Abstract

Semiconductor plasmons have potential for terahertz generation. Because practical device formats may be quasi-optical, we studied theoretically distributed plasmonic reflectors that comprise multiple interfaces between cascaded two-dimensional electron channels. Employing a mode-matching technique, we show that transmission through and reflection from a single interface depend on the magnitude and direction of a dc current flowing in the channels. As a result, plasmons can be amplified at an interface, and the cumulative effect of multiple interfaces increases the total gain, leading to plasmonic reflection coefficients exceeding unity. Reversing the current direction in a distributed reflector, however, has the opposite effect of plasmonic deamplification. Consequently, we propose structurally asymmetric resonators comprising two different distributed reflectors and predict that they are capable of terahertz oscillations at low threshold currents.

© 2012 OSA

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  1. J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
    [CrossRef]
  2. D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
    [CrossRef]
  3. E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
    [CrossRef] [PubMed]
  4. S. A. Mikhailov, “Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems,” Phys. Rev. B58, 1517–1532 (1998).
    [CrossRef]
  5. S. Riyopoulos, “THz instability by streaming carriers in high mobility solid-state plasmas,” Phys. Plasmas12, 070704 (2005).
    [CrossRef]
  6. S. M. Kukhtaruk, “High-frequency properties of systems with drifting electrons and polar optical phonons,” Sem. Phys. Quant. Electr. & Optoelectr.11, 43–49 (2008).
  7. O. Sydoruk, V. Kalinin, and L. Solymar, “Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels,” Appl. Phys. Lett.97, 062107 (2010).
    [CrossRef]
  8. M. Dyakonov and M. Shur, “Shallow water analogy for a ballistic field-effect transistor: new mechanism of plasma wave generation by a dc current,” Phys. Rev. Lett.71, 2465–2468 (1993).
    [CrossRef] [PubMed]
  9. F. J. Crowne, “Contact boundary conditions and the Dyakonov–Shur instability in high electron mobility transistors,” J. Appl. Phys.82, 1242–1254 (1997).
    [CrossRef]
  10. M. V. Cheremisin and G. G. Samsonidze, “D’yakonov–Shur instability in a ballistic field-effect transistor with a spatially nonuniform channel,” Semiconductors33, 578–585 (1999).
    [CrossRef]
  11. M. Dyakonov and M. Shur, “Current instability and plasma waves generation in ungated two-dimensional electron layers,” Appl. Phys. Lett.87(11), 111501 (2005).
    [CrossRef]
  12. O. Sydoruk, R. R. A. Syms, and L. Solymar, “Plasma oscillations and terahertz instability in field-effect transistors with Corbino geometry,” Appl. Phys. Lett.97, 263504 (2010).
    [CrossRef]
  13. J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
    [CrossRef]
  14. Y. Tsuda, T. Komori, A. El Fatimy, K. Horiike, T. Suemitsu, and T. Otsuji, “Application of plasmon-resonant microchip emitters to broadband terahertz spectroscopic measurement,” J. Opt. Soc. Am. B26, A52–A57 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
    [CrossRef]
  20. S. Thongrattanasiri, J. Elser, and V. A. Podolskiy, “Quasi-planar optics: computing light propagation and scattering in planar waveguide arrays,” J. Opt. Soc. Am. B26, B102–B110 (2009).
    [CrossRef]
  21. U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
    [CrossRef]
  22. Z. Knittl, Optics of Thin Films (Wiley, London, 1981).

2011 (1)

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

2010 (3)

O. Sydoruk, R. R. A. Syms, and L. Solymar, “Plasma oscillations and terahertz instability in field-effect transistors with Corbino geometry,” Appl. Phys. Lett.97, 263504 (2010).
[CrossRef]

O. Sydoruk, V. Kalinin, and L. Solymar, “Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels,” Appl. Phys. Lett.97, 062107 (2010).
[CrossRef]

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

2009 (2)

2008 (2)

S. M. Kukhtaruk, “High-frequency properties of systems with drifting electrons and polar optical phonons,” Sem. Phys. Quant. Electr. & Optoelectr.11, 43–49 (2008).

