  The two-photon luminescence (TPL) of gold nanoparticles (NP) was shown to
result from the excitation of hot carriers, the plasmonic NP resonances playing
an important role both for plasmon enhanced absorption and plasmon enhanced
emission. However, the exact parameters enabling to control or optimize the NP
nonlinear luminescence still need to be understood in detail. In this paper, we
report the two-photon excited photoluminescence of single gold nanorods
exhibiting identical aspect ratio (close to 4) and thus identical plasmonic
resonances, but increasing volumes V (707 <V< 160 103 nm3 i.e. rod diameters
varying between 6 and 40 nm). The two-photon luminescence intensity of a high
number of colloidal nanorods was investigated at the single object level,
combining polarization resolved TPL and simultaneously acquired topography.
Non-monotonic TPL variations are evidenced, nanorods with an intermediate size
(diameter around 10 nanometers) exhibiting the highest TPL signal intensity. A
model is proposed considering both the local field enhancement effects at the
NP and the size-dependent electron thermalization processes. BEM (Boundary
Elements Method) simulations are used to compute the fields at both the
transverse and longitudinal plasmon resonance. A good fitting of the
experimental data is obtained considering integration of the fields over the
whole the NP volume.
