## Relation between near–field and far–field properties of plasmonic Fano resonances |

Optics Express, Vol. 19, Issue 22, pp. 22167-22175 (2011)

http://dx.doi.org/10.1364/OE.19.022167

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### Abstract

The relation between the near–field and far–field properties of plasmonic nanostructures that exhibit Fano resonances is investigated in detail. We show that specific features visible in the asymmetric lineshape far–field response of such structures originate from particular polarization distributions in their near–field. In particular we extract the central frequency and width of plasmonic Fano resonances and show that they cannot be directly found from far–field spectra. We also address the effect of the modes coupling onto the frequency, width, asymmetry and modulation depth of the Fano resonance. The methodology described in this article should be useful to analyze and design a broad variety of Fano plasmonic systems with tailored near–field and far–field spectral properties.

© 2011 OSA

## 1. Introduction

2. U. Fano, “Effects of configuration interaction on
intensities and phase shifts,” Phys.
Rev. **124**, 1866 (1961). [CrossRef]

3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic
nanostructures and metamaterials,” Nat.
Mater. **9**, 707–715
(2010). [CrossRef]

4. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale
structures,” Rev. Mod. Phys. **82**, 2257–2298
(2010). [CrossRef]

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

12. Z.-J. Yang, Z.-S. Zhang, L.-H. Zhang, Q.-Q. Li, Z.-H. Hao, and Q.-Q. Wang, “Fano resonances in dipole-quadrupole
plasmon coupling nanorod dimers,” Opt.
Lett. **36**, 1542–1544
(2011). [CrossRef] [PubMed]

## 2. Results and discussion

3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic
nanostructures and metamaterials,” Nat.
Mater. **9**, 707–715
(2010). [CrossRef]

*ω*: where

*a*is the maximum amplitude of the resonance,

*ω*the resonance frequency and

_{s}*W*its spectral width for

_{s}*W*≪

_{s}*ω*. Contrary to a quantum mechanical formulation, the electromagnetic modes’ eigenvalues are expressed in eV

_{s}^{2}and their resonance shape are expressed as function of

*ω*

^{2}(see for instance Eq. (1) in Ref. [13

13. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in
plasmonic nanostructures and metamaterials,”
Phys. Rev. B **83**, 235427 (2011). [CrossRef]

3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic
nanostructures and metamaterials,” Nat.
Mater. **9**, 707–715
(2010). [CrossRef]

14. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic
metamaterial at optical wavelength,” Nano
Lett. **8**, 2171–2175
(2008). [CrossRef] [PubMed]

15. N. Verellen, P. Van Dorpe, D. Vercruysse, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Dark and bright localized surface
plasmons in nanocrosses,” Opt.
Express **19**, 11034–11051
(2011). [CrossRef] [PubMed]

13. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in
plasmonic nanostructures and metamaterials,”
Phys. Rev. B **83**, 235427 (2011). [CrossRef]

*ω*is the central spectral position,

_{a}*W*the spectral width for

_{a}*W*≪

_{a}*ω*,

_{a}*q*the asymmetry parameter introduced by Fano in his quantum theory [2

2. U. Fano, “Effects of configuration interaction on
intensities and phase shifts,” Phys.
Rev. **124**, 1866 (1961). [CrossRef]

*b*the modulation damping parameter appearing with intrinsic losses. Note that Eq. (2) is a generalization of the original Fano formula for systems with losses, such as plasmonic materials [13

13. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in
plasmonic nanostructures and metamaterials,”
Phys. Rev. B **83**, 235427 (2011). [CrossRef]

*q*= 0, the lineshape of Eq. (2) becomes the one of an antiresonance centered around

*ω*with minimum value

_{a}*b*and width

*W*. As the absolute value of the asymmetry parameter

_{a}*q*increases, the lineshape of Eq. (2) becomes comparable to a lorentzian profile (

*q*= ±∞). Equation (2) with constant parameters is valid in a small frequency interval around the frequency of a single resonant dark mode, and assumes that the dark mode’s spectral width is smaller than the bright mode’s spectral width [13

**83**, 235427 (2011). [CrossRef]

*R*[Eq. (1)] modulated by

_{b}*σ*[Eq. (2)]: Let us now discuss the validity of Eq. (3). If two dark modes interact with the same continuum but their respective asymmetric lineshapes do not spectrally overlap, Eq. (3) becomes the product of the background resonance

