Abstract

We develop a rigorous theory of the enhancement of spontaneous emission from a light-emitting device via coupling the radiant energy in and out of surface plasmon polaritons (SPPs) on the metal-dielectric interface. We show that while the efficiency of coupling into the SPP mode can be quite high, the radiative efficiency of the SPP itself is relatively low, with a substantial fraction of the energy lost in the metal. Using the GaNAg system as an example we obtain easy-to-interpret analytical results that unequivocally indicate that using SPP pays off only for emitters that have medium-to-low luminescence efficiency; thus the SPP applications should be limited to those in sensing and analysis rather than in the development of efficient light sources.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  5. J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
    [CrossRef]
  6. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
    [CrossRef]
  7. S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
    [CrossRef] [PubMed]
  8. M. Moskovits, "Surface-enhanced spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985).
    [CrossRef]
  9. C. K. Chen, A. R. B. de Castro, and Y. R. Shen, "Surface-enhanced second-harmonic generation," Phys. Rev. Lett. 46, 145-148 (1981).
    [CrossRef]
  10. I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
    [CrossRef]
  11. A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
    [CrossRef]
  12. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
    [CrossRef] [PubMed]
  13. K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
    [CrossRef]
  14. T. D. Neal, K. Okamoto, and A. Scherer, "Surface plasmon enhanced emission from dye doped polymer layers," Opt. Express 13, 5522-5527 (2005).
    [CrossRef] [PubMed]
  15. J. Feng, T. Okamoto, and S. Kawata, "Enhancement of electroluminescence through a two-dimension corrugated metal film by grating-induced surface-plasmon cross coupling," Opt. Lett. 30, 2302-2304 (2005).
    [CrossRef] [PubMed]
  16. S. Wedge, J. A. E. Wasey, W. L. Barnes, and I. Sage, "Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure," Appl. Phys. Lett. 85, 182-184 (2004).
    [CrossRef]
  17. S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
    [CrossRef]
  18. P. T. Worthing and W. L. Barnes, "Efficient coupling of surface plasmon portions to radiation using bi-grating," Appl. Phys. Lett. 79, 3035-3037 (2001).
    [CrossRef]
  19. J. Vuckovic, M. Loncar, and A. Scherer, "Surface plasmon enhanced light-emitting diode," IEEE J. Quantum Electron. 36, 1131-1144 (2000).
    [CrossRef]
  20. W. L. Barnes, "Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices," J. Lightwave Technol. 17, 2170-2182 (1999).
    [CrossRef]
  21. R. Paiella, "Tunable surface plasmons in coupled metallic-dielectric multiple layers for light-emission efficiency enhancement," Appl. Phys. Lett. 87, 111104 (2005).
    [CrossRef]
  22. H. Metiu, "Surface enhanced spectroscopy," Prog. Surf. Sci. 17, 153-320 (1984).
    [CrossRef]
  23. G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
    [CrossRef]
  24. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).
    [CrossRef]
  25. E. Ejder, "Refractive index of GaN," Phys. Status Solidi A 6, 445-448 (1971).
    [CrossRef]
  26. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]

2006

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

2005

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

T. D. Neal, K. Okamoto, and A. Scherer, "Surface plasmon enhanced emission from dye doped polymer layers," Opt. Express 13, 5522-5527 (2005).
[CrossRef] [PubMed]

J. Feng, T. Okamoto, and S. Kawata, "Enhancement of electroluminescence through a two-dimension corrugated metal film by grating-induced surface-plasmon cross coupling," Opt. Lett. 30, 2302-2304 (2005).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

R. Paiella, "Tunable surface plasmons in coupled metallic-dielectric multiple layers for light-emission efficiency enhancement," Appl. Phys. Lett. 87, 111104 (2005).
[CrossRef]

2004

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

S. Wedge, J. A. E. Wasey, W. L. Barnes, and I. Sage, "Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure," Appl. Phys. Lett. 85, 182-184 (2004).
[CrossRef]

2002

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

2001

P. T. Worthing and W. L. Barnes, "Efficient coupling of surface plasmon portions to radiation using bi-grating," Appl. Phys. Lett. 79, 3035-3037 (2001).
[CrossRef]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

