  It is well known that impurities play a central role in the linear and
nonlinear response of graphene at optical and terahertz frequencies. In this
work, we calculate the bands and intraband dipole connection elements for
nitrogen-doped monolayer graphene using a density functional tight binding
approach. Employing these results, we calculate the linear and nonlinear
response of the doped graphene to terahertz pulses using a density-matrix
approach in the length gauge. We present the results for the linear and
nonlinear mobility as well as third harmonic generation in graphene for
adsorbed and substitutional nitrogen doping for a variety of doping densities.
We show that the conduction bands are more parabolic in graphene structures
with substitutional nitrogen doping than for those with adsorbed nitrogen. As a
result, substitutional doping has a greater impact on the terahertz mobility
and nonlinear response of graphene than adsorbed nitrogen does.
