The physical processes underlying the complex nanoscale optical responses of metal nanoparticles must be understood
both experimentally and theoretically if they are to be developed for use in photonic devices. While
many linear optical measurements have been performed on gold nanoparticle arrays, only a handful of nonlinear
measurements have been reported. Here, we discuss a collection of experiments of both types on arrays of gold
nanoparticles. However, on nanoscale-rough metal surfaces, such as nanoparticles with small-scale defects, local
electric fields may vary rapidly and strong field gradients can induce significant multipolar contributions, making
a theoretical description of second-harmonic generation (SHG) from nanoparticle arrays infeasible at present.
A macroscopic nonlinear response tensor approach based on the input and output fields to the system avoids
with these complications. Contributions from higher multipoles are implicitly included, and electric-dipole-type
selection rules can be applied to address symmetry issues. While the experimental geometry constrains the
formalism, additional insight into the underlying physical processes is expected from experimental variations.
Good agreement with direct SHG tensor measurements validates the formalism, providing the framework for a
deeper understanding of the nanoscale optical responses of metal nanoparticles.