Propagation of optical excitations by dipolar interactions in metal nanoparticle chains

Abstract

Dispersion relations for dipolar modes propagating along a chain of metal nanoparticles are calculated by solving the full Maxwell equations, including radiation damping. The nanoparticles are treated as point dipoles, which means the results are valid only for $a∕d\ensuremath{\leqslant}\frac{1}{3}$, where $a$ is the particle radius and $d$ the spacing. The discrete modes for a finite chain are first calculated, then these are mapped onto the dispersion relations appropriate for the infinite chain. Computed results are given for a chain of $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.2em}{0ex}}\mathrm{diam}$ Ag spheres spaced by $75\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. We find large deviations from previous quasistatic results: Transverse modes interact strongly with the light line. Longitudinal modes develop a bandwidth more than twice as large, resulting in a group velocity that is more than doubled. All modes for which ${k}_{\text{mode}}\ensuremath{\leqslant}\ensuremath{\omega}∕c$ show strongly enhanced decay due to radiation damping.