Abstract

Amplification of the single-interface and long-range surface plasmon-polariton modes is studied in planar metallic structures incorporating gain media formed by Rhodamine 6G dye molecules in solution. We employ a theoretical model that accounts for the nonuniformity of the gain medium close to the metal surface due to position-dependent dipole lifetime and pump irradiance. The results of this model are used as a baseline for a comparative study against two simplified models: one neglects the position-dependent dipole lifetime while the other assumes a uniform gain medium. The discrepancies between the models are explained in terms of the mode overlap with the gain distribution near the metal. For the cases under analysis, the simplified models estimate the required pump irradiance with deviation factors that vary from 1.45 at the lossless conditions to 8 for gains near saturation. The relevance of describing properly the amount of gain interacting with the SPP mode and the role played by the dipole quantum efficiency are discussed.

© 2009 Optical Society of America

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  22. I. Z. Kozma, P. Krok, and E. Riedle, "Direct measurement of the group-velocity mismatch and derivation of the refractive-index dispersion for a variety of solvents in the ultraviolet," J. Opt. Soc. Am. B 22, 1479 (2005).
    [CrossRef]
  23. A. Penzkofer and W. Leupacher, "Fluorescence behaviour of highly concentrated rhodamine 6G solutions," J. Lumin. 37, 61 (1978).
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  24. W. Falkenstein, A. Penzkofer, and W. Kaiser, "Amplified spontaneous emission in rhodamine dyes: Generation of picosecond light pulses and determination of excited state absorption and relaxation," Opt. Commun. 27, 151 (1978).
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  25. E. Sahar and D. Treves, "Excited singlet-state absorption in dyes and their effect on dye lasers," IEEE J. Quantum Electron. QE-13, 962 (1977).
    [CrossRef]
  26. H. J. Eichler, U. Klein, and D. Langhans, "Measurement of orientational relaxation times of rhodamine 6G with a streak camera," Chem. Phys. Lett. 67, 21 (1979).
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  30. C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260 (2000).
    [CrossRef] [PubMed]
  31. P. Berini, "Bulk and surface sensitivities of surface plasmon waveguides," New J. Phys. 10, 105010 (2008).
    [CrossRef]
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    [CrossRef]

2009 (3)

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

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

T. Okamoto, F. H’Dhili, and S. Kawata, "Plasmonic crystal for efficient energy transfer from fluorescent molecules to long-range surface plasmons," Opt. Express. 17, 8294 (2009).
[CrossRef] [PubMed]

2008 (4)

I. De Leon and P. Berini, "Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media," Phys. Rev. B 78, 161401 (2008).
[CrossRef]

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

P. Berini, "Bulk and surface sensitivities of surface plasmon waveguides," New J. Phys. 10, 105010 (2008).
[CrossRef]

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, "Compensation of loss in propagating surface plasmons polariton by gain in adjacent dielectric medium," Opt. Express 16, 1385 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

S. A. Maier, "Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides," Opt. Comm. 258, 295 (2006).
[CrossRef]

G. Winter, S. Wedge, and W. L. Barnes, "Can lasing at visible wavelength be achieved using the low-loss long range surface plasmon-polariton mode?," New J. Phys. 8, 125 (2006).
[CrossRef]

2005 (3)

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

I. Z. Kozma, P. Krok, and E. Riedle, "Direct measurement of the group-velocity mismatch and derivation of the refractive-index dispersion for a variety of solvents in the ultraviolet," J. Opt. Soc. Am. B 22, 1479 (2005).
[CrossRef]

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

2004 (4)

T. Okamoto, F. H’Dhili, and S. Kawata, "Towards plasmonic band gap laser," App. Phys. Lett. 85, 3968 (2004).
[CrossRef]

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

M. P. Nezhad, K. Tetz, and Y. Fainman, "Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides," Opt. Express 17, 4072 (2004).
[CrossRef]

I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
[CrossRef]

2003 (2)

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

2002 (1)

S. Astilean and W. L. Barnes, "Quantum efficiency and the photonic control of molecular fluorescence in the solid state," App. Phys. B 75, 591 (2002).
[CrossRef]

2000 (1)

1998 (1)

W. L. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661 (1998).
[CrossRef]

1996 (1)

W. Svendsen, O. Ellegaard, and J. Schou, "Laser ablation deposition measurements from silver and nickel," Appl. Phys. A 63247 (1996).
[CrossRef]

