Abstract

We develop a fundamental formulation for electrically-pumped plasmonic semiconductor nanolasers based on a metallic bowtie structure. Because of the negative dielectric constant of the metal at optical frequencies, the effective modal volume of the plasmonic mode can be compressed to the nanometer scale. In addition, the curvature effect of the bowtie tips provides additional field enhancement in the bowtie gap and further reduces the modal volume. With this small modal volume, the required volume of the active region is reduced correspondingly, which significantly decreases the threshold current. The huge field enhancement due to the small modal volume at the gap of the bowtie may overcome the material and radiation losses by increasing both the spontaneous and stimulated emission rates, and it makes the lasing action possible.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Haus and C. Shank, "Antisymmetric taper of distributed feedback lasers," IEEE J. Quantum Electron. 12, 532-539 (1976).
    [CrossRef]
  2. H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
    [CrossRef]
  3. E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
    [CrossRef]
  4. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
    [CrossRef] [PubMed]
  5. S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
    [CrossRef] [PubMed]
  6. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
    [CrossRef] [PubMed]
  7. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
    [CrossRef]
  8. T. Baba, "Photonic crystals and microdisk cavities based on GaInAsP-InP system," IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
    [CrossRef]
  9. M. Fujita, A. Sakai, and T. Baba, "Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
    [CrossRef]
  10. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  11. C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
    [CrossRef]
  12. M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
    [CrossRef]
  13. B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
    [CrossRef]
  14. S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
    [CrossRef]
  15. E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
    [CrossRef]
  16. M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F.W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, "Lasing in metallic-coated nanocavities," Nat. Photonics 1, 589-594 (2007).
    [CrossRef]
  17. E. Yablonovitch, T. J. Gmitter, and R. Bhat, "Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures," Phys. Rev. Lett. 61, 2546-2549 (1988).
    [CrossRef] [PubMed]
  18. J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
    [CrossRef]
  19. J. M. Gerard and B. Gayral, "Strong Purcell effect for InAs quantum boxes in three-dimensionalsolid-state microcavities," J. Lightwave Technol. 17, 2089-2095 (1999).
    [CrossRef]
  20. G. S. Solomon, M. Pelton, and Y. Yamamoto, "Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity," Phys. Rev. Lett. 86, 3903-3906 (2001).
    [CrossRef] [PubMed]
  21. D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef] [PubMed]
  22. I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
    [CrossRef]
  23. J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
    [CrossRef] [PubMed]
  24. A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
    [CrossRef]
  25. E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Elsevier Butterworth-Heinemann, 1984).
  26. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).
  27. E. Feigenbaum and M. Orenstein, "Optical 3D cavity modes below the diffraction-limit using slow-wave surfaceplasmon-polaritons," Opt. Express 15, 2607-2612 (2007).
    [CrossRef] [PubMed]
  28. G. Bjork, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50, 1675-1680 (1994).
    [CrossRef] [PubMed]
  29. P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
    [CrossRef] [PubMed]
  30. M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots," Phys. Rev. B 65, R041308 (2002).
    [CrossRef]

2007

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

E. Feigenbaum and M. Orenstein, "Optical 3D cavity modes below the diffraction-limit using slow-wave surfaceplasmon-polaritons," Opt. Express 15, 2607-2612 (2007).
[CrossRef] [PubMed]

2006

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

2005

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

2004

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

2002

M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots," Phys. Rev. B 65, R041308 (2002).
[CrossRef]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

2001

G. S. Solomon, M. Pelton, and Y. Yamamoto, "Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity," Phys. Rev. Lett. 86, 3903-3906 (2001).
[CrossRef] [PubMed]

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

2000

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

1999

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

M. Fujita, A. Sakai, and T. Baba, "Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

J. M. Gerard and B. Gayral, "Strong Purcell effect for InAs quantum boxes in three-dimensionalsolid-state microcavities," J. Lightwave Technol. 17, 2089-2095 (1999).
[CrossRef]

1998

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

1997

T. Baba, "Photonic crystals and microdisk cavities based on GaInAsP-InP system," IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
[CrossRef]

1995

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

1994

G. Bjork, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50, 1675-1680 (1994).
[CrossRef] [PubMed]

1993

1992

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

1988

E. Yablonovitch, T. J. Gmitter, and R. Bhat, "Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures," Phys. Rev. Lett. 61, 2546-2549 (1988).
[CrossRef] [PubMed]

1987

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

1976

H. Haus and C. Shank, "Antisymmetric taper of distributed feedback lasers," IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

1946

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).

