  Surface plasmon resonances, the coherent oscillation of free electrons, can
concentrate incident field into small volumes much smaller than the incident
wavelength. The intense fields at these \textit{hot spots} enhance the
light-matter interactions and may lead to the appearance of nonlinearity.
Controlling such nonlinearities is significant for various practical
applications. Here we report that by coupling dark modes to the first and the
generated second harmonic modes separately, one can gain control over both
fields. We find that by engineering path interferences (Fano resonances)
between bright and dark plasmon modes it is possible to enhance the fundamental
mode without increasing the nonlinear field, enhance the nonlinear field
without modifying the fundamental mode, and enhance the second harmonic field
with enhanced fundamental mode.