1988 (1)

1986 (1)

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

1984 (1)

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

1982 (1)

L. G. Nair, "Dye Lasers," Prog. Quantum Electron. 7, 153 (1982).
[CrossRef]

1979 (1)

H. J. Eichler, U. Klein, and D. Langhans, "Measurement of orientational relaxation times of rhodamine 6G with a streak camera," Chem. Phys. Lett. 67, 21 (1979).
[CrossRef]

1978 (2)

A. Penzkofer and W. Leupacher, "Fluorescence behaviour of highly concentrated rhodamine 6G solutions," J. Lumin. 37, 61 (1978).
[CrossRef]

W. Falkenstein, A. Penzkofer, and W. Kaiser, "Amplified spontaneous emission in rhodamine dyes: Generation of picosecond light pulses and determination of excited state absorption and relaxation," Opt. Commun. 27, 151 (1978).
[CrossRef]

1977 (1)

E. Sahar and D. Treves, "Excited singlet-state absorption in dyes and their effect on dye lasers," IEEE J. Quantum Electron. QE-13, 962 (1977).
[CrossRef]

Adegoke, J. A.

Aitchison, J.S.

Alam, M. Z.

Ambati, M.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

Astilean, S.

S. Astilean and W. L. Barnes, "Quantum efficiency and the photonic control of molecular fluorescence in the solid state," App. Phys. B 75, 591 (2002).
[CrossRef]

Avrutsky, I.

I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
[CrossRef]

Bahoura, M.

Barnes, W. L.

G. Winter, S. Wedge, and W. L. Barnes, "Can lasing at visible wavelength be achieved using the low-loss long range surface plasmon-polariton mode?," New J. Phys. 8, 125 (2006).
[CrossRef]

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

S. Astilean and W. L. Barnes, "Quantum efficiency and the photonic control of molecular fluorescence in the solid state," App. Phys. B 75, 591 (2002).
[CrossRef]

W. L. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661 (1998).
[CrossRef]

Bartal, G.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

Becker, M. F.

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]

Berini, P.

I. De Leon and P. Berini, "Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media," Phys. Rev. B 78, 161401 (2008).
[CrossRef]

P. Berini, "Bulk and surface sensitivities of surface plasmon waveguides," New J. Phys. 10, 105010 (2008).
[CrossRef]

C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, "Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media," Opt. Express 7, 260 (2000).
[CrossRef] [PubMed]

Bouhelier, A.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[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 (1986).
[CrossRef]

Chen, C.

Colas des Francs, G.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

De Leon, I.

I. De Leon and P. Berini, "Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media," Phys. Rev. B 78, 161401 (2008).
[CrossRef]

Dereux, A.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

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

Ebbesen, T. W.

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

Eichler, H. J.

H. J. Eichler, U. Klein, and D. Langhans, "Measurement of orientational relaxation times of rhodamine 6G with a streak camera," Chem. Phys. Lett. 67, 21 (1979).
[CrossRef]

Ellegaard, O.

W. Svendsen, O. Ellegaard, and J. Schou, "Laser ablation deposition measurements from silver and nickel," Appl. Phys. A 63247 (1996).
[CrossRef]

Eng, L.

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Fainman, Y.

M. P. Nezhad, K. Tetz, and Y. Fainman, "Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides," Opt. Express 17, 4072 (2004).
[CrossRef]

Falkenstein, W.

W. Falkenstein, A. Penzkofer, and W. Kaiser, "Amplified spontaneous emission in rhodamine dyes: Generation of picosecond light pulses and determination of excited state absorption and relaxation," Opt. Commun. 27, 151 (1978).
[CrossRef]

Fedenev, A. V.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Feng, D.

Finot, C.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

Ford, G. W.

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

Geluk, E. J.

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

Genov, D. A.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

Goncharenko, I. M.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Grafstrom, S.

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Grandidier, J.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

H’Dhili, F.

T. Okamoto, F. H’Dhili, and S. Kawata, "Plasmonic crystal for efficient energy transfer from fluorescent molecules to long-range surface plasmons," Opt. Express. 17, 8294 (2009).
[CrossRef] [PubMed]

T. Okamoto, F. H’Dhili, and S. Kawata, "Towards plasmonic band gap laser," App. Phys. Lett. 85, 3968 (2004).
[CrossRef]

Hill, M. T.

