Abstract

We report a theoretical study of lasing when plasmonic metallic structures are embedded in a gain medium. The model used is a dynamic semi-quantum approach that accounts for stimulated and spontaneous emission wherein molecules constituting the laser dye are described using a four-level rate equation model, which is coupled to an electrodynamics description of the entire system including metal particles. Based on 3D simulations in which electromagnetic fields for both the pump and emitted photons are accurately determined for an array of elliptical gold nanorods, we numerically demonstrate lasing action above an intensity threshold for a narrow range of wavelengths close to the plasmon maximum. We also show numerically that this lasing action clamps the population inversion above threshold. The dye molecule photophysics near the nanoparticle was also studied, and it is demonstrated that stimulated emission dominates over spontaneous emission above threshold, with most of the stimulated emission being associated with the near-field region near the metal nanorods. The effect of the Purcell factor on the lasing action is also studied. This theoretical work provides the basic framework for investigation and optimization of light emission arising from the coupling of gain media and plasmonic nanostructures.

© 2013 Optical Society of America

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  10. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
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    [CrossRef]
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    [CrossRef]
  34. J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
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2013 (1)

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

2012 (1)

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

2011 (3)

J. Trieschmann, S. Xiao, L. J. Prokopeva, V. P. Drachev, and A. V. Kildishev, “Experimental retrieval of the kinetic parameters of a dye in a solid film,” Opt. Express 19, 18253–18259 (2011).
[CrossRef]

P. Berini and I. de Leon, “Surface plasmon-polaritons amplifiers and lasers,” Nat. Photonics 6, 16–24 (2011).
[CrossRef]

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

2010 (6)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382–387 (2010).
[CrossRef]

M. Tatsunosuke and K. Masahiro, “Finite-difference time-domain analysis of laser action in cholesteric photonic liquid crystal,” Appl. Phys. Express 3, 061701 (2010).
[CrossRef]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

A. F. Koenderink, “On the use of Purcell factor for plasmon antenna,” Opt. Lett. 35, 4208–4210 (2010).
[CrossRef]

2009 (3)

2008 (7)

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticles arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (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, 3998–4001 (2008).
[CrossRef]

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (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 plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16, 1385–1392 (2008).
[CrossRef]

B. Redding, S. Shi, T. Creazzo, and D. W. Prather, “Electromagnetic modeling of active silicon nanocrystal waveguides,” Opt. Express 16, 8792–8799 (2008).
[CrossRef]

2005 (2)

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (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]

2004 (2)

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

M. P. Maziar, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12, 4072–4079 (2004).
[CrossRef]

2003 (1)

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectral of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).

2000 (1)

Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A 61, 033808 (2000).
[CrossRef]

1999 (3)

J.-K. Hwang, H.-Y. Ryu, and Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688–4695 (1999).
[CrossRef]

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Oainter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16, 465–474 (1999).
[CrossRef]

1998 (2)

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58, 7252–7259 (1998).

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

Adegoke, J. A.

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, 3998–4001 (2008).
[CrossRef]

Bahoura, M.

Barchiesi, D.

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[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, 3998–4001 (2008).
[CrossRef]

Belov, P.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

Berini, P.

P. Berini and I. de Leon, “Surface plasmon-polaritons amplifiers and lasers,” Nat. Photonics 6, 16–24 (2011).
[CrossRef]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382–387 (2010).
[CrossRef]

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

Bohringer, K.

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[CrossRef]

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Choi, J.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Chu, Y.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticles arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Co, D. T.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Creazzo, T.

Crozier, K. B.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticles arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Dai, L.

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

de la Chapelle, M. L.

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

de Leon, I.

P. Berini and I. de Leon, “Surface plasmon-polaritons amplifiers and lasers,” Nat. Photonics 6, 16–24 (2011).
[CrossRef]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382–387 (2010).
[CrossRef]

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

Drachev, V. P.