2000

J. Vuckovic, M. Loncar, and A. Scherer, "Surface plasmon enhanced light-emitting diode," IEEE J. Quantum Electron. 36, 1131-1144 (2000).
[CrossRef]

1999

W. L. Barnes, "Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices," J. Lightwave Technol. 17, 2170-2182 (1999).
[CrossRef]

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

1986

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1985

M. Moskovits, "Surface-enhanced spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985).
[CrossRef]

1984

H. Metiu, "Surface enhanced spectroscopy," Prog. Surf. Sci. 17, 153-320 (1984).
[CrossRef]

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
[CrossRef]

1981

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, "Surface-enhanced second-harmonic generation," Phys. Rev. Lett. 46, 145-148 (1981).
[CrossRef]

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

1972

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

1971

E. Ejder, "Refractive index of GaN," Phys. Status Solidi A 6, 445-448 (1971).
[CrossRef]

1946

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

1941

Barnes, W. L.

S. Wedge, J. A. E. Wasey, W. L. Barnes, and I. Sage, "Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure," Appl. Phys. Lett. 85, 182-184 (2004).
[CrossRef]

P. T. Worthing and W. L. Barnes, "Efficient coupling of surface plasmon portions to radiation using bi-grating," Appl. Phys. Lett. 79, 3035-3037 (2001).
[CrossRef]

W. L. Barnes, "Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices," J. Lightwave Technol. 17, 2170-2182 (1999).
[CrossRef]

Boroditsky, M.

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Catchpole, K. R.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Chen, C. K.

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, "Surface-enhanced second-harmonic generation," Phys. Rev. Lett. 46, 145-148 (1981).
[CrossRef]

Christy, R. W.

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

Contijo, I.

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

de Castro, A. R. B.

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, "Surface-enhanced second-harmonic generation," Phys. Rev. Lett. 46, 145-148 (1981).
[CrossRef]

DenBaars, S. P.

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

Ejder, E.

E. Ejder, "Refractive index of GaN," Phys. Status Solidi A 6, 445-448 (1971).
[CrossRef]

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Everitt, H. O.

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Fano, U.

Feng, J.

Ford, G. W.

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
[CrossRef]

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Hvam, J. M.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Johnson, P. B.

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

Kawakami, Y.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

Kawata, S.

Keller, S.

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

Kuroda, T.

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Lee, C. W.

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Leosson, K.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Loncar, M.

J. Vuckovic, M. Loncar, and A. Scherer, "Surface plasmon enhanced light-emitting diode," IEEE J. Quantum Electron. 36, 1131-1144 (2000).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Metiu, H.

H. Metiu, "Surface enhanced spectroscopy," Prog. Surf. Sci. 17, 153-320 (1984).
[CrossRef]

Mishra, U. K.

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

Moskovits, M.

M. Moskovits, "Surface-enhanced spectroscopy," Rev. Mod. Phys. 57, 783-826 (1985).
[CrossRef]

Mukai, T.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

Narukawa, Y.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

Neal, T. D.

Neogi, A.

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Niki, I.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

Okamoto, K.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

T. D. Neal, K. Okamoto, and A. Scherer, "Surface plasmon enhanced emission from dye doped polymer layers," Opt. Express 13, 5522-5527 (2005).
[CrossRef] [PubMed]

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

Okamoto, T.

Paiella, R.

R. Paiella, "Tunable surface plasmons in coupled metallic-dielectric multiple layers for light-emission efficiency enhancement," Appl. Phys. Lett. 87, 111104 (2005).
[CrossRef]

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Purcell, E. M.

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

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

Sage, I.

S. Wedge, J. A. E. Wasey, W. L. Barnes, and I. Sage, "Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure," Appl. Phys. Lett. 85, 182-184 (2004).
[CrossRef]

Sarid, D.

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Scherer, A.