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

Ishigure, T.

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Jee, Y.

Kaiser, W.

W. Falkenstein, A. Penzkofer, and W. Kaiser, "Amplified spontaneous emission in rhodamine dyes: Generation of picosecond light pulses and determination of excited state absorption and relaxation," Opt. Commun. 27, 151 (1978).
[CrossRef]

Karouta, F.

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

Kawata, S.

T. Okamoto, F. H’Dhili, and S. Kawata, "Plasmonic crystal for efficient energy transfer from fluorescent molecules to long-range surface plasmons," Opt. Express. 17, 8294 (2009).
[CrossRef] [PubMed]

T. Okamoto, F. H’Dhili, and S. Kawata, "Towards plasmonic band gap laser," App. Phys. Lett. 85, 3968 (2004).
[CrossRef]

Klein, U.

H. J. Eichler, U. Klein, and D. Langhans, "Measurement of orientational relaxation times of rhodamine 6G with a streak camera," Chem. Phys. Lett. 67, 21 (1979).
[CrossRef]

Koike, Y.

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Koval, N. N.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Kozma, I. Z.

Krok, P.

Langhans, D.

H. J. Eichler, U. Klein, and D. Langhans, "Measurement of orientational relaxation times of rhodamine 6G with a streak camera," Chem. Phys. Lett. 67, 21 (1979).
[CrossRef]

Leong, E. S.

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

Leupacher, W.

A. Penzkofer and W. Leupacher, "Fluorescence behaviour of highly concentrated rhodamine 6G solutions," J. Lumin. 37, 61 (1978).
[CrossRef]

Lipatov, E. I.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Maier, S. A.

S. A. Maier, "Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides," Opt. Comm. 258, 295 (2006).
[CrossRef]

Marell, M.

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

Markey, L.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

Massenot, S.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

Mayy, M.

Meier, J.

Mikes, F.

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Mojahedi, M.

Nair, L. G.

L. G. Nair, "Dye Lasers," Prog. Quantum Electron. 7, 153 (1982).
[CrossRef]

Nam, S. H.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

Nezhad, M. P.

M. P. Nezhad, K. Tetz, and Y. Fainman, "Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides," Opt. Express 17, 4072 (2004).
[CrossRef]

Ning, C.

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

Noginov, M. A.

Notzel, R.

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

Oei, Y.

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

Okamoto, T.

T. Okamoto, F. H’Dhili, and S. Kawata, "Plasmonic crystal for efficient energy transfer from fluorescent molecules to long-range surface plasmons," Opt. Express. 17, 8294 (2009).
[CrossRef] [PubMed]

T. Okamoto, F. H’Dhili, and S. Kawata, "Towards plasmonic band gap laser," App. Phys. Lett. 85, 3968 (2004).
[CrossRef]

Okamoto, Y.

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Orlovskii, V. M.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Penzkofer, A.

A. Penzkofer and W. Leupacher, "Fluorescence behaviour of highly concentrated rhodamine 6G solutions," J. Lumin. 37, 61 (1978).
[CrossRef]

W. Falkenstein, A. Penzkofer, and W. Kaiser, "Amplified spontaneous emission in rhodamine dyes: Generation of picosecond light pulses and determination of excited state absorption and relaxation," Opt. Commun. 27, 151 (1978).
[CrossRef]

Podolskiy, V. A.

Reynolds, K.

Riedle, E.

Ritzo, B. A.

Sahar, E.

E. Sahar and D. Treves, "Excited singlet-state absorption in dyes and their effect on dye lasers," IEEE J. Quantum Electron. QE-13, 962 (1977).
[CrossRef]

Schou, J.

W. Svendsen, O. Ellegaard, and J. Schou, "Laser ablation deposition measurements from silver and nickel," Appl. Phys. A 63247 (1996).
[CrossRef]

Seidel, J.

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Shulepov, M. A.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Smalbrugge, B.

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

Smit, M. K.

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

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 (1986).
[CrossRef]

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]

Sun, M.

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

Svendsen, W.

W. Svendsen, O. Ellegaard, and J. Schou, "Laser ablation deposition measurements from silver and nickel," Appl. Phys. A 63247 (1996).
[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 (1986).
[CrossRef]

Tanev, S.

