Abstract

It is shown that the decay of the weakly coupled to radiation (dark) modes of subwavelength plasmonic nanostructures is strongly nonexponential. Their lifetime is overestimated by conventional exponential relaxation time obtained in the standard Markovian approximation. These effects are manifestations of the strong dispersion and near-field feedback. The developed theoretical framework introduces an ensemble of local relaxation degrees of freedom coupled to plasmonic mode in order to describe its decay due to material losses. The macroscopic description of the decay process leads to the specific memory function of the system, evaluated from the modal and material dispersions of the plasmonic nanostructure. Proper knowledge of the relaxation behavior is vital for various applications relying on light-matter interactions of emitters with nanoscale objects, such as fluorescence manipulation, bio-imaging, sensing, spasers, sub-diffraction optics, Raman scattering, and quantum optics.

© 2012 OSA

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2011 (5)

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011).
[CrossRef]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[CrossRef]

J. K. Kitur, V. A. Podolskiy, and M. A. Noginov, “Stimulated emission of surface plasmon polaritons in a microcylinder cavity,” Phys. Rev. Lett. 106(18), 183903 (2011).
[CrossRef] [PubMed]

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nano-particles,” Nano Lett. 11(6), 2329–2333 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[CrossRef] [PubMed]

2010 (7)

P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, “Nonlocal ponderomotive nonlinearity in plasmonics,” Opt. Lett. 35(10), 1551–1553 (2010).
[CrossRef] [PubMed]

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4(9), 5269–5276 (2010).
[CrossRef] [PubMed]

N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett. 10(4), 1405–1408 (2010).
[CrossRef] [PubMed]

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010).
[CrossRef]

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt. 12(2), 024004 (2010).
[CrossRef]

Z. Jacob, J. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef] [PubMed]

2009 (6)

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

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(7264), 629–632 (2009).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Guided propagation along quadrupolar chains of plasmonic nanoparticles,” Phys. Rev. B 79(23), 235412 (2009).
[CrossRef]

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[CrossRef] [PubMed]

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9(1), 399–404 (2009).
[CrossRef] [PubMed]

2008 (3)

G. A. Wurtz and A. V. Zayats, “Nonlinear surface plasmon polaritonic crystals,” Laser Photonics Rev. 2(3), 125–135 (2008).
[CrossRef]

A. V. Kildishev, W. Cai, U. K. Chettiar, and V. M. Shalaev, “Transformation optics: approaching broadband electromagnetic cloaking,” New J. Phys. 10(11), 115029 (2008).
[CrossRef]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
[CrossRef] [PubMed]

2007 (4)

B. N. Khlebtsov and N. G. Khlebtsov, “Multipole plasmons in metal nanorods: scaling properties and dependence on particle size, shape, orientation, and dielectric environment,” J. Phys. Chem. C 111(31), 11516–11527 (2007).
[CrossRef]

I. D. Mayergoyz, Z. Zhang, and G. Miano, “Analysis of dynamics of excitation and dephasing of plasmon resonance modes in nanoparticles,” Phys. Rev. Lett. 98(14), 147401 (2007).
[CrossRef] [PubMed]

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

J. B. Khurgin, G. Sun, and R. A. Soref, “Enhancement of luminescence efficiency using surface plasmon polaritons: figures of merit,” J. Opt. Soc. Am. B 24(8), 1968–1980 (2007).
[CrossRef]

2006 (1)

N. A. R. Bhat and J. E. Sipe, “Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media,” Phys. Rev. A 73(6), 063808 (2006).
[CrossRef]

2005 (3)

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005).
[CrossRef]

C. Loo, A. Lowery, N. Halas, J. West, and R. Drezek, “Immunotargeted nanoshells for integrated cancer imaging and therapy,” Nano Lett. 5(4), 709–711 (2005).
[CrossRef] [PubMed]

I. I. Smolyaninov, “Quantum fluctuations of the refractive index near the interface between a metal and a nonlinear dielectric,” Phys. Rev. Lett. 94(5), 057403 (2005).
[CrossRef] [PubMed]

