  We study theoretically the strong-field absorption of an ultrafast optical
pulse by a gapped graphene monolayer. At low field amplitudes, the absorbance
in the pristine graphene is equal to the universal value of $2.3$ percent.
Although the ultrafast optical absorption for low field amplitudes is
independent of the polarization, linear or circular, of the applied optical
pulse, for high field amplitudes, the absorption strongly depends on the pulse
polarization. For a linearly polarized pulse, the optical absorbance is
saturated at the value of $\approx 1.4$ percent for the pulse's amplitude of
$\geq 0.4~\mathrm{V/\AA}$, but no such saturation is observed for a circularly
polarized pulse. For the gapped graphene, the absorption of a linearly
polarized pulse has a weak dependence on the bandgap, while for a circularly
polarized pulse, the absorption is very sensitive to the bandgap. %Opening a
bandgap in graphene by placing in on, for example, SiC substrate strongly
modify the ultrafast absorption at small field amplitudes.