Ajili, L.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Baba, T.

M. Fujita, A. Sakai, and T. Baba, "Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

T. Baba, "Photonic crystals and microdisk cavities based on GaInAsP-InP system," IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
[CrossRef]

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bayer, M.

M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots," Phys. Rev. B 65, R041308 (2002).
[CrossRef]

Beere, H.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Bhat, R.

E. Yablonovitch, T. J. Gmitter, and R. Bhat, "Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures," Phys. Rev. Lett. 61, 2546-2549 (1988).
[CrossRef] [PubMed]

Bimberg, D.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Bjork, G.

G. Bjork, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50, 1675-1680 (1994).
[CrossRef] [PubMed]

Borri, P.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Capasso, F.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Cho, A. Y.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Costard, E.

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Crozier, K. B.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Cubukcu, E.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Davies, G.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

de Vries, T.

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

de Waardt, H.

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

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Eijkemans, T. J.

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

Eisler, H.-J.

J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Faist, J.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Farahani, J. N.

J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Feigenbaum, E.

Forchel, A.

M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots," Phys. Rev. B 65, R041308 (2002).
[CrossRef]

Fromm, D. P.

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Fujita, M.

M. Fujita, A. Sakai, and T. Baba, "Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

Gayral, B.

J. M. Gerard and B. Gayral, "Strong Purcell effect for InAs quantum boxes in three-dimensionalsolid-state microcavities," J. Lightwave Technol. 17, 2089-2095 (1999).
[CrossRef]

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Geluk, E. J.

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

Gerard, J. M.

J. M. Gerard and B. Gayral, "Strong Purcell effect for InAs quantum boxes in three-dimensionalsolid-state microcavities," J. Lightwave Technol. 17, 2089-2095 (1999).
[CrossRef]

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, and R. Bhat, "Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures," Phys. Rev. Lett. 61, 2546-2549 (1988).
[CrossRef] [PubMed]

Haus, H.

H. Haus and C. Shank, "Antisymmetric taper of distributed feedback lasers," IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

Hecht, B.

J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Hill, M. T.

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

Hu, Q.

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Hutchinson, A. L.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Imai, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Ishikawa, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Ju, Y. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Karlsson, A.

G. Bjork, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50, 1675-1680 (1994).
[CrossRef] [PubMed]

Kim, I. I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Kim, S. B.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kim, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Kino, G. S.

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Kohen, S.

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

Kort, E. A.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Kotaki, Y.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Kumar, S.

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Kwon, S. H.

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

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Langbein, W.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Lee, Y. H.

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

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Legrand, B.

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Linfield, E.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Moerner, W. E.

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Noda, S.

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Notzel, R.

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

O???Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

O???Reilly, E. P.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Oei, Y. S.

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

Orenstein, M.

Ouyang, D.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Park, H. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Pelton, M.

G. S. Solomon, M. Pelton, and Y. Yamamoto, "Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity," Phys. Rev. Lett. 86, 3903-3906 (2001).
[CrossRef] [PubMed]

Pohl, D.

J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Protsenko, I. E.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Purcell, E. M.

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).

Reno, J. L.

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Ritchie, D.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Rochat, M.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Sakai, A.

M. Fujita, A. Sakai, and T. Baba, "Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

Samoilov, V. N.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Schneider, S.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Schuck, P. J.

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Sellin, R. L.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Sermage, B.

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Shank, C.

H. Haus and C. Shank, "Antisymmetric taper of distributed feedback lasers," IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

Sirtori, C.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Sivco, D. L.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Smalbrugge, B.

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

Smit, M. K.

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

Soda, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Solomon, G. S.

G. S. Solomon, M. Pelton, and Y. Yamamoto, "Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity," Phys. Rev. Lett. 86, 3903-3906 (2001).
[CrossRef] [PubMed]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Sudo, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Sundaramurthy, A.

