Colombelli, R.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[CrossRef]

Davies, A. G.

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. B30, 6051–6056 (1984).
[CrossRef]

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).
[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, 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]

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[CrossRef]

Dupont, E.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

Eaves, L.

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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R. M. Feenstra, D. Jena, and G. Gu, “Single-particle tunneling in doped graphene-insulator-graphene junctions,” J. Appl. Phys111, 043711 (2012).
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F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
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L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
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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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L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
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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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
[CrossRef]

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

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L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
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R. M. Feenstra, D. Jena, and G. Gu, “Single-particle tunneling in doped graphene-insulator-graphene junctions,” J. Appl. Phys111, 043711 (2012).
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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,” Nat. Nanotechnol.7, 100–103 (2013).

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. B30, 6051–6056 (1984).
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Hormoz, S.

Hwang, H. Y.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[CrossRef]

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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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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R. M. Feenstra, D. Jena, and G. Gu, “Single-particle tunneling in doped graphene-insulator-graphene junctions,” J. Appl. Phys111, 043711 (2012).
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L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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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,” Nat. Nanotechnol.7, 100–103 (2013).

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F. T. Vasko and A. V. Kuznetsov, Electronic States and Optical Transitions in Semiconductor Heterostructures (Springer, 1999)
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Leiman, V. G.

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

Leist, J.

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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Liu, M.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett.12, 1482–1485 (2012).
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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,” Nat. Nanotechnol.7, 100–103 (2013).

Martin, M. J.

R. Rengel and M. J. Martin, “Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene,” J. Appl. Phys.114, 143702 (2013).
[CrossRef]

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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
[CrossRef]

Mishenko, A.

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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Mitin, V.

V. Ryzhii, M. Ryzhii, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (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. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (2013).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys.110, 094503 (2011).
[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]

Mitin, V. V.

F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
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Morozov, S. 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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
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Ndebeka-Bandou, C.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

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,” Nat. Nanotechnol.7, 100–103 (2013).

Novoselov, K. S.

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
[CrossRef]

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

Otsuji, T.

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, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (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. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (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]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (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. B85, 035443 (2012).
[CrossRef]

F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, and M. S. Shur, “Double graphene-layer plasma resonances terahertz detector,” J. Phys. D Appl. Phys.45, 302001 (2012).
[CrossRef]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys.110, 094503 (2011).
[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]

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
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V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys.101, 083114 (2007).
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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. B87, 155304 (2013).

Peres, N. M. R.

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

Pershoguba, S. S.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B76, 153410 (2007).
[CrossRef]

Ponomarenko, L. A.

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (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,” Nat. Nanotechnol.7, 100–103 (2013).

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

Rengel, R.

R. Rengel and M. J. Martin, “Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene,” J. Appl. Phys.114, 143702 (2013).
[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. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (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, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (2013).
[CrossRef]

T. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (2013).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, and M. S. Shur, “Double graphene-layer plasma resonances terahertz detector,” J. Phys. D Appl. Phys.45, 302001 (2012).
[CrossRef]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys.110, 094503 (2011).
[CrossRef]

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[CrossRef]

M. Ryzhii and V. Ryzhii, “”Population inversion in optically and electrically pumped graphene,” Physica E40, 317–320 (2007).
[CrossRef]

M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys.46, L151–L153 (2007).
[CrossRef]

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

Ryzhii, V.

T. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (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]

V. Ryzhii, M. Ryzhii, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (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]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (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. B85, 035443 (2012).
[CrossRef]

F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, and M. S. Shur, “Double graphene-layer plasma resonances terahertz detector,” J. Phys. D Appl. Phys.45, 302001 (2012).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys.110, 094503 (2011).
[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]

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[CrossRef]

M. Ryzhii and V. Ryzhii, “”Population inversion in optically and electrically pumped graphene,” Physica E40, 317–320 (2007).
[CrossRef]

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

M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys.46, L151–L153 (2007).
[CrossRef]

Satou, A.

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, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (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. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (2013).
[CrossRef]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (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. B85, 035443 (2012).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[CrossRef]

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]

Shedin, F.

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

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. B87, 155304 (2013).

Shibayama, H.

