  The reflectivity properties of graphene with nonzero mass-gap parameter are
investigated in the framework of Dirac model using the polarization tensor in
(2+1)-dimensional space-time. For this purpose, a more simple explicit
representation for the polarization tensor along the real frequency axis is
found. The approximate analytic expressions for the polarization tensor and for
the reflectivities of graphene are obtained in different frequency regions at
any temperature. We show that the nonzero mass-gap parameter has a profound
effect on the reflectivity of graphene. Specifically, at zero temperature the
reflectivity of gapped graphene goes to zero with vanishing frequency. At
nonzero temperature the same reflectivities are equal to unity at zero
frequency. We also find the resonance behavior of the reflectivities of gapped
graphene at both zero and nonzero temperature at the border frequency
determined by the width of the gap. At nonzero temperature the reflectifities
of graphene drop to zero in the vicinity of some frequency smaller than the
border frequency. Our analytic results are accompanied with numerical
computations performed over a wide frequency region. The developed formalism
can be used in devising nanoscale optical detectors, optoelectronic switches
and in other optical applications of graphene.
