A surface integral eigenvalue based technique for the direct calculation of resonance values of the permittivity of nanoparticles, and hence resonance frequencies, is discussed. General physical properties of electrostatic (plasmon) resonances are presented. Strong orthogonality properties of resonance modes, a two-dimensional phenomenon of “twin” spectrum and explicit estimates of resonance frequencies in terms of geometrical characteristics of convex nanoparticles are reported. Second-order corrections for resonance values of the dielectric permittivity are derived. Tunability and optical controllability of plasmon resonances in semiconductor nanoparticles are discussed and, as a digression, a plausible plasmon resonance mechanism for nucleation and formation of ball lightning is outlined. An efficient numerical algorithm for the calculation of resonance frequencies is developed and illustrated by extensive computational results that are compared with theoretical results and available experimental data.

• Received 12 April 2005

DOI:https://doi.org/10.1103/PhysRevB.72.155412