H. Kanaya, H. Shibayama, R. Sogabe, S. Suzuki, and M. Asada, “Fundamental oscillation up to 1.31 THz in resonant tunneling diodes with thin well and barriers”, Appl. Phys. Express5, 124101 (2012).
[CrossRef]

Shur, M. S.

V. Ryzhii, M. Ryzhii, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (2013).
[CrossRef]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (2013).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, and M. S. Shur, “Double graphene-layer plasma resonances terahertz detector,” J. Phys. D Appl. Phys.45, 302001 (2012).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (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]

Sivco, D. L.

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[CrossRef]

Sogabe, R.

H. Kanaya, H. Shibayama, R. Sogabe, S. Suzuki, and M. Asada, “Fundamental oscillation up to 1.31 THz in resonant tunneling diodes with thin well and barriers”, Appl. Phys. Express5, 124101 (2012).
[CrossRef]

Strasser, G.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

Suzuki, S.

H. Kanaya, H. Shibayama, R. Sogabe, S. Suzuki, and M. Asada, “Fundamental oscillation up to 1.31 THz in resonant tunneling diodes with thin well and barriers”, Appl. Phys. Express5, 124101 (2012).
[CrossRef]

Svintsov, D.

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]

Tredicucci, A.

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Top. Quantum Electron.20, 8500109 (2014).

Unterrainer, K.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[CrossRef]

Varlamov, A. A.

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B56, 281–284 (2007).
[CrossRef]

Vasko, F. T.

F. T. Vasko, “Resonant and nondissipative tunneling in independently contacted graphene structures,” Phys. Rev. B87, 075424 (2013).
[CrossRef]

F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
[CrossRef]

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

Vitiello, M. S.

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Top. Quantum Electron.20, 8500109 (2014).

Vyurkov, V.

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]

Wacker, A.

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

Watanabe, 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]

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. B85, 035443 (2012).
[CrossRef]

Williams, B. S.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1, 517 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1964).

Ya. Aleshkin, V.

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. 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, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[CrossRef]

Ya. Aleshkin., V.

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[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]

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. B87, 155304 (2013).

Yin, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett.12, 1482–1485 (2012).
[CrossRef] [PubMed]

Yurchenko, S. O.

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett.12, 1482–1485 (2012).
[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. B87, 155304 (2013).

Appl. Phys. Express (2)

A. A. Dubinov, V. Ya. Aleshkin., M. Ryzhii, T. Otsuji, and V. Ryzhii, “Terahertz laser with optically pumped graphene layers and Fabry-Perot resonator,” Appl. Phys. Express2, 092301 (2009).
[CrossRef]

H. Kanaya, H. Shibayama, R. Sogabe, S. Suzuki, and M. Asada, “Fundamental oscillation up to 1.31 THz in resonant tunneling diodes with thin well and barriers”, Appl. Phys. Express5, 124101 (2012).
[CrossRef]

Appl. Phys. Lett. (2)

K. Unterrainer, R. Colombelli, C. Gmachl, F. Capasso, H. Y. Hwang, D. L. Sivco, and A. Y. Cho, “Quantum cascade lasers with double metal-semiconductor waveguide resonators, Appl. Phys. Lett.80, 3060 (2002).
[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. B56, 281–284 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

T. Otsuji, S. A. Boubanga Tombet, A. Satou, M. Ryzhii, and V. Ryzhii, “Terahertz-wave generation using graphene - toward new types of terahertz lasers,” IEEE J. Sel. Top. Quantum Electron.19, 8400209 (2013).
[CrossRef]

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Top. Quantum Electron.20, 8500109 (2014).

J. Appl. Phys (1)

R. M. Feenstra, D. Jena, and G. Gu, “Single-particle tunneling in doped graphene-insulator-graphene junctions,” J. Appl. Phys111, 043711 (2012).
[CrossRef]

J. Appl. Phys. (8)

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]

R. Rengel and M. J. Martin, “Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene,” J. Appl. Phys.114, 143702 (2013).
[CrossRef]

V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. A. Dubinov, and V. Ya. Aleshkin, “Feasibility of terahertz lasing in optically pumped expitaxial multiple graphene layer structures,” J. Appl. Phys.106, 084507 (2009).
[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, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys.110, 094503 (2011).
[CrossRef]

