  In this article, we develop a classical electrodynamic theory to study the
optical nonlinearities of metallic nanoparticles. The quasi-free electrons
inside the metal are approximated as a classical Coulomb-interacting electron
gas, and their motion under the excitation of an external electromagnetic field
is described by the plasma equations. This theory is further tailored to study
second-harmonic generation. Through detailed experiment-theory comparisons, we
validate this classical theory as well as the associated numerical algorithm.
It is demonstrated that our theory not only provides qualitative agreement with
experiments, it also reproduces the overall strength of the experimentally
observed second-harmonic signals.
