  Using long-range surface plasmon polaritons light can propagate in metal
nano-scale waveguides for ultracompact opto-electronic devices. Gold is an
important material for plasmonic waveguides, but although its linear optical
properties are fairly well understood, the nonlinear response is still under
investigation. We consider propagation of pulses in ultrathin gold strip
waveguides, modeled by the nonlinear Schr\"odinger equation. The nonlinear
response of gold is accounted for by the two-temperature model, revealing it as
a delayed nonlinearity intrinsic in gold. The consequence is that the measured
nonlinearities are strongly dependent on pulse duration. This issue has so far
only been addressed phenomenologically, but we provide an accurate estimate of
the quantitative connection as well as a phenomenological theory to understand
the enhanced nonlinear response as the gold thickness is reduced. In comparison
with the previous works, the analytical model for the power-loss equation has
been improved, and can be applied now to cases with a high laser peak power. We
show new fits to experimental data from literature and provide updated values
for the real and imaginary part of the nonlinear susceptibility of gold for
various pulse durations and gold layer thicknesses. Our simulations show that
the nonlinear loss is inhibiting efficient nonlinear interaction with low-power
laser pulses. We therefore propose to design waveguides suitable for the
mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over
the delayed hot-electron nonlinearity and provide a suitable plasmonics
platform for efficient ultrafast nonlinear optics.
