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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 12 — Jun. 9, 2008
  • pp: 8570–8580
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Dispersion and extinction of surface plasmons in an array of gold nanoparticle chains: influence of the air/glass interface

Tian Yang and Kenneth B. Crozier  »View Author Affiliations


Optics Express, Vol. 16, Issue 12, pp. 8570-8580 (2008)
http://dx.doi.org/10.1364/OE.16.008570


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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

2. Experiments

The structure under consideration consists of an array of gold nanoparticle chains on a glass substrate. Each chain consisted of gold cylinders that were spaced by 140 nm. Each cylinder had a diameter of ~90 nm and a height of 55 nm. Adjacent chains were spaced by 300 nm. The sample was fabricated by the standard electron beam lithography and lift-off processes. A 5 nm chrome layer was deposited prior to the gold deposition to improve adhesion. The glass substrate was coated with a 15 to 30 nm thick layer of indium tin oxide (ITO) to prevent charging during electron beam writing. Figure 1 is scanning electron micrographs of the sample. Details of the fabrication processes can be found in 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]

].

Fig. 1. Scanning electron micrographs of an array of gold nanoparticle chains on a glass substrate.

To characterize the transmission and reflection properties of the array of gold nanoparticle chains over a wide range of incidence angles, the sample was illuminated from the glass side by a collimated beam from a Xenon lamp. The illumination beam was angled along the direction of the chains and was s-polarized in order to excite surface plasmons transversely polarized along the air/glass interface. The incidence angle θ was varied in order to excite surface plasmon modes at different kx values. kx 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]

].

Fig. 2. Power transmission and reflection spectra for an array of gold nanoparticle chains at an air/glass interface. The incidence angle θ is 0° (red), 13° (wine), 25° (brown), and 35° (olive) for the transmission spectra, and 48° (green), 55° (blue), and 61° (magenta) for the reflection spectra. The TIR critical angle is 41.5°. (a) Experimental results; (b) FDTD simulation results. Inset: schematic diagram for illumination with s-polarization and definition of x, y and z directions.

Power transmission spectra were taken for angles (θ) outside the TIR regime [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]

], where θ is smaller than the critical angle. Reflection spectra were taken for angles (θ) within the TIR regime, where θ is greater than the critical angle. The 140 nm spacing along the x direction and 300 nm spacing along the y direction did not produce any higher order scattering modes for the range of wavelengths discussed in this paper. Figure 2(a) shows the experimental spectra at several incidence angles (θ). In addition, spectra obtained by a numerical approach are presented in Fig. 2(b), and can be seen to be in good agreement with the experiment. The numerical modeling approach is discussed in greater detail in the following section. The dispersion relation was extracted from these spectra and plotted as Fig. 3. The orange points in Fig. 3 are experimental values of the resonance frequencies at different kx 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 kx 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 kx value will change with frequency as the incidence angle changes and consequently shift the minimum position of a fixed kx 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 kx 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.

Fig. 3. Dispersion relation for an array of gold nanoparticle chains at an air/glass interface. Orange: experimental results; Green: FDTD simulation results.
Fig. 4. Electric field E at an air/glass interface for an s-polarized plane wave incident from the glass side towards the air side (no metal nanoparticles). (a) |E|2/incident power; (b) phase of E compared to the electric field of the incident plane wave at the interface.

3. Numerical simulations

To gain insight into our experimental observation of a distinctive change in the dispersion relation across the TIR line (or the light line of air), we developed a numerical simulation method to obtain the transmission and reflection spectra of metal nanoparticle periodic structures. With this method, the transmission and reflection coefficients are obtained for a range of frequency values in a single simulation. The simulation was done with the FDTD software Fullwave from the RSOFT Design Group, Inc.

In each simulation, a time domain electromagnetic wave pulse covering the spectral regime of interest was launched from the glass side at a single kx 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 kx 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 kx value were obtained. Multiple simulations were done to obtain results for all the kx 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 kx values. In our simulation, we have simulated kx values with an interval of 0.2π/µm.

Since each simulation contained a range of frequencies, there existed plane wave components with frequencies close to the light lines of air and glass, which propagated approximately parallel to the x axis, either on the air side or on the glass side. These wave components were not efficiently absorbed by PML’s [20

20. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Ch. 7 (Artech House Antennas and Propagation Library, 2000).

], and bounced back and forth inside the simulation domain, causing unphysical oscillatory features in the entire spectral regime of Fourier Transforms for a finite time window if not treated appropriately. To resolve this problem, we calculated the reflected power -1/2 Re(E 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, Hx=H cos(θ) approaches 0 as θ approaches 90°, while Ey=E does not change with θ. Therefore, the Fourier Transform of the time domain Hx values suffered much less from the bouncing wave components with large θ values than the Fourier Transform of Ey. 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.

