## Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface

Optics Express, Vol. 16, Issue 12, pp. 8570-8580 (2008)

http://dx.doi.org/10.1364/OE.16.008570

Acrobat PDF (1280 KB)

### Abstract

We investigate the dispersion relation and extinction properties of surface plasmons in an array of gold nanoparticle chains under s-polarized plane wave excitations, through experiment and simulation. Our results reveal that the dispersion and extinction properties of gold nanoparticle chains at an air/glass interface are significantly different from those in a uniform medium. Under total internal reflection, the dispersion is much larger than that above total internal reflection and 100% extinction can be reached. We show that the large dispersion under total internal reflection can be explained by dipole fields and coupling at the air/glass interface.

© 2008 Optical Society of America

## 1. Introduction

1. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. **23**, 1331–1333 (1998). [CrossRef]

4. N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. **82**, 3095–3097 (2003). [CrossRef]

2. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B **62**, R16356–16359 (2000). [CrossRef]

13. W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B **70**, 125429 (2004). [CrossRef]

5. J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. **82**, 2590–2593 (1999). [CrossRef]

12. E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography,” Nano Lett. **5**, 1065–1070 (2005). [CrossRef] [PubMed]

17. J. Sung, E. M. Hicks, R. P. Van Duyne, and K. G. Spears, “Nanoparticle Spectroscopy: Dipole Coupling in Two-Dimensional Arrays of L-shaped Silver Nanoparticles,” J. Phys. Chem. C **111**, 10368–10376 (2007). [CrossRef]

18. P. Ghenuche, I. G. Cormack, G. Badenes, P. Loza-Alvarez, and R. Quidant, “Cavity resonances in finite plasmonic chains,” Appl. Phys. Lett. **90**, 041109 (2007). [CrossRef]

19. K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express **15**, 17482–17493 (2007). [CrossRef] [PubMed]

2. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B **62**, R16356–16359 (2000). [CrossRef]

13. W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B **70**, 125429 (2004). [CrossRef]

## 2. Experiments

19. K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express **15**, 17482–17493 (2007). [CrossRef] [PubMed]

_{x}values. k

_{x}was the wave vector component along the direction of the chains. The inset of Fig. 2(a) is a schematic diagram of the experiment and also gives the definition of x, y and z directions in this paper. Details of the experiment were similar to that of Ref [19

19. K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express **15**, 17482–17493 (2007). [CrossRef] [PubMed]

**15**, 17482–17493 (2007). [CrossRef] [PubMed]

_{x}values for the full range of incidence angles, i.e., above the light line of glass. The green points are the numerical results. The resonance frequencies were taken from the positions of the minima of the transmission spectra for incidence angles above the TIR regime and from the positions of the minima of the reflection spectra for incidence angles within the TIR regime. To mitigate against the effects of experimental noise, we fit each spectrum with a fifth order polynomial near the resonance frequency before finding the minimum. It is worth mentioning that that we took the minima of the spectra at each angle instead of the minima of the spectra at each k

_{x}value. This was due to the consideration that, at a constant incident illuminating power, the amplitude of the electric field at an air/glass interface changes significantly with the incidence angle near and inside the TIR regime, as shown in Fig. 4. Therefore, the coupling between the illuminating beam and the surface plasmon mode at a constant k

_{x}value will change with frequency as the incidence angle changes and consequently shift the minimum position of a fixed k

_{x}spectrum away from the actual resonance frequency by a considerable amount. Although by extracting the minima from spectra with fixed incidence angles we were actually comparing surface plasmon modes with different k

_{x}values, this method more closely indicates where the resonances are positioned. A distinctive feature of the dispersion relation in Fig. 3 is that the dispersion is much larger within the TIR regime. We discuss our interpretation of this phenomenon with the aid of numerical simulations in the following sections of this paper.

