We present an all-dielectric germanium nanosystem exhibiting a strong third order
nonlinear response and efficient third harmonic generation in the optical regime. A thin germanium
nanodisk shows a pronounced valley in its scattering cross section close to the dark anapole mode,
while the electric field energy inside the disk is maximized due to high confinement within the
dielectric. We investigate the dependence of the third harmonic signal on disk size and pump
wavelength to reveal the nature of the anapole mode. Each germanium nanodisk generates a high
effective third order susceptibility of
(3) = 4.3 10−9 , corresponding to an associated third
harmonic conversion efficiency of 0.0001% at a wavelength of 1650 nm, which is four orders of
magnitude greater than the case of an unstructured germanium reference film. Furthermore, the
nonlinear conversion via the anapole mode outperforms that via the radiative dipolar resonances
by about one order of magnitude, which is consistent with our numerical simulations. These
findings open new possibilities for the optimization of upconversion processes on the nanoscale
through the appropriate engineering of suitable dielectric materials.