Abstract

Nonlocal effects have been shown to be responsible for a variety of nontrivial optical effects in small-size plasmonic nanoparticles, beyond classical electrodynamics. However, it is not clear whether optical mode descriptions can be applied to such extreme confinement regimes. Here, we present a powerful quasinormal mode description of the nonlocal optical response for three-dimensional plasmonic nanoresonators. The nonlocal hydrodynamical model and a generalized nonlocal optical response model for plasmonic nanoresonators are used to construct an intuitive modal theory and to compare to the local Drude model response theory. Using the example of a gold nanorod, we show how an efficient quasinormal mode picture is able to accurately capture the blueshift of the resonances, the higher damping rates in plasmonic nanoresonators, and the modified spatial profile of the plasmon quasinormal modes, even at the single mode level. We exemplify the use of this theory by calculating the Purcell factors of single quantum emitters, the electron energy loss spectroscopy spatial maps, and the Mollow triplet spectra of field-driven quantum dots with and without nonlocal effects for different size nanoresonators. Our nonlocal quasinormal mode theory offers a reliable and efficient technique to study both classical and quantum optical problems in nanoplasmonics.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Enhancing ultraviolet spontaneous emission with a designed quantum vacuum

Duncan McArthur, Benjamin Hourahine, and Francesco Papoff
Opt. Express 25(4) 4162-4179 (2017)

Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes

Jakob Rosenkrantz de Lasson, Jesper Mørk, and Philip Trøst Kristensen
J. Opt. Soc. Am. B 30(7) 1996-2007 (2013)

References

  • View by:
  • |
  • |
  • |

  1. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
    [Crossref]
  2. K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
    [Crossref]
  3. R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
    [Crossref]
  4. M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
    [Crossref]
  5. M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
    [Crossref]
  6. T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast room-temperature single photon emission from quantum dots coupled to plasmonic nanocavities,” Nano Lett. 16, 270–275 (2016).
    [Crossref]
  7. S. I. Bozhevolnyi and N. A. Mortensen, “Plasmonics for emerging quantum technologies,” Nanophotonics 6, 1185–1188 (2017).
    [Crossref]
  8. R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31, 1434–1437 (1973).
    [Crossref]
  9. R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
    [Crossref]
  10. P. T. Leung, “Decay of molecules at spherical surfaces: nonlocal effects,” Phys. Rev. B 42, 7622–7625 (1990).
    [Crossref]
  11. F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112, 17983–17987 (2008).
    [Crossref]
  12. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097405 (2009).
    [Crossref]
  13. S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
    [Crossref]
  14. T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
    [Crossref]
  15. N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
    [Crossref]
  16. A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
    [Crossref]
  17. L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
    [Crossref]
  18. R. Filter, C. Bösel, G. Toscano, F. Lederer, and C. Rockstuhl, “Nonlocal effects: relevance for the spontaneous emission rates of quantum emitters coupled to plasmonic structures,” Opt. Lett. 39, 6118–6121 (2014).
    [Crossref]
  19. P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photon. 1, 2–10 (2014).
    [Crossref]
  20. M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission for a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A 95, 013846 (2017).
    [Crossref]
  21. P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
    [Crossref]
  22. P. T. Kristensen, C. P. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
    [Crossref]
  23. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
    [Crossref]
  24. P. T. Kristensen, R. C. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
    [Crossref]
  25. Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
    [Crossref]
  26. E. A. Muljarov and W. Langbein, “Exact mode volume and Purcell factor of open optical systems,” Phys. Rev. B 94, 235438 (2016).
    [Crossref]
  27. E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
    [Crossref]
  28. G. Ford and W. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [Crossref]
  29. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [Crossref]
  30. G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84, 5500–5503 (2000).
    [Crossref]
  31. M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A 70, 053823 (2004).
    [Crossref]
  32. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
    [Crossref]
  33. S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
    [Crossref]
  34. V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient ‘On Chip’ single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
    [Crossref]
  35. C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B 85, 075303 (2012).
    [Crossref]
  36. W. Yan, N. A. Mortensen, and M. Wubs, “Green’s function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments,” Phys. Rev. B 88, 155414 (2013).
    [Crossref]
  37. R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
    [Crossref]
  38. M. Kamandar Dezfouli and S. Hughes, “Quantum optics model of surface-enhanced Raman spectroscopy for arbitrarily shaped plasmonic resonators,” ACS Photon. 4, 1245–1256 (2017).
    [Crossref]
  39. F. J. García De Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100, 106804 (2008).
    [Crossref]
  40. D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
    [Crossref]
  41. O. Nicoletti, M. Wubs, N. A. Mortensen, W. Sigle, P. A. van Aken, and P. A. Midgley, “Surface plasmon modes of a single silver nanorod: an electron energy loss study,” Opt. Express 19, 15371–15379 (2011).
    [Crossref]
  42. Z. Mohammadi, C. P. Van Vlack, S. Hughes, J. Bornemann, and R. Gordon, “Vortex electron energy loss spectroscopy for near-field mapping of magnetic plasmons,” Opt. Express 20, 15024–15034 (2012).
    [Crossref]
  43. G. Boudarham and M. Kociak, “Modal decompositions of the local electromagnetic density of states and spatially resolved electron energy loss probability in terms of geometric modes,” Phys. Rev. B 85, 245447 (2012).
    [Crossref]
  44. M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
    [Crossref]
  45. T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
    [Crossref]
  46. S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
    [Crossref]
  47. A. Hörl, A. Trügler, and U. Hohenester, “Full three-dimensional reconstruction of the dyadic green tensor from electron energy loss spectroscopy of plasmonic nanoparticles,” ACS Photon. 2, 1429–1435 (2015).
    [Crossref]
  48. R.-C. Ge and S. Hughes, “Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructures,” J. Opt. 18, 054002 (2016).
    [Crossref]
  49. R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
    [Crossref]
  50. P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
    [Crossref]
  51. I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
    [Crossref]
  52. R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
    [Crossref]
  53. R.-C. Ge and S. Hughes, “Design of an efficient single photon source from a metallic nanorod dimer: a quasi-normal mode finite-difference time-domain approach,” Opt. Lett. 39, 4235–4238 (2014).
    [Crossref]
  54. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
    [Crossref]
  55. C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
    [Crossref]
  56. S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
    [Crossref]
  57. G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).
    [Crossref]
  58. C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
    [Crossref]
  59. “COMSOL Multiphysics,” https://www.comsol.com .
  60. A. A. Sukhorukov, I. V. Shadrivov, and Y. S. Kivshar, “Wave scattering by metamaterial wedges and interfaces,” Int. J. Numer. Model. 19, 105–117 (2006).
    [Crossref]
  61. H. Wallén, H. Kettunen, and A. Sihvola, “Surface modes of negative-parameter interfaces and the importance of rounding sharp corners,” Metamaterials 2, 113–121 (2008).
    [Crossref]
  62. S. I. Bozhevolnyi and J. B. Khurgin, “The case for quantum plasmonics,” Nat. Photonics 11, 398–400 (2017).
    [Crossref]
  63. S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
    [Crossref]

