Particle plasmons: Why shape matters

Simple analytic expressions for the polarizability of metallic nanoparticles are in wide use in the field of plasmonics, but their origins are not obvious. In this article, expressions for the polarizability of a particle are derived in the quasistatic limit in a manner that allows the physical origin of the terms to be clearly seen. The discussion is tutorial in nature, with particular attention given to the role of particle shape since this is a controlling factor in particle plasmon resonances.