## 3. Numerical simulations

_{x}value, with a periodic boundary condition applied along the x axis and a symmetric boundary condition applied along the y axis. Therefore, the launch was composed of plane wave components within a range of frequencies, the launching angle of each plane wave component determined by its frequency and k

_{x}values. Perfectly Matched Layers (PML) were applied at the top and bottom z-boundaries of the unit cell simulation domain to absorb the transmitted and reflected electromagnetic waves. The transmitted power was found from 1/2 Re(E

_{y}H

_{x}

^{*}), where E and H monitors were placed on the air side. The reflected power was found from -1/2 Re(E

_{y}H

_{x}

^{*}), where E and H monitors were placed on the glass side. E and H were Fourier Transforms of the time domain electromagnetic field values. To find the reflected E and H fields, we subtracted the incident fields from the total fields. Because only the fundamental scattering mode exists for the frequency range of interest in the far field, the transmitted and reflected powers can be determined from field monitor points on the air and glass sides, respectively. There is therefore no need to integrate the Poynting vector over a surface in the x–y plane in our case. In each simulation, the transmission and reflection coefficients over a range of frequencies and at one k

_{x}value were obtained. Multiple simulations were done to obtain results for all the k

_{x}values of interest. The transmission and reflection coefficients at an arbitrary angle were then obtained by linear interpolations of the transmission and reflection coefficients at the same frequency and the nearest k

_{x}values. In our simulation, we have simulated k

_{x}values with an interval of 0.2π/µm.

_{y}H

_{x}

^{*}) as -1/2 η|H

_{x}|

^{2}/cos(θ), where η was the characteristic impedance of electromagnetic waves in glass. For an s-polarized plane wave at an incidence angle θ, H

_{x}=H cos(θ) approaches 0 as θ approaches 90°, while E

_{y}=E does not change with θ. Therefore, the Fourier Transform of the time domain H

_{x}values suffered much less from the bouncing wave components with large θ values than the Fourier Transform of E

_{y}. This method was found to be effective at reducing the effects of the unphysical wave components that bounced between the glass side PML and the air/glass interface due to TIR.

_{y}H

_{x}

^{*}) for the transmitted power instead of 1/2 η|H

_{x}|

^{2}/cos(θ) because H

_{x}was non-zero for the evanescent waves on the air side. Part of these evanescent waves on the air side was from the large angle bouncing waves on the glass side and did not disappear with time efficiently. This problem did not present itself for the reflected power.

^{-32}. The simulation time was 100 µm/c, where c is the speed of light in vacuum.

21. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. **37**, 5271–5283 (1998). [CrossRef]

_{x}values. The extinction was found from (1 - transmission - reflection), which is equal to the ohmic absorption. Large differences in dispersion and extinction are clearly present between the above and within TIR regimes. In the TIR regime, the extinction at resonance can reach almost 100%, which means an efficient excitation of surface plasmons. This originates from destructive interference between the surface plasmon radiation and the illuminating plane wave’s reflection, which leads to critical coupling condition between the surface plasmon mode and the TIR plane wave mode. Although there is no radiation loss at a 100% extinction, the linewidth of the resonance spectrum still contains the contribution from radiation, or coupling between the surface plasmon and the TIR plane wave. Efficient excitation is important for some plasmonic devices [22].

## 4. Explanation of dispersion relation

2. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B **62**, R16356–16359 (2000). [CrossRef]

13. W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B **70**, 125429 (2004). [CrossRef]

15. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B **74**, 033402 (2006). [CrossRef]

**70**, 125429 (2004). [CrossRef]

15. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B **74**, 033402 (2006). [CrossRef]

**70**, 125429 (2004). [CrossRef]

15. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B **74**, 033402 (2006). [CrossRef]

23. W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. **67**, 1607–1615 (1977). [CrossRef]

_{y}and changes with frequency and k

_{x}. We see from Fig. 7 that the E

_{y}pattern along the air/glass interface has both the periodicity of the wavelength in air and the periodicity of the wavelength in glass. Figure 8(a) shows the amplitude and phase of E

_{y}along x-axis at the air/glass interface. Figure 8(b) shows the amplitude and phase of E

_{y}along x-axis for the same line of dipoles but in a uniform glass environment for comparison with Fig. 8(a). We see that the field along an air/glass interface decays faster than in a uniform dielectric environment.

_{y}values of (…, E

_{-1}, E

_{0}, E

_{1}, E

_{2}, …) at x=(…, -140 nm, 0 nm, 140 nm, 280 nm, …) on the x-axis. The induced surface plasmon dipole in nanoparticle line 0 through coupling to surface plasmon dipole fields from the other nanoparticle lines is P

_{indu}=α E

_{indu}, where α is the polarizability of a single line of nanoparticles, and E

_{indu}is a sum of E

_{y}field values at the origin from all the other nanoparticle lines. When the in-plane wave vector is k

_{x}, we have

_{indu}has a positive real part, it is in phase with the point dipoles in line 0 and decreases the restoring force on the surface plasmon, which results in a red shift of the surface plasmon resonance; for the same reason, when E

_{indu}has a negative real part, there will be a blue shift of the surface plasmon resonance.

