Abstract

Microcavities and nanoresonators are characterized by their quality factors (Q) and mode volumes (V). While Q is unambiguously defined, there are still questions on V and, in particular, on its complex-valued character, whose imaginary part is linked to the non-Hermitian nature of open systems. Helped by cavity perturbation theory and near-field experimental data, we clarify the physics captured by the imaginary part of V and show how a mapping of the spatial distribution of both the real and imaginary parts can be directly inferred from perturbation measurements. This result shows that the mathematically abstract complex mode V, in fact, is directly observable.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Generalized effective mode volume for leaky optical cavities

P. T. Kristensen, C. Van Vlack, and S. Hughes
Opt. Lett. 37(10) 1649-1651 (2012)

Semianalytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity–waveguide structures

Jakob Rosenkrantz de Lasson, Philip Trøst Kristensen, Jesper Mørk, and Niels Gregersen
Opt. Lett. 40(24) 5790-5793 (2015)

Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots

Kartik Srinivasan, Matthew Borselli, Oskar Painter, Andreas Stintz, and Sanjay Krishna
Opt. Express 14(3) 1094-1105 (2006)

References

  • View by:
  • |
  • |
  • |

  1. H. A. Bethe and J. Schwinger, “Perturbation theory for cavities,” (Cornell University, 1943).
  2. R. A. Waldron, “Perturbation theory of resonant cavities,” Proc. IEEE 107, 272–274 (1960).
    [Crossref]
  3. O. Klein, D. M. Dressel, and G. Grüner, “Microwave cavity perturbation techniques: part I: principles,” Int. J. Infrared Millim. Waves 14, 2423–2457 (1993).
    [Crossref]
  4. L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
    [Crossref]
  5. L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
    [Crossref]
  6. M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
    [Crossref]
  7. L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17, 123008 (2015).
    [Crossref]
  8. P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
    [Crossref]
  9. J.-M. Gérard, “Solid-state cavity-quantum electrodynamics with self-assembled quantum dots,” in Single Quantum Dots, Topics in Applied Physics (2003), Vol. 90, p. 269.
  10. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [Crossref]
  11. K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
    [Crossref]
  12. A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
    [Crossref]
  13. A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
    [Crossref]
  14. S. Mujumdar, A. F. Koenderink, T. Sünner, B. C. Buchler, M. Kamp, A. Forchel, and V. Sandoghdar, “Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity,” Opt. Express 15, 17214–17220 (2007).
    [Crossref]
  15. F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
    [Crossref]
  16. N. Le Thomas and R. Houdré, “Inhibited emission of electromagnetic modes confined in subwavelength cavities,” Phys. Rev. B 84, 035320 (2011).
    [Crossref]
  17. F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
    [Crossref]
  18. S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
    [Crossref]
  19. 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]
  20. E. A. Muljarov and W. Langbein, “Resonant-state expansion of dispersive optical open systems: creating gold from sand,” Phys. Rev. B 93, 075417 (2016).
    [Crossref]
  21. J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439 (2015).
    [Crossref]
  22. T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
    [Crossref]
  23. A. Oskooi and S. G. Johnson, “Electromagnetic wave source conditions,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House, 2013), Chap. 4.
  24. N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
    [Crossref]
  25. Q-increases by modifying cavity geometry have been previously reported using slabs [16] and scatterer gratings [17] in near-fields, but not with a localized perturbation, nor with scanning through the mode to determine the relation between changes and mode distributions. Perturbations by extended structures, like slabs, have been understood as radiation pattern engineering to control.
  26. W. Yan, R. Faggiani, and P. Lalanne, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422 (2018).
    [Crossref]
  27. QNMEig and companion Matlab Toolboxes are available on the webpage of L. Lalanne.
  28. https://www.comsol.com/ (Version 5.2a).
  29. The present theory is derived for isotropic and non-magnetic perturbers for the sake of simplicity, but these assumptions can be easily removed.
  30. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), Chap. 15.
  31. E. Lassale, N. Bonod, T. Durt, and B. Stout, “Interplay between spontaneous decay rates and Lamb shifts in open photonic systems,” Opt. Lett. 43, 1950–1953 (2018).
    [Crossref]

2018 (3)

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[Crossref]

W. Yan, R. Faggiani, and P. Lalanne, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422 (2018).
[Crossref]

E. Lassale, N. Bonod, T. Durt, and B. Stout, “Interplay between spontaneous decay rates and Lamb shifts in open photonic systems,” Opt. Lett. 43, 1950–1953 (2018).
[Crossref]

2017 (1)

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

2016 (2)

E. A. Muljarov and W. Langbein, “Resonant-state expansion of dispersive optical open systems: creating gold from sand,” Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

2015 (4)

