  Graphene has two very important optical properties of population inversion of
electrons, and broadband optical gain. As a result, graphene has potential for
use in lasers and amplifiers. In this work, we presented a quantum master model
and analyzed the properties for the electrically pumped single-AGNR
vertical-cavity surface-emitting lasers (VCSELs) to investigate the lasing
action and laser properties for realistic experimental parameters. A
semiclassical approximation for the output power and laser linewidth is also
derived. The laser threshold power was several orders of magnitude lower than
that currently achievable with semiconductor microlasers. Our results have
demonstrated that a single-AGNR VCSEL can serve as a nanolaser with ultralow
lasing threshold. Implementation of such a GNR-based VCSEL is especially
promising for optical interconnection systems since VCSELs emit low optical
power and single longitudinal mode over a wide wavelength spectral range
through tailoring GNRs.