Tarasenko, V. F.

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Teraoka, I.

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Tetz, K.

M. P. Nezhad, K. Tetz, and Y. Fainman, "Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides," Opt. Express 17, 4072 (2004).
[CrossRef]

Treves, D.

E. Sahar and D. Treves, "Excited singlet-state absorption in dyes and their effect on dye lasers," IEEE J. Quantum Electron. QE-13, 962 (1977).
[CrossRef]

Tzolov, V.

Ulin-Avila, E.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

van Veldhoven, P. J.

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

Walser, R. M.

Weber, W. H.

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

Wedge, S.

G. Winter, S. Wedge, and W. L. Barnes, "Can lasing at visible wavelength be achieved using the low-loss long range surface plasmon-polariton mode?," New J. Phys. 8, 125 (2006).
[CrossRef]

Weeber, J. C.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

Winter, G.

G. Winter, S. Wedge, and W. L. Barnes, "Can lasing at visible wavelength be achieved using the low-loss long range surface plasmon-polariton mode?," New J. Phys. 8, 125 (2006).
[CrossRef]

Yang, Y.

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Zhang, X.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

Zhu, G.

Zhu, Y.

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

App. Phys. B (1)

S. Astilean and W. L. Barnes, "Quantum efficiency and the photonic control of molecular fluorescence in the solid state," App. Phys. B 75, 591 (2002).
[CrossRef]

App. Phys. Lett. (1)

T. Okamoto, F. H’Dhili, and S. Kawata, "Towards plasmonic band gap laser," App. Phys. Lett. 85, 3968 (2004).
[CrossRef]

Appl. Phys. A (1)

W. Svendsen, O. Ellegaard, and J. Schou, "Laser ablation deposition measurements from silver and nickel," Appl. Phys. A 63247 (1996).
[CrossRef]

Chem. Phys. Lett. (1)

H. J. Eichler, U. Klein, and D. Langhans, "Measurement of orientational relaxation times of rhodamine 6G with a streak camera," Chem. Phys. Lett. 67, 21 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Sahar and D. Treves, "Excited singlet-state absorption in dyes and their effect on dye lasers," IEEE J. Quantum Electron. QE-13, 962 (1977).
[CrossRef]

J. Lumin. (1)

A. Penzkofer and W. Leupacher, "Fluorescence behaviour of highly concentrated rhodamine 6G solutions," J. Lumin. 37, 61 (1978).
[CrossRef]

J. Mod. Opt. (1)

W. L. Barnes, "Fluorescence near interfaces: the role of photonic mode density," J. Mod. Opt. 45, 661 (1998).
[CrossRef]

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

Macromolecules (1)

F. Mikes, Y. Yang, I. Teraoka, T. Ishigure, Y. Koike, and Y. Okamoto, "Synthesis and Characterization of an Amorphous Perfluoropolymer Poly(perfluoro-2-methylene-4-methyl-13-dioxolane)," Macromolecules 38, 4237 (2005).

Nano Lett. (2)

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Observation of Stimulated Emission of Surface Plasmon Polaritons," Nano Lett. 8, 3998 (2008)
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. C.  Weeber, C. Finot, and A. Dereux, "Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength," Nano Lett. 9, 2935 (2009).
[CrossRef] [PubMed]

Nature (1)

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

New J. Phys. (2)

P. Berini, "Bulk and surface sensitivities of surface plasmon waveguides," New J. Phys. 10, 105010 (2008).
[CrossRef]

G. Winter, S. Wedge, and W. L. Barnes, "Can lasing at visible wavelength be achieved using the low-loss long range surface plasmon-polariton mode?," New J. Phys. 8, 125 (2006).
[CrossRef]

Opt. Comm. (1)

S. A. Maier, "Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides," Opt. Comm. 258, 295 (2006).
[CrossRef]

Opt. Commun. (1)

W. Falkenstein, A. Penzkofer, and W. Kaiser, "Amplified spontaneous emission in rhodamine dyes: Generation of picosecond light pulses and determination of excited state absorption and relaxation," Opt. Commun. 27, 151 (1978).
[CrossRef]

Opt. Express (4)

Opt. Express. (2)

T. Okamoto, F. H’Dhili, and S. Kawata, "Plasmonic crystal for efficient energy transfer from fluorescent molecules to long-range surface plasmons," Opt. Express. 17, 8294 (2009).
[CrossRef] [PubMed]

