Optical propagation via dipolar coupling in metal nanoparticle chains

Electromagnetic propagation in metal nanoparticle chains offers the potential for nano-sized integrated optical circuits. Dispersion relations for dipolar modes propagating along such a chain 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 \quad \le $ 1/3, where $a$ is the particle radius and $d$ the spacing.$^{1}$ 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-nm diameter Ag spheres spaced by 75 nm.$^{2}$ We find large deviations from previous quasistatic results:$^{3}$ 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_{mode} \quad \le $ \textit{$\omega $/c} show strongly enhanced decay due to radiation damping. These features are consistent with recent calculations by Citrin.$^{4}$ $^{1}$ S. Y. Park and D. Stroud, Phys. Rev. B \textbf{69}, 125418 (2004). $^{2}$ W. H. Weber and G. W. Ford, Phys. Rev. B \textbf{70}, 125429 (2004). $^{3}$ M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B \textbf{62}, 16356 (2000). $^{4}$ D. S. Citrin, Nano Lett. \textbf{4}, 1561 (2004).