T. D. Neal, K. Okamoto, and A. Scherer, "Surface plasmon enhanced emission from dye doped polymer layers," Opt. Express 13, 5522-5527 (2005).
[CrossRef] [PubMed]

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, "Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy," Appl. Phys. Lett. 87, 071102 (2005).
[CrossRef]

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

J. Vuckovic, M. Loncar, and A. Scherer, "Surface plasmon enhanced light-emitting diode," IEEE J. Quantum Electron. 36, 1131-1144 (2000).
[CrossRef]

Shen, Y. R.

C. K. Chen, A. R. B. de Castro, and Y. R. Shen, "Surface-enhanced second-harmonic generation," Phys. Rev. Lett. 46, 145-148 (1981).
[CrossRef]

Shvartser, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells," Nat. Mater. 3, 601-605 (2004).
[CrossRef] [PubMed]

Skovgaard, P. M. W.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Takemuchi, A.

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Van Duzer, T.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

Vuckovic, J.

J. Vuckovic, M. Loncar, and A. Scherer, "Surface plasmon enhanced light-emitting diode," IEEE J. Quantum Electron. 36, 1131-1144 (2000).
[CrossRef]

Wasey, J. A. E.

S. Wedge, J. A. E. Wasey, W. L. Barnes, and I. Sage, "Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure," Appl. Phys. Lett. 85, 182-184 (2004).
[CrossRef]

Weber, W. H.

G. W. Ford and W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).
[CrossRef]

Wedge, S.

S. Wedge, J. A. E. Wasey, W. L. Barnes, and I. Sage, "Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure," Appl. Phys. Lett. 85, 182-184 (2004).
[CrossRef]

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

Worthing, P. T.

P. T. Worthing and W. L. Barnes, "Efficient coupling of surface plasmon portions to radiation using bi-grating," Appl. Phys. Lett. 79, 3035-3037 (2001).
[CrossRef]

Yablonovich, E.

A. Neogi, C. W. Lee, H. O. Everitt, T. Kuroda, A. Takemuchi, and E. Yablonovich, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling," Phys. Rev. B 66, 153305 (2002).
[CrossRef]

I. Contijo, M. Boroditsky, E. Yablonovich, S. Keller, U. K. Mishra, and S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons," Phys. Rev. B 60, 11564-11567 (1999).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Zhang, G.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Zhao, J.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, "Enhanced emission from Si-based light emitting diodes using surface plasmons," Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Appl. Phys. Lett.

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Figures (18)

Fig. 1
Fig. 1

Light emission through coupling of SPP to radiation modes by a grating placed at (a) bottom interface for emission from the same side and (b) top interface for emission from the opposite side of the emitter. The gray (green) circle is the radiating center.

Fig. 2
Fig. 2

Effective width of SPP modes as a function of the propagation constant β p .

Fig. 3
Fig. 3

SPP dispersion curve.

Fig. 4
Fig. 4

(a) Purcell factor and (b) group velocity as a function of the photon energy.

Fig. 5
Fig. 5

Profiles of electric field for SPP and radiation modes.

Fig. 6
Fig. 6

Top view of (a) 1D and (b) 2D grating patterns along with their first-order wave vectors in reciprocal space.

Fig. 7
Fig. 7

κ pr f 1 2 versus the SPP propagation constant β p that couples into various radiation modes β r to illustrate the trend of radiative decay constant.

Fig. 8
Fig. 8

(a) SPP-radiation in-plane propagation constant coupling in reciprocal space, (b) emission cone with polar angle θ.

Fig. 9
Fig. 9

Coupling efficiency for bottom emission as a function of the polar angle θ with (a) 1D and (b) 2D grating.

Fig. 10
Fig. 10

Coupling efficiency for top emission through a thin metal layer d M = 50 nm as a function of the polar angle θ by (a) 1D and (b) 2D grating.

Fig. 11
Fig. 11

Top emission coupling efficiency between the SPP mode with β p = 1.40 and the radiation mode with β r = 0 (normal emission of θ = 0 ) as a function of metal thickness.

Fig. 12
Fig. 12

Integrated SPP coupling efficiency as a function of β p for bottom and top emission ( d M = 50 nm ) with θ max = π 2 by (a) 1D and (b) 2D grating.

