Universal optical polarizability for plasmonic nanostructures

We develop an analytical model for calculation of optical spectra for metal nanostructures of arbitrary shape supporting localized surface plasmons (LSPs). For plasmonic systems with characteristic size below the diffraction limit, we obtain an explicit expression for optical polarizability that describes the lineshape of optical spectra solely in terms of the metal dielectric function and LSP frequency. The amplitude of the LSP spectral band is determined by the effective system volume that, for long-wavelength LSPs, can significantly exceed the physical volume of metal nanostructure. Within the quasistatic approach, we derive the exact LSP Green's function and establish general spectral properties of LSPs, including the distribution and oscillator strength of the LSP states. These results can be used to model or interpret the experimental spectra of plasmonic nanostructures and to tune their optical properties for various applications.