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Thierry-Mieg, V.

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

Turkiewicz, J. P.

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

Uskov, A. V.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

van Otten, F.W. M.

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

van Veldhoven, P. J.

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

Willenberg, H.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Williams, B. S.

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Woggon, U.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, and R. Bhat, "Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures," Phys. Rev. Lett. 61, 2546-2549 (1988).
[CrossRef] [PubMed]

Yamakoshi, S.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Yamamoto, Y.

G. S. Solomon, M. Pelton, and Y. Yamamoto, "Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity," Phys. Rev. Lett. 86, 3903-3906 (2001).
[CrossRef] [PubMed]

G. Bjork, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50, 1675-1680 (1994).
[CrossRef] [PubMed]

Yang, J. K.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Zaimidoroga, O. A.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Zhu, Y.

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

Appl. Phys. Lett.

C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 �??m wavelength," Appl. Phys. Lett. 66, 3242-3244 (1995).
[CrossRef]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, "Low-threshold terahertz quantum-cascade lasers," Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, "Terahertz quantum-cascade laser at ? �?? 100 ?m using metal waveguide for mode confinement," Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

S. Kumar, B. S. Williams, S. Kohen, Q. Hu, and J. L. Reno, "Continuous-wave operation of terahertz quantumcascade lasers above liquid-nitrogen temperature," Appl. Phys. Lett. 84, 2494-2496 (2004).
[CrossRef]

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, "Plasmonic laser antenna," Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

IEEE J. Quantum Electron.

H. Haus and C. Shank, "Antisymmetric taper of distributed feedback lasers," IEEE J. Quantum Electron. 12, 532-539 (1976).
[CrossRef]

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. Baba, "Photonic crystals and microdisk cavities based on GaInAsP-InP system," IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, "Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor," IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nat. Photonics

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

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

S. Noda, A. Chutinan, and M. Imada, "Trapping and emission of photons by a single defect in a photonic bandgap structure," Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev.

E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).

Phys. Rev. A

G. Bjork, A. Karlsson, and Y. Yamamoto, "Definition of a laser threshold," Phys. Rev. A 50, 1675-1680 (1994).
[CrossRef] [PubMed]

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O�??Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Phys. Rev. B

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, "Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip Au nanotriangles," Phys. Rev. B 72, 165409 (2005).
[CrossRef]

M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.60Ga0.40As/GaAs self-assembled quantum dots," Phys. Rev. B 65, R041308 (2002).
[CrossRef]

Phys. Rev. Lett.

P. Borri,W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, "Ultralong dephasing time in InGaAs quantum dots," Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

J. N. Farahani, D. Pohl, H.-J. Eisler, and B. Hecht, "Single quantum dot coupled to a scanning optical antenna: a tunable superemitter," Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, and R. Bhat, "Inhibited and enhanced spontaneous emission from optically thin AlGaAs/GaAs double heterostructures," Phys. Rev. Lett. 61, 2546-2549 (1988).
[CrossRef] [PubMed]

J. M. Gerard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).
[CrossRef]

G. S. Solomon, M. Pelton, and Y. Yamamoto, "Single-mode spontaneous emission from a single quantum dot in a three-dimensional microcavity," Phys. Rev. Lett. 86, 3903-3906 (2001).
[CrossRef] [PubMed]

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Science

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447 (2004).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�??Brien, P. D. Dapkus, and I. I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Other

E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Elsevier Butterworth-Heinemann, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

The geometry of a plasmonic bowtie antenna laser using (a) quantum dots (QDs), and (b) multiple quantum wells (MQWs). QDs are placed in the bowtie gap while MQWs are located below the metallic bowtie. The dashed lines in the figure are the field distribution along the tip-to-tip direction. The bowtie tips reduce the effective volume of the cavity mode and lead to the field enhancement around the bowtie tips, which increases the stimulated and spontaneous emission rates.

Fig. 2.
Fig. 2.

