Collective electronic states in inhomogeneous media at critical and subcritical metal concentrations

The excitation of collective electronic states, surface plasmons (SPs), is studied for semicontinuous metal films at various metal concentrations. A previously unexpected strong optical response, manifested through an increase in the exponents of the local field moments, is predicted at noncritical metal concentrations. This phenomenon results from an increase in SP localization away from the percolation threshold, which is opposite to the general understanding that a decrease in the number of scatters leads to weaker mode localization. Experimental results from near-field optical microscopy are found to be in good agreement with the theory, validating the role of SP localization in the optical response. Possible applications in improving the sensitivity of spectroscopic measurements such as surface-enhanced Raman scattering and harmonic generation are considered.

Figure 1

Random metal-dielectric films synthesized by laser ablation of a solid silver target onto a glass substrate. The metal concentration $p$ is varied by control over the deposition time. At a low concentration $p=0.2$ (a), the sample constitutes of dispersed metal particles with sizes $a=10–20\mathrm{nm}$, while close to the percolation threshold $p=0.65$ (b), large metal clusters span the entire system.

Figure 2

The surface plasmon density of states (a), and localization length (b), are calculated as a function of the eigenvalue $\Lambda$ for an ensemble of 100 metal-dielectric films, each with size $1\mu \mathrm{m}$. Four different metal filling fractions are investigated: $p=0.1$ (dashed black line), $p=0.2$ (dashed gray line), $p=0.3$ (black line), and $p=p_c=0.5$ (gray line). The singularity at the band center and its dependence on the metal concentration are closely inspected in the insets.

Figure 3

Slope of local field moments vs metal concentration for numerical (lines) and experimental (connected squares) data. The wavelengths of the incident light are $\lambda =543\mathrm{nm}$ (solid lines) and $\lambda =633\mathrm{nm}$ (dashed lines), respectively.

Figure 4

Electromagnetic enhancement for surface-enhanced Raman scattering from a silver-glass composite at various metal concentrations. A local minimum is observed at the percolation threshold while maximum enhancement factors of $2\times {10}^6$ for $\lambda =543\mathrm{nm}$ (solid line) and $6\times {10}^6$ for $\lambda =633\mathrm{nm}$ (dashed line) are obtained at $\Delta p_c=-0.3$ and $\Delta p_c=-0.27$, respectively.