  New propagation regimes for light arise from the ability to tune the
dielectric permittivity to extremely low values. Here we demonstrate a
universal approach based on the low linear permittivity values attained in the
epsilon-near-zero (ENZ) regime for enhancing the nonlinear refractive index,
which enables remarkable light-induced changes of the material properties.
Experiments performed on Al-doped ZnO (AZO) thin films show a six-fold increase
of the Kerr nonlinear refractive index ($n_2$) at the ENZ wavelength, located
in the 1300 nm region. This in turn leads to ultrafast light-induced refractive
index changes of the order of unity, thus representing a new paradigm for
nonlinear optics.
