Abstract

Semiconductor plasmonic lasers at submicron and nanometer scales exhibit many characteristics distinct from those of their conventional counterparts at micron scales. The differences originate from their small sizes and the presence of metal plasma surrounding the cavity. To design a laser of this type, features such as metal dispersion, optical energy confinement, and group velocity have to be taken into account properly. In this paper, we provide a comprehensive approach to the design and performance evaluation of plasmonic Fabry-Perot nanolasers. In particular, we show the proper procedure to obtain the key parameters, especially the quality factor and threshold gain, which are usually neglected in conventional semiconductor Fabry-Perot lasers but become important for nanolasers.

© 2010 Optical Society of America

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  1. C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  3. 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]
  4. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
    [CrossRef] [PubMed]
  5. C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
    [CrossRef]
  6. S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1004–1013 (2009).
    [CrossRef]
  7. A. V. Maslov and C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
    [CrossRef]
  8. A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE 6468, 64680I (2007).
    [CrossRef]
  9. S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express 16, 10580–10595 (2008).
    [CrossRef] [PubMed]
  10. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  11. A. Kapoor and G. S. Singh, “Mode classification in cylindrical dielectric waveguide,” J. Lightwave Technol. 18, 849 (2000).
    [CrossRef]
  12. C. S. Lee, S. W. Lee, and S. L. Chuang, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34, 773 (1986).
    [CrossRef]
  13. T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
    [CrossRef]
  14. S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
    [CrossRef]
  15. COMSOL Inc, http://www.comsol.com.
  16. C. Y. Lu, S. W. Chang, S. H. Yang, and S. L. Chuang, “Quantum-dot laser with a metal-coated waveguide under continuous-wave operation at room temperature,” Appl. Phys. Lett. 95, 233507 (2009).
    [CrossRef]
  17. S. W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
    [CrossRef]
  18. M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micro-pillar cavity quality factors calculated with finite element methods,” Opt. Express 17, 1144 (2009).
    [CrossRef] [PubMed]
  19. E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
    [CrossRef]
  20. Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
    [CrossRef]

2010 (2)

C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

2009 (5)

2008 (1)

2007 (2)

A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE 6468, 64680I (2007).
[CrossRef]

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]

2005 (1)

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

2003 (2)

A. V. Maslov and C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

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

2000 (1)

1997 (1)

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[CrossRef]

1993 (1)

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

1992 (1)

E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
[CrossRef]

1986 (1)

C. S. Lee, S. W. Lee, and S. L. Chuang, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34, 773 (1986).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Barnes, W. L.

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

Bimberg, D.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

Blok, H.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[CrossRef]

Burger, S.

Chang, S. W.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

C. Y. Lu, S. W. Chang, S. H. Yang, and S. L. Chuang, “Quantum-dot laser with a metal-coated waveguide under continuous-wave operation at room temperature,” Appl. Phys. Lett. 95, 233507 (2009).
[CrossRef]

S. W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
[CrossRef]

S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1004–1013 (2009).
[CrossRef]

S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express 16, 10580–10595 (2008).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Chuang, S. L.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

C. Y. Lu, S. W. Chang, S. H. Yang, and S. L. Chuang, “Quantum-dot laser with a metal-coated waveguide under continuous-wave operation at room temperature,” Appl. Phys. Lett. 95, 233507 (2009).
[CrossRef]

S. W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
[CrossRef]

S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1004–1013 (2009).
[CrossRef]

S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express 16, 10580–10595 (2008).
[CrossRef] [PubMed]

C. S. Lee, S. W. Lee, and S. L. Chuang, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34, 773 (1986).
[CrossRef]

Crawford, F. D.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

Dapkus, P.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[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]

Demeulenaere, B.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[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]

Geluk, E. J.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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]

Germann, T. D.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
[CrossRef]

Grodzinski, P.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

Hetterich, M.

Hill, M. T.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kalt, H.

Kapoor, A.

Karl, M.

Karouta, F.

Kettner, B.

Kohen, S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

Koza, M. A.

E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
[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]

Lee, C. S.

C. S. Lee, S. W. Lee, and S. L. Chuang, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34, 773 (1986).
[CrossRef]

Lee, S. W.

C. S. Lee, S. W. Lee, and S. L. Chuang, “Normal modes in an overmoded circular waveguide coated with lossy material,” IEEE Trans. Microw. Theory Tech. 34, 773 (1986).
[CrossRef]

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]

Lenstra, D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[CrossRef]

Leong, E. S. P.

Lu, C. Y.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

C. Y. Lu, S. W. Chang, S. H. Yang, and S. L. Chuang, “Quantum-dot laser with a metal-coated waveguide under continuous-wave operation at room temperature,” Appl. Phys. Lett. 95, 233507 (2009).
[CrossRef]

Marell, M.

Maslov, A. V.

A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE 6468, 64680I (2007).
[CrossRef]

A. V. Maslov and C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

Ni, C. Y. A.

Ning, C. Z.

