  The graphene membrane irradiated by weak activating alternative electric
field in terahertz range was considered. The quantum approach based on the
time-dependent density matrix method was used. The exact solution was obtained
for graphene membrane density matrix equation in linear on the external field
approximation. The graphene electromagnetic response was studied i.e. the
formulae for the induced current and conductivity were found and analyzed
neglecting loss. The obtained formula for the conductivity showed that the
graphene membrane was an oscillating contour and its fundamental eigen
frequency coincided with a singularity point of the conductivity. This formula
allowed us to calculate the graphene membrane inductivity and the capacitance.
So the graphene membrane could be used as an antenna or a transistor. It was
shown that its eigen frequency could be tuned by doping as its value was found
to depend on electrons concentration. It was obtained that the eigen frequency
could be tuned in a rather large frequency range 1-100 terahertz as electrons
concentration in graphene may differ considerably. The found dependence on
concentration correlates with experiments. It would be useful to take the
obtained results into account when constructing devices containing graphene
membrane nanoantenna allowing wireless communications among nanosystems. This
could be promising research area of energy harvesting applications.
