  All-optical signal processing based on nonlinear optical devices is promising
for ultrafast information processing in optical communication systems. Recent
advances in two-dimensional (2D) layered materials with unique structures and
distinctive properties have opened up new ave-nues for nonlinear optics and the
fabrication of related devices with high performance. This paper reviews the
recent advances in research on third-order optical nonlinearities of 2D
materials, focus-ing on all-optical processing applications in the optical
telecommunications band near 1550 nm. First, we provide an overview of the
material properties of different 2D materials. Next, we review different
methods for characterizing the third-order optical nonlinearities of 2D
materials, including the Z-scan technique, third-harmonic generation (THG)
measurement, and hybrid device character-ization, together with a summary of
the measured n2 values in the telecommunications band. Fi-nally, the current
challenges and future perspectives are discussed.