*R*with two independant lineshapes

_{b}*σ*and

*σ*′. For the case of two bright modes, where one does not interact with the dark mode, the additional bright mode alters the total reflectance

*R*. The approach shown here is therefore valid only for a single bright and a single dark mode that are spectrally and spatially overlapping, and requires a preliminary insight into the eigenmode spectrum of the structure, as shown in Figure 2 of Ref. [13

**83**, 235427 (2011). [CrossRef]

16. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in
metamaterials,” Phys. Rev. Lett. **101**, 047401 (2008). [CrossRef] [PubMed]

17. N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent
plasmonic nanocavities,” Nano Lett. **9**, 1663–1667
(2009). [CrossRef] [PubMed]

*ω*, the bright mode of the single beam is resonantly excited. The dark mode is perturbed by the coupling to the bright mode and resonates at a frequency

_{s}*ω*slightly detuned from its original resonance frequency, and the width of this resonance is determined by both the modes coupling and intrinsic losses [13

_{a}**83**, 235427 (2011). [CrossRef]

*ω*= 1.37 × 10

_{p}^{16}s

^{−1}and damping

*γ*= 1.23 × 10

^{14}s

^{−1}, which corresponds to the dielectric permittivity of gold. The black dashed line in Fig. 1(b) shows the reflectance spectrum of the array under normal illumination, calculated using the surface integral method [18

18. B. Gallinet and O. J. F. Martin, “Scattering on plasmonic nanostructures
arrays modeled with a surface integral formulation,”
Photon. Nanostruct. **8**, 278–284
(2010). [CrossRef]

19. B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of
electromagnetic scattering on periodic nanostructures with a surface
integral approach,” J. Opt. Soc. Am.
A **27**, 2261–2271
(2010). [CrossRef]

*a*< 1 is imposed in order to fulfill energy conservation. The fit parameters are

*a*= 1.00,

*ω*= 1.29 eV,

_{s}*W*= 0.12 eV,

_{s}*ω*= 1.08 eV,

_{a}*W*= 0.03 eV,

_{a}*q*= −0.96,

*b*= 0.34, and the corresponding curve is drawn as a solid red line in Fig. 1(b). In Fig. 2(a), the same geometry and illumination conditions are considered, but for a single dolmen instead of an array. Due to retardation effect, the quadrupolar mode can be excited from the far–field at grazing incidence [17

17. N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent
plasmonic nanocavities,” Nano Lett. **9**, 1663–1667
(2009). [CrossRef] [PubMed]

*a*= 2.63,

*ω*= 1.33 eV,

_{s}*W*= 0.10 eV,

_{s}*ω*= 0.98 eV,

_{a}*W*= 0.05 eV,

_{a}*q*= −1.83,

*b*= 1.80) is not as satisfying as the fit of Fig. 2(b) (with parameters

*a*= 1.00,

*ω*= 1.29 eV,

_{s}*W*= 0.03 eV,

_{s}*ω*= 1.00 eV,

_{a}*W*= 0.03 eV,

_{a}*q*= −3.88,

*b*= 3.75) or the fit of Fig. 1(b). In a periodic array, near–field interactions between nearest neighbors have to be taken into account, as will be seen later.

19. B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of
electromagnetic scattering on periodic nanostructures with a surface
integral approach,” J. Opt. Soc. Am.
A **27**, 2261–2271
(2010). [CrossRef]

21. A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules
near realistic plasmonic nanostructures,”
Nano Lett. **11**, 482–487
(2011). [CrossRef] [PubMed]

*ω*found from the fit in Fig. 1(b). The points of maximal near-field enhancement are located at (

_{a}*x,z*) = (±80,0)nm, i.e. at the two top interior corners of the beam pair [Fig. 1(d)]. Figures 1(d) to (f), which show the normalized intensity enhancement and the corresponding polarization charges through the structure, indicate that the quadrupolar mode of the double beam structure is resonantly excited at

*ω*. The second peak in Fig. 1(c) corresponds to the excitation of the bright mode. The maximum intensity enhancement is found at 1.29 eV, which also corresponds exactly to its resonance frequency

_{a}*ω*found from the fit in Fig. 1(b). The maximum intensity enhancement observed at

_{s}*ω*is about 2.3 times the maximum intensity enhancement observed for the excitation of the bright mode at

_{a}*ω*. This significant near–field enhancement originates from the fact that the dark mode does not suffer from radiative losses and is therefore able to store a larger amount of electromagnetic energy than the bright mode. Figure 1(e) also shows that the phase of the instantaneous electric field switches by

