  We have revealed from a numerical study that the Hall plateaus are retained
in the optical Hall conductivity $\sigma_{xy}(\omega)$ in the ac ($\sim$ THz)
regime in both of the ordinary two-dimensional electron gas and graphene in the
quantum Hall regime, although the plateau height in ac deviates from integer
multiples of $e^2/h$. The effect remains unexpectedly robust against a
significant strength of disorder, which we attribute to an effect of
localization. We predict the ac Hall plateaus are observable through the
Faraday rotation with the rotation angle characterized by the fine-structure
constant $\alpha$. In this paper we clarify the relationship between plateau
structures and the disorder strength by performing numerical calculation.
