Abstract

We develop a theoretical model to compute the local density of states in a confined plasmonic waveguide. Based on this model, we derive a simple formula with a clear physical interpretation for the lifetime modification of emitters embedded in the waveguide. The gain distribution within the active medium is then computed following the formalism developed in a recent work [Phys. Rev. B 78, 161401 (2008)], by taking rigorously into account the pump irradiance and emitters lifetime modifications in the system. We finally apply this formalism to describe gain-assisted propagation in a dielectric-loaded surface plasmon polariton waveguide.

© 2010 Optical Society of America

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  1. D. K. Gramotnev, and S. I. Bozhelvonyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
    [CrossRef]
  2. S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Integrated power monitor for long-range surface plasmon polaritons,” Opt. Commun. 255, 51–56 (2005).
    [CrossRef]
  3. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
    [CrossRef] [PubMed]
  4. J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
    [CrossRef] [PubMed]
  5. R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
    [CrossRef] [PubMed]
  6. I. De Leon, and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics, (2010).
    [CrossRef]
  7. M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
    [CrossRef]
  8. J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
    [CrossRef] [PubMed]
  9. A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
    [CrossRef]
  10. P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
    [CrossRef] [PubMed]
  11. 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]
  12. I. De Leon, and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express 17, 20191–20202 (2009).
    [CrossRef] [PubMed]
  13. I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
    [CrossRef] [PubMed]
  14. G. Winter, S. Wedge, and W. L. Barnes, “Can lasing at visible wavelengths be achieved using the low-loss long range surface plasmon-polariton mode?” N. J. Phys. 8, 125 (2006).
    [CrossRef]
  15. J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
    [CrossRef] [PubMed]
  16. G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
    [CrossRef]
  17. D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004).
    [CrossRef]
  18. Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
    [CrossRef]
  19. W. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998).
    [CrossRef]
  20. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1986).
  21. E. Hecht, Optics (1987).
  22. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007).
    [CrossRef]
  23. A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
    [CrossRef] [PubMed]

2010 (8)

D. K. Gramotnev, and S. I. Bozhelvonyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

I. De Leon, and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics, (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
[CrossRef]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
[CrossRef]

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

2009 (6)

I. De Leon, and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express 17, 20191–20202 (2009).
[CrossRef] [PubMed]

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
[CrossRef] [PubMed]

2008 (1)

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]

2007 (1)

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007).
[CrossRef]

2006 (1)

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

2005 (1)

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Integrated power monitor for long-range surface plasmon polaritons,” Opt. Commun. 255, 51–56 (2005).
[CrossRef]

2004 (2)

D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004).
[CrossRef]

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
[CrossRef] [PubMed]

1998 (1)

W. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998).
[CrossRef]

Andersen, T. B.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

Atwater, H. A.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007).
[CrossRef]

Barnes, W.

W. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998).
[CrossRef]

Barnes, W. L.

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

Bartal, G.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Berini, P.

I. De Leon, and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics, (2010).
[CrossRef]

I. De Leon, and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express 17, 20191–20202 (2009).
[CrossRef] [PubMed]

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]

Bernussi, A. A.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
[CrossRef]

Bolger, P. M.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

Bouhelier, A.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Bozhelvonyi, S. I.

D. K. Gramotnev, and S. I. Bozhelvonyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Bozhevolnyi, S. I.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Integrated power monitor for long-range surface plasmon polaritons,” Opt. Commun. 255, 51–56 (2005).
[CrossRef]

Chen, Y.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

Colas des Francs, G.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Dai, L.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
[CrossRef]

De Leon, I.

I. De Leon, and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics, (2010).
[CrossRef]

I. De Leon, and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express 17, 20191–20202 (2009).
[CrossRef] [PubMed]

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. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Dickson, W.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

Finot, C.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

Frisbie, S. P.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
[CrossRef]

Fussell, D. P.

D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004).
[CrossRef]

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
[CrossRef]

Gladden, C.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Gorbach, A. V.

A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
[CrossRef] [PubMed]

Gosciniak, J.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev, and S. I. Bozhelvonyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

Grandidier, J.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Grave de Peralta, L.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
[CrossRef]

Gregersen, N.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

Gryczynski, I.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
[CrossRef] [PubMed]

Gryczynski, Z.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
[CrossRef] [PubMed]

Heinis, D.

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

Hickey, S. G.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

Hoogenboom, J. P.

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

Kjelstrup-Hansen, J.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

Krasavin, A. V.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

Krishnan, A.

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
[CrossRef]

Lakowicz, J. R.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
[CrossRef] [PubMed]

Legay, G.

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

Leosson, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
[CrossRef]

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Integrated power monitor for long-range surface plasmon polaritons,” Opt. Commun. 255, 51–56 (2005).
[CrossRef]

Lezec, H. J.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007).
[CrossRef]

Liebscher, L.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

Lodahl, P.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

Ma, R.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Malicka, J.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
[CrossRef] [PubMed]

Marini, A.

A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
[CrossRef] [PubMed]

Markey, L.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

Martijn de Sterke, C.

D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004).
[CrossRef]

Massenot, S.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

McPhedran, R. C.

D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004).
[CrossRef]

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
[CrossRef]

Mork, J.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

Nielsen, T. R.

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

Nikolajsen, T.

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Integrated power monitor for long-range surface plasmon polaritons,” Opt. Commun. 255, 51–56 (2005).
[CrossRef]

Oulton, R.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Pacifici, D.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007).
[CrossRef]

Sanchez-Mosteiro, G.

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

Skryabin, D. V.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
[CrossRef] [PubMed]

Sorger, V.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

van Hulst, N. F.

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

Volkov, V. S.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

Wedge, S.