_{s}*π*around

*ω*. Two pathways have to be considered in the excitation from the far–field: the direct excitation of the bright mode and the excitation of the dark mode through its coupling to the bright mode. These two pathways interfere to produce the asymmetric lineshape observed in Fig. 1(b) around

_{a}*ω*(Eq. (22) of [13

_{a}**83**, 235427 (2011). [CrossRef]

*q*parameter, while the modulation damping by intrinsic losses is described by the

*b*parameter. The latter prevents the reflectance spectrum to reach zero values and can be understood as the ratio of the energy that is lost in heat to the metallic structure, to the energy that is transferred from the continuum to the dark mode (see Section IV of [13

**83**, 235427 (2011). [CrossRef]

*ω*. This shows that locating the central resonance frequency

_{s}*ω*is a critical point for applications such as refractive index sensing or lasing [3

_{a}**9**, 707–715
(2010). [CrossRef]

22. D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplification by
Stimulated Emission of Radiation: Quantum Generation of Coherent Surface
Plasmons in Nanosystems,” Phys. Rev.
Lett. **90**, 027402 (2003). [CrossRef] [PubMed]

23. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,”
Nat. Photonics **2**, 351–354
(2008). [CrossRef]

14. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic
metamaterial at optical wavelength,” Nano
Lett. **8**, 2171–2175
(2008). [CrossRef] [PubMed]

*a*= 0.84,

*ω*= 1.88 eV,

_{s}*W*= 0.37 eV,

_{s}*ω*= 1.38 eV,

_{a}*W*= 0.13 eV,

_{a}*q*= 0.66, and

*b*= 0.27. The electric field is sampled at each frequency on a 1 nm homogeneous grid of positions at 1 nm from the nanostructures surface. The maximal electric field intensity for each frequency is then reported in Fig. 3(b). The maximal intensity in the spectrum of Fig. 3(b) is fitted with a lorentzian profile similar to Eq. (1). Its central frequency is found at approximately 1.39 eV and has a width of 0.06 eV. These values agree well with the values of

*ω*and

_{a}*W*found from the fit of Fig. 3(a). At this frequency, the maximum intensity enhancement is about 16 times the one observed for the excitation of the bright mode at

_{a}*ω*. This lets us conclude that the dark mode is resonantly excited at this frequency. The near-field distribution in Fig. 3(c) also indicates a quadrupolar charges configuration in the structure at

_{s}*ω*. The points of maximal near-field enhancement are located at (

_{a}*x,z*) = (±50,14)nm, i.e. at the two bottom corners of the top nanoparticle. Let us emphasize that it is not possible to determine

*a priori*the resonance frequency

*ω*from a Fano resonance spectrum such as the black dashed curve in Fig. 1(b) or in Fig. 3(a), since its shape is determined by many parameters and

_{a}*ω*does not correspond to a specific point in the spectrum (for instance a local minimum or maximum). However, the fit with Eq. (3) is able to extract

_{a}*ω*easily, without detailed knowledge of the near–field interactions.

_{a}*ω*. The same procedure as in Fig. 1 is repeated for this structure. The fit parameters are now

_{s}*a*= 1.00,

*ω*= 1.25 eV,

_{s}*W*= 0.12 eV,

_{s}*ω*= 1.55 eV,

_{a}*W*= 0.02 eV,

_{a}*q*= 1.30, and

*b*= 0.15. The asymmetric resonance appears now on the other shoulder of the bright mode’s resonance, compare Fig. 1(b) and Fig. 4(b). The shift in the modes frequency is a function of their spectral detuning. As a result, the resonance frequency of the bright mode red shifts from 1.38 eV to 1.25 eV. Since the asymmetry parameter depends on the frequency difference

**83**, 235427 (2011). [CrossRef]

*ω*in this configuration. The resonance is now at a higher frequency than the dip’s frequency, because the asymmetry parameter is positive. The absolute value of

_{a}*q*is larger than in the case of Fig. 1, which pushes the resonance frequency towards the second reflectance peak (Fig. 1 in Ref. [2

2. U. Fano, “Effects of configuration interaction on
intensities and phase shifts,” Phys.
Rev. **124**, 1866 (1961). [CrossRef]

*x,z*) = (±161,100)nm, i.e. at the two exterior bottom corners of the beam pair. A phase shift of the dark mode similar to the case of Fig. 1 occurs in a frequency region around

*ω*[Fig. 4(e)]. The first peak in Fig. 4(c) is attributed to the bright mode’s excitation and is centered around 1.25 eV, in agreement with the value

_{a}*ω*= 1.25 eV found from the fit.