C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE 6468, 64680I (2007).
[CrossRef]

A. V. Maslov and C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

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]

Nötzel, R.

Oei, Y. S.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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]

Osinski, J. S.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

Rideout, W. C.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

Schlafer, J.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

Schmidt, F.

Sharfin, W. F.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

Singh, G. S.

Smalbrugge, B.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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]

Sun, M.

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]

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, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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]

Visser, T. D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[CrossRef]

Williams, B. S.

S. Kohen, B. S. Williams, and Q. Hu, “Electromagnetic modeling of terahertz quantum cascade laser waveguides and resonators,” J. Appl. Phys. 97, 053106 (2005).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
[CrossRef]

Yang, S. H.

C. Y. Lu, S. W. Chang, S. H. Yang, and S. L. Chuang, “Quantum-dot laser with a metal-coated waveguide under continuous-wave operation at room temperature,” Appl. Phys. Lett. 95, 233507 (2009).
[CrossRef]

Zah, C. E.

E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
[CrossRef]

Zhu, Y.

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107 (2009).
[CrossRef] [PubMed]

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]

Zou, Y.

Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

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C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[CrossRef]

A. V. Maslov and C. Z. Ning, “Reflection of guided modes in a semiconductor nanowire laser,” Appl. Phys. Lett. 83, 1237 (2003).
[CrossRef]

C. Y. Lu, S. W. Chang, S. H. Yang, and S. L. Chuang, “Quantum-dot laser with a metal-coated waveguide under continuous-wave operation at room temperature,” Appl. Phys. Lett. 95, 233507 (2009).
[CrossRef]

E. Yablonovitch, C. E. Zah, T. J. Gmitter, and M. A. Koza, “Nearly ideal InP/In0.53Ga0.47As heterojunction regrowth on chemically prepared In0.53Ga0.47As surfaces,” Appl. Phys. Lett. 60, 371 (1992).
[CrossRef]

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Y. Zou, J. S. Osinski, P. Grodzinski, P. Dapkus, W. C. Rideout, W. F. Sharfin, J. Schlafer, and F. D. Crawford, “Experimental study of Auger recombination, gain, and temperature sensitivity of 1.5 μm compressively strained semiconductor lasers,” IEEE J. Quantum Electron. 29, 1565–1575 (1993).
[CrossRef]

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[CrossRef]

S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1004–1013 (2009).
[CrossRef]

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Nat. Photonics (1)

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).
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A. V. Maslov and C. Z. Ning, “Size reduction of a semiconductor nanowire laser by using metal coating,” Proc. SPIE 6468, 64680I (2007).
[CrossRef]

Other (1)

COMSOL Inc, http://www.comsol.com.

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Figures (11)

Fig. 1.
Fig. 1.

Two Ag-coated circular structures: (a) the nanocavity with a short vertical post and a subwavelength cross section, and (b) the micron-long cylinder (with a subwavelength cross section) which acts as the FP nanolaser cavity. In both cases, the In0.53Ga0.47As bulk semiconductor is used as the gain medium.

Fig. 2.
Fig. 2.

(a) The effective index of the plasmonic circular waveguide shown in Fig. 1(b). The TM0 mode and each of HE m1 (m ≥ 1) will evolve into the SPP m modes as the photon energy increases. (b) The counterpart of (a) but with silver replaced by the perfect electric conductor. The guided modes in (a) and (b) both show the cutoff behavior (n eff → 0).

Fig. 3.
Fig. 3.

(a) The real parts of effective indices of a few guided modes obtained by 2D FEM (symbol) and by the calculation of lossless waveguide (line). (b) The modal losses of the same modes obtained by 2D FEM (symbol) and variational approach (line). The results from two methods agree very well except near the cutoff and plasmon resonance.

Fig. 4.
Fig. 4.

(a) The standing-wave pattern of the the x-polarized field in the xz plane for the HE11 mode at λ = 1443.65 nm. The facet at z = 0 is waveguide/air interface. (b) The curve fitting of normalized ∣��x (z)∣ at ρ = 0. Due to the contamination of the near field near the facet, the fitted curve slightly deviates from the original data there. The obtained reflection coefficient has a magnitude of 0.881 and phase angle of −0.165 π.

Fig. 5.
Fig. 5.

(a) The material group index n g,a(ω) of In0.53Ga0.47As and waveguide group indices n g,z (ω) of the HE11 and SPP1 modes as a function of photon energy. The two waveguide group indices are always larger than that of In0.53Ga0.47As, and the deviation can be significant near the waveguide cutoff of HE11 mode or plasmon resonance of SPP1 mode. (b) The waveguide confinement factor Γ wg and energy confinement factor ΓE for the HE11 and SPP1 modes. The waveguide confinement factors follow the trends of waveguide group indices while the energy confinement factor is always smaller than unity.

Fig. 6.
Fig. 6.

The resonance spectrum of the store energy for the FP cavity with waveguide/air interfaces.

