  We report on the response of graphene to high intensity mid-IR radiation and
show that graphene exhibits saturable absorption and significant two-photon
absorption in the spectral region from 1.55 $\mu$m to 3.50 $\mu$m (0.35 eV to
0.80 eV). We find that the effective modulation depth of multilayer graphene is
limited by two-photon absorption which will affect its performance as a laser
mode-locking element. The measured saturation intensities of femtosecond pulses
were found to depend on the third power of photon energy when we combined our
results with others reported in literature, while those of longer pulses were
found to have a square root dependence.