_{s}16. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in
metamaterials,” Phys. Rev. Lett. **101**, 047401 (2008). [CrossRef] [PubMed]

17. N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent
plasmonic nanocavities,” Nano Lett. **9**, 1663–1667
(2009). [CrossRef] [PubMed]

**83**, 235427 (2011). [CrossRef]

*b*giving the ratio between the power lost in the metallic structure and the power transferred from the bright mode to the dark mode. The near–field intensity enhancement maps in Figs. 1 and 4 indicate that the most efficient way to change the coupling is by tuning the gap size

*g*between the single beam and the pair of parallel beams, Fig. 5. For high coupling, in the spectral minimum in the reflectance response, the Fano interference opens a narrow transparency window for the incoming light, whose magnitude depends on the

*b*parameter. As

*g*increases, the coupling between the two modes decreases, the

*b*parameter drastically increases and the resonance modulation depth is reduced. As a result, the reflectance of the system approaches that of the bright mode alone [Fig. 5(a)]. This effect appears only in the presence of intrinsic losses and goes along with a reduction of the absolute value of the asymmetry parameter (from −1.68 for

*g*= 15 nm to −0.21 for

*g*= 50 nm). As the coupling decreases, the resonance becomes more symmetric and its frequency shifts towards the reflectance dip. In addition, the resonance frequency blue shifts, and converges to the non–perturbed resonance frequency of the dark mode [13

**83**, 235427 (2011). [CrossRef]

*ω*extracted from a fit with Eq. (3); this frequency is indicated by a red dot in panel (a). The correlation between near–field and far–field is also verified in this case: as the two modes decouple, the power transfer between the two parallel beams and the third becomes less effective. This results in a decrease of the field intensity in the two parallel beams, leading finally to field enhancement solely at the extremities of the single beam, when both structures are decoupled and the Fano resonance has disappeared,

_{a}*g*≃ 60 nm (Fig. 5). As mentioned previously, the structures are placed in an array to ensure that the quadrupolar mode is a true dark mode. Although its subwavelength character does not produce grating effects, this configuration is accompanied by strong near–field interactions between nearest neighbors. The gap size of

*g*=60 nm in Fig. 5 leading to a complete vanishing of the Fano resonance corresponds to a configuration for which the dipolar beam is placed at the same distance from its two adjacent beam pairs, i.e. to a configuration for which the array has a

*y*= 0 symmetry plane. Moving the dipolar bar from this position induces the symmetry breaking required for the excitation of the dark mode, which explains the high sensitivity of the resonance lineshape to the gap size

*g*.

## 3. Conclusion

## Acknowledgments

## References and links

1. | U. Fano, “Effects of configuration interaction on
intensities and phase shifts,” Citations
Classics |

2. | U. Fano, “Effects of configuration interaction on
intensities and phase shifts,” Phys.
Rev. |

3. | B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic
nanostructures and metamaterials,” Nat.
Mater. |

4. | A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale
structures,” Rev. Mod. Phys. |

5. | E. Prodan, C. Radloff, N. Halas, and P. Nordlander, “A hybridization model for the plasmon
response of complex nanostructures,”
Science |

6. | A. Christ, Y. Ekinci, H. H. Solak, N. A. Gippius, S. G. Tikhodeev, and O. J. F. Martin, “Controlling the Fano interference in a
plasmonic lattice,” Phys. Rev. B |

7. | N. A. Mirin, K. Bao, and P. Nordlander, “Fano Resonances in Plasmonic
Nanoparticle Aggregates,” J. Phys. Chem.
A |

8. | N. Liu, L. Langguth, T. Weiss, J. Kaestel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of
electromagnetically induced transparency at the drude damping
limit,” Nat. Mater. |

9. | J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle
clusters,” Science |

10. | K. Bao, N. A. Mirin, and P. Nordlander, “Fano resonances in planar silver
nanosphere clusters,” Appl. Phys. A, Mater.
Sci. Process. |

11. | Y. Sonnefraud, N. Verellen, H. Sobhani, G. A. E. Vandenbosch, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Experimental realization of subradiant,
superradiant, and fano resonances in ring/disk plasmonic
nanocavities,” ACS Nano |