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

Weeber, J.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

Weeber, J.-C.

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

Winter, G.

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

Zayats, A. V.

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
[CrossRef] [PubMed]

Zentgraf, T.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Zhang, X.

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. Krishnan, S. P. Frisbie, L. Grave de Peralta, and A. A. Bernussi, “Plasmon stimulated emission in arrays of bimetallic structures coated with dye-doped dielectric,” Appl. Phys. Lett. 96, 111104 (2010).
[CrossRef]

J. Microsc. (1)

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Leakage radiation microscopy of surface plasmon coupled emission: investigation of gain assisted propagation in an integrated plasmonic waveguide,” J. Microsc., (2010).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

W. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661–699 (1998).
[CrossRef]

J. Phys. Chem. B (1)

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108, 12568–12574 (2004).
[CrossRef] [PubMed]

N. J. Phys. (1)

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

Nano Lett. (2)

J. P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N. F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett. 9, 1189–1195 (2009).
[CrossRef] [PubMed]

J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

Nat. Photonics (4)

D. K. Gramotnev, and S. I. Bozhelvonyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[CrossRef]

I. De Leon, and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics, (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics, (2010).
[CrossRef]

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007).
[CrossRef]

Nature (1)

R. Oulton, V. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Integrated power monitor for long-range surface plasmon polaritons,” Opt. Commun. 255, 51–56 (2005).
[CrossRef]

Opt. Express (2)

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010).
[CrossRef] [PubMed]

I. De Leon, and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express 17, 20191–20202 (2009).
[CrossRef] [PubMed]

Opt. Lett. (2)

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35, 1197–1199 (2010).
[CrossRef] [PubMed]

A. Marini, A. V. Gorbach, D. V. Skryabin, and A. V. Zayats, “Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover,” Opt. Lett. 34, 2864–2866 (2009).
[CrossRef] [PubMed]

Phys. Rev. B (3)

Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mork, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81, 125431 (2010).
[CrossRef]

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]

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J. Weeber, and A. Dereux, “Integrated plasmonic waveguides: a mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Phys. Rev. E (1)

D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004).
[CrossRef]

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1986).

E. Hecht, Optics (1987).

Cited By

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Figures (4)

Fig. 1.
Fig. 1.

a) DLSPPW configuration. A w × h dielectric strip (optical index nd = ε 1/2 d ) is deposited on a gold film, supported by a substrate. b) Corresponding so-called reference geometry consisting of the same system without the dielectric strip.

Fig. 2.
Fig. 2.

LDOS calculated at the waveguide center (a) and edge (b) in function of both normalized propagation constant ky /k 0 and height z in the dielectric strip. DLSPPW is a w = 400 nm × h = 600 nm polymer strip (nd = 1.5) on a 40 nm thick gold film. The wavelength is λ = 1.55 µm.

Fig. 3.
Fig. 3.

2D-DOS variation in function of wavector component ky along the DSLPPW axis. The inset shows a zoom near the Au/air SPP mode effective index.

Fig. 4.
Fig. 4.

a) Small gain coefficient within the doped wavequide calculated using Eq. 15 at pump irradiance 1000W.cm −2 incident from the top at incident angle 45° and wavelength λ = 532 nm. b) Guided SPP mode profile. c) Guided modes DOS calculated for null pump irradiance (passive) and Ip = 1000 W.cm −2 pump irradiance (gain). An offset has been added so that the two curves coincide far from the resonance. The complex mode effective index, deduced from a Lorentzian fit, is indicated on the figure.

Equations (18)

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

ρ 2 D ( k y ) = 2 k y π Im d r ε ( r ) G 2 D ( r , r , k y ) , [ r = ( x , z ) ] .
ρ 2 D ( r , k y ) = 2 k y π Im G 2 D ( r , r , k y ) ,
Δ ρ 2 D ( k y ) = ρ 2 D ( k y ) ρ ref 2 D ( k y ) g s π 1 2 L SPP ( k y k y 0 ) 2 + ( 1 2 L SPP ) 2 .
Δ ρ 2 D ( r , k y ) Δ ρ 2 D ( r , k y 0 ) ( 2 L SPP ) 2 1 ( k y k y 0 ) 2 + ( 1 2 L SPP ) 2 .
ρ ( r ) = k 0 2 π ω ImTr G ( r , r ) .
G ( r , r ) = + dk y G 2 D ( r , r , k y ) e ik y ( y y )
ρ ( r ) = k 0 2 π ω ImTr G ( r , r )
= k 0 2 π ω ImTr + dk y G 2 D ( r , r , k y )
= k 0 2 π ω + dk y ImTr G 2 D ( r , r , k y )
= ρ ref ( r ) k 0 2 π ω + dk y ImTr Δ G 2 D ( r , r , k y ) ,
with Δ G 2 D = G 2 D G ref 2 D .
ρ ( r ) = ρ ref ( r ) k 0 2 2 ω L SPP ImTr Δ G 2 D ( r , r , k y 0 )
= ρ ref ( r ) + π k 0 2 4 ω k y 0 1 L SPP Δ ρ 2 D ( r ) ,
with Δ ρ 2 D ( r ) = 2 k y π ImTr Δ G 2 D ( r , r , k y 0 ) .
g ( x , z ) = N I p ( x , z ) τ ( x , z ) σ p σ e σ a h ¯ ω p I p ( x , z ) τ ( x , z ) σ p + h ¯ ω p
τ ( x , z ) τ 0 = ρ 0 ρ ( x , z ) ,
I p ( x , z ) = ε 0 c 2 n d E p ( x , z ) 2
E p ( r ) = E inc ( r ) + k 0 2 d r G 2 D ( r , r , k y inc ) ( ε ref ε d ) E inc ( r )

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