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

2007 (1)

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
[CrossRef]

2006 (1)

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

2005 (3)

S. Riyopoulos, “THz instability by streaming carriers in high mobility solid-state plasmas,” Phys. Plasmas12, 070704 (2005).
[CrossRef]

M. Dyakonov and M. Shur, “Current instability and plasma waves generation in ungated two-dimensional electron layers,” Appl. Phys. Lett.87(11), 111501 (2005).
[CrossRef]

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

2004 (1)

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

1999 (1)

M. V. Cheremisin and G. G. Samsonidze, “D’yakonov–Shur instability in a ballistic field-effect transistor with a spatially nonuniform channel,” Semiconductors33, 578–585 (1999).
[CrossRef]

1998 (1)

S. A. Mikhailov, “Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems,” Phys. Rev. B58, 1517–1532 (1998).
[CrossRef]

1997 (1)

F. J. Crowne, “Contact boundary conditions and the Dyakonov–Shur instability in high electron mobility transistors,” J. Appl. Phys.82, 1242–1254 (1997).
[CrossRef]

1993 (1)

M. Dyakonov and M. Shur, “Shallow water analogy for a ballistic field-effect transistor: new mechanism of plasma wave generation by a dc current,” Phys. Rev. Lett.71, 2465–2468 (1993).
[CrossRef] [PubMed]

1984 (1)

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

1958 (1)

A. D. Bresler, G. H. Joshi, and N. Marcuvitz, “Orthogonality properties for modes in passive and active uniform wave guides,” J. Appl. Phys.29, 794–799 (1958).
[CrossRef]

Beinvogl, W.

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

Bolivar, P. H.

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

Bollaert, S.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Bonn, M.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

Bresler, A. D.

A. D. Bresler, G. H. Joshi, and N. Marcuvitz, “Orthogonality properties for modes in passive and active uniform wave guides,” J. Appl. Phys.29, 794–799 (1958).
[CrossRef]

Cappy, A.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Cheremisin, M. V.

M. V. Cheremisin and G. G. Samsonidze, “D’yakonov–Shur instability in a ballistic field-effect transistor with a spatially nonuniform channel,” Semiconductors33, 578–585 (1999).
[CrossRef]

Collin, R. E.

R. E. Collin, Foundations for Microwave Engineering (Wiley-IEEE Press, Hoboken, New Jersey, 2001).
[CrossRef]

Crowne, F. J.

F. J. Crowne, “Contact boundary conditions and the Dyakonov–Shur instability in high electron mobility transistors,” J. Appl. Phys.82, 1242–1254 (1997).
[CrossRef]

Delage, S.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Dmitriev, A. P.

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

Dyakonov, M.

M. Dyakonov and M. Shur, “Current instability and plasma waves generation in ungated two-dimensional electron layers,” Appl. Phys. Lett.87(11), 111501 (2005).
[CrossRef]

M. Dyakonov and M. Shur, “Shallow water analogy for a ballistic field-effect transistor: new mechanism of plasma wave generation by a dc current,” Phys. Rev. Lett.71, 2465–2468 (1993).
[CrossRef] [PubMed]

Dyakonova, N.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

El Fatimy, A.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Y. Tsuda, T. Komori, A. El Fatimy, K. Horiike, T. Suemitsu, and T. Otsuji, “Application of plasmon-resonant microchip emitters to broadband terahertz spectroscopic measurement,” J. Opt. Soc. Am. B26, A52–A57 (2009).
[CrossRef]

El Moutaouakil, A.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Elser, J.

Gaquiere, C.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Garcia-Vidal, F. J.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

Gómez Rivas, J.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

Gonzalez, T.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Heitmann, D.

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

Hendry, E.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

Hibbins, A. P.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

Horiike, K.

Joshi, G. H.

A. D. Bresler, G. H. Joshi, and N. Marcuvitz, “Orthogonality properties for modes in passive and active uniform wave guides,” J. Appl. Phys.29, 794–799 (1958).
[CrossRef]

Kachorovskii, V. Y.

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

Kalinin, V.

O. Sydoruk, V. Kalinin, and L. Solymar, “Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels,” Appl. Phys. Lett.97, 062107 (2010).
[CrossRef]

Karasawa, H.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Karpierz, K.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Knap, W.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1981).

Komori, T.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Y. Tsuda, T. Komori, A. El Fatimy, K. Horiike, T. Suemitsu, and T. Otsuji, “Application of plasmon-resonant microchip emitters to broadband terahertz spectroscopic measurement,” J. Opt. Soc. Am. B26, A52–A57 (2009).
[CrossRef]

Kotthaus, J. P.