J. Trieschmann, S. Xiao, L. J. Prokopeva, V. P. Drachev, and A. V. Kildishev, “Experimental retrieval of the kinetic parameters of a dye in a solid film,” Opt. Express 19, 18253–18259 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Dridi, M.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[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]

Fainman, Y.

Fang, A.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

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, 3998–4001 (2008).
[CrossRef]

Giannini, V.

Gladden, C.

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

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Grimault, A. S.

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Hamm, J. M.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef]

Hess, O.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef]

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[CrossRef]

Hwang, J.-K.

J.-K. Hwang, H.-Y. Ryu, and Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688–4695 (1999).
[CrossRef]

Iorsh, I.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

Janel, N.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

Kelly, K. L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectral of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).

Kildishev, A. V.

J. Trieschmann, S. Xiao, L. J. Prokopeva, V. P. Drachev, and A. V. Kildishev, “Experimental retrieval of the kinetic parameters of a dye in a solid film,” Opt. Express 19, 18253–18259 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Kim, C. H.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Kim, S.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Kim, S. W.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Kim, Y.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Kivshar, Y. S.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

Kling, M. F.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Koenderink, A. F.

Koschny, T.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Lee, D.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Lee, R. K.

Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A 61, 033808 (2000).
[CrossRef]

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Oainter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16, 465–474 (1999).
[CrossRef]

Lee, Y.-H.

J.-K. Hwang, H.-Y. Ryu, and Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688–4695 (1999).
[CrossRef]

Ma, R. M.

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

Macias, D.

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Maier, S. A.

S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).

Masahiro, K.

M. Tatsunosuke and K. Masahiro, “Finite-difference time-domain analysis of laser action in cholesteric photonic liquid crystal,” Appl. Phys. Express 3, 061701 (2010).
[CrossRef]

Mayy, M.

Maziar, M. P.

Muskens, O. L.

Nagra, A. S.

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[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, 3998–4001 (2008).
[CrossRef]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Noginov, M. A.

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Oainter, O. J.

Odom, T. W.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Orlov, A.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

Oulton, R. F.

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

Painter, O.

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

Park, I.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Pendry, J. B.

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58, 7252–7259 (1998).

Poddubny, A.

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

Podolskiy, V. A.

Prather, D. W.

Prokopeva, L. J.

Pusch, A.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef]

Redding, B.

Reynolds, K.

Ritzo, B. A.

Rivas, J. G.

Ryu, H.-Y.

J.-K. Hwang, H.-Y. Ryu, and Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688–4695 (1999).
[CrossRef]

Sanchez-Gil, J. A.

Schatz, G. C.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectral of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

Scherer, A.

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Oainter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16, 465–474 (1999).
[CrossRef]

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

Schonbrun, E.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticles arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[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]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Shi, S.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1976).

Sorger, V. J.

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

Soukoulis, C. M.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

Stockman, M. I.

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

Suh, J. Y.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Tatsunosuke, M.

M. Tatsunosuke and K. Masahiro, “Finite-difference time-domain analysis of laser action in cholesteric photonic liquid crystal,” Appl. Phys. Express 3, 061701 (2010).
[CrossRef]

Tetz, K.

Trieschmann, J.

Tsakmakidis, K. L.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef]

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, 3998–4001 (2008).
[CrossRef]

Vial, A.

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Vuckovic, J.

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

Vuckovic, J. S.

Ward, A. J.

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58, 7252–7259 (1998).

Wasielewski, M. R.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Wuestner, S.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef]

Xiao, S.

J. Trieschmann, S. Xiao, L. J. Prokopeva, V. P. Drachev, and A. V. Kildishev, “Experimental retrieval of the kinetic parameters of a dye in a solid film,” Opt. Express 19, 18253–18259 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Xu, Y.

Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A 61, 033808 (2000).
[CrossRef]

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Oainter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16, 465–474 (1999).
[CrossRef]

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

Yang, T.

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticles arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

Yariv, A.

Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A 61, 033808 (2000).
[CrossRef]

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

Y. Xu, J. S. Vuckovic, R. K. Lee, O. J. Oainter, A. Scherer, and A. Yariv, “Finite-difference time-domain calculation of spontaneous emission lifetime in a microcavity,” J. Opt. Soc. Am. B 16, 465–474 (1999).
[CrossRef]

York, R. A.

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

Yuan, H. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

Zentgraf, T.

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

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[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, 3998–4001 (2008).
[CrossRef]

Zhao, L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectral of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).

Zhou, W.

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Zhu, G.

Zou, S.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

Appl. Phys. Express (1)

M. Tatsunosuke and K. Masahiro, “Finite-difference time-domain analysis of laser action in cholesteric photonic liquid crystal,” Appl. Phys. Express 3, 061701 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, “Experimental observation of narrow surface plasmon resonances in gold nanoparticles arrays,” Appl. Phys. Lett. 93, 181108 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Vuckovic, O. Painter, Y. Xu, A. Yariv, and A. Scherer, “Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,” IEEE J. Quantum Electron. 35, 1168–1175 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antennas Propag. 46, 334–340 (1998).
[CrossRef]

J. Chem. Phys. (1)

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004).
[CrossRef]

J. Opt. (1)

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

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

J. Phys. Chem. B (1)

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectral of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).

Nano Lett. (1)

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, 3998–4001 (2008).
[CrossRef]

Nat. Nanotechnol. (1)

W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays,” Nat. Nanotechnol. 8, 506–511 (2013).
[CrossRef]

Nat. Photonics (3)

I. Park, S. Kim, J. Choi, D. Lee, Y. Kim, M. F. Kling, M. I. Stockman, and S. W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).
[CrossRef]

P. Berini and I. de Leon, “Surface plasmon-polaritons amplifiers and lasers,” Nat. Photonics 6, 16–24 (2011).
[CrossRef]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382–387 (2010).
[CrossRef]

Nature (2)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef]

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

Opt. Express (5)

Opt. Lett. (1)

Phys. Lett. A (1)

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[CrossRef]

Phys. Rev. A (1)

Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A 61, 033808 (2000).
[CrossRef]

Phys. Rev. B (3)

J.-K. Hwang, H.-Y. Ryu, and Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60, 4688–4695 (1999).
[CrossRef]

A. J. Ward and J. B. Pendry, “Calculating photonic Green’s functions using a nonorthogonal finite-difference time-domain method,” Phys. Rev. B 58, 7252–7259 (1998).

A. Vial, A. S. Grimault, D. Macias, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef]

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[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]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Prog. Quantum Electron. (1)

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159–246 (2008).
[CrossRef]

Other (3)

S. A. Maier, Plasmonics Fundamentals and Applications (Springer, 2007).

A. E. Siegman, Lasers (University Science Books, 1976).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

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Figures (10)

Fig. 1.
Fig. 1.

Four-level model used to describe the dye molecule: the dashed arrow lines are for spontaneous transitions and continuous lines are for stimulated transitions.

Fig. 2.
Fig. 2.

Description of the plasmonic structure, where the passive structure has a resonance wavelength λ=733nm with a spectral bandwidth Δλ=80nm.

Fig. 3.
Fig. 3.

Optical response of the structure. (a) Normalized emitted light spectra for various input energies: a narrow peak emerges at λ=738nm with an intensity exhibiting a threshold behavior. (b) Nonlinear behavior of the emission intensities at λ=738nm.

Fig. 4.
Fig. 4.

Model used to show that only dyes close to the NP contribute efficiently to the lasing action. (a) Spatial distribution of the dye concentration in the computational volume. (b) Calculated emission intensity as a function of input for different spatial distributions of the gain (a=0nm, the gain is everywhere, a=12.5nm: dyes are removed from the NP edge at all directions).

Fig. 5.
Fig. 5.

