  We use the robust nearest-neighbour tight-binding approximation to study on
the same footing interband dipole transitions in narrow-bandgap carbon
nanotubes and graphene nanoribbons. It is demonstrated that curvature effects
in metallic single-walled carbon nanotubes and edge effects in gapless graphene
nanoribbons not only open up bang gaps, which typically correspond to THz
frequencies, but also result in a giant enhancement of the probability of
optical transitions across these gaps. Moreover, the matrix element of the
velocity operator for these transitions has a universal value (equal to the
Fermi velocity in graphene) when the photon energy coincides with the band-gap
energy. Upon increasing the excitation energy, the transition matrix element
first rapidly decreases (for photon