  We present theoretical and experimental evidence of high-gain far-detuned
nonlinear frequency conversion, extending towards both the visible and the
mid-infrared, in a few-mode graded-index silica fiber pumped at 1.064 $\mu$m,
and more specifically achieving gains of hundreds of dB per meter below 0.65
$\mu$m and beyond 3.5 $\mu$m. Our findings highlight the potential of
graded-index fibers in terms of strong modal confinement over an ultrabroad
spectral range for enabling high-gain wavelength conversion. Such advancements
require an accurate interpretation of intramodal and intermodal four-wave
mixing processes.