_{indu}at a single frequency of 1.6 c/µm for k

_{x}values in the first irreducible Brillouin Zone found from Equation (1) and the calculations plotted as Fig. 8. The k

_{x}interval between the nearest points in Fig. 9 is a constant. In this calculation we summed up 71 E

_{y}values on the second line of equation (1) which corresponds to a 10 µm long simulation domain on one side of line 0, as shown in Fig. 7 and 8. From Fig. 9(b), we see that E

_{indu}in a uniform dielectric environment has a sharp and large amplitude peak at the light line. If we assume that the dipole fields vary as exp[i(-ωt+kx)], then the dipole lines interfere constructively at the light line of glass through the first term of the second line of Equation (1). This results in the large amplitude peak. The abrupt change of E

_{indu}across the light line of glass is qualitatively consistent with the theoretical calculations of dispersion relations in refs [13

**70**, 125429 (2004). [CrossRef]

**74**, 033402 (2006). [CrossRef]

_{indu}of point dipole lines at an air/glass interface is different. For the uniform glass environment case in Fig. 9(b), E

_{indu}undergoes an abrupt change across the lightline; while for the air/glass interface case in Fig. 9(a), the abrupt change in E

_{indu}across the light line for the uniform glass environment case is expanded to a fast change across the whole TIR regime. The fast change of the real part of E

_{indu}in the TIR regime indicates a corresponding large dispersion, which is consistent with our experimental and simulation results. We have found that in the TIR regime, the value of E

_{indu}is also predominantly determined by the first term on the second line of equation (1), which is similar to constructive interference as what occurs at the light line for the uniform glass environment case.

## 5. Summary

## Acknowledgments

## References and links

1. | M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. |

2. | M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B |

3. | S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. |

4. | N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, “Optimized surface-enhanced Raman scattering on gold nanoparticle arrays,” Appl. Phys. Lett. |

5. | J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. |

6. | B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance,” Phys. Rev. Lett. |

7. | S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B |

8. | S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss,” Appl. Phys. Lett. |

9. | Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, “Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains,” Nano Lett. |

10. | C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, “Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays,” Phys. Chem. B |

11. | S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. |

12. | E. M. Hicks, S. Zou, G. C. Schatz, K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, “Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography,” Nano Lett. |

13. | W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B |

14. | S. Y. Park and D. Stroud, “Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation,” Phys. Rev. B |

15. | A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B |

16. | A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B |

17. | J. Sung, E. M. Hicks, R. P. Van Duyne, and K. G. Spears, “Nanoparticle Spectroscopy: Dipole Coupling in Two-Dimensional Arrays of L-shaped Silver Nanoparticles,” J. Phys. Chem. C |

18. | P. Ghenuche, I. G. Cormack, G. Badenes, P. Loza-Alvarez, and R. Quidant, “Cavity resonances in finite plasmonic chains,” Appl. Phys. Lett. |

19. | K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express |

20. | A. Taflove and S. C. Hagness, |

21. | A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. |

22. | J. Lu, C. Petre, J. Conway, and E. Yablonovitch, “Numerical optimization of a grating coupler for the efficient excitation of surface plasmons at an Ag-SiO |

23. | W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. |

24. | W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. Radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am. |

25. | W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation,” J. Opt. Soc. Am. |

26. | J. Mertz, “Radiative absorption, fluorescence, and scattering of a classical dipole near a lossless interface: a unified description,” J. Opt. Soc. Am. B |

27. | S. J. Radzeviciusa, C.-C. Chenb, L. Peters Jr., and J. J. Daniels, “Near-field dipole radiation dynamics through FDTD modeling,” J. Appl. Geophys. |

28. | L. Luan, P. R. Sievert, and J. B. Ketterson, “Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space,” New J. Phys. |

29. | L. Novotny L. and B. Hecht, |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(290.5820) Scattering : Scattering measurements

(230.4555) Optical devices : Coupled resonators

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: May 16, 2008

Manuscript Accepted: May 20, 2008

Published: May 27, 2008

**Virtual Issues**

Vol. 3, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Tian Yang and Kenneth B. Crozier, "Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface," Opt. Express **16**, 8570-8580 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8570

