We present an advanced numerical formulation to calculate the optical properties of 3D nanoparticles (single or coupled) of arbitrary shape and lack of symmetry. The method is based on the (formally exact) surface integral equation formulation, implemented for parametric surfaces describing particles with arbitrary shape through a unified treatment (Gielis' formula). Extinction, scattering, and absorption spectra of a variety of metal nanoparticles are shown, thus determining rigorously the localised surface-plasmon resonances of nanocubes, nanostars, and nanodimers. Far-field and near-field patterns for such resonances are also calculated, revealing their nature. The flexibility and reliability of the formulation makes it specially suitable for complex scattering problems in Nano-Optics and Plasmonics.
