  The ability to control the laser modes within a subwavelength resonator is of
key relevance in modern optoelectronics. This work deals with the theoretical
research on optical properties of a PT--symmetric nano--scaled dimer formed by
two dielectric wires, one is with loss and the other with gain, wrapped with
graphene sheets. We show the existence of two non--radiating trapped modes
which transform into radiating modes by increasing the gain--loss parameter.
Moreover, these modes reach the lasing condition for suitable values of this
parameter, a fact that makes these modes to achieve an ultra high quality
factor that is manifested on the response of the structure when it is excited
by a plane wave. Unlike other mechanism that transform trapped modes into
radiating modes, we show that the variation of gain--loss parameter in the
balanced loss--gain structure here studied leads to a variation in the phase
difference between induced dipole moments on each wires, without appreciable
variation in the modulus of these dipole moments. We provide an approximated
method that reproduces the main results provided by the rigorous calculation.
Our theoretical findings reveal the possibility to develop unconventional
optical devices and structures with enhanced functionality.
