  Second harmonic (SH) radiation in metal nanoparticles is generated by both
nonlocal-bulk and local-surface SH sources, induced by the electromagnetic
field at the fundamental frequency. We propose a surface integral equation
(SIE) method for evaluating the SH radiation generated by metal nanoparticles
with arbitrary shapes, considering all SH sources. We demonstrate that the
contribution of the nonlocal-bulk SH sources to the SH electromagnetic field
can be taken into account through equivalent surface electric and magnetic
currents. We numerically solve the SIE problem by using the Galerkin method and
the Rao-Wilton-Glisson basis functions in the framework of the distribution
theory. The accuracy of the proposed method is verified by comparison with the
SH-Mie analytical solution. As an example of a complex-shaped particle, we
investigate the SH scattering by a triangular nano-prism. This method paves the
way for a better understanding of the SH generation process in arbitrarily
shaped nanoparticles and can also have a high impact in the design of novel
nanoplasmonic devices with enhanced SH emission.