V. Ryzhii, T. Otsuji, M. Ryzhii, V. G. Leiman, S. O. Yurchenko, V. Mitin, and M. S. Shur, “Effect of plasma resonances on dynamic characteristics of double-graphene layer optical modulators,” J. Appl. Phys.112, 104507 (2012).
[CrossRef]

V. Ryzhii, M. Ryzhii, V. Mitin, M. S. Shur, A. Satou, and T. Otsuji, “Terahertz photomixing using plasma resonances in double-graphene-layer structures,” J. Appl. Phys.113, 174506 (2013).
[CrossRef]

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

J. Phys. D Appl. Phys. (2)

V. Ryzhii, T. Otsuji, M. Ryzhii, and M. S. Shur, “Double graphene-layer plasma resonances terahertz detector,” J. Phys. D Appl. Phys.45, 302001 (2012).
[CrossRef]

V. Ryzhii, A. Satou, T. Otsuji, M. Ryzhii, V. Mitin, and M. S. Shur, “Dynamic effects in double-graphene-layer structures with inter-layer resonant-tunneling negative differential conductivity,” J. Phys. D Appl. Phys.46, 315107 (2013).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Ryzhii and V. Ryzhii, “Injection and population inversion in electrically induced p-n junction in graphene with split gates,” Jpn. J. Appl. Phys.46, L151–L153 (2007).
[CrossRef]

Nano Lett. (1)

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett.12, 1482–1485 (2012).
[CrossRef] [PubMed]

Nat. Commun. (1)

L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Ponomarenko, A. Mishchenko, M. T. Greenaway, T. M. Fromhold, K. S. Novoselov, and L. Eaves, “Resonant tunneling and negative differential conductance in graphene transistors,” Nat. Commun.4, 1794–1799 (2013).
[CrossRef]

Nat. Nanotechnol. (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,” Nat. Nanotechnol.7, 100–103 (2013).

Nat. Photonics (1)

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics1, 517 (2007).
[CrossRef]

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 (1)

Phys. Rev. B (7)

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. B30, 6051–6056 (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. B87, 155304 (2013).

F. T. Vasko, “Resonant and nondissipative tunneling in independently contacted graphene structures,” Phys. Rev. B87, 075424 (2013).
[CrossRef]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B76, 153410 (2007).
[CrossRef]

F. Carosella, C. Ndebeka-Bandou, R. Ferreira, E. Dupont, K. Unterrainer, G. Strasser, A. Wacker, and G. Bastard, “Free carrier absorption in quantum cascade structures,” Phys. Rev. B85, 085310 (2012).
[CrossRef]

F. T. Vasko, V. V. Mitin, V. Ryzhii, and T. Otsuji, “Interplay of intra- and interband absorption in a disordered graphene,” Phys. Rev. B86, 235424 (2012)
[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. B85, 035443 (2012).
[CrossRef]

Physica E (1)

M. Ryzhii and V. Ryzhii, “”Population inversion in optically and electrically pumped graphene,” Physica E40, 317–320 (2007).
[CrossRef]

Science (1)

L. Britnell, R. V. Gorbachev, R. Jalil, B.D. Belle, F. Shedin, A. Mishenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov, N. M. R. Peres, J. Leist, A. K. Geim, K. S. Novoselov, and L. A. Ponomarenko, “Field-effect tunneling transistor based on vertical graphene heterostructures,” Science335, 947–950 (2012).
[CrossRef] [PubMed]

Other (3)

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

K. J. Ebeling, Integrated Optoelectronics: Waveguide Optics, Photonics, Semiconductors (Springer, 1993).
[CrossRef]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1964).

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Figures (7)

Fig. 1
Fig. 1

Schematic views of double-GL laser cross-sections (a) with the side monopolar injection to each independently contacted GL, tunneling barrier layer, and MM waveguide (device ”a”) and (b) with the injection of electrons and holes from p- and n-contacts to each GL and dielectric waveguide (device ”b”).

Fig. 2
Fig. 2

Band diagrams of laser structures with (a) inter-GL and (b) intra-GL radiative transitions. Wavy arrows indicate the inter-GL and intra-GL radiative cc, vv, and cv transitions in devices ”a” and ”b”, respectively.

