  Strong second-harmonic generation has recently been experimentally observed
from metamaterials consisting of periodic arrays of metal split ring resonators
with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To
explore the underlying physical mechanism, a classical model derived from
microscopic theory is employed here. 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 cold-plasma wave equations. Through numerical simulations, it is
demonstrated that the microscopic theory includes the dominant physical
mechanisms bothqualitatively and quantitatively.