2017 (6)

S. I. Bozhevolnyi and N. A. Mortensen, “Plasmonics for emerging quantum technologies,” Nanophotonics 6, 1185–1188 (2017).
[Crossref]

M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission for a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A 95, 013846 (2017).
[Crossref]

M. Kamandar Dezfouli and S. Hughes, “Quantum optics model of surface-enhanced Raman spectroscopy for arbitrarily shaped plasmonic resonators,” ACS Photon. 4, 1245–1256 (2017).
[Crossref]

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

S. I. Bozhevolnyi and J. B. Khurgin, “The case for quantum plasmonics,” Nat. Photonics 11, 398–400 (2017).
[Crossref]

2016 (7)

C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
[Crossref]

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
[Crossref]

R.-C. Ge and S. Hughes, “Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructures,” J. Opt. 18, 054002 (2016).
[Crossref]

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

E. A. Muljarov and W. Langbein, “Exact mode volume and Purcell factor of open optical systems,” Phys. Rev. B 94, 235438 (2016).
[Crossref]

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast room-temperature single photon emission from quantum dots coupled to plasmonic nanocavities,” Nano Lett. 16, 270–275 (2016).
[Crossref]

2015 (5)

M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
[Crossref]

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

A. Hörl, A. Trügler, and U. Hohenester, “Full three-dimensional reconstruction of the dyadic green tensor from electron energy loss spectroscopy of plasmonic nanoparticles,” ACS Photon. 2, 1429–1435 (2015).
[Crossref]

P. T. Kristensen, R. C. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

2014 (6)

R.-C. Ge and S. Hughes, “Design of an efficient single photon source from a metallic nanorod dimer: a quasi-normal mode finite-difference time-domain approach,” Opt. Lett. 39, 4235–4238 (2014).
[Crossref]