The large angle (θ) transmitted wave components on the air side corresponded to wave components on the glass side with smaller propagation angles (due to Snell’s Law), and therefore underwent reasonable absorption inside the glass side PML. As long as these wave components completely disappeared within the finite simulation time window through absorption by the glass side PML, they do not affect Fourier Transform at other frequencies. Since these wave components would bounce back and forth several times on the air side before they reached the glass side PML, a sufficiently long simulation time was required. We used 1/2 Re(E y H x *) for the transmitted power instead of 1/2 η|H x|2/cos(θ) because Hx 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.

Several other factors needed to be carefully considered in the FDTD simulation in order to obtain accurate transmission and reflection spectra. The transmission and reflection monitors should be located some distance from the metal nanoparticles in order not to detect the near field of the surface plasmons. The pulsed plane wave launch plane should be located some distance from the metal nanoparticles because the pulsed plane wave launch contained an evanescent near field. To ensure adequate absorption by the PML’s of waves at relatively large incidence angles, the PML’s must be sufficiently long. The simulation time must be suitably long in order for most wave components to disappear completely via PML absorption within the simulation time. In our simulation, we placed the transmission E and H monitors 0.9 µm above the air/glass interface in air and the reflection E and H monitors 0.9 µm below the interface in glass. The pulsed plane wave launch plane was 1 µm below the interface. The PML’s were 2 µm long, with a normal incidence reflectivity of 10-32. The simulation time was 100 µm/c, where c is the speed of light in vacuum.

In our simulation, the refractive index of glass was taken as 1.51. The dielectric properties of gold were fit to the Drude-Lorentzian model based on ref [21

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]

]. Chrome and ITO were not taken into consideration for simulation results reported in this article. A non-uniform cubic mesh with 5 nm grid size at and near the particles was used. The time step was 2.5nm/c.

The simulation and experimental results agree nicely with each other as exhibited in Fig. 2 and 3. We noticed that by including a 15 to 30 nm thick ITO layer into the simulation, the resonance frequencies red shift, but maintain similar relative changes in dispersion and extinction across the light line of air. The nice agreement between simulation and experiments in Fig. 2 and 3 could be due to the differences in various parameters between simulation and experiments cancelling each other. In Fig. 5, the extinction has been simulated for a wide range of frequencies and kx 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

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-SiO2 interface,” arXiv:physics/0703036v1 [physics.optics] (2007).

].

Fig. 5. Simulation of extinction in the first irreducible Brillouin Zone for an array of gold nanoparticle chains at an air/glass interface. The two white lines are, left: the light line of air, right: the light line of glass.

4. Explanation of dispersion relation

Fig. 6. Simulated dispersion relations for an array of gold nanoparticle chains. Green: 55 nm tall nanoparticles at an air/glass interface; blue: 30 nm tall nanoparticles at an air/glass interface; purple: 55 nm tall nanoparticles in a uniform glass environment.

Fig. 7. The y=0 cross section of the Ey field pattern from a line of point dipoles. The point dipoles in the line were spaced by 320 nm along y axis at an air/glass interface. One point dipole was sitting at origin. The point dipoles were polarized in +y direction and continuously oscillating at a frequency of 1.6 c/µm. The amplitude of Ey has been raised to the power of 0.6 in the plot in order to improve the visual contrast. Inset: definitions of nanoparticle chain and nanoparticle line in this paper.
Fig. 8. Amplitude (blue, in log scale) and phase (green) of Ey along x-axis. Ey was the field from a line of point dipoles. The point dipoles in the line were spaced by 320 nm along y axis. One point dipole was sitting at origin. The point dipoles were polarized in +y direction and continuously oscillating at a frequency of 1.6 c/µm. (a) The point dipole line was at an air/glass interface; (b) the point dipole line was in a uniform glass medium.

To conveniently describe the coupling between surface plasmons or point dipoles, we name the lines of nanoparticles or lines of point dipoles at x=(…, -140 nm, 0 nm, 140 nm, 280 nm, …) as (…line -1, line 0, line 1, line 2, …). In Fig. 8, the field from point dipole line 0 has Ey values of (…, E-1, E0, E1, E2, …) 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 Pindu=α Eindu, where α is the polarizability of a single line of nanoparticles, and Eindu is a sum of Ey field values at the origin from all the other nanoparticle lines. When the in-plane wave vector is kx, we have

Eindu=n=,n0Enexp(ikx·n·140nm)
=n=1Enexp(ikx·n·140nm)+Enexp(ikx·n·140nm)
(1)

The phase of the point dipoles in line 0 is set to 0 in our simulation. When Eindu 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 Eindu has a negative real part, there will be a blue shift of the surface plasmon resonance.