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439 (2015).
[Crossref]

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17, 123008 (2015).
[Crossref]

2013 (1)

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]

2011 (1)

N. Le Thomas and R. Houdré, “Inhibited emission of electromagnetic modes confined in subwavelength cavities,” Phys. Rev. B 84, 035320 (2011).
[Crossref]

2010 (2)

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

2009 (1)

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
[Crossref]

2008 (2)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

2007 (2)

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

S. Mujumdar, A. F. Koenderink, T. Sünner, B. C. Buchler, M. Kamp, A. Forchel, and V. Sandoghdar, “Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity,” Opt. Express 15, 17214–17220 (2007).
[Crossref]

2005 (2)

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
[Crossref]

1993 (1)

O. Klein, D. M. Dressel, and G. Grüner, “Microwave cavity perturbation techniques: part I: principles,” Int. J. Infrared Millim. Waves 14, 2423–2457 (1993).
[Crossref]

1960 (1)

R. A. Waldron, “Perturbation theory of resonant cavities,” Proc. IEEE 107, 272–274 (1960).
[Crossref]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Atatüre, M.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Badolato, A.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Balet, L.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Bao, W.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Bargioni, A. W.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Bethe, H. A.

H. A. Bethe and J. Schwinger, “Perturbation theory for cavities,” (Cornell University, 1943).

Bonod, N.

Buchler, B. C.

S. Mujumdar, A. F. Koenderink, T. Sünner, B. C. Buchler, M. Kamp, A. Forchel, and V. Sandoghdar, “Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity,” Opt. Express 15, 17214–17220 (2007).
[Crossref]

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
[Crossref]

Burresi, M.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

Caselli, N.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Chang, D. E.

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17, 123008 (2015).
[Crossref]

Cluzel, B.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Colocci, M.

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

De Fornel, F.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Doeleman, H. M.

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

Dreiser, J.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Dressel, D. M.

O. Klein, D. M. Dressel, and G. Grüner, “Microwave cavity perturbation techniques: part I: principles,” Int. J. Infrared Millim. Waves 14, 2423–2457 (1993).
[Crossref]

Durt, T.

Faggiani, R.

W. Yan, R. Faggiani, and P. Lalanne, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422 (2018).
[Crossref]

Fiore, A.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Forchel, A.

Francardi, M.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Gérard, J.-M.

J.-M. Gérard, “Solid-state cavity-quantum electrodynamics with self-assembled quantum dots,” in Single Quantum Dots, Topics in Applied Physics (2003), Vol. 90, p. 269.

Gerardino, A.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Giessen, H.

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439 (2015).
[Crossref]

Goldsmith, R. H.

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Grüner, G.

O. Klein, D. M. Dressel, and G. Grüner, “Microwave cavity perturbation techniques: part I: principles,” Int. J. Infrared Millim. Waves 14, 2423–2457 (1993).
[Crossref]

Gurioli, M.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Hadji, E.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), Chap. 15.

Hendrikx, R.

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

Hennessy, K.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Heylman, K. D.

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Horak, E. H.

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Houdré, R.

N. Le Thomas and R. Houdré, “Inhibited emission of electromagnetic modes confined in subwavelength cavities,” Phys. Rev. B 84, 035320 (2011).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Hu, E.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Hughes, S.

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
[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]

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Hugonin, J.-P.

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[Crossref]

Imamoglu, A.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Intonti, F.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Johnson, S. G.

A. Oskooi and S. G. Johnson, “Electromagnetic wave source conditions,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House, 2013), Chap. 4.

Kafesaki, M.

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
[Crossref]

Kamp, M.

Kampfrath, T.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

Klein, O.

O. Klein, D. M. Dressel, and G. Grüner, “Microwave cavity perturbation techniques: part I: principles,” Int. J. Infrared Millim. Waves 14, 2423–2457 (1993).
[Crossref]

Knapper, K. A.

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Koenderink, A. F.

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

S. Mujumdar, A. F. Koenderink, T. Sünner, B. C. Buchler, M. Kamp, A. Forchel, and V. Sandoghdar, “Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity,” Opt. Express 15, 17214–17220 (2007).
[Crossref]

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
[Crossref]

Kuipers, L.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

La China, F.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Lalanne, P.

W. Yan, R. Faggiani, and P. Lalanne, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422 (2018).
[Crossref]

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439 (2015).
[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]

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Lalouat, L.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Langbein, W.

E. A. Muljarov and W. Langbein, “Resonant-state expansion of dispersive optical open systems: creating gold from sand,” Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Lassale, E.

Le Thomas, N.

N. Le Thomas and R. Houdré, “Inhibited emission of electromagnetic modes confined in subwavelength cavities,” Phys. Rev. B 84, 035320 (2011).
[Crossref]

Li, L.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Li, L. H.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Linfield, E. H.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[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]

Mesch, M.