Fig. 13
Fig. 13

Integrated SPP coupling efficiency as a function of β p for bottom and top emission ( d M = 50 nm ) with θ max = sin 1 ( 1 ε D ) by (a) 1D and (b) 2D grating.

Fig. 14
Fig. 14

Integrated SPP coupling efficiency as a function of β p for bottom and top emission ( d M = 50 nm ) with NA = 1 by (a) 1D and (b) 2D grating.

Fig. 15
Fig. 15

Overall enhancement factor for bottom emission by (a) 1D and (b) 2D grating.

Fig. 16
Fig. 16

Overall enhancement factor for top emission through a metal layer d M = 50 nm by (a) 1D and (b) 2D grating.

Fig. 17
Fig. 17

Optimal β p , opt as a function of the radiative efficiency η rad .

Fig. 18
Fig. 18

Overall optimal SPP enhancement for bottom emission as a function of the original radiative efficiency of the emitter at optimal value β p , opt .

Equations (45)

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η rad = τ rad 1 τ rad 1 + τ nrad 1 = τ nrad τ nrad + τ rad ,
ρ FS ( ω ) = n 3 ω 2 π 2 c 3 ,
τ SPP 1 = F P τ rad 1 ,
F P ρ SPP ρ FS ,
η pr = κ pr κ pr + κ nr ,
η SPP = η pr F P τ rad 1 F P τ rad 1 + τ nrad 1 .
F SPP = η SPP η rad = η pr η rad + ( 1 η rad ) F P 1 η pr η rad .
ε = ε D 1 ( 1 ω p 2 ω 2 + j ω Γ ) ,
H p , y ( ω , β p ) = { a p e q M x e j ( β p z ω t ) x > 0 a p e q D x e j ( β p z ω t ) x < 0 } ,
ε = β p 2 1 β p 2 , q D = β p 2 1 , q M = β p 2 β p 2 1 , q D + q M = 2 β p 2 1 β p 2 1 .
e p ( β p , x ) = { 2 ε w p 1 2 2 β p 2 1 ( j β p x ̂ + q M z ̂ ) e q M x x > 0 2 w p 1 2 2 β p 2 1 ( j β p x ̂ q D z ̂ ) e q D x x < 0 } ,
w p = 1 2 ( 2 β p 2 1 ) [ 2 β p 2 1 β p 2 1 + 1 ε 2 ( ω ε ) ω 2 β p 2 ε β p 2 ε ] 1 2 ( 2 β p 2 1 ) [ 2 β p 2 1 β p 2 1 + ( 2 ε D ε 2 1 ε ) 2 β p 2 ε β p 2 ε ] ,
ρ P = ρ SPP k D 3 = 1 2 π β p w p v g 1 ,
1 v g = β p ω + β p ω β p 0 ω [ β p 0 2 + ( β p 0 2 1 ) 2 ε D β p 0 2 ] .
F P = ρ P ρ D e q D h D = π 2 w p [ β p 4 + ε D 1 ( β p 2 1 ) 2 ] e q D h D = π ( 2 β p 2 1 ) [ β p 4 + ε D 1 ( β p 2 1 ) 2 ] [ 2 β p 2 1 β p 2 1 + ( 2 ε D ε 2 1 ε ) 2 β p 2 ε β p 2 ε ] 1 e q D h D .
β p = 1 2 ε ε β p 0 ( β p 0 2 1 ) 1 2 Γ ω β p 0 ( β p 0 2 1 ) .
γ loss = v g β p 1 2 Γ β p 0 ( β p 0 2 1 ) β p 0 3 ,
H r , y ( ω , β r ) = { a r e q r x e j ( β r z ω t ) x > 0 [ a r cos ( k r x ) + b r sin ( k r x ) ] e j ( β r z ω t ) x < 0 } ,