Figure 9 shows Eindu at a single frequency of 1.6 c/µm for kx values in the first irreducible Brillouin Zone found from Equation (1) and the calculations plotted as Fig. 8. The kx interval between the nearest points in Fig. 9 is a constant. In this calculation we summed up 71 Ey 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 Eindu 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 Eindu across the light line of glass is qualitatively consistent with the theoretical calculations of dispersion relations in refs [13

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

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]

], which have a sharp red shift of resonances near the light line.

Fig. 9. Eindu for an array of point dipole lines oscillating at a frequency of 1.6 c/µm. The point dipole lines were polarized in +y direction and were spaced by 140 nm in x direction. kx spans the first irreducible Brillouin Zone from 0 to π/d with a fixed interval. (a) The point dipoles were on an air/glass interface; (b) the point dipoles were in a uniform glass medium.

Eindu of point dipole lines at an air/glass interface is different. For the uniform glass environment case in Fig. 9(b), Eindu undergoes an abrupt change across the lightline; while for the air/glass interface case in Fig. 9(a), the abrupt change in Eindu 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 Eindu 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 Eindu 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.

Fig. 10. Eindu for a single chain of point dipoles on an air/glass interface, which are oscillating at a frequency of 1.6 c/µm. The point dipoles were polarized in +y direction and were spaced by 140 nm in x direction. kx spans the first irreducible Brillouin Zone from 0 to π/d with a fixed interval.

5. Summary

We have experimentally obtained the dispersion and extinction properties for the s-polarized surface plasmon mode in an array of gold nanoparticles chains at an air/glass interface by measuring the transmission and reflection spectra. The dispersion is significantly larger within the total internal reflection (TIR) regime. 100% extinction can be reached under TIR. We have outlined an FDTD numerical approach that rejects spurious unphysical waves propagating at large angles. The accuracy of this FDTD approach was verified through comparison with experiment. The large change in dispersion between the above and within TIR regimes has been explained by considering the field pattern of dipoles at an air-glass interface, and the resulting influence upon the coupling between the dipoles.

Acknowledgments

We thank the Defense Advanced Research Projects Agency (DARPA), the Charles Stark Draper Laboratory and the Harvard Nanoscale Science and Engineering Center (NSEC) for the financial support of this work. The Harvard NSEC is supported by the National Science Foundation (NSF). Fabrication work was carried out at the Harvard Center for Nanoscale Systems (CNS), which is also supported by the NSF.

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. 23, 1331–1333 (1998). [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]

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. 2, 229–232 (2003). [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]

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]

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. 84, 4721–4724 (2000). [CrossRef] [PubMed]

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 65, 193408 (2002). [CrossRef]

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. 81, 1714–1716 (2002). [CrossRef]

9.

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]

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 107, 7337–7342 (2003). [CrossRef]

11.

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]

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]

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]

14.

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]

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]

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 76, 201403(R) (2007). [CrossRef]

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]

20.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Ch. 7 (Artech House Antennas and Propagation Library, 2000).

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]

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-SiO2 interface,” arXiv:physics/0703036v1 [physics.optics] (2007).

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]

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. 67, 1615–1619 (1977). [CrossRef]

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. 69, 1495–1503 (1979). [CrossRef]

26.

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]

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. 52, 75–91 (2003). [CrossRef]

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. 8, 264 (2006). [CrossRef]

29.

L. Novotny L. and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Ch. 10.

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

  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]
  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]
  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," Nat. Mater. 2, 229-232 (2003). [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]
  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]
  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. 84, 4721-4724 (2000). [CrossRef] [PubMed]
  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 65, 193408 (2002). [CrossRef]
  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. 81, 1714-1716 (2002). [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  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]
  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]
  14. 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]
  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]
  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 76, 201403(R) (2007). [CrossRef]
  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]
  20. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Ch. 7 (Artech House Antennas and Propagation Library, 2000).
  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]
  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-SiO2 interface," arXiv:physics/0703036v1 [physics.optics] (2007).
  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]
  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. 67, 1615-1619 (1977). [CrossRef]
  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. 69, 1495-1503 (1979). [CrossRef]
  26. 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]
  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. 52, 75-91 (2003). [CrossRef]
  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. 8, 264 (2006). [CrossRef]
  29. L. Novotny L., and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Ch. 10.

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