Abstract

The propagation of surface plasmon polaritons on metallic waveguides adjacent to a gain medium is considered. It is shown that the presence of the gain medium can compensate for the absorption losses in the metal. The conditions for existence of a surface plasmon polariton and its lossless propagation and wavefront behavior are derived analytically for a single infinite metal-gain boundary. In addition, the cases of thin slab and stripe geometries are also investigated using finite element simulations. The effect of a finite gain layer and its distance from the SPP waveguide is also investigated. The calculated gain requirements suggest that lossless gain-assisted surface plasmon polariton propagation can be achieved in practice for infrared wavelengths.

© 2004 Optical Society of America

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  1. C. Vassalo, Optical waveguide concepts (Elsevier, 1991).
  2. F. A. Fernández and Y. Lu, Microwave and optical waveguide analysis by the finite element method, (Wiley, 1996).
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  4. G. A. Plotz, H. J. Simon, and J. M. Tucciarone, “Enhanced total reflection with surface plasmons,” JOSA 69, 419–421 (1979).
    [CrossRef]
  5. B. Ya Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100 (1972).
  6. A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys.Tech. Phys. 34, 764–766 (1989).
  7. H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer Verlag, 1988).
  8. C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, “Long-wavelength (λ=8-11.5 µm) semiconductor lasers with waveguides based on surface plasmons,” Opt. Lett. 23, 1366 (1998).
    [CrossRef]
  9. E. D. Palik, Handbook of optical constants of solidsvol. I (Academic Press, 1985).
  10. T. Saitoh and T Mukai, “1.5 µm GaInAsP traveling-wave semiconductor laser amplifier,” IEEE J. Quant. Elec. QE-23, 1010–1020 (1987).
    [CrossRef]
  11. N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
    [CrossRef]
  12. K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
    [CrossRef]
  13. P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
    [CrossRef]
  14. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
    [CrossRef]
  15. L.A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, (Wiley, 1995).
  16. N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
    [CrossRef]
  17. S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
    [CrossRef]
  18. N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
    [CrossRef]
  19. J. R. Sambles, “Grain-boundary scattering and surface-plasmon attenuation in noble-metal films,” Solid State Comm. 49, 343–345 (1984).
    [CrossRef]

2003 (1)

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

2002 (1)

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
[CrossRef]

2000 (3)

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
[CrossRef]

1999 (1)

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

1998 (1)

1996 (1)

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

1994 (1)

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

1989 (1)

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys.Tech. Phys. 34, 764–766 (1989).

1987 (1)

T. Saitoh and T Mukai, “1.5 µm GaInAsP traveling-wave semiconductor laser amplifier,” IEEE J. Quant. Elec. QE-23, 1010–1020 (1987).
[CrossRef]

1984 (1)

J. R. Sambles, “Grain-boundary scattering and surface-plasmon attenuation in noble-metal films,” Solid State Comm. 49, 343–345 (1984).
[CrossRef]

1979 (1)

G. A. Plotz, H. J. Simon, and J. M. Tucciarone, “Enhanced total reflection with surface plasmons,” JOSA 69, 419–421 (1979).
[CrossRef]

1972 (1)

B. Ya Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100 (1972).

Alferov, Z. I.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Aoyagi, Y.

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

Auxier, J.

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

Barnes, W. L.

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

Berini, P.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Bimberg, D.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Borrelli, N. F.

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

Capasso, F.

Cho, A. Y.

Coldren, L. A.

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

Coldren, L.A.

L.A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, (Wiley, 1995).

Corzine, S. W.

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

L.A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, (Wiley, 1995).

Demkovich, P. A.

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys.Tech. Phys. 34, 764–766 (1989).

Dereux, A.

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

Domen, K.

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

Ebbesen, T. W.

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

Egorov, A. Y.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Faist, J.

Fernández, F. A.

F. A. Fernández and Y. Lu, Microwave and optical waveguide analysis by the finite element method, (Wiley, 1996).

Gmachl, C.

Gossard, A.C.

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

Hacke, P.

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

Hatori, N.

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

Horino, K.

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

Hu, S. Y.

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

Hutchinson, A. L.

Ishikawa, H.

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

Kirstaedter, N.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Kopev, P.S.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Kuramata, A.

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

Lebedev, S. A.

B. Ya Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100 (1972).

Ledentsov, N. N.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Lu, Y.