R. Filter, C. Bösel, G. Toscano, F. Lederer, and C. Rockstuhl, “Nonlocal effects: relevance for the spontaneous emission rates of quantum emitters coupled to plasmonic structures,” Opt. Lett. 39, 6118–6121 (2014).
[Crossref]

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photon. 1, 2–10 (2014).
[Crossref]

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

2013 (7)

W. Yan, N. A. Mortensen, and M. Wubs, “Green’s function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments,” Phys. Rev. B 88, 155414 (2013).
[Crossref]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref]

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

2012 (9)

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).
[Crossref]

P. T. Kristensen, C. P. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[Crossref]

Z. Mohammadi, C. P. Van Vlack, S. Hughes, J. Bornemann, and R. Gordon, “Vortex electron energy loss spectroscopy for near-field mapping of magnetic plasmons,” Opt. Express 20, 15024–15034 (2012).
[Crossref]

G. Boudarham and M. Kociak, “Modal decompositions of the local electromagnetic density of states and spatially resolved electron energy loss probability in terms of geometric modes,” Phys. Rev. B 85, 245447 (2012).
[Crossref]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref]

C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B 85, 075303 (2012).
[Crossref]

2011 (3)

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

O. Nicoletti, M. Wubs, N. A. Mortensen, W. Sigle, P. A. van Aken, and P. A. Midgley, “Surface plasmon modes of a single silver nanorod: an electron energy loss study,” Opt. Express 19, 15371–15379 (2011).
[Crossref]

2010 (1)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
[Crossref]

2009 (1)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097405 (2009).
[Crossref]

2008 (3)

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112, 17983–17987 (2008).
[Crossref]

F. J. García De Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100, 106804 (2008).
[Crossref]

H. Wallén, H. Kettunen, and A. Sihvola, “Surface modes of negative-parameter interfaces and the importance of rounding sharp corners,” Metamaterials 2, 113–121 (2008).
[Crossref]

2007 (1)

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient ‘On Chip’ single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

2006 (2)

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[Crossref]

A. A. Sukhorukov, I. V. Shadrivov, and Y. S. Kivshar, “Wave scattering by metamaterial wedges and interfaces,” Int. J. Numer. Model. 19, 105–117 (2006).
[Crossref]

2004 (2)

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[Crossref]

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A 70, 053823 (2004).
[Crossref]

2000 (1)

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84, 5500–5503 (2000).
[Crossref]

1999 (1)

S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
[Crossref]

1994 (1)

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref]

1990 (1)

P. T. Leung, “Decay of molecules at spherical surfaces: nonlocal effects,” Phys. Rev. B 42, 7622–7625 (1990).
[Crossref]

1987 (2)

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[Crossref]

J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
[Crossref]

1984 (1)

G. Ford and W. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

1973 (1)

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31, 1434–1437 (1973).
[Crossref]

1946 (1)

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Agarwal, G. S.

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84, 5500–5503 (2000).
[Crossref]

Aharonovich, I.

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
[Crossref]

Aizpurua, J.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Akselrod, G. M.

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast room-temperature single photon emission from quantum dots coupled to plasmonic nanocavities,” Nano Lett. 16, 270–275 (2016).
[Crossref]

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[Crossref]

Axelrod, S.

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

Bai, Q.

Barbry, M.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

Baumberg, J. J.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Berggren, K. K.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[Crossref]

Borisov, A. G.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Bornemann, J.

Bösel, C.

Botton, G. A.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

Boudarham, G.

G. Boudarham and M. Kociak, “Modal decompositions of the local electromagnetic density of states and spatially resolved electron energy loss probability in terms of geometric modes,” Phys. Rev. B 85, 245447 (2012).
[Crossref]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi and N. A. Mortensen, “Plasmonics for emerging quantum technologies,” Nanophotonics 6, 1185–1188 (2017).
[Crossref]

S. I. Bozhevolnyi and J. B. Khurgin, “The case for quantum plasmonics,” Nat. Photonics 11, 398–400 (2017).
[Crossref]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

Busch, K.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Chilkoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

Christensen, T.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

Ciracì, C.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

Claro, F.

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[Crossref]

Couillard, M.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

Dalili, N.

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

Di Vece, M.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

Englund, D.

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
[Crossref]

Esteban, R.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref]

Fernández-Domínguez, A. I.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

Filter, R.

Ford, G.

G. Ford and W. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

Fuchs, R.

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[Crossref]

Gaind, V.

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

García De Abajo, F. J.

F. J. García De Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100, 106804 (2008).
[Crossref]

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112, 17983–17987 (2008).
[Crossref]

García-González, P.

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

García-Vidal, F. J.