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### References

- M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333 (1998). [CrossRef]
- M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-16359 (2000). [CrossRef]
- S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003). [CrossRef]
- N. Félidj, J. Aubard, G. Lévi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R. Aussenegg, "Optimized surface-enhanced Raman scattering on gold nanoparticle arrays," Appl. Phys. Lett. 82, 3095-3097 (2003). [CrossRef]
- J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, and J. P. Goudonnet, "Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles," Phys. Rev. Lett. 82, 2590-2593 (1999). [CrossRef]
- B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, "Metal Nanoparticle Gratings: Influence of Dipolar Particle Interaction on the Plasmon Resonance," Phys. Rev. Lett. 84, 4721-4724 (2000). [CrossRef] [PubMed]
- S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408 (2002). [CrossRef]
- S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002). [CrossRef]
- Q.-H. Wei, K.-H. Su, S. Durant, and X. Zhang, "Plasmon Resonance of Finite One-Dimensional Au Nanoparticle Chains," Nano Lett. 4, 1067-1071 (2004). [CrossRef]
- Q1. C. L. Haynes, A. D. McFarland, L. L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. J. Kall, "Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays," Phys. Chem. B 107, 7337-7342 (2003). [CrossRef]
- S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004). [CrossRef] [PubMed]
- E. M. Hicks, S. Zou, G. C. Schatz; K. G. Spears, R. P. V. Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, "Controlling Plasmon Line Shapes through Diffractive Coupling in Linear Arrays of Cylindrical Nanoparticles Fabricated by Electron Beam Lithography," Nano Lett. 5, 1065-1070 (2005). [CrossRef] [PubMed]
- W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125429 (2004). [CrossRef]
- S. Y. Park and D. Stroud, "Surface-plasmon dispersion relations in chains of metallic nanoparticles: An exact quasistatic calculation," Phys. Rev. B 69, 125418 (2004). [CrossRef]
- A. F. Koenderink and A. Polman, "Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains," Phys. Rev. B 74, 033402 (2006). [CrossRef]
- A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, "Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides," Phys. Rev. B 76, 201403(R) (2007). [CrossRef]
- J. Sung, E. M. Hicks, R. P. Van Duyne, and K. G. Spears, "Nanoparticle Spectroscopy: Dipole Coupling in Two-Dimensional Arrays of L-shaped Silver Nanoparticles," J. Phys. Chem. C 111, 10368-10376 (2007). [CrossRef]
- P. Ghenuche, I. G. Cormack, G. Badenes, P. Loza-Alvarez, and R. Quidant, "Cavity resonances in finite plasmonic chains," Appl. Phys. Lett. 90, 041109 (2007). [CrossRef]
- K. B. Crozier, E. Togan, E. Simsek, and T. Yang, "Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains," Opt. Express 15, 17482-17493 (2007). [CrossRef] [PubMed]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Ch. 7 (Artech House Antennas and Propagation Library, 2000).
- A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998). [CrossRef]
- J. Lu, C. Petre, J. Conway, and E. Yablonovitch, "Numerical optimization of a grating coupler for the efficient excitation of surface plasmons at an Ag-SiO2 interface," arXiv:physics/0703036v1 [physics.optics] (2007).
- W. Lukosz and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power," J. Opt. Soc. Am. 67, 1607-1615 (1977). [CrossRef]
- W. Lukosz and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. Radiation patterns of perpendicular oriented dipoles," J. Opt. Soc. Am. 67, 1615-1619 (1977). [CrossRef]
- W. Lukosz and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation," J. Opt. Soc. Am. 69, 1495-1503 (1979). [CrossRef]
- J. Mertz, "Radiative absorption, fluorescence, and scattering of a classical dipole near a lossless interface: a unified description," J. Opt. Soc. Am. B 17, 1906-1913 (2000). [CrossRef]
- S. J. Radzeviciusa, C.-C. Chenb, L. Peters Jr., and J. J. Daniels, "Near-field dipole radiation dynamics through FDTD modeling," J. Appl. Geophys. 52, 75-91 (2003). [CrossRef]
- L. Luan, P. R. Sievert, and J. B. Ketterson, "Near-field and far-field electric dipole radiation in the vicinity of a planar dielectric half space," New J. Phys. 8, 264 (2006). [CrossRef]
- L. Novotny L., and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Ch. 10.

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