Extremely Narrow Plasmon Resonances Based on Diffraction Coupling of Localized Plasmons in Arrays of Metallic Nanoparticles

We experimentally demonstrate extremely narrow plasmon resonances with half-width of just several nanometers in regular arrays of metallic nanoparticles. These resonances are observed at Rayleigh’s cutoff wavelengths for Wood anomalies and based on diffraction coupling of localized plasmons. We show experimentally that reflection from an array of nanoparticles can be completely suppressed at certain wavelengths. As a result, our metal nanostructures exhibit $\pi$-jump for the phase of the reflected light.

Figure 1

Wood anomalies for the single dot Au nanoarray with the period $a=320\mathrm{nm}$, the dot diameter $d=100\mathrm{nm}$, the dot height $h=90\mathrm{nm}$. Spectral dependences observed at $\mathrm{AOI}=62°$ (orange curves), 64° (green), 66° (blue), 68° (brown) for (a) $\Psi$-value. The inset shows a zoom of the reflection dip at $\mathrm{AOI}=64°$. ${\lambda }_{R_{-}1}^{\mathrm{air}}$ and ${\lambda }_{R_{-}1}^{\mathrm{sub}}$ are given by (1) with the sign “$+$.” (b) Phase $\Delta$. The inset on the left shows the experimental geometry for the incident light of $p$ polarization. The inset on the right shows a zoom of the phase jump at $\mathrm{AOI}=64°$. (c) Reflection $R_p$ and $R_s$ for light of $p$ and $s$ polarizations, respectively. (d) Extinction for $p$ polarization. The inset shows the electron micrograph of the array. The arrow indicates the position of the weak narrow resonance in absorption.

Figure 2

Wood anomalies and supernarrow resonances for the double-dot Au nanoarray with the period $a=320\mathrm{nm}$, the dot diameter $d=108\mathrm{nm}$, the dot height $h=90\mathrm{nm}$. $\mathrm{AOI}=62°$ (orange curves), 64° (green), 66° (blue), 68° (brown) for (a) $\Psi$-value. The inset shows a zoom of the reflection dip at $\mathrm{AOI}=64°$. ${\lambda }_{R_{-}m}^{\mathrm{air}}$ and ${\lambda }_{R_{-}m}^{\mathrm{sub}}$ are given by (1) with the sign “$+$.” (b) Phase $\Delta$. The inset on the left shows the experimental geometry for the incident light of $p$ polarization. The inset on the right shows a zoom of the phase jump at $\mathrm{AOI}=64°$. (c) Reflection $R_p$ and $R_s$ for light of $p$ and $s$ polarizations, respectively. (d) Extinction for $p$ polarization. The electric field of the incident wave is perpendicular to the line connecting neighboring dots. The left inset shows the electron micrograph of the array. The right inset shows a zoom of a peak in extinction at $\mathrm{AOI}=64°$.

Figure 3

Properties of supernarrow resonances. (a) The spectral dependence of extinction for the double-dot array of Fig. 2 plotted for $\mathrm{AOIs}=50–74°$ for $p$ polarization. (b) The 2D plot of the extinction shown in (a), image color scale CS from 0 to 12. (c) The angular dependence of the resonance half-width and the value of ${\Psi }_{\min }$ at the Wood anomaly for the single dot array of Fig. 1. The color maps of $\Psi$ for the double-dot arrays with $d\approx 100\mathrm{nm}$, $h=90\mathrm{nm}$ and (d) $a=320\mathrm{nm}$, CS from 0° to 40°. (e) $a=400\mathrm{nm}$, CS from 1° to 36°. (f) $a=500\mathrm{nm}$, CS from 3° to 36°. The dotted white lines show ${\lambda }_{R_{-}m}^{\mathrm{air}}$ and ${\lambda }_{R_{-}m}^{\mathrm{sub}}$, which are given by (1) with the sign $+$.

Figure 4

Properties of the double-dot Au nanoarray with the period $a=320\mathrm{nm}$, the dot diameter $d=110\mathrm{nm}$, the dot height $h=90\mathrm{nm}$. (a) The micrograph of the array obtained under a tilted angle. (b) 3D plot of $\Psi$-value as a function of AOI and wavelength, CS from 0° to 35°. ${\lambda }_{R_{-}m}^{\mathrm{air}}$ and ${\lambda }_{R_{-}m}^{\mathrm{sub}}$ are given by (1) with the sign $+$ (c) 3D-plot of phase $\Delta$, CS from 0° to 180°. (d) 3D plot of digital derivative of phase $\Delta$.