Fundamental limits to extinction by metallic nanoparticles.

We show that there are shape-independent upper bounds to the extinction cross section per unit volume of dilute, randomly arranged nanoparticles, given only material permittivity. Underlying the limits are restrictive sum rules that constrain the distribution of quasistatic eigenvalues. Surprisingly, optimally designed spheroids, with only a single quasistatic degree of freedom, reach the upper bounds for four permittivity values. Away from these permittivities, we demonstrate computationally optimized structures that surpass spheroids and approach the fundamental limits.