  Epsilon-near-zero (ENZ) materials have emerged as viable platforms for strong
nonlinear optical (NLO) interactions. The NLO phase shift in materials
exhibiting an ENZ condition is extremely large, however, direct experimental
measurements of the magnitude and time dynamics of this phenomenon,
particularly nondegenerate NLO phase shifts, have so far been lacking. Here, we
directly measure the NLO phase shift of an Indium-Tin-Oxide (ITO) thin film
using three different techniques. By characterizing the excitation-induced,
time resolved Beam Deflection (BD) of a probe beam, we measure the
nondegenerate NLO effects, allowing a separate determination of the effects of
excitation and probe wavelengths on the NLO phase shift as they are varied
across the ENZ region. These experiments reveal that having the probe pulse
centered at ENZ greatly contributes to this enhancement; however, the NLO phase
shift is less sensitive to the excitation wavelength, which only slightly
enhances the nonlinearity for obliquely incident TM-polarized light. We also
find that the spectral shift of the probe pulse induced by the excitation
follows both the magnitude and time dynamics of the NLO phase shift measured
via the BD experiments. We observe large, ultrafast cross-phase modulation in
agreement with a redistribution of carriers in the conduction band. Finally
using the Z-Scan method, we measure the degenerate nonlinear refraction at ENZ
near normal incidence. The results of all three measurements agree, revealing a
gigantic sub-picosecond NLO phase shift in ITO. At its largest, we consistently
measure an effective induced index change that is greater than the linear
index.