2004 (3)

P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004).
[CrossRef] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69(20), 205414 (2004).
[CrossRef]

2003 (2)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

2002 (1)

C. Cao, J. Tian, and H. Cao, “Non-Markovian correlation function and direct analysis of spontaneous emission of an excited two-level atom,” Phys. Lett. A 303(5-6), 318–327 (2002).
[CrossRef]

1999 (1)

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, “Giant enhancement of surface second harmonic generation in BaTiO3 due to photorefractive surface wave excitation,” Phys. Rev. Lett. 83(12), 2429–2432 (1999).
[CrossRef]

1996 (1)

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry‐Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[CrossRef]

1990 (1)

C. Benkert, M. O. Scully, and G. Süssmann, “Memory correlation effects on quantum noise in lasers and masers,” Phys. Rev. A 41(11), 6119–6128 (1990).
[CrossRef] [PubMed]

1988 (1)

J. Seke and W. N. Herfort, “Deviations from exponential decay in the case of spontaneous emission from a two-level atom,” Phys. Rev. A 38(2), 833–840 (1988).
[CrossRef] [PubMed]

1978 (1)

L. Fonda, G. C. Ghirardi, and A. Rimini, “Decay theory of unstable quantum systems,” Rep. Prog. Phys. 41(4), 587–631 (1978).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1970 (1)

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3(3), 233–245 (1970).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Alù, A.

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Guided propagation along quadrupolar chains of plasmonic nanoparticles,” Phys. Rev. B 79(23), 235412 (2009).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Atkinson, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Barrier, D.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry‐Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[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(7264), 629–632 (2009).
[CrossRef] [PubMed]

Belov, P. A.

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011).
[CrossRef]

Benkert, C.

C. Benkert, M. O. Scully, and G. Süssmann, “Memory correlation effects on quantum noise in lasers and masers,” Phys. Rev. A 41(11), 6119–6128 (1990).
[CrossRef] [PubMed]

Berkovitch, N.

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nano-particles,” Nano Lett. 11(6), 2329–2333 (2011).
[CrossRef] [PubMed]

N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett. 10(4), 1405–1408 (2010).
[CrossRef] [PubMed]

P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, “Nonlocal ponderomotive nonlinearity in plasmonics,” Opt. Lett. 35(10), 1551–1553 (2010).
[CrossRef] [PubMed]

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, “Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media,” Phys. Rev. A 73(6), 063808 (2006).
[CrossRef]

Blanco, L. A.

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69(20), 205414 (2004).
[CrossRef]

Boltasseva, A.

Z. Jacob, J. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Bondarenko, O.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010).
[CrossRef]

Cai, W.

A. V. Kildishev, W. Cai, U. K. Chettiar, and V. M. Shalaev, “Transformation optics: approaching broadband electromagnetic cloaking,” New J. Phys. 10(11), 115029 (2008).
[CrossRef]

Cao, C.

C. Cao, J. Tian, and H. Cao, “Non-Markovian correlation function and direct analysis of spontaneous emission of an excited two-level atom,” Phys. Lett. A 303(5-6), 318–327 (2002).
[CrossRef]

Cao, H.

C. Cao, J. Tian, and H. Cao, “Non-Markovian correlation function and direct analysis of spontaneous emission of an excited two-level atom,” Phys. Lett. A 303(5-6), 318–327 (2002).
[CrossRef]

Chen, C. H.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9(1), 399–404 (2009).
[CrossRef] [PubMed]

Chettiar, U. K.

A. V. Kildishev, W. Cai, U. K. Chettiar, and V. M. Shalaev, “Transformation optics: approaching broadband electromagnetic cloaking,” New J. Phys. 10(11), 115029 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Chu, M. W.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9(1), 399–404 (2009).
[CrossRef] [PubMed]

Costard, E.

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[CrossRef] [PubMed]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Pollard, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Prodan, E.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4(9), 5269–5276 (2010).
[CrossRef] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[CrossRef]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Righini, M.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[CrossRef]

Rimini, A.