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

Ge, R. C.

P. T. Kristensen, R. C. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

Ge, R.-C.

R.-C. Ge and S. Hughes, “Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructures,” J. Opt. 18, 054002 (2016).
[Crossref]

R.-C. Ge and S. Hughes, “Design of an efficient single photon source from a metallic nanorod dimer: a quasi-normal mode finite-difference time-domain approach,” Opt. Lett. 39, 4235–4238 (2014).
[Crossref]

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

Goodman, S. A.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Gordon, R.

M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission for a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A 95, 013846 (2017).
[Crossref]

Z. Mohammadi, C. P. Van Vlack, S. Hughes, J. Bornemann, and R. Gordon, “Vortex electron energy loss spectroscopy for near-field mapping of magnetic plasmons,” Opt. Express 20, 15024–15034 (2012).
[Crossref]

Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
[Crossref]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097405 (2009).
[Crossref]

Hawkeye, M. M.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Helmy, A. S.

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

Hill, R. T.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

Hoang, T. B.

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast room-temperature single photon emission from quantum dots coupled to plasmonic nanocavities,” Nano Lett. 16, 270–275 (2016).
[Crossref]

Hobbs, R. G.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Hohenester, U.

A. Hörl, A. Trügler, and U. Hohenester, “Full three-dimensional reconstruction of the dyadic green tensor from electron energy loss spectroscopy of plasmonic nanoparticles,” ACS Photon. 2, 1429–1435 (2015).
[Crossref]

Hörl, A.

A. Hörl, A. Trügler, and U. Hohenester, “Full three-dimensional reconstruction of the dyadic green tensor from electron energy loss spectroscopy of plasmonic nanoparticles,” ACS Photon. 2, 1429–1435 (2015).
[Crossref]

Horsfield, A. P.

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

Hughes, S.

M. Kamandar Dezfouli and S. Hughes, “Quantum optics model of surface-enhanced Raman spectroscopy for arbitrarily shaped plasmonic resonators,” ACS Photon. 4, 1245–1256 (2017).
[Crossref]

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission for a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A 95, 013846 (2017).
[Crossref]

R.-C. Ge and S. Hughes, “Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructures,” J. Opt. 18, 054002 (2016).
[Crossref]

P. T. Kristensen, R. C. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

R.-C. Ge and S. Hughes, “Design of an efficient single photon source from a metallic nanorod dimer: a quasi-normal mode finite-difference time-domain approach,” Opt. Lett. 39, 4235–4238 (2014).
[Crossref]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photon. 1, 2–10 (2014).
[Crossref]

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B 85, 075303 (2012).
[Crossref]

Z. Mohammadi, C. P. Van Vlack, S. Hughes, J. Bornemann, and R. Gordon, “Vortex electron energy loss spectroscopy for near-field mapping of magnetic plasmons,” Opt. Express 20, 15024–15034 (2012).
[Crossref]

P. T. Kristensen, C. P. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient ‘On Chip’ single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[Crossref]

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Hugonin, J.-P.

Husnik, M.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Irsen, S.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Jacob, Z.

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

Jauho, A. P.

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

Jauho, A.-P.

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

Kadkhodazadeh, S.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

Kamada, H.

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[Crossref]

Kamandar Dezfouli, M.

M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission for a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A 95, 013846 (2017).
[Crossref]

M. Kamandar Dezfouli and S. Hughes, “Quantum optics model of surface-enhanced Raman spectroscopy for arbitrarily shaped plasmonic resonators,” ACS Photon. 4, 1245–1256 (2017).
[Crossref]

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

Kettunen, H.

H. Wallén, H. Kettunen, and A. Sihvola, “Surface modes of negative-parameter interfaces and the importance of rounding sharp corners,” Metamaterials 2, 113–121 (2008).
[Crossref]

Khurgin, J. B.

S. I. Bozhevolnyi and J. B. Khurgin, “The case for quantum plasmonics,” Nat. Photonics 11, 398–400 (2017).
[Crossref]

Kivshar, Y. S.

A. A. Sukhorukov, I. V. Shadrivov, and Y. S. Kivshar, “Wave scattering by metamaterial wedges and interfaces,” Int. J. Numer. Model. 19, 105–117 (2006).
[Crossref]

Knöll, L.

S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
[Crossref]

Kociak, M.

G. Boudarham and M. Kociak, “Modal decompositions of the local electromagnetic density of states and spatially resolved electron energy loss probability in terms of geometric modes,” Phys. Rev. B 85, 245447 (2012).
[Crossref]

F. J. García De Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100, 106804 (2008).
[Crossref]

Koval, P.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

Kristensen, P. T.