Comparison between spontaneous emission decay rate (spatial average of (N2/τ21)) and stimulated emission rate [spatial average of (1/h¯ω21)E⃗·(dP⃗21/dt)] above threshold for an input energy equal to 30mJ·cm2 (both rates are normalized with the initial concentration C). The stimulated emission process has an ultrafast dynamics with a rate that is much higher than the spontaneous emission rate.

Fig. 6.
Fig. 6.

Spatial profile of the gain (the steady state value of the N2N1 population density in log10 scale. (a) Below the threshold: higher gain is observed in close vicinity of the NP due to the plasmon near field. (b) Above the threshold: the gain in the vicinity of the NP is lower than far from the NP, and the inversion is clamped near the NP.

Fig. 7.
Fig. 7.

Population inversion as a function of the input intensities.

Fig. 8.
Fig. 8.

Calculation of the Pf close to the plasmonics nanocavity: an extremely high Pf is achieved in the close vicinity of the NP.

Fig. 9.
Fig. 9.

(a) Emission as a function of input energy for different decay rates: including the Pf leads to a decrease of the threshold intensity. (b) Comparison of population inversion ΔN=N2N1 for different decay rates: including the Pf leads to a decrease in gain. ΔN was calculated by integrating over a volume V surrounding the NP defined by the distance a=50nm from the NP edge.

Fig. 10.
Fig. 10.

Comparison of the coupling strength (κΔN) between the plasmon and the dye (a) without accounting for the Pf and (b) with accounting for the Pf. Due to the Pf the coupling strength increases, leading to a decrease of the threshold intensity.

Equations (16)

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

d2μ⃗i(t)dt2+γidμ⃗idt+ωi2μ⃗i=e2mE⃗.
d2P⃗(t)dt2+γdP⃗dt+ωr2P⃗=Ne2mE⃗,
d2P⃗(t)dt2+ΔωrdP⃗dt+ωr2P⃗=κΔN(t)E⃗.
×E⃗(t)=μ0H⃗(t)t×H⃗(t)=ϵE⃗(t)t+iP⃗i(t)t.
dN3(t)dt=N3(t)τ32N3(t)τ30+1h¯ω30E⃗(t)·dP⃗30(t)dt,
dN2(t)dt=N3(t)τ32N2(t)τ21+1h¯ω21E⃗(t)·dP⃗21(t)dt,
dN1(t)dt=N2(t)τ21N1(t)τ101h¯ω21E⃗(t)·dP⃗21(t)dt,
dN0(t)dt=N1(t)τ10+N3(t)τ301h¯ω30E⃗(t)·dP⃗30(t)dt,
dN3(t)dt=N3(t)τ32N3(t)τ30+1h¯ω30E⃗(t)·dP⃗30(t)dt.
N3|i1/2,j+1/2,k+1n+1/2=N3n1/2(2τ32τ30Δt(τ32+τ30)2τ32τ30+Δt(τ32+τ30))+1h¯ω30E⃗·dP⃗30dt(2τ30τ32Δt2τ30τ32+Δt(τ30+τ32)).
Ex|i1/2,j+1/2,k+1=14(Ex|i,j+1/2,k+1/2+Ex|i1,j+1/2,k+1/2+Ex|i1,j+1/2,k+3/2+Ex|i,j+1/2,k+3/2)Ey|i1/2,j+1/2,k+1=14(Ey|i1/2,j+1,k+1/2+Ey|i1/2,j+1,k+3/2+Ey|i1/2,j,k+3/2+Ey|i1/2,j,k+1/2).
τ30=τ21=1nsτ32=τ10=10fs.
dN2(t)dt=N3(t)τ32N2(t)τ21+1h¯ω21E⃗(t)·dP⃗21(t)dt.
F=3Q4π2V(λ2n)3,
J⃗(t)=d⃗δ(x⃗x⃗0)1Ω2+Γ2eΓt[Ωcos(Ωt)Γsin(Ωt)],
γcavityγfree=εcavityεfree,

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