12. | Z.-J. Yang, Z.-S. Zhang, L.-H. Zhang, Q.-Q. Li, Z.-H. Hao, and Q.-Q. Wang, “Fano resonances in dipole-quadrupole
plasmon coupling nanorod dimers,” Opt.
Lett. |

13. | B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in
plasmonic nanostructures and metamaterials,”
Phys. Rev. B |

14. | A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic
metamaterial at optical wavelength,” Nano
Lett. |

15. | N. Verellen, P. Van Dorpe, D. Vercruysse, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Dark and bright localized surface
plasmons in nanocrosses,” Opt.
Express |

16. | S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in
metamaterials,” Phys. Rev. Lett. |

17. | N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent
plasmonic nanocavities,” Nano Lett. |

18. | B. Gallinet and O. J. F. Martin, “Scattering on plasmonic nanostructures
arrays modeled with a surface integral formulation,”
Photon. Nanostruct. |

19. | B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of
electromagnetic scattering on periodic nanostructures with a surface
integral approach,” J. Opt. Soc. Am.
A |

20. | A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D
simulations of plasmonic and high permittivity
nanostructures,” J. Opt. Soc. Am. A |

21. | A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules
near realistic plasmonic nanostructures,”
Nano Lett. |

22. | D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplification by
Stimulated Emission of Radiation: Quantum Generation of Coherent Surface
Plasmons in Nanosystems,” Phys. Rev.
Lett. |

23. | N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,”
Nat. Photonics |

24. | P. B. Johnson and R. W. Christy, “Optical-constants of
noble-metals,” Phys. Rev. B |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(260.5740) Physical optics : Resonance

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Plasmonics

**History**

Original Manuscript: July 27, 2011

Revised Manuscript: September 16, 2011

Manuscript Accepted: October 14, 2011

Published: October 24, 2011

**Virtual Issues**

Collective Phenomena (2011) *Optics Express*

**Citation**

Benjamin Gallinet and Olivier J. F. Martin, "Relation between near–field and far–field properties of plasmonic Fano resonances," Opt. Express **19**, 22167-22175 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-22167

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### References

- U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Citations Classics27, 219 (1977).
- U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124, 1866 (1961). [CrossRef]
- B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9, 707–715 (2010). [CrossRef]
- A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82, 2257–2298 (2010). [CrossRef]
- E. Prodan, C. Radloff, N. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302, 419–422 (2003). [CrossRef] [PubMed]
- A. Christ, Y. Ekinci, H. H. Solak, N. A. Gippius, S. G. Tikhodeev, and O. J. F. Martin, “Controlling the Fano interference in a plasmonic lattice,” Phys. Rev. B76, 201405 (2007).
- N. A. Mirin, K. Bao, and P. Nordlander, “Fano Resonances in Plasmonic Nanoparticle Aggregates,” J. Phys. Chem. A113, 4028–4034 (2009). [CrossRef] [PubMed]
- N. Liu, L. Langguth, T. Weiss, J. Kaestel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater.8, 758–762 (2009). [CrossRef] [PubMed]
- J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science328, 1135–1138 (2010). [CrossRef] [PubMed]
- K. Bao, N. A. Mirin, and P. Nordlander, “Fano resonances in planar silver nanosphere clusters,” Appl. Phys. A, Mater. Sci. Process.100, 333–339 (2010). [CrossRef]
- Y. Sonnefraud, N. Verellen, H. Sobhani, G. A. E. Vandenbosch, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Experimental realization of subradiant, superradiant, and fano resonances in ring/disk plasmonic nanocavities,” ACS Nano4, 1664–1670 (2010). [CrossRef] [PubMed]
- Z.-J. Yang, Z.-S. Zhang, L.-H. Zhang, Q.-Q. Li, Z.-H. Hao, and Q.-Q. Wang, “Fano resonances in dipole-quadrupole plasmon coupling nanorod dimers,” Opt. Lett.36, 1542–1544 (2011). [CrossRef] [PubMed]
- B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B83, 235427 (2011). [CrossRef]
- A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8, 2171–2175 (2008). [CrossRef] [PubMed]
- N. Verellen, P. Van Dorpe, D. Vercruysse, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Dark and bright localized surface plasmons in nanocrosses,” Opt. Express19, 11034–11051 (2011). [CrossRef] [PubMed]
- S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008). [CrossRef] [PubMed]
- N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett.9, 1663–1667 (2009). [CrossRef] [PubMed]
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