Fig. 3
Fig. 3

Spatial distributions of the photon electric field components: (a) | E z a ( x , z , ω ) |, (b) | E y a ( x , z , ω ) | in the TM mode in MM waveguide (in device ”a”), (c) E x b ( x , z , ω ) | in the TE mode (in device ”b”), and (d) amplitudes of electric field components at GL plane (z = 0) for ω/2π = 8 THz). White horizontal strips correspond to GLs with the barrier layer in between.

Fig. 4
Fig. 4

Dependences of (a) the inter-GL matrix element |zu,l|2 and (b) depolarization shift Δdep on the energy separation between the Dirac points Δ calculated for different values of spacing between GLs d.

Fig. 5
Fig. 5

Frequency dependences of gain-overlap factors Γ j j a , b ( ω ) (solid lines) and waveguide absorption coefficients αa,b(ω) (dashed lines): (a) L = 5 μm and W = 5 μm and (b) L = 15 μm and W = 5 μm.

Fig. 6
Fig. 6

THz gain ga(ω) versus frequency dependences (solid lines) for different values of energy separation between the Dirac points Δ and THz gain gb(ω) (dashed lines) for different Fermi energies in GLs: (a) L = 5 μm and W = 5 μm and (b) L = 15 μm and W = 5 μm.

Fig. 7
Fig. 7

Tuning of frequency ωmax corresponding to peak of the THz gain ga(ω) by (a) bias voltage V and (b) gate voltage Vg.

Equations (12)

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Σ = Σ i + κ Δ 4 π e 2 d ,
Δ / e = V + V 0 2 V V 0 + V 0 2 + V t 2 , μ = e 2 ( 2 V V 0 + V 0 2 + V t 2 V 0 ) ,
Re σ y y a ( ω ) 2 ( e 2 4 h ¯ ) [ 2 exp ( μ k B T ) sinh ( h ¯ ω 2 k B T ) + 4 γ μ π ( h ¯ 2 ω 2 + γ 2 ) ] ,
Re σ z z a ( ω ) = ( e 2 h ¯ ) 2 | z u , l | 2 Σ i ( 1 + Δ / Δ i ) γ h ¯ ω [ h ¯ 2 ( ω ω max ) 2 + γ 2 ] ,
h ¯ ω max = Δ 8 π e 2 | z u , l | 2 Σ i ( 1 + Δ / Δ i ) κ d = Δ + Δ dep ,
Re σ x x b ( ω ) = 2 ( e 2 4 h ¯ ) [ tanh ( h ¯ ω 2 μ 4 k B T ) + 4 γ μ π ( h ¯ 2 ω 2 + γ 2 ) ] , Re σ z z b = 0 .
g a ( ω ) = 4 π c κ [ Re σ y y a ( ω ) Γ y y a ( ω ) + Re σ z z a ( ω ) Γ z z a ( ω ) ] α a ( ω ) ,
g b ( ω ) = 4 π c κ Re σ x x b ( ω ) Γ x x b ( ω ) α b ( ω ) ,
Γ j j a , b ( ω ) = L L d x | E j a , b ( x , 0 , ω ) | 2 L L W W d x d z | E j a , b ( x , z , ω ) | 2 ( j = x , y , z ) ,
g a ( ω ) = 2 π e 2 h ¯ c κ { [ 2 exp ( μ k B T ) sinh ( h ¯ ω 2 k B T ) + 4 γ μ π ( h ¯ 2 ω 2 + γ 2 ) ] Γ y y a ( ω ) + 4 | z u , l | 2 Σ i ( 1 + Δ / Δ i ) γ h ¯ ω [ h ¯ 2 ( ω ω max ) 2 + γ 2 ] Γ z z a ( ω ) } α a ( ω ) ,
g a ( ω ) = ( 8 π e 2 h ¯ c κ ) | z u , l | 2 Σ i ( 1 + Δ / Δ i ) γ h ¯ ω [ h ¯ 2 ( ω ω max ) 2 + γ 2 ] Γ z z a ( ω ) α a ( ω ) ,
g b ( ω ) = ( 2 π e 2 h ¯ c κ ) [ tanh ( 2 μ h ¯ ω 4 k B T ) 4 γ μ π ( h ¯ 2 ω 2 + γ 2 ) ] Γ x x b ( ω ) α b ( ω ) .

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