P. T. Kristensen, R. C. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photon. 1, 2–10 (2014).
[Crossref]

C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B 85, 075303 (2012).
[Crossref]

P. T. Kristensen, C. P. Van Vlack, and S. Hughes, “Generalized effective mode volume for leaky optical cavities,” Opt. Lett. 37, 1649–1651 (2012).
[Crossref]

Kumacheva, E.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

Lagendijk, A.

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A 70, 053823 (2004).
[Crossref]

Lalanne, P.

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Langbein, W.

E. A. Muljarov and W. Langbein, “Exact mode volume and Purcell factor of open optical systems,” Phys. Rev. B 94, 235438 (2016).
[Crossref]

Lederer, F.

Leung, P. T.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref]

P. T. Leung, “Decay of molecules at spherical surfaces: nonlocal effects,” Phys. Rev. B 42, 7622–7625 (1990).
[Crossref]

Linden, S.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Liu, S. Y.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref]

Liu, Z.

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

Maack, J. R.

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

Maier, S. A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

Maksymov, I. S.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Malac, M.

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

Manfrinato, V. R.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Manga Rao, V. S. C.

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient ‘On Chip’ single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

Marchesin, F.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

McMahon, J. M.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
[Crossref]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097405 (2009).
[Crossref]

Meldrum, A.

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

Midgley, P. A.

Mikkelsen, M. H.

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast room-temperature single photon emission from quantum dots coupled to plasmonic nanocavities,” Nano Lett. 16, 270–275 (2016).
[Crossref]

Mock, J. J.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

Mohammadi, Z.

Mortensen, N. A.

S. I. Bozhevolnyi and N. A. Mortensen, “Plasmonics for emerging quantum technologies,” Nanophotonics 6, 1185–1188 (2017).
[Crossref]

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
[Crossref]

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

W. Yan, N. A. Mortensen, and M. Wubs, “Green’s function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments,” Phys. Rev. B 88, 155414 (2013).
[Crossref]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).
[Crossref]

O. Nicoletti, M. Wubs, N. A. Mortensen, W. Sigle, P. A. van Aken, and P. A. Midgley, “Surface plasmon modes of a single silver nanorod: an electron energy loss study,” Opt. Express 19, 15371–15379 (2011).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

Muljarov, E. A.

E. A. Muljarov and W. Langbein, “Exact mode volume and Purcell factor of open optical systems,” Phys. Rev. B 94, 235438 (2016).
[Crossref]

Nicoletti, O.

Niegemann, J.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Nordlander, P.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref]

Novotny, L.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[Crossref]

Pelton, M.

M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
[Crossref]

Pendry, J. B.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

Perrin, M.

Pound, R. V.

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Purcell, E. M.

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Raza, S.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

Rockstuhl, C.

Rossouw, D.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

Rubio, A.

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

Ruppin, R.

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31, 1434–1437 (1973).
[Crossref]

Sánchez-Portal, D.

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

Sauvan, C.

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Savage, K. J.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Schatz, G. C.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
[Crossref]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097405 (2009).
[Crossref]

Scheel, S.

S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
[Crossref]

Shadrivov, I. V.

A. A. Sukhorukov, I. V. Shadrivov, and Y. S. Kivshar, “Wave scattering by metamaterial wedges and interfaces,” Int. J. Numer. Model. 19, 105–117 (2006).
[Crossref]

Shekhar, P.

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

Sigle, W.

Sihvola, A.

H. Wallén, H. Kettunen, and A. Sihvola, “Surface modes of negative-parameter interfaces and the importance of rounding sharp corners,” Metamaterials 2, 113–121 (2008).
[Crossref]

Sipe, J. E.

Smith, D. R.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

Søndergaard, T.

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

Stach, E. A.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Stefanou, N.

C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
[Crossref]

Stella, L.

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

Stenger, N.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

Sukhorukov, A. A.

A. A. Sukhorukov, I. V. Shadrivov, and Y. S. Kivshar, “Wave scattering by metamaterial wedges and interfaces,” Int. J. Numer. Model. 19, 105–117 (2006).
[Crossref]

Suttorp, L. G.

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A 70, 053823 (2004).
[Crossref]

Teperik, T. V.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref]

Tong, S. S.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref]

Torrey, H. C.

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Toscano, G.

Toth, M.

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
[Crossref]

Trügler, A.

