Microscopic Origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures

We report spatial domain measurements of the damping of surface-plasmon excitations in metal films with periodic nanohole arrays. The measurements reveal a short coherent propagation length of a few $\mu \mathrm{m}$ inside nanohole arrays, consistent with delays of about 10 fs in ultrafast transmission experiments. This implies that the transmission spectra of the entire plasmonic band-gap structure are homogeneously broadened by radiative damping of surface-plasmon excitations. We show that a Rayleigh-like scattering of surface plasmons by the periodic hole array is the microscopic origin of this damping, allowing the reradiation rate to be controlled.

Figure 1

(a) Transmission spectrum of a gold nanohole array with $a_0=761\mathrm{n}\mathrm{m}$ and $r=125\mathrm{n}\mathrm{m}$. (b) Near-field transmission image at an excitation wavelength of 820 nm.

Figure 2

(a) Schematics of the experiment. The incident polarization is along x, the SP propagation direction (arrow). (b),(c) Near-field images of the intensity $I_{\mathrm{S}\mathrm{P}}(x,y)$ on the nonilluminated grating side within a scan area of $5\times 5\mu {\mathrm{m}}^2$. The excitation was at 760 nm (b) and 830 nm (c), close to the AM $[1,0]$ resonance (790 nm) .

Figure 3

(a) Decay of $\int I_{\mathrm{S}\mathrm{P}}(x,y)dy$ of Figs. 2b, 2c, versus distance $x$. The excitation was at 760 nm (top) and 830 nm (bottom). Dashed line: exponential decay. (b) Top (experiment): cross correlations of fs pulse transmission ($\lambda =790\mathrm{n}\mathrm{m}$) through a nanohole array (filled circles) and through the substrate only (open circles). Solid line: curve calculated from Eq. (1) assuming $\tau =10\mathrm{f}\mathrm{s}$.

Figure 4

(a) Log-log plot of line widths $\Gamma$ versus peak wavelengths $\lambda$ for different nanohole arrays with $r=125\mathrm{n}\mathrm{m}$. The solid line is a fit of $\Gamma$ to ${\lambda }^{-n}$, with $n=3.4$. Inset: transmission spectrum for a gold sample with $a_0=800\mathrm{n}\mathrm{m}$ and $r=125\mathrm{n}\mathrm{m}$. A, B, and C correspond to AM $[1,0]$, SM $[1,1]$, and SM $[1,0]$ resonances. (b) $\Gamma$ vs $\lambda$ for various incident angles for the SM $[1,0]$ peak and fit to ${\lambda }^{-4}$ (line). Inset: transmission spectra of the SM $[1,0]$ resonance as a function of incident angle $\theta$.

Figure 5

(a) Far-field emission patterns from various single holes with radii decreasing from 267 nm (top) to 110 nm (bottom). The images are recorded at a tip-to-sample distance of $0.6\mu \mathrm{m}$. (b) Log-log plot of the spatially integrated emission intensity around the single holes plotted against their hole radius $r$. The dotted line is a fit to the fourth power of $r$.