e r = { 2 k r L x ( q r 2 + ε 2 k r 2 ) ( j β r x ̂ + q r z ̂ ) e q r x x > 0 2 k r L x ( q r 2 + ε 2 k r 2 ) { j β r [ ε cos ( k r x ) ( q r k r ) sin ( k r x ) ] x ̂ + [ ε k r sin ( k r x ) + q r cos ( k r x ) ] z ̂ } x < 0 } ,
δ ε ( x ) = { 0 x > h M 1 ε 0 < x < h M ε 1 h D < x < 0 0 x < h D } ,
E = E r + E p = [ A r ( z , t ) e r ( x ) e i ( β r z ω r t ) + A p ( z , t ) e p ( x ) e j ( β p z ω t ) ] ,
2 j ω r A r t + ω p 2 A p e j ( ω r ω ) t C pr = 0 ,
A r t = j ω p 2 2 ω r C pr A p e j ( ω r ω ) t ,
C pr = f 1 2 δ ε ( x ) e p ( x ) e r * ( x ) d x .
A r ( z , t ) 2 = ω 4 4 ω r 2 C pr 2 A p 2 t 2 [ sin [ ( ω r ω ) t 2 ] ( ω r ω ) t 2 ] 2 .
A rad 2 = ω 4 4 ω r 2 C pr 2 A p 2 t 2 [ sin [ ( ω ω r ) t 2 ] ( ω ω r ) t 2 ] 2 ρ ( ω r ) d ω r π 2 ω 2 C pr 2 A p 2 ρ ( ω ) t ,
ρ ( ω r ) = L x 2 π ω r k r = L x 2 π ω r 1 β r 2 .
t A p ( t ) 2 = γ ( β r , β p ) A p ( t ) 2 ,
γ ( β r , β p ) = L x ω 4 1 β r 2 C pr 2 .
z A p ( z , t ) 2 = 1 v g t A p ( z , t ) 2 = κ pr A p ( z , t ) 2 ,
κ pr = γ ( β r , β p ) v g .
κ pr = β p 4 1 β r 2 [ β p 2 + ( β p 2 1 ) 2 ε D β p 2 ] L x C pr 2 .
κ pr = ( ε 1 ) 2 f 1 2 2 w p ( 2 β p 2 1 ) [ β p 2 + ( β p 2 1 ) 2 ε D β p 2 ] β p k r q r 2 + ε 2 k r 2 × { β p β r q r + ε k r 2 q D q D 2 + k r 2 [ 1 e q D h D [ ( q D k r ) sin ( k r h D ) + cos ( k r h D ) ] ] + ε β p β r q D q D 2 q r q D 2 + k r 2 [ 1 e q D h D [ cos ( k r h D ) ( k r q D ) sin ( k r h D ) ] ] + ( β p β r + q M q r ) ε ( q M + q r ) [ 1 e ( q M + q r ) h M ] } 2 .
η pr ( b ) = χ pr 1 + χ pr ,
f ( z ) = 1 2 f 1 e j G z + f 1 e j G z , f 1 = j π ,
f ( r ) = f 0 + f 1 n = 1 6 e j G n r , f 1 = 0.087 ,
E ( ω , β p ) = [ A t ( z ) e t ( x ) e j ( β p z ω t ) + A b ( z ) e b ( x ) e j ( β p z ω t ) ] ,
A t z = j κ bt A b κ pr 2 A t β p A t ,
A b z = j κ bt A t β p A b ,
κ bt = 1 ε 4 β p 0 e b ( x ) e t * ( x ) d x = ( ε 1 ) β p β p 2 1 ε w p ( 2 β p 2 1 ) 2 e q M d ,
A t ( z ) 2 = κ bt 2 κ bt 2 κ pr 2 16 A 0 2 e [ ( κ pr 2 ) + 2 β p ] z sin 2 ( κ bt 2 κ pr 2 16 z ) .
A rad 2 = κ rad A t ( z ) 2 d z = κ pr κ bt 2 κ pr 2 + 2 β p A 0 2 2 β p 2 + 2 κ bt 2 + β p κ pr .
η pr ( t ) = A rad 2 A 0 2 = χ pr 2 + χ pr ( 1 1 + χ pr 1 + χ pr + 4 χ bt 2 ) ,
η pr , all = N G 2 π φ m φ m η pr d φ ,
F SPP , opt = η SPP ( θ max , β p , opt ) η rad ( 1 cos θ max ) ,

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