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Monat, C.

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Mujumdar, S.

Muljarov, E. A.

E. A. Muljarov and W. Langbein, “Resonant-state expansion of dispersive optical open systems: creating gold from sand,” Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Neumeier, L.

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17, 123008 (2015).
[Crossref]

Noda, S.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), Chap. 15.

Oskooi, A.

A. Oskooi and S. G. Johnson, “Electromagnetic wave source conditions,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House, 2013), Chap. 4.

Pagliano, F.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Petroff, P. M.

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Peyrade, D.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Picard, E.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Prangsma, J. C.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

Quidant, R.

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17, 123008 (2015).
[Crossref]

Ramunno, L.

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
[Crossref]

Rea, M. T.

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Riboli, F.

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Ruesink, F.

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

Sandoghdar, V.

S. Mujumdar, A. F. Koenderink, T. Sünner, B. C. Buchler, M. Kamp, A. Forchel, and V. Sandoghdar, “Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity,” Opt. Express 15, 17214–17220 (2007).
[Crossref]

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
[Crossref]

Sauvan, C.

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[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]

Schäferling, M.

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Schwinger, J.

H. A. Bethe and J. Schwinger, “Perturbation theory for cavities,” (Cornell University, 1943).

Song, B. S.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

Stout, B.

Sünner, T.

van Oosten, D.

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

Vanga, S. K.

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Velha, P.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

Verhagen, E.

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

Vignolini, S.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Vinattieri, A.

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

Vynck, K.

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[Crossref]

Waldron, R. A.

R. A. Waldron, “Perturbation theory of resonant cavities,” Proc. IEEE 107, 272–274 (1960).
[Crossref]

Weiss, T.

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Wiersma, D. S.

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Yan, W.

W. Yan, R. Faggiani, and P. Lalanne, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422 (2018).
[Crossref]

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[Crossref]

Yang, J.

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439 (2015).
[Crossref]

Zinoni, C.

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

Adv. Mater. (1)

K. D. Heylman, K. A. Knapper, E. H. Horak, M. T. Rea, S. K. Vanga, and R. H. Goldsmith, “Optical microresonators for sensing and transduction: a materials perspective,” Adv. Mater. 29, 1700037 (2017).
[Crossref]

Int. J. Infrared Millim. Waves (1)

O. Klein, D. M. Dressel, and G. Grüner, “Microwave cavity perturbation techniques: part I: principles,” Int. J. Infrared Millim. Waves 14, 2423–2457 (1993).
[Crossref]

Laser Photon. Rev. (1)

P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, “Light interaction with photonic and plasmonic resonances,” Laser Photon. Rev. 12, 1700113 (2018).
[Crossref]

Light Sci. Appl. (1)

N. Caselli, F. Intonti, F. La China, F. Riboli, A. Gerardino, W. Bao, A. W. Bargioni, L. Li, E. H. Linfield, F. Pagliano, A. Fiore, and M. Gurioli, “Ultra-subwavelength phase-sensitive Fano-imaging of localized photonic modes,” Light Sci. Appl. 4, e326 (2015).
[Crossref]

Nano Lett. (1)

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439 (2015).
[Crossref]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

New J. Phys. (1)

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17, 123008 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (6)

E. A. Muljarov and W. Langbein, “Resonant-state expansion of dispersive optical open systems: creating gold from sand,” Phys. Rev. B 93, 075417 (2016).
[Crossref]

F. Intonti, S. Vignolini, F. Riboli, A. Vinattieri, D. S. Wiersma, M. Colocci, L. Balet, C. Monat, C. Zinoni, L. H. Li, R. Houdré, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Spectral tuning and near-field imaging of photonic crystal microcavities,” Phys. Rev. B 78, 041401 (2008).
[Crossref]

N. Le Thomas and R. Houdré, “Inhibited emission of electromagnetic modes confined in subwavelength cavities,” Phys. Rev. B 84, 035320 (2011).
[Crossref]

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. De Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B 76, 041102 (2007).
[Crossref]

L. Ramunno and S. Hughes, “Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities,” Phys. Rev. B 79, 161303 (2009).
[Crossref]

W. Yan, R. Faggiani, and P. Lalanne, “Rigorous modal analysis of plasmonic nanoresonators,” Phys. Rev. B 97, 205422 (2018).
[Crossref]

Phys. Rev. Lett. (6)

M. Burresi, T. Kampfrath, D. van Oosten, J. C. Prangsma, B. S. Song, S. Noda, and L. Kuipers, “Magnetic light-matter interactions in a photonic crystal nanocavity,” Phys. Rev. Lett. 105, 123901 (2010).
[Crossref]