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

Phys. Rep. (1)

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

Phys. Rev. B (3)

I. De Leon and P. Berini, "Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media," Phys. Rev. B 78, 161401 (2008).
[CrossRef]

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

I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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]

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

L. G. Nair, "Dye Lasers," Prog. Quantum Electron. 7, 153 (1982).
[CrossRef]

Quantum Electron. (1)

A. V. Fedenev, E. I. Lipatov, V. F. Tarasenko, V. M. Orlovskii, M. A. Shulepov, N. N. Koval, and I. M. Goncharenko, "Disturbance of adhesion upon ablation of thin films by laser pulses," Quantum Electron. 34, 375 (2004).
[CrossRef]

Other (3)

P. Yeh, Optical waves in layered media (Wiley, New York, 1988).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer, Berlin, 1988).

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, New York, 1985).

Supplementary Material (4)

» Media 1: MOV (489 KB)     
» Media 2: MOV (302 KB)     
» Media 3: MOV (512 KB)     
» Media 4: MOV (310 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

(a) Thin-film active structure (Structure 1). (b) Semi-infinite metal active structure (Structure 2). (c) Multi-level energy model used for R6G molecules.

Fig. 2.
Fig. 2.

Normalized pump irradiance distribution (solid lines) across (a) structure 1 and (b) structure 2. The dashed lines are computed for I 0 p satisfying the bottom form in Eq. (4). The irradiance in the metal region in both structures is magnified 20 times.

Fig. 3.
Fig. 3.

Normalized power dissipation density of an isotropically oriented dipole located at the labeled metal-dipole separations for (a) Structure 1 and (b) Structure 2.

Fig. 4.
Fig. 4.

Normalized lifetime distribution of an isotropically oriented dipole in structure 1 (dashed lines) and structure 2 (solid lines) for both concentrations, Ca (black) and Cb (red).

Fig. 5.
Fig. 5.

Dye’s gain coefficient distribution, g(y), and the normalized |Ey |2 distribution for the LRSPP mode using concentration (a) Ca (Media 1) and (b) Cb (Media 2), and for the single-interface SPP mode using concentrations (c) Ca (Media 3) and (d) Cb (Media 4).

Fig. 6.
Fig. 6.

Comparative analysis of G(I 0 p ). The curves for the three different models are plotted for the LRSPP mode using concentration (a) Ca and (b)Cb , and for the single-interface SPP mode using concentrations (c) Ca and (d) Cb .

Fig. 7.
Fig. 7.

Pump irradiance increment factors, fB and fC , for the LRSPP mode using concentration (a) Ca and (b) Cb , and for the single-interface SPP mode using concentrations (c) Ca and (d) Cb . The vertical dashed lines represent the lossless condition, GA =0

Tables (2)

Tables Icon

Table 1. Relative permittivities (εr ) at λp =532 nm and λe =560 nm.

Tables Icon

Table 2. Photophysical parameters of Rhodamine 6G. The last four parameters (below horizontal line) are assumed to be concentration-independent. * Values for monomers.

Equations (15)

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

g=N1σe*N0σa0,
N1(y)=NIp(y)τ(y)σp0Ip(y)τ(y)σp0+ωp
dIp(y)dy=Ip(y)[Nσp0N1(y)σp0+N1(y)σp1] ,
g(y)=NIp(y)τ(y)σp0σe*σa0ωpIp(y)τ(y)σp0+ωp.
dIp(y)dy{Ip(y)Nσp0,ifIp(y)ωpσp0τ(y)Ip(y)Nσp1,ifIp(y)ωpσp1τ(y),
εr,p=εr,piλe2πNσp(εr,p)12 ,
Ip(y)=Reη(y)2η(y)2 Ep(y)2 ,
γ̂μ(y)=γ̂nr+ϕ0Pμ(u,y)du,
P(u,y)=Re 32 u31u2 {1+rpexp(i2ky)}
P(u,y)=Re 34 u1u2 {(1+rsexp(i2ky))+(1u2)(1rpexp(i2ky))} ,
Puy=23Puy+13Puy.
τ(y)=γ̂(y)1 τ ,
εr,e(y)=εr,e+iλe2πg(y)(εr,e)1/2,
G=2α .
fx=Ip,AIp,x,

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