(a) The transition lineshape Lcv (ħω) and photon density of states ρn (ħω). The relative magnitudes of the two curves are plotted up to a scaling factor. (b) The spontaneousemission efficiency as a function of the dipole transition energy Ecv . When the energy difference Ecv -ħωn is within the HWHM linewidth Γcv+ħΔωn , the spontaneous-emission efficiency becomes significant, and it reaches its maximum when Ecv =ħωn .

Fig. 3.
Fig. 3.

The geometrical parameters which specify the bowtie cavity shown in Fig. 1.

Fig. 4.
Fig. 4.

(a) A logarithmic plot of |fx (r)|2 along the x axis at one half of the bowtie thickness. The maximum of the field strength is located at the bowtie tips and decays exponentially into the metal. The modal profile can be regarded as the symmetrically-coupled mode of the two bowtie modes. (b) A contour plot of |fx (r)|2 near the tips in the x-y plane.

Fig. 5.
Fig. 5.

(a) Stimulated (R st(n)S) and spontaneous emission (R sp(n)) rates, and the nonradiative recombination (R nr(n)) rate of plasmonic nanolaser using three quantum dots placed in the bowtie gap. The field enhancement and peaked gain on the gain spectrum help to overcome the high material loss from the metallic plasmons. The nonradiative recombination rate is nearly negligible compared with the other two rates, indicating a high intrinsic quantum efficiency. (b) R st(n)S and R sp(n) at a small injection current. The stimulated absorption is gradually converted to the stimulated emission. At 0.5 µA, R st(n)S exceeds R sp(n). (c) The light output power vs. injection current of the QD-based plasmonic nanolaser. Since β sp is close to unity, the LI curve shows a thresholdless behavior.

Fig. 6.
Fig. 6.

(a) Various transition rates of the plasmonic nanolaser using five quantum wells placed below the bowtie. Since carriers are inefficiently utilized both spectrally and spatially, the stimulated emission rate (R st(n)S) is much lower than the spontanneous emission (R sp(n)) and non-radiative recombination (R nr(n)) rate. This means that the stimulated emission rate cannot overcome the loss for the MQW case. (b) The light output power vs. injection current of the MQW-based plasmonic device. The device is actually an LED.

Fig. 7.
Fig. 7.

(a) Various transition rates of the plasmonic nanolaser using five quantum wells placed below the bowtie after Q is improved to 100. The stimulated emission rate can overcome the loss of the cavity and make the device lase. (b) The corresponding LI curve. Since the spontaneous emission factor β sp is less than unity (β sp⋍0.3 after the stimulated emission takes over), a smooth turn-on behavior is present on the LI curve.

Tables (2)

Tables Icon

Table 1. The parameters which characterizes the geometry of the bowtie cavity.

Tables Icon

Table 2. The dipole moment between conduction and valence bands. ed 0=〈S|ex|X〉 is the dipole moment between Bloch states.

Equations (51)