F. A. Fernández and Y. Lu, Microwave and optical waveguide analysis by the finite element method, (Wiley, 1996).

Maximov, M. V.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Mukai, K.

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

Mukai, T

T. Saitoh and T Mukai, “1.5 µm GaInAsP traveling-wave semiconductor laser amplifier,” IEEE J. Quant. Elec. QE-23, 1010–1020 (1987).
[CrossRef]

Nakata, Y.

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of optical constants of solidsvol. I (Academic Press, 1985).

Peyghambarian, N.

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

Pikhtin, N. A.

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
[CrossRef]

Plotz, G. A.

G. A. Plotz, H. J. Simon, and J. M. Tucciarone, “Enhanced total reflection with surface plasmons,” JOSA 69, 419–421 (1979).
[CrossRef]

Raether, H.

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer Verlag, 1988).

Ramvall, P.

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

Saitoh, T.

T. Saitoh and T Mukai, “1.5 µm GaInAsP traveling-wave semiconductor laser amplifier,” IEEE J. Quant. Elec. QE-23, 1010–1020 (1987).
[CrossRef]

Sambles, J. R.

J. R. Sambles, “Grain-boundary scattering and surface-plasmon attenuation in noble-metal films,” Solid State Comm. 49, 343–345 (1984).
[CrossRef]

Schmidt, O. G.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Schulzgen, A.

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

Simon, H. J.

G. A. Plotz, H. J. Simon, and J. M. Tucciarone, “Enhanced total reflection with surface plasmons,” JOSA 69, 419–421 (1979).
[CrossRef]

Sirtori, C.

Sivco, D. L.

Sliptchenko, S. O.

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
[CrossRef]

Sokolova, Z. N.

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
[CrossRef]

Sudarkin, A. N.

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys.Tech. Phys. 34, 764–766 (1989).

Sugawara, M.

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

Tarasov, I. S.

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
[CrossRef]

Tucciarone, J. M.

G. A. Plotz, H. J. Simon, and J. M. Tucciarone, “Enhanced total reflection with surface plasmons,” JOSA 69, 419–421 (1979).
[CrossRef]

Ustinov, V. M.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Vassalo, C.

C. Vassalo, Optical waveguide concepts (Elsevier, 1991).

Volkov, V. M.

B. Ya Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100 (1972).

Wundke, K.

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

Ya Kogan, B.

B. Ya Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100 (1972).

Young, D. B.

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

Zhukov, A.E.

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

Appl. Phys. Lett. (4)

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata, and H. Ishikawa, “Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1–1.3 µm semiconductor lasers,” Appl. Phys. Lett. 77, 773–775 (2000).
[CrossRef]

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 µm in PbS-doped glasses,” Appl. Phys. Lett. 75, 3060–3062 (1999).
[CrossRef]

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen, and K. Horino, “Doping-dependent optical gain in GaN,” Appl. Phys. Lett. 76, 2994–2996 (2000).
[CrossRef]

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev, and Z. I. Alferov, “Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,” Appl. Phys. Lett. 69, 1226–1228 (1996).
[CrossRef]

IEEE J. Quant. Elec. (1)

T. Saitoh and T Mukai, “1.5 µm GaInAsP traveling-wave semiconductor laser amplifier,” IEEE J. Quant. Elec. QE-23, 1010–1020 (1987).
[CrossRef]

J. of Appl. Physics (1)

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, and L. A. Coldren, “High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,” J. of Appl. Physics 76, 3932–3934 (1994).
[CrossRef]

JETP Lett. (1)

B. Ya Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100 (1972).

JOSA (1)

G. A. Plotz, H. J. Simon, and J. M. Tucciarone, “Enhanced total reflection with surface plasmons,” JOSA 69, 419–421 (1979).
[CrossRef]

Nature (1)

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

Opt. Lett. (1)

Phys. Rev. B (1)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Semiconductors (1)

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova, and I. S. Tarasov, “Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,” Semiconductors 36, 344–353 (2002).
[CrossRef]

Solid State Comm. (1)

J. R. Sambles, “Grain-boundary scattering and surface-plasmon attenuation in noble-metal films,” Solid State Comm. 49, 343–345 (1984).
[CrossRef]

Sov. Phys.Tech. Phys. (1)

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys.Tech. Phys. 34, 764–766 (1989).

Other (5)

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer Verlag, 1988).