A. Hörl, A. Trügler, and U. Hohenester, “Full three-dimensional reconstruction of the dyadic green tensor from electron energy loss spectroscopy of plasmonic nanoparticles,” ACS Photon. 2, 1429–1435 (2015).
[Crossref]

Tserkezis, C.

C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
[Crossref]

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

Urzhumov, Y.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

van Aken, P. A.

Van Vlack, C.

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B 85, 075303 (2012).
[Crossref]

Van Vlack, C. P.

Vickery, J.

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

Von Cube, F.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Wallén, H.

H. Wallén, H. Kettunen, and A. Sihvola, “Surface modes of negative-parameter interfaces and the importance of rounding sharp corners,” Metamaterials 2, 113–121 (2008).
[Crossref]

Weber, W.

G. Ford and W. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

Wegener, M.

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Welsch, D.-G.

S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
[Crossref]

Wiener, A.

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

Wong, H. M. K.

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

Wubs, M.

C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
[Crossref]

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

W. Yan, N. A. Mortensen, and M. Wubs, “Green’s function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments,” Phys. Rev. B 88, 155414 (2013).
[Crossref]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20, 4176–4188 (2012).
[Crossref]

O. Nicoletti, M. Wubs, N. A. Mortensen, W. Sigle, P. A. van Aken, and P. A. Midgley, “Surface plasmon modes of a single silver nanorod: an electron energy loss study,” Opt. Express 19, 15371–15379 (2011).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A 70, 053823 (2004).
[Crossref]

Yan, W.

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

W. Yan, N. A. Mortensen, and M. Wubs, “Green’s function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments,” Phys. Rev. B 88, 155414 (2013).
[Crossref]

Yang, Y.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Yao, P.

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

Young, J. F.

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

Young, K.

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref]

Zhang, L.

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

Zhang, P.

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

ACS Nano (1)

T. Christensen, W. Yan, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Nonlocal response of metallic nanospheres probed by light, electrons, and atoms,” ACS Nano 8, 1745–1758 (2014).
[Crossref]

ACS Photon. (4)

A. Hörl, A. Trügler, and U. Hohenester, “Full three-dimensional reconstruction of the dyadic green tensor from electron energy loss spectroscopy of plasmonic nanoparticles,” ACS Photon. 2, 1429–1435 (2015).
[Crossref]

P. Shekhar, M. Malac, V. Gaind, N. Dalili, A. Meldrum, and Z. Jacob, “Momentum-resolved electron energy loss spectroscopy for mapping the photonic density of states,” ACS Photon. 4, 1009–1014 (2017).
[Crossref]

P. T. Kristensen and S. Hughes, “Modes and mode volumes of leaky optical cavities and plasmonic nanoresonators,” ACS Photon. 1, 2–10 (2014).
[Crossref]

M. Kamandar Dezfouli and S. Hughes, “Quantum optics model of surface-enhanced Raman spectroscopy for arbitrarily shaped plasmonic resonators,” ACS Photon. 4, 1245–1256 (2017).
[Crossref]

Int. J. Numer. Model. (1)

A. A. Sukhorukov, I. V. Shadrivov, and Y. S. Kivshar, “Wave scattering by metamaterial wedges and interfaces,” Int. J. Numer. Model. 19, 105–117 (2006).
[Crossref]

J. Opt. (1)

R.-C. Ge and S. Hughes, “Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructures,” J. Opt. 18, 054002 (2016).
[Crossref]

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

J. Phys. Chem. C (2)

L. Stella, P. Zhang, F. J. García-Vidal, A. Rubio, and P. García-González, “Performance of nonlocal optics when applied to plasmonic nanostructures,” J. Phys. Chem. C 117, 8941–8949 (2013).
[Crossref]

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112, 17983–17987 (2008).
[Crossref]

Metamaterials (1)

H. Wallén, H. Kettunen, and A. Sihvola, “Surface modes of negative-parameter interfaces and the importance of rounding sharp corners,” Metamaterials 2, 113–121 (2008).
[Crossref]

Nano Lett. (5)

R. G. Hobbs, V. R. Manfrinato, Y. Yang, S. A. Goodman, L. Zhang, E. A. Stach, and K. K. Berggren, “High-energy surface and volume plasmons in nanopatterned sub-10  nm aluminum nanostructures,” Nano Lett. 16, 4149–4157 (2016).
[Crossref]

D. Rossouw, M. Couillard, J. Vickery, E. Kumacheva, and G. A. Botton, “Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe,” Nano Lett. 11, 1499–1504 (2011).
[Crossref]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12, 3308–3314 (2012).
[Crossref]