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

n ( r ) = i 2 ħ ω n ε 0 f n ( r ) , 𝓗 n ( r ) = 1 μ 0 2 ħ ε 0 ω n × f n ( r ) ,
× × f n ( r ) = ( ω n c ) 2 ε ̂ R ( r , ω n ) f n ( r ) , · [ ε ̂ R ( r , ω n ) f n ( r ) ] = 0 ,
ε ̂ ( r , ω ) = ε ̂ R ( r , ω ) + i ε ̂ I ( r , ω ) = ε ( r , ω ) + i σ f ( r , ω ) ( ε 0 ω ) .
V d r 1 2 [ [ ω ε ̂ R ( r , ω ) ] ω ω = ω 0 + ε ̂ R ( r , ω 0 ) ] f n * ( r ) · f n ( r ) = δ n n , ω n ~ ω n ~ ω 0 .
r sp , cv , n ( r ) = 2 π ħ ( ħ ω n 2 ε 0 ) e d cv · f n ( r ) 2 δ ( ħ ω n E cv ) ,
r st , cv , n ( r ) N ph , n = 2 π ħ ( ħ ω n 2 ε 0 ) e d cv · f n ( r ) 2 N ph , n δ ( ħ ω n E cv ) ,
δ ( ħ ω n E cv ) L cv ( ħ ω n ) = 1 π Γ cv ( ħ ω n E cv ) 2 + Γ cv 2 ,
ρ n ( ħ ω ) = δ ( ħ ω ħ ω n ) 1 π ħ Δ ω n ( ħ ω ħ ω n ) 2 + ( ħ Δ ω n ) 2 ,
R ̂ sp , n = 1 V a c , v , r i V a ( π ω n ε 0 ) d ( ħ ω ) ρ n ( ħ ω ) e d cv , i · f n ( r i ) 2 L cv , i ( ħ ω ) f c , i ( 1 f v , i ) ,
d ( ħ ω ) ρ n ( ħ ω ) L cv , i ( ħ ω ) = 1 π ( ħ Δ ω + Γ cv , i ) ( ħ ω n E cv , i ) 2 + ( ħ Δ ω + Γ cv , i ) 2 .
R ̂ st , n = V eff V a c , v , r i V a ( π ω n ε 0 ) e d cv , i · f n ( r i ) 2 L cv , i ( ħ ω n ) ( f c , i f v , i ) ,
V eff = [ n ¯ 2 f ( r ) max 2 ] 1 ,
n t = η i I e V a R nr ( n ) R sp ( n ) R st ( n ) S ,
S t = S τ p + V a V eff β sp ( n ) R sp ( n ) + V a V eff R st ( n ) S ,
τ p 1 = τ p , rad 1 + τ p , mat 1 ,
n = n c = n h = N V a ,
S = N ph V eff ,
R nr ( n ) = n τ nr + C n 3 ,
1 Q t = 1 Q V a V eff R st ( n ) ω L = 2 Δ ω ω L = 1 τ p ω L ,
1 Q = 1 Q rad + 1 Q mat ,
P = V eff S ( ħ ω L τ p , rad ) = N ph ( ħ ω L τ p , rad ) .
S = τ p β sp ( n ) R sp ( n ) ( V a V eff ) 1 R st ( n ) τ p ( V a V eff ) .
n th = s n d 2 + ε 0 2 π Q [ 1 π Γ cv V a d r e d cv · f ( r ) 2 ( E cv ħ ω L ) 2 + Γ cv 2 ] 1 ,
n th = s n d 2 + V eff Q ε 0 n ¯ 2 2 π V a e d cv ¯ 2 [ 1 π Γ cv ( E cv ħ ω L ) 2 + Γ cv 2 ] 1 ,
e d cv 2 ¯ V a d r e d cv · f ( r ) 2 V a f ( r ) max 2 ,
n th = s n d 2 + V eff Q ε 0 n ¯ 2 Γ cv 2 V a e d cv ¯ 2 .
R ̂ sp , n = 1 V a c , v ( π ω n ε 0 ) V a d r D ( r ) d ( ħ ω ) ρ n ( ħ ω ) e d cv , r · f n ( r ) 2 L cv , r ( ħ ω ) f c , r ( 1 f v , r ) ,
R sp , n = 1 V a c , v ( π ω n ε 0 ) V a d r D ( r ) d E 𝒢 cv ( E )
× e d cv ( E ) · f n ( r ) 2 1 π ( Γ cv + ħ Δ ω n ) f c ( E ̂ c ) [ 1 f v ( E ̂ v ) ] ( ħ ω n E ) 2 + ( Γ cv + ħ Δ ω n ) 2 ,
R sp = n C R sp , n + c , v d E 𝒢 cv ( E ) f c ( E ̂ c ) [ 1 f v ( E ̂ v ) ]
× 1 V a V a d r D ( r ) { n R ( π ω n ε 0 ) 1 π ( Γ cv + ħ Δ ω n ) e d cv ( E ) · f n ( r ) 2 ( ħ ω n E ) 2 + ( Γ cv + ħ Δ ω n ) 2 } .