E. D. Palik, Handbook of optical constants of solidsvol. I (Academic Press, 1985).

C. Vassalo, Optical waveguide concepts (Elsevier, 1991).

F. A. Fernández and Y. Lu, Microwave and optical waveguide analysis by the finite element method, (Wiley, 1996).

L.A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, (Wiley, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic illustration of various SPP propagation regimes as a function of ε1.

Fig. 2.
Fig. 2.

Plots of: (a) Im(kx ), (b) propagation length, (c) wavefront tilt angle and (d) Im( k z 1 ) versus gain. The points corresponding to lossless propagation, zero wavefront tilt and bound surface wave limit, respectively, are also shown.

Fig. 3.
Fig. 3.

FEA simulations of total electric field for SPPs propagating on a silver interface embedded in an InGaAsP-based gain medium: (a) Symmetric mode in slab configuration without gain, kx =14.06+i0.0197 µm-1. (b) Symmetric mode in slab configuration with gain, kx =14.06 µm-1. (c) Symmetric mode in stripe configuration without gain, kx =13.76+i0.0094 µm -1. (d) Symmetric mode in stripe configuration with gain, kx =13.76 µm-1.

Fig. 4.
Fig. 4.

(a) Metallic stripe waveguide of Fig. 3 in proximity to a gain layer with finite thickness. (b) FEA generated results showing variation of gain required for lossless propagation as the gap d increases. Each curve corresponds to a different value of gain layer thickness h.

Equations (12)

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{ E j = ( E x , 0 , E z j ) exp ( i ( k x x + k z j z ω t ) ) H j = ( 0 , H y , 0 ) exp ( i ( k x x + k z j z ω t ) ) , j = 1 , 2
{ ε 1 k z 1 = ε 2 k z 2 k z 2 + k z i 2 = ε i k 0 2 E x = k z i ω ε i H y , E z i = k x ω ε i H y i = 1 , 2
{ k x 2 = k 0 2 ε 1 ε 2 ε 1 + ε 2 ( a ) k z i 2 = k 0 2 ε i 2 ε 1 + ε 2 ( b )
{ k x 2 = k 0 2 ( ε 1 + i ε 1 ) ( ε 2 + i ε 2 ) ( ε 1 + ε 2 ) + i ( ε 1 + ε 2 ) ( a ) k z i 2 = k 0 2 ( ε i + i ε i ) 2 ( ε 1 + ε 2 ) + i ( ε 1 + ε 2 ) ( b )
k z 1 k 0 ε 1 + ε 2 ( ε 1 + ε 2 ) 2 + ( ε 1 + ε 2 ) 2 ( ε 1 + i ε 1 ) ( 1 i ( ε 1 + ε 2 ) 2 ( ε 1 + ε 2 ) )
( ε 1 ) 2 + ε 2 ε 1 + 2 ε 1 ( ε 1 + ε 2 ) < 0
ε 2 ( ε 2 ) 2 8 ε 1 ( ε 1 + ε 2 ) 2 < ε 1 < ε 2 + ( ε 2 ) 2 8 ε 1 ( ε 1 + ε 2 ) 2
k x 2 = k 0 2 ( ε 1 + ε 2 ) 2 + ( ε 1 + ε 2 ) 2 [ ε 1 ( ( ε 2 ) 2 + ε 1 2 ε 1 ε 2 + ( ε 2 ) 2 ) + i ε 2 ( ( ε 1 ) 2 + ε 2 2 ε 2 ε 1 + ( ε 1 ) 2 ) ]
ε 1 = ε 2 2 2 ε 2 ( 1 ± 1 4 ( ε 1 ε 2 ) 2 ε 2 4 ) { ε 2 2 ε 2 + ( ε 1 ) 2 ε 2 ε 2 2 ( a ) ( ε 1 ) 2 ε 2 ε 2 2 ( b )
γ 0 = 2 π λ 0 ε 2 ( ε 1 ) 3 2 ( ε 2 ) 2 + ( ε 2 ) 2
P = 1 2 Re ( E 1 × H * ) = H y 2 2 ω [ Re ( k x ε 1 ) x ̂ + Re ( k z 1 ε 1 ) z ̂ ]
Re ( k z 1 ε 1 ) = Re ( k 0 ε 1 + ε 2 + i ( ε 1 + ε 2 ) ) k 0 ( ε 1 + ε 2 ) 2 ( ε 1 + ε 2 ) 3 2

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