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

Kukhtaruk, S. M.

S. M. Kukhtaruk, “High-frequency properties of systems with drifting electrons and polar optical phonons,” Sem. Phys. Quant. Electr. & Optoelectr.11, 43–49 (2008).

Kurz, H.

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

Kuttge, M.

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

Liu, Y.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
[CrossRef]

Lockyear, M. J.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

Lusakowski, J.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Mackens, U.

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

Madjour, K.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Marcuvitz, N.

A. D. Bresler, G. H. Joshi, and N. Marcuvitz, “Orthogonality properties for modes in passive and active uniform wave guides,” J. Appl. Phys.29, 794–799 (1958).
[CrossRef]

Martin-Moreno, L.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

Mateos, J.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Meziani, Y.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Mikhailov, S. A.

S. A. Mikhailov, “Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems,” Phys. Rev. B58, 1517–1532 (1998).
[CrossRef]

Otsuji, T.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Y. Tsuda, T. Komori, A. El Fatimy, K. Horiike, T. Suemitsu, and T. Otsuji, “Application of plasmon-resonant microchip emitters to broadband terahertz spectroscopic measurement,” J. Opt. Soc. Am. B26, A52–A57 (2009).
[CrossRef]

Oulton, R. F.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
[CrossRef]

Podolskiy, V. A.

Poisson, M. A.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Prager, L.

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

Prystawko, P.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Riyopoulos, S.

S. Riyopoulos, “THz instability by streaming carriers in high mobility solid-state plasmas,” Phys. Plasmas12, 070704 (2005).
[CrossRef]

Roelens, Y.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Ryzhii, V.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Samsonidze, G. G.

M. V. Cheremisin and G. G. Samsonidze, “D’yakonov–Shur instability in a ballistic field-effect transistor with a spatially nonuniform channel,” Semiconductors33, 578–585 (1999).
[CrossRef]

Sánchez-Gil, J. A.

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

Sano, E.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Satou, A.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Shur, M.

M. Dyakonov and M. Shur, “Current instability and plasma waves generation in ungated two-dimensional electron layers,” Appl. Phys. Lett.87(11), 111501 (2005).
[CrossRef]

M. Dyakonov and M. Shur, “Shallow water analogy for a ballistic field-effect transistor: new mechanism of plasma wave generation by a dc current,” Phys. Rev. Lett.71, 2465–2468 (1993).
[CrossRef] [PubMed]

Shur, M. S.

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

Skierbiszewski, C.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Solymar, L.

O. Sydoruk, R. R. A. Syms, and L. Solymar, “Plasma oscillations and terahertz instability in field-effect transistors with Corbino geometry,” Appl. Phys. Lett.97, 263504 (2010).
[CrossRef]

O. Sydoruk, V. Kalinin, and L. Solymar, “Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels,” Appl. Phys. Lett.97, 062107 (2010).
[CrossRef]

Suemitsu, M.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Suemitsu, T.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Y. Tsuda, T. Komori, A. El Fatimy, K. Horiike, T. Suemitsu, and T. Otsuji, “Application of plasmon-resonant microchip emitters to broadband terahertz spectroscopic measurement,” J. Opt. Soc. Am. B26, A52–A57 (2009).
[CrossRef]

Sydoruk, O.

O. Sydoruk, V. Kalinin, and L. Solymar, “Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels,” Appl. Phys. Lett.97, 062107 (2010).
[CrossRef]

O. Sydoruk, R. R. A. Syms, and L. Solymar, “Plasma oscillations and terahertz instability in field-effect transistors with Corbino geometry,” Appl. Phys. Lett.97, 263504 (2010).
[CrossRef]

Syms, R. R. A.

O. Sydoruk, R. R. A. Syms, and L. Solymar, “Plasma oscillations and terahertz instability in field-effect transistors with Corbino geometry,” Appl. Phys. Lett.97, 263504 (2010).
[CrossRef]

Teppe, F.

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

Theron, D.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Thongrattanasiri, S.

Tsuda, Y.

Vandenbrouk, S.

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

Varani, L.

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

Veksler, D.

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

Watanabe, T.

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

Zhang, X.