L. Fonda, G. C. Ghirardi, and A. Rimini, “Decay theory of unstable quantum systems,” Rep. Prog. Phys. 41(4), 587–631 (1978).
[CrossRef]

Rivera, T.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry‐Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[CrossRef]

Scully, M. O.

C. Benkert, M. O. Scully, and G. Süssmann, “Memory correlation effects on quantum noise in lasers and masers,” Phys. Rev. A 41(11), 6119–6128 (1990).
[CrossRef] [PubMed]

Seke, J.

J. Seke and W. N. Herfort, “Deviations from exponential decay in the case of spontaneous emission from a two-level atom,” Phys. Rev. A 38(2), 833–840 (1988).
[CrossRef] [PubMed]

Shalaev, V. M.

Z. Jacob, J. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

A. V. Kildishev, W. Cai, U. K. Chettiar, and V. M. Shalaev, “Transformation optics: approaching broadband electromagnetic cloaking,” New J. Phys. 10(11), 115029 (2008).
[CrossRef]

Shor, I.

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nano-particles,” Nano Lett. 11(6), 2329–2333 (2011).
[CrossRef] [PubMed]

Simic, A.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010).
[CrossRef]

Sipe, J. E.

N. A. R. Bhat and J. E. Sipe, “Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media,” Phys. Rev. A 73(6), 063808 (2006).
[CrossRef]

Slutsky, B.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010).
[CrossRef]

Smalbrugge, B.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Smit, M. K.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, “Quantum fluctuations of the refractive index near the interface between a metal and a nonlinear dielectric,” Phys. Rev. Lett. 94(5), 057403 (2005).
[CrossRef] [PubMed]

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, “Giant enhancement of surface second harmonic generation in BaTiO3 due to photorefractive surface wave excitation,” Phys. Rev. Lett. 83(12), 2429–2432 (1999).
[CrossRef]

Soref, R. A.

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(7264), 629–632 (2009).
[CrossRef] [PubMed]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Stockman, M.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[CrossRef] [PubMed]

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt. 12(2), 024004 (2010).
[CrossRef]

Sun, G.

Süssmann, G.

C. Benkert, M. O. Scully, and G. Süssmann, “Memory correlation effects on quantum noise in lasers and masers,” Phys. Rev. A 41(11), 6119–6128 (1990).
[CrossRef] [PubMed]

Tanaka, K.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef] [PubMed]

Thierry-Mieg, V.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry‐Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[CrossRef]

Tian, J.

C. Cao, J. Tian, and H. Cao, “Non-Markovian correlation function and direct analysis of spontaneous emission of an excited two-level atom,” Phys. Lett. A 303(5-6), 318–327 (2002).
[CrossRef]

Turkiewicz, J. P.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Uchino, T.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef] [PubMed]

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

van Otten, F. W. M.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

van Veldhoven, P. J.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Vanmaekelbergh, D.

P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004).
[CrossRef] [PubMed]

Vos, W. L.

P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004).
[CrossRef] [PubMed]

West, J.

C. Loo, A. Lowery, N. Halas, J. West, and R. Drezek, “Immunotargeted nanoshells for integrated cancer imaging and therapy,” Nano Lett. 5(4), 709–711 (2005).
[CrossRef] [PubMed]

Wurtz, G. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

G. A. Wurtz and A. V. Zayats, “Nonlinear surface plasmon polaritonic crystals,” Laser Photonics Rev. 2(3), 125–135 (2008).
[CrossRef]

Zayats, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

G. A. Wurtz and A. V. Zayats, “Nonlinear surface plasmon polaritonic crystals,” Laser Photonics Rev. 2(3), 125–135 (2008).
[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(7264), 629–632 (2009).
[CrossRef] [PubMed]

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(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zhang, Z.

I. D. Mayergoyz, Z. Zhang, and G. Miano, “Analysis of dynamics of excitation and dephasing of plasmon resonance modes in nanoparticles,” Phys. Rev. Lett. 98(14), 147401 (2007).
[CrossRef] [PubMed]

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005).
[CrossRef]

Zheludev, N. I.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef] [PubMed]

Zhu, Y.