R sp n C R sp , n + c , v R sp , cv rad d E D 𝒢 cv ( E ) f c ( E ̂ c ) [ 1 f v ( E ̂ v ) ] ,
R sp , cv rad 1 V a n R ( π ω n ε 0 ) V a d r D ( r ) D 1 π [ ( Γ cv + ħ Δ ω n ) + e d cv ( E ) · f n ( r ) 2 ( ħ ω n E ) 2 + ( Γ cv + ħ Δ ω n ) 2 ] , ¯
R st , n = V eff V a c , v ( π ω n ε 0 ) V a d r D ( r ) d E π 𝒢 c v ( E ) e d c v ( E ) · f n ( r ) 2 Γ c v [ f c ( E ̂ c ) f v ( E ̂ v ) ] ( ħ ω n E ) 2 + Γ c v 2 .
f c ( E ̂ c ) = [ exp ( E ̂ c E Fc k B T ) + 1 ] 1 , f v ( E ̂ v ) = [ exp ( E ̂ v E Fv k B T ) + 1 ] 1 .
R sp , n = 1 V a ( π ω n ε 0 ) s n d π ( Γ cv + ħ Δ ω n ) f c ( E c ) [ 1 f v ( E v ) ] ( E cv ħ ω n ) 2 + ( Γ cv + ħ Δ ω n ) 2 [ V a d r e d cv · f n ( r ) 2 ]
= 1 s n d V a ( π ω n ε 0 ) 1 π ( Γ cv + ħ Δ ω n ) ( E cv ħ ω n ) 2 + ( Γ cv + ħ Δ ω n ) 2 [ V a d r e d cv · f n ( r ) 2 ] n c n h
R sp = n C R sp , n + R sp rad n d f c ( E c ) [ 1 f v ( E v ) ] = n C R sp , n + R sp rad n d n c n h ( s n d ) 2 ,
R st , n = V eff V a ( π ω n ε 0 ) s n d π Γ cv [ f c ( E c ) f v ( E v ) ] ( E cv ħ ω n ) 2 + Γ cv 2 [ V a d r e d cv · f n ( r ) 2 ]
= V eff V a ( π ω n ε 0 ) 1 π Γ cv ( E cv ħ ω n ) 2 + Γ cv 2 [ V a d r e d cv · f n ( r ) 2 ] ( n c + n h s n d )
n c = s n d f c ( E c ) , n h = s n d [ 1 f v ( E v ) ] .
R sp , n = 1 V a c , v ( π ω n ε 0 ) V a d r d k t ( 2 π ) 2 L w 1 π e d cv , k t · f n ( r ) 2 ( Γ cv + ħ Δ ω n ) f c , k t ( 1 f v , k t ) ( E c , k t E v , k t ħ ω n ) 2 + ( Γ c v + ħ Δ ω n ) 2 ,
R st , n = V eff V a c , v ( π ω n ε 0 ) V a d r d k t ( 2 π ) 2 L w 1 π e d cv , k t · f n ( r ) 2 Γ cv ( f c , k t f v , k t ) ( E c , k t E v , k t ħ ω n ) 2 + Γ cv 2 .
E c , k t = E c + ħ 2 k t 2 2 m c , E v , k t = E v ħ 2 k t 2 2 m v ,
E c , k t E v , k t = E c E v + ħ 2 k t 2 2 m r , cv , 1 m r , cv = 1 m c + 1 m v ,
E = ħ 2 k t 2 2 m r , cv , ρ cv , 0 ( E ) = m r , cv 2 π ħ 2 L w .
R sp , n = 1 V a c , v ( π ω n ε 0 ) V a d r e d cv · f n ( r ) 2 0 d E π ρ cv , 0 ( E ) ( Γ cv + ħ Δ ω n ) f c ( E ) ( 1 f v ( E ) ) ( E cv + E ħ ω n ) 2 + ( Γ cv + ħ Δ ω n ) 2 ,
R st , n = V eff V a c , v ( π ω n ε 0 ) V a d r e d cv · f n ( r ) 2 0 d E π ρ cv , 0 ( E ) Γ cv [ f c ( E ) f v ( E ) ] ( E cv + E ħ ω n ) 2 + Γ c v 2 ,
R sp = n R sp , n + c , v R sp , cv rad 0 d E ρ cv , 0 ( E ) f c ( E ) [ 1 f v ( E ) ]
f c ( E ) = { exp [ 1 k B T ( E c + m r , c v m c E E f c ) ] + 1 } 1 ,
f v ( E ) = { exp [ 1 k B T ( E v + m r , c v m v E E fv ) ] + 1 } 1 .

Metrics