Fig. 7.
Fig. 7.

(a) The resonance spectrum for a silver coating of thickness t = 10 nm on the waveguide facet at z = 0. (b) The standing-wave pattern of the cavity mode at λ = 1414.63 nm in the yz plane. The 10 nm silver coating reduces the mirror loss and sharpens the standingwave pattern. The transmitted power is lower than that of the uncoated waveguide/air interface at z = 0 shown in Fig. 4(a).

Fig. 8.
Fig. 8.

(a) The resonance spectrum for a silver coating of a thickness t = 30 nm. (b) The standing-wave pattern of the cavity mode at λ = 1405.65 nm in the yz plane. Most of the power is reflected back into the waveguide due to the thin silver coating on the facet, which results in an even sharper standing-wave pattern than that in Fig. 7(b).

Fig. 9.
Fig. 9.

The gain spectra of bulk In0.53Ga0.47As under different carrier densities.

Fig. 10.
Fig. 10.

(a) The stimulated emission rates of the four FP modes and nonradiative recombination rate by solving coupled Eqs. (1a)–(1e) for four modes. Around a current of 0.79 mA, the stimulated emission rate of the mode at λ = 1529.59 nm surpasses the nonradiative recombination rate and indicates that the lasing action begins to dominate. (b) The spontaneous emission rates of the four FP modes. Although only the mode at λ = 1529.59 nm lases, the four spontaneous emission rates are close in magnitude.

Fig. 11.
Fig. 11.

The output powers of four FP modes by solving coupled Eqs. (1a)–(1e). They resemble the trends of stimulated emission rates in Fig. 10(a) once the population inversion is reached.

Tables (3)

Tables Icon

Table 1. The reflectivities, quality factors, and threshold material gain of the resonance modes for the FP cavity with waveguide/air interfaces. Q (FP) is obtained using Eq. (8b). Q (3D) is obtained using FEM in Fig. 6.

Tables Icon

Table 2. The reflectivities, quality factors, and threshold material gains of the resonance modes for the FP cavity with the 10 nm Ag coating. Q (FP) is obtained using Eq. (8b). Q (3D) is obtained using FEM in Fig. 7(a).

Tables Icon

Table 3. The reflectivities, quality factors, and threshold material gains of the resonance modes for the FP cavity with the 30 nm Ag coating. Q (FP) is obtained using Eq. (8b). Q (3D) is obtained using FEM in Fig. 8(a).

Equations (21)

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n t = η i I q V a R nr ( n ) R sp , cont ( n ) Σ b R sp , b ( n ) Σ b R st , b ( n ) s b ,
S b t = S b τ p , b + Γ E , b R sp , b ( n ) + Γ E , b R st , b ( n ) S b ,
R nr ( n ) = A n + C n 3 ,
R sp , cont ( n ) = 1 τ rad 1 V a Σ c , v , k f c , k ( 1 f v , k ) ,
R st , b ( n ) = v g , a ( ω b ) g ( ω b , n ) ,
α i = ω ε 0 2 P z A d ρ Im [ ε ( ρ , ω ) ] ( ρ ) 2 = 1 2 η 0 P z A d ρ ( ρ ) 2 n ( ρ , ω ) α ( ρ , ω ) ,
P z = A d ρ 1 2 Re [ ( ρ ) × * ( ρ ) ] · z ̂ ,
SWR E max E min ,
r = SWR 1 SWR + 1 = E max E min E max + E min .
( z ) = inc e i k z ( z z facet ) + r inc e i k z ( z z facet )
= inc e 2 Im [ k z ] ( z z facet ) + r 2 e 2 Im [ k z ] ( z z facet ) + 2 r cos { 2 Re [ k z ] ( z z facet ) θ r } ,
r = r e i θ r ,
1 τ p = v g , z ( ω ) [ α i + 1 2 L ln ( 1 R 2 ) ] ,
1 Q = 1 ω τ p = v g , z ( ω ) ω [ α i + 1 L ln ( 1 R ) ] = 1 Q abs + 1 Q mir ,
1 Q abs = v g , z ( ω ) α i ω , 1 Q mir = v g , z ( ω ) ω 1 L ln ( 1 R ) ,
1 τ p v g , z ( ω ) Γ wg g th = v g , a ( ω ) Γ E g th ,
Γ wg = n a ( ω ) 2 η 0 P z A a d ρ ( ρ ) 2 ,
Γ E = A a d ρ ε 0 4 { ε g , a ( ω ) + Re [ ε a ( ω ) ] } ( ρ ) 2 A d ρ ε 0 4 { ε g ( ρ , ω ) + Re [ ε ( ρ , ω ) ] } ( ρ ) 2 .
U = V a d r ε 0 4 { ε g , a ( ω ) + Re [ ε a ( ω ) ] } ( r ) 2 ,
Q λ r Δ λ .
P b = ω b V a S b Γ E , b [ T b 1 R b v g , z ( ω b ) L ln ( 1 R b ) ] ,

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