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Zuloaga, J.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4(9), 5269–5276 (2010).
[CrossRef] [PubMed]

ACS Nano (1)

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4(9), 5269–5276 (2010).
[CrossRef] [PubMed]

Appl. Phys. B (1)

Z. Jacob, J. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry‐Mieg, and T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Appl. Phys. Lett. 69(4), 449–451 (1996).
[CrossRef]

J. Opt. (1)

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt. 12(2), 024004 (2010).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3(3), 233–245 (1970).
[CrossRef]

J. Phys. Chem. C (1)

B. N. Khlebtsov and N. G. Khlebtsov, “Multipole plasmons in metal nanorods: scaling properties and dependence on particle size, shape, orientation, and dielectric environment,” J. Phys. Chem. C 111(31), 11516–11527 (2007).
[CrossRef]

Laser Photonics Rev. (1)

G. A. Wurtz and A. V. Zayats, “Nonlinear surface plasmon polaritonic crystals,” Laser Photonics Rev. 2(3), 125–135 (2008).
[CrossRef]

Nano Lett. (5)

N. Berkovitch, P. Ginzburg, and M. Orenstein, “Concave plasmonic particles: broad-band geometrical tunability in the near-infrared,” Nano Lett. 10(4), 1405–1408 (2010).
[CrossRef] [PubMed]

P. Ginzburg, N. Berkovitch, A. Nevet, I. Shor, and M. Orenstein, “Resonances on-demand for plasmonic nano-particles,” Nano Lett. 11(6), 2329–2333 (2011).
[CrossRef] [PubMed]

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9(1), 399–404 (2009).
[CrossRef] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

C. Loo, A. Lowery, N. Halas, J. West, and R. Drezek, “Immunotargeted nanoshells for integrated cancer imaging and therapy,” Nano Lett. 5(4), 709–711 (2005).
[CrossRef] [PubMed]

Nat. Mater. (1)

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Nat. Photonics (3)

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[CrossRef]

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010).
[CrossRef]

Nature (3)

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(7264), 629–632 (2009).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004).
[CrossRef] [PubMed]

New J. Phys. (1)

A. V. Kildishev, W. Cai, U. K. Chettiar, and V. M. Shalaev, “Transformation optics: approaching broadband electromagnetic cloaking,” New J. Phys. 10(11), 115029 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

C. Cao, J. Tian, and H. Cao, “Non-Markovian correlation function and direct analysis of spontaneous emission of an excited two-level atom,” Phys. Lett. A 303(5-6), 318–327 (2002).
[CrossRef]

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (4)

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011).
[CrossRef]

J. Seke and W. N. Herfort, “Deviations from exponential decay in the case of spontaneous emission from a two-level atom,” Phys. Rev. A 38(2), 833–840 (1988).
[CrossRef] [PubMed]

N. A. R. Bhat and J. E. Sipe, “Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media,” Phys. Rev. A 73(6), 063808 (2006).
[CrossRef]

C. Benkert, M. O. Scully, and G. Süssmann, “Memory correlation effects on quantum noise in lasers and masers,” Phys. Rev. A 41(11), 6119–6128 (1990).
[CrossRef] [PubMed]

Phys. Rev. B (4)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005).
[CrossRef]

A. Alù and N. Engheta, “Guided propagation along quadrupolar chains of plasmonic nanoparticles,” Phys. Rev. B 79(23), 235412 (2009).
[CrossRef]

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69(20), 205414 (2004).
[CrossRef]

Phys. Rev. Lett. (8)

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

M. Liu, T. W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, “Excitation of dark plasmons in metal nanoparticles by a localized emitter,” Phys. Rev. Lett. 102(10), 107401 (2009).
[CrossRef] [PubMed]

J. K. Kitur, V. A. Podolskiy, and M. A. Noginov, “Stimulated emission of surface plasmon polaritons in a microcylinder cavity,” Phys. Rev. Lett. 106(18), 183903 (2011).
[CrossRef] [PubMed]

