Collective Resonances in Gold Nanoparticle Arrays

We present experimental evidence of sharp spectral features in the optical response of 2D arrays of gold nanorods. A simple coupled dipole model is used to describe the main features of the observed spectral line shape. The resonance involves an interplay between the excitation of plasmons localized on the particles and diffraction resulting from the scattering by the periodic arrangement of these particles. We investigate this interplay by varying the particle size, aspect ratio, and interparticle spacing, and observe the effect on the position, width, and intensity of the sharp spectral feature.

Figure 1

Top: Calculated isolated particle extinction cross section for an ellipsoidal particle (semiaxes: $a=60\mathrm{nm}$, $b=40\mathrm{nm}$, $c=15\mathrm{nm}$, surrounding medium: $n=1.46$, incident light polarized along $a$). Solid red curve: Same particle in an array. Inset: Effect of pitch variation. The pitch values $h$ are 454, 476, and 497 nm for the thin blue curves and 519, 534, 548 nm for the thick red curves. Bottom: Corresponding calculated array factor (real and imaginary part). The finite number of dipoles ($400\times 400$) creates spurious fast oscillations in the array factor $S$, which were smoothed before insertion in Eq. (3) (continuous lines).

Figure 2

Transmittance spectra for gold nanorod arrays in an homogeneous index environment (top, oil immersion $n=1.46$) and asymmetric refractive index configuration (bottom, incident light in air), for five particle separations. Nominal particle sizes: $100\mathrm{nm}\times 90\mathrm{nm}\times 35\mathrm{nm}$ (top), $120\mathrm{nm}\times 90\mathrm{nm}\times 35\mathrm{nm}$ (bottom). The vertical lines indicate the position of the $⟨1,0⟩$ and $⟨1,1⟩$ diffraction edges for the two refractive index environment configurations.

Figure 3

Extinction spectra (per particle) for several gold nanoparticle arrays. The average particle size was $123\mathrm{nm}\times 85\mathrm{nm}\times 35\mathrm{nm}$. Inset (nominal particle size $120\mathrm{nm}\times 90\mathrm{nm}\times 35\mathrm{nm}$): When the diffraction edge is on the blue side of the main resonance, a much weaker effect is observed. Interestingly, complete transmission can be obtained near the diffraction edge; see especially the curve for 420 nm pitch in the inset.

Figure 4

Extinction spectra, normalized by the occupancy for two polarization states (long axis: solid lines; short-axis: dashed lines). The colors refer to two arrays of particles both of pitch 540 nm for which the particle volume is approximately the same, but the particles have different aspect ratios.