M. Barbry, P. Koval, F. Marchesin, R. Esteban, A. G. Borisov, J. Aizpurua, and D. Sánchez-Portal, “Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics,” Nano Lett. 15, 3410–3419 (2015).
[Crossref]

T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast room-temperature single photon emission from quantum dots coupled to plasmonic nanocavities,” Nano Lett. 16, 270–275 (2016).
[Crossref]

Nanophotonics (2)

S. I. Bozhevolnyi and N. A. Mortensen, “Plasmonics for emerging quantum technologies,” Nanophotonics 6, 1185–1188 (2017).
[Crossref]

M. Husnik, F. Von Cube, S. Irsen, S. Linden, J. Niegemann, K. Busch, and M. Wegener, “Comparison of electron energy-loss and quantitative optical spectroscopy on individual optical gold antennas,” Nanophotonics 2, 241–245 (2013).
[Crossref]

Nanoscale (1)

C. Tserkezis, N. Stefanou, M. Wubs, and N. A. Mortensen, “Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects,” Nanoscale 8, 17532–17541 (2016).
[Crossref]

Nat. Commun. (3)

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref]

Nat. Photonics (3)

M. Pelton, “Modified spontaneous emission in nanophotonic structures,” Nat. Photonics 9, 427–435 (2015).
[Crossref]

S. I. Bozhevolnyi and J. B. Khurgin, “The case for quantum plasmonics,” Nat. Photonics 11, 398–400 (2017).
[Crossref]

I. Aharonovich, D. Englund, and M. Toth, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641 (2016).
[Crossref]

Nature (1)

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

New J. Phys. (1)

R. C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics,” New J. Phys. 16, 113048 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rep. (1)

G. Ford and W. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

Phys. Rev. (1)

E. M. Purcell, H. C. Torrey, and R. V. Pound, “Resonance absorption by nuclear magnetic moments in a solid,” Phys. Rev. 69, 37–38 (1946).
[Crossref]

Phys. Rev. A (5)

M. Kamandar Dezfouli, R. Gordon, and S. Hughes, “Modal theory of modified spontaneous emission for a hybrid plasmonic photonic-crystal cavity system,” Phys. Rev. A 95, 013846 (2017).
[Crossref]

P. T. Leung, S. Y. Liu, S. S. Tong, and K. Young, “Time-independent perturbation-theory for quasi-normal modes in leaky optical cavities,” Phys. Rev. A 49, 3068–3073 (1994).
[Crossref]

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A 70, 053823 (2004).
[Crossref]

P. T. Kristensen, R. C. Ge, and S. Hughes, “Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators,” Phys. Rev. A 92, 053810 (2015).
[Crossref]

S. Scheel, L. Knöll, and D.-G. Welsch, “Spontaneous decay of an excited atom in an absorbing dielectric,” Phys. Rev. A 60, 4094–4104 (1999).
[Crossref]

Phys. Rev. B (11)

R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, “Accessing quantum nanoplasmonics in a hybrid quantum dot-metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle,” Phys. Rev. B 87, 205425 (2013).
[Crossref]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
[Crossref]

G. Boudarham and M. Kociak, “Modal decompositions of the local electromagnetic density of states and spatially resolved electron energy loss probability in terms of geometric modes,” Phys. Rev. B 85, 245447 (2012).
[Crossref]

S. Axelrod, M. Kamandar Dezfouli, H. M. K. Wong, A. S. Helmy, and S. Hughes, “Hyperbolic metamaterial nanoresonators make poor single-photon sources,” Phys. Rev. B 95, 155424 (2017).
[Crossref]

S. Hughes and H. Kamada, “Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide,” Phys. Rev. B 70, 195313 (2004).
[Crossref]

C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B 85, 075303 (2012).
[Crossref]

W. Yan, N. A. Mortensen, and M. Wubs, “Green’s function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments,” Phys. Rev. B 88, 155414 (2013).
[Crossref]

E. A. Muljarov and W. Langbein, “Exact mode volume and Purcell factor of open optical systems,” Phys. Rev. B 94, 235438 (2016).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987).
[Crossref]

P. T. Leung, “Decay of molecules at spherical surfaces: nonlocal effects,” Phys. Rev. B 42, 7622–7625 (1990).
[Crossref]

Phys. Rev. Lett. (8)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097405 (2009).
[Crossref]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref]

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett. 31, 1434–1437 (1973).
[Crossref]

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84, 5500–5503 (2000).
[Crossref]

F. J. García De Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100, 106804 (2008).
[Crossref]

V. S. C. Manga Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient ‘On Chip’ single photon gun,” Phys. Rev. Lett. 99, 193901 (2007).
[Crossref]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Sci. Rep. (1)

C. Tserkezis, J. R. Maack, Z. Liu, M. Wubs, and N. A. Mortensen, “Robustness of the far-field response of nonlocal plasmonic ensembles,” Sci. Rep. 6, 28441 (2016).
[Crossref]

Science (1)

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[Crossref]

Other (1)

“COMSOL Multiphysics,” https://www.comsol.com .

