Unusual resonances in nanoplasmonic structures due to nonlocal response

We study the nonlocal response of a confined electron gas within the hydrodynamical Drude model. We address the question as to whether plasmonic nanostructures exhibit nonlocal resonances that have no counterpart in the local-response Drude model. Avoiding the usual quasistatic approximation, we find that such resonances do indeed occur, but only above the plasma frequency. Thus the recently found nonlocal resonances at optical frequencies for very small structures, obtained within quasistatic approximation, are unphysical. As a specific example we consider nanosized metallic cylinders, for which extinction cross sections and field distributions can be calculated analytically.

Figure 1

Extinction cross sections ${\sigma }_{\mathrm{ext}}$ as a function of frequency for TM-polarized light normally incident on a metallic cylinder in vacuum. Parameters for Au as in Ref. 14: $\hslash {\omega }_{\mathrm{p}}=8.812\mathrm{eV}$, $\hslash \gamma =0.0752\mathrm{eV}$, and $v_{\mathrm{F}}=1.39\times {10}^6\mathrm{m}/\mathrm{s}$. Inset: Frequency shift of the maximum ${\sigma }_{\mathrm{ext}}\left(\omega \right)$ for nonlocal against local response, as a function of radius.

Figure 2

Field distributions in the three different models, for TM-polarized light normally incident on a cylinder of radius $a=2$ nm. (a) Normalized displacement field ${\left|\mathit{D}\right|}^2/{\left|{\mathit{D}}_{\mathrm{in}}\right|}^2$ at the frequency $\omega =0.6503{\omega }_{\mathrm{p}}$ (P1 in Fig. 1). ${\mathit{D}}_{\mathrm{in}}={\varepsilon }_0{\mathit{E}}_{\mathrm{in}}$ and ${\mathit{E}}_{\mathrm{in}}$ is the incident electric field. (b) Analogous plots of ${\left|\mathit{E}\right|}^2/{\left|{\mathit{E}}_{\mathrm{in}}\right|}^2$ for $\omega =1.1963{\omega }_{\mathrm{p}}$ (P2 in Fig. 1).