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

O. Sydoruk, V. Kalinin, and L. Solymar, “Terahertz instability of optical phonons interacting with plasmons in two-dimensional electron channels,” Appl. Phys. Lett.97, 062107 (2010).
[CrossRef]

M. Dyakonov and M. Shur, “Current instability and plasma waves generation in ungated two-dimensional electron layers,” Appl. Phys. Lett.87(11), 111501 (2005).
[CrossRef]

O. Sydoruk, R. R. A. Syms, and L. Solymar, “Plasma oscillations and terahertz instability in field-effect transistors with Corbino geometry,” Appl. Phys. Lett.97, 263504 (2010).
[CrossRef]

J. Appl. Phys. (4)

J. Lusakowski, W. Knap, N. Dyakonova, L. Varani, J. Mateos, T. Gonzalez, Y. Roelens, S. Bollaert, A. Cappy, and K. Karpierz, “Voltage tuneable terahertz emission from a ballistic nanometer InGaAs/InAlAs transistor,” J. Appl. Phys.97, 064307 (2005).
[CrossRef]

F. J. Crowne, “Contact boundary conditions and the Dyakonov–Shur instability in high electron mobility transistors,” J. Appl. Phys.82, 1242–1254 (1997).
[CrossRef]

A. El Fatimy, N. Dyakonova, Y. Meziani, T. Otsuji, W. Knap, S. Vandenbrouk, K. Madjour, D. Theron, C. Gaquiere, M. A. Poisson, S. Delage, P. Prystawko, and C. Skierbiszewski, “AlGaN/GaN high electron mobility transistors as a voltage-tunable room temperature terahertz sources,” J. Appl. Phys.107, 024504 (2010).
[CrossRef]

A. D. Bresler, G. H. Joshi, and N. Marcuvitz, “Orthogonality properties for modes in passive and active uniform wave guides,” J. Appl. Phys.29, 794–799 (1958).
[CrossRef]

J. Infrared Milli. Terahz. Waves (1)

T. Otsuji, T. Watanabe, A. El Moutaouakil, H. Karasawa, T. Komori, A. Satou, T. Suemitsu, M. Suemitsu, E. Sano, W. Knap, and V. Ryzhii, “Emission of terahertz radiation from two-dimensional electron systems in semiconductor nano- and heterostructures,” J. Infrared Milli. Terahz. Waves32, 629–645 (2011).
[CrossRef]

J. Opt. Soc. Am. B (2)

Phys. Plasmas (1)

S. Riyopoulos, “THz instability by streaming carriers in high mobility solid-state plasmas,” Phys. Plasmas12, 070704 (2005).
[CrossRef]

Phys. Rev. B (3)

D. Veksler, F. Teppe, A. P. Dmitriev, V. Y. Kachorovskii, W. Knap, and M. S. Shur, “Detection of terahertz radiation in gated two-dimensional structures governed by dc current,” Phys. Rev. B73, 125328 (2006).
[CrossRef]

S. A. Mikhailov, “Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems,” Phys. Rev. B58, 1517–1532 (1998).
[CrossRef]

R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B76, 035,408 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

U. Mackens, D. Heitmann, L. Prager, J. P. Kotthaus, and W. Beinvogl, “Minigaps in the plasmon dispersion of a two-dimensional electron gas with spatially modulated charge density,” Phys. Rev. Lett.53, 1485–1488 (1984).
[CrossRef]

J. Gómez Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett.93, 256804 (2004).
[CrossRef]

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. Gómez Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901 (2008).
[CrossRef] [PubMed]

M. Dyakonov and M. Shur, “Shallow water analogy for a ballistic field-effect transistor: new mechanism of plasma wave generation by a dc current,” Phys. Rev. Lett.71, 2465–2468 (1993).
[CrossRef] [PubMed]

Sem. Phys. Quant. Electr. & Optoelectr. (1)

S. M. Kukhtaruk, “High-frequency properties of systems with drifting electrons and polar optical phonons,” Sem. Phys. Quant. Electr. & Optoelectr.11, 43–49 (2008).