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

S. Vignolini, F. Intonti, F. Riboli, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, D. S. Wiersma, and M. Gurioli, “Magnetic imaging in photonic crystal microcavities,” Phys. Rev. Lett. 105, 123902 (2010).
[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]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, “From dark to bright: first-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing,” Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

A. F. Koenderink, M. Kafesaki, B. C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904 (2005).
[Crossref]

Proc. IEEE (1)

R. A. Waldron, “Perturbation theory of resonant cavities,” Proc. IEEE 107, 272–274 (1960).
[Crossref]

Science (1)

A. Badolato, K. Hennessy, M. Atatüre, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoğlu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005).
[Crossref]

Other (8)

J.-M. Gérard, “Solid-state cavity-quantum electrodynamics with self-assembled quantum dots,” in Single Quantum Dots, Topics in Applied Physics (2003), Vol. 90, p. 269.

A. Oskooi and S. G. Johnson, “Electromagnetic wave source conditions,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House, 2013), Chap. 4.

Q-increases by modifying cavity geometry have been previously reported using slabs [16] and scatterer gratings [17] in near-fields, but not with a localized perturbation, nor with scanning through the mode to determine the relation between changes and mode distributions. Perturbations by extended structures, like slabs, have been understood as radiation pattern engineering to control.

QNMEig and companion Matlab Toolboxes are available on the webpage of L. Lalanne.

https://www.comsol.com/ (Version 5.2a).

The present theory is derived for isotropic and non-magnetic perturbers for the sake of simplicity, but these assumptions can be easily removed.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006), Chap. 15.

H. A. Bethe and J. Schwinger, “Perturbation theory for cavities,” (Cornell University, 1943).

Supplementary Material (1)

NameDescription
» Supplement 1       supplement

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 (3)

Fig. 1.
Fig. 1. Experimental results. (a) Sketch of the PhC cavity. (b) Wavelength-shift map as the tip is scanned over the cavity, with superimposed holes. (c) Photoluminescence recorded for three tip positions, A, B, and C shown in (a). Curves are Lorentzian fits of the data small points. The black and red points are blue-shifted by 0.05 and 0.08 nm to ease the visual comparison for cavity Q ’s. (d) Perturbation-induced Q map. (e)  Q as a function of the offset distance z d min between the tip and the PhC membrane. Conclusively, the same tip may either enhance or decrease the intrinsic Q = 2300 ± 40 , depending on its position. The PhC parameters are lattice period a = 331 nm , hole diameter 206 nm , and GaAs-membrane thickness 320 nm.
Fig. 2.
Fig. 2. Numerical test of Eq. (2) for the cavity used in the experiment. (a) Maps of | E ˜ | 2 . (b) Comparison between the Δ Q maps predicted with Eq. (2) (left) and exact values (right) for α = 166 α 0 . (c) Validity of Eq. (2) for increasing values of the polarizability and for the three tip positions, A, B, and C, used in the experiment. α 0 denotes the static polarizability of a 10-nm-radius silica sphere in air, so that the full horizontal scale covers silica spheres with radii from 10 to 70 nm. Note that Eq. (1) predicts Δ Q = 0 for all positions and all α . In (b) and (c), the point-dipole perturber is assumed to be located in a plane 30 nm above the semiconductor PhC membrane, and the exact values are computed by iteratively searching the complex-frequency pole of Eq. (4) for E b = 0 with the regularized scattering tensor Δ G ( r , r , ω ) computed with COMSOL Multiphysics [27].
Fig. 3.
Fig. 3. Maps of (a)  Re ( V ˜ 1 ) and (b)  Im ( V ˜ 1 ) computed with the QNM solver 30 nm above the semiconductor membrane (bottom) and directly inferred from the Δ ω ˜ measurements using Eq. (2) with a tip polarizability α tip = 166 α 0 (top). Note that the experimental values are all rescaled by a factor of ¼.

Equations (4)

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

Δ ω ˜ ω ˜ α ε ( r 0 ) | E ˜ ( r 0 ) | 2 [ ε | E ˜ | 2 + μ 0 | H ˜ | 2 ] d 3 r α 2 V ( r 0 ) ,
Δ ω ˜ ω ˜ α ε ( r 0 ) E ˜ 2 [ ε E ˜ 2 μ 0 H ˜ 2 ] d 3 r α 2 V ˜ ( r 0 ) .
p = α ( ω ) { E b + μ 0 ω 2 Δ G ( r 0 , r 0 , ω ) p } ,
Δ G ( r , r , ω ) = ω ˜ E ˜ N ( r ) E ˜ N ( r ) μ 0 ω 2 ( ω ω ˜ ) + δ G ( r , r , ω ) ,

Metrics