  In this paper, we develop a theory of edge effects in graphene for its
applications to nanoantennas in the terahertz, infrared, and visible frequency
ranges. Its characteristic feature is selfconsistence reached due the
formulation in terms of dynamical conductance instead of ordinary used surface
conductivity. The physical model of edge effects is based on using the concept
of Dirac fermions. The surface conductance is considered as a general
susceptibility and is calculated via the Kubo approach. In contrast with
earlier models, the surface conductance becomes nonhomogeneous and nonlocal.
The spatial behavior of the surface conductance depends on the length of the
sheet and the electrochemical potential. Results of numerical simulations are
presented for lengths in the range of 2.1-800 nm and electrochemical potentials
ranging between 0.1-1.0 eV. It is shown that if the length exceeded 800 nm, our
model agrees with the classical Drude conductivity model with a relatively high
degree of accuracy. For rather short lengths, the conductance usually exhibits
spatial oscillations, which absent in conductivity and strongly affect the
properties of graphene based antennas. The period and amplitude of such spatial
oscillations, strongly depend on the electrochemical potential. The new theory
opens the way for realizing electrically controlled nanoantennas by changing
the electrochemical potential may of the gate voltage. The obtained results may
be applicable for the design of carbon based nanodevices in modern quantum
technologies.
