  Plasmonic waveguides provide an integrated platform to develop efficient
nanoscale ultrafast photonic devices. Theoretical models that describe
nonlinear optical phenomena in plasmonic waveguides, usually, only incorporate
bulk nonlinearities, while nonlinearities that arise from metallic constituents
remained unexplored. In this work, we present a method that enables a
generalized treatment of the nonlinearities present in plasmonic waveguides and
use it to calculate second-harmonic generation from free electrons through a
hydrodynamic nonlocal description. As a general application of our method we
also consider nonlinearities arising from the quantum hydrodynamic theory with
electron spill-out. Our results may find applicability in design and analysis
of integrated photonic platforms for nonlinear optics incorporating wide
variety of nonlinear materials such as heavily doped semiconductors for
mid-infrared applications.