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, “Giant enhancement of surface second harmonic generation in BaTiO3 due to photorefractive surface wave excitation,” Phys. Rev. Lett. 83(12), 2429–2432 (1999).
[CrossRef]

I. D. Mayergoyz, Z. Zhang, and G. Miano, “Analysis of dynamics of excitation and dephasing of plasmon resonance modes in nanoparticles,” Phys. Rev. Lett. 98(14), 147401 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, “Quantum fluctuations of the refractive index near the interface between a metal and a nonlinear dielectric,” Phys. Rev. Lett. 94(5), 057403 (2005).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101(16), 163902 (2008).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

L. Fonda, G. C. Ghirardi, and A. Rimini, “Decay theory of unstable quantum systems,” Rep. Prog. Phys. 41(4), 587–631 (1978).
[CrossRef]

Science (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Other (4)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), 3rd ed.

S. A. Maier, Plasmonics: Fundamentals and Applications, New York, Springer, 2007.

Z. Jacob, I. Smolyaninov, and E. Narimanov, “Broadband Purcell effect: radiative decay engineering with metamaterials,” e-print arXiv:0910.3981.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge 1997).

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Figures (3)

Fig. 1
Fig. 1

The electric field distribution associated with a quadrupolar mode of a spherical nanoparticle in the quasistatic approximation. Color maps of (a) radial and (b) azimuthal electric field components. The quadrupole resonance condition is ε(ω) = - 1.5εd . All distances are normalized to the sphere radius. Color scale represents the electric field amplitude in arbitrary units. Inset in (a) illustrates the assembly of local oscillators acting as the damping reservoir; qk,qk are the creation and annihilation operators corresponding to kth oscillator.

Fig. 2
Fig. 2

(a) The time evolution of the plasmonic quadrupole mode’s power for different loss parameters in the quasistatic regime. Blue (red) and green (black) lines correspond to the memory-effect-based model (conventional exponential decay) for ε=1.5+0.5i and ε=1.5+0.1i , respectively. (b) Deviation of the decay process from the exponential law [ log( | a( t ) | 2 ) Γ C t ]: 4 curves correspond to different material loss parameters ε im =[ 0.5;0.1;0.05;0.01 ] . Horizontal dashed line y = 0 corresponds to the exponential decay.

Fig. 3
Fig. 3

(a) Absorption (red), scattering (blue) and extinction (black) cross-sections for the silver particles with the radii of 50 nm (solid lines) and 20 nm (dashed lines) and permittivity from [44]. (b) The time evolution of the dipolar plasmonic mode’s power: red line corresponds to the standard Weisskopf-Wigner theory; blue line is the full numerical solution using the memory equation. Insert shows the zoomed area of the same curve.

Equations (7)

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

Γ C =2 ω 0 dV ε 0 ε im | E ( r , ω 0 ) | 2 U tot ,
Γ C = 41 ω p 2 γ ω 0 2 ( ω 0 2 + γ 2 ) 2 [ 41 2 ( 1 ω p 2 ( ω 0 2 + γ 2 ) + 2 ω p 2 ω 0 2 ( ω 0 2 + γ 2 ) 2 )+ 189 8 ε d ] ,
Η ^ = Η ^ 0 + Η ^ I Η ^ 0 = ω 0 a a+ q ω k q k q k ; Η ^ I = k g k ( q k a+ a q k ) ,
a ˜ ( t )= a( t ) R e i ω 0 t a ˜ ˙ = k ( g k 2 0 t dt' a ˜ ( t' ) e i( ω 0 ω k )( tt' ) )  .
a ˜ ˙ = 0 t F(tτ) a ˜ ( τ ) dτ,
F(t)= Γ C 2π 0 ( ω 0 2 + γ 2 ω 2 + γ 2 ) ω 0 ω e i( ω 0 ω )t dω   .
a(t)= 1 2π a(0) is+ Γ C 2 ( ω 0 2 + γ 2 ( ω 0 s ) 2 + γ 2 ) ω 0 ( ω 0 s ) e ist ds  .

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