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Comparison between the local QNM (a, c, e), |f˜(x,z,y0)|2 and nonlocal GNOR QNM (b, d, f), |f˜nl(x,z,y0)|2 for nanorods of different heights, h=20  nm, h=10  nm, and h=5  nm, where y0=0 is at the center of the nanorods. Same geometrical aspect ratio of 2 is used corresponding to a radius of r=5  nm for the largest resonator. Double arrow in (a) shows the location of the dipole emitter at 10 nm away from the metallic surface that is kept the same for all QNM calculations, and the green box represents the metallic border.

Fig. 2.
Fig. 2.

Top: generalized Purcell factor for a dipole emitter placed 10-nm away form a gold nanorod of height h=20  nm and radius of r=5  nm, using Drude QNM, nonlocal HDM QNM, and nonlocal GNOR QNM. The inset shows the agreement between full dipole calculations (with no approximations) and GNOR QNM results. Bottom: corresponding QNM effective mode volume, Veff, is shown for a range of locations above the nanorod. Note that z=10  nm is at the surface of the metallic nanoparticle. Inset shows the modal absolute magnitude for completeness.

Fig. 3.
Fig. 3.

Size-dependent discrepancy in Purcell factor between the local Drude model and nonlocal GNOR model. Results are derived from analytical QNM calculations when the dipole emitter is kept 10-nm away along the z-axis. Complex resonance frequencies for both models are also shown in each case.

Fig. 4.
Fig. 4.

Comparison between the EELS map of the plasmonic nanorod using the local Drude model, (a, c, e) and nonlocal GNOR model, (b, d, f), where each map is calculated at the corresponding plasmonic peak frequency. Same geometries as in Fig. 1 are used, and green box represents the metallic border.

Fig. 5.
Fig. 5.

Detected spectra (S evaluated at rD=200  nm) of a field-driven QD coupled to plasmonic nanoparticles, where the same ordering of the particle size and QD location as in Fig. 1 is followed, and we use an effective Rabi field of Ω=50  meV. Plasmonic enhancement is also shown in dashed-gray in background. Nonlocal investigations on the right predict relatively stronger side peaks for the Mollow triplet with narrower linewidths.

Tables (1)

Tables Icon

Table 1. Linewidth of the Central Mollow Peak for the Three Nanoparticles, Using Both Drude Model and GNOR Modela

Equations (13)

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

××f˜μ(r)(ω˜μc)2ϵ(r,ω)f˜μ(r)=0,
××f˜μnl(r)(ω˜μnlc)2f˜μnl(r)=iω˜μnlμ0Jμ,
ξ2[·Jμ]+ω˜μnl(ω˜μnl+iγp)Jμ=iω˜μnlωp2ϵ0f˜μnl(r),
FP(r)=34π2(λcnb)3QVeff(r),
Gscnl(r1,r2;ω)=μω22ω˜μnl(ω˜μnlω)f˜μnl(r1)f˜μnl(r2),
F(r;ω)=1+6πc3ω3nbn·Im{Gscnl(r,r;ω)}·n,
f˜c(r0)·d=d·Gsc(r0,r0;ω˜c)·dA(ω˜c),
f˜c(r)=Gsc(r,r0;ω˜c)·dA(ω˜c)[d·Gsc(r0,r0;ω˜c)·d],
Γ(x,z;ω)=4e2v2dtdtIm{eiω(tt)Gyy(re(t),re(t);ω)},
H=dr0dωωf^(r,ω)f^(r,ω)+ωxσ+σ[σ+0dωd·E^(rd,ω)+H.c.]+Ω2(σ+eiωL+σeiωL),
ρt=1i[HS,ρ]+0tdτ{J˜ph(τ)[σ+σ(τ)ρ+σ(τ)ρσ+]+H.c.},
S0(ω)=limtRe[0dτ(σ+(tτ)σ(t)σ+(t)σ(t))ei(ωLω)τ],
S(rD;ω)=2ϵ0|G(rD,r0;ω)·d|2S0(ω).