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 $a∕d⩽\frac{1}{3}$, 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 $50\mathrm{nm}\mathrm{diam}$ Ag spheres spaced by $75\mathrm{nm}$. 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 $k_{\text{mode}}⩽\omega ∕c$ show strongly enhanced decay due to radiation damping.