Semiconductors (1)

M. V. Cheremisin and G. G. Samsonidze, “D’yakonov–Shur instability in a ballistic field-effect transistor with a spatially nonuniform channel,” Semiconductors33, 578–585 (1999).
[CrossRef]

Other (2)

R. E. Collin, Foundations for Microwave Engineering (Wiley-IEEE Press, Hoboken, New Jersey, 2001).
[CrossRef]

Z. Knittl, Optics of Thin Films (Wiley, London, 1981).

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Figures (6)

Fig. 1
Fig. 1

Cascaded two-dimensional channels form a distributed reflector (a). In the presence of dc current, counter-propagating plasmons have different dispersion characteristics (b) leading to different transverse field profiles, shown schematically on the dispersion curves.

Fig. 2
Fig. 2

Schematic presentation (a) of an interface between two different channels, where the step shows the change in the dc electron density. The presence of dc current affects the (b) reflection and (c) transmission coefficients of the plasmon incident from the channel with a larger electron density. Both coefficients can increase when the current flows away from the interface.

Fig. 3
Fig. 3

To obtain the boundary conditions for the current, we surround the interface by a cylinder with a small radius δ. As the radius decreases, the difference between the magnetic fields at the cylinder surface vanishes leading to continuity of the current.

Fig. 4
Fig. 4

The effect of the dc current depends on the structure of a distributed reflectors. In the absence of the current, (b) and (f), the plasmonic reflection coefficient can be close to unity in several frequency bands. It can increase and exceed unity for negative current densities, (d) and (h), and decrease for positive current densities, (c) and (g). The effect of the dc current is larger for the reflector (a) comprising channels with low electron density.

Fig. 5
Fig. 5

Two different reflectors form an asymmetric resonator (a) whose roundtrip gain can exceed unity. The reflection and transmission coefficients of plasmons incident on the resonator do not exceed unity in the absence of the dc current (b), but oscillations occur at 1 THz when the threshold current density is reached (c) and (d). The oscillation frequency was controlled by choosing the length of the middle section.

Fig. 6
Fig. 6

A plasmonic reflection coefficient clearly shows threshold oscillation behavior. Oscillations occur at current densities exceeding 0.029 A/cm.

Equations (15)

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

E z | x = + 0 = E z | x = 0 E x | x = + 0 E x | x = 0 = e n / ( ε 0 ε d ) H y | x = + 0 H y | x = 0 = J
H y = A cos k x ( x w ) cos k x w ,
n tot = n 0 + n v tot = v 0 + v
J tot = e ( n 0 + n ) ( v 0 + v ) e n 0 v 0 + e n 0 v + e n v 0 ,
j ( ω k z v 0 ) v = e m E z | x = 0 ,
Ω p 2 k x tan k x w ( ω k z v 0 ) 2 = 1 ,
E x ( 1 ) | z = 0 = E x ( 2 ) | z = 0 H y ( 1 ) | z = 0 = H y ( 2 ) | z = 0
J ( 1 ) , ( 2 ) ( z ) = 2 H y ( 1 ) , ( 2 ) ( z ) | x = 0 ,
H y ( 1 ) | z = δ x = 0 H y ( 1 ) | z = 0 x = δ H y ( 2 ) | z = δ x = 0 H y ( 2 ) | z = 0 x = δ
J ( 1 ) | z = 0 = J ( 2 ) | z = 0 .
n ( 1 ) | z = 0 = n ( 2 ) | z = 0 .
v ( 2 ) | z = 0 = n 0 ( 1 ) v ( 1 ) | z = 0 + ( v 0 ( 1 ) v 0 ( 2 ) ) n ( 1 ) | z = 0 n 0 ( 2 ) .
E x 1 ( 1 ) + + α R α E x α ( 1 ) = α T α E x α ( 2 ) + H y 1 ( 1 ) + + α R α H y α ( 1 ) = α T α H y α ( 2 ) +
0 w ( E x α ( 1 , 2 ) H y β ( 1 , 2 ) + E x β ( 1 , 2 ) H y α ( 1 , 2 ) ) d x + m v 0 ( 1 , 2 ) 2 e ( J α ( 1 , 2 ) v β ( 1 , 2 ) + J β ( 1 , 2 ) v α ( 1 , 2 ) ) = 0 , α β ,
R N ( + ) = R N 1 ( + ) + T N 1 ( + ) T N 1 ( ) r N ( + ) e j [ k N 1 ( + ) k N 1 ( ) ] L N 1 1 r N ( + ) R N 1 ( ) e j [ k N 1 ( + ) k N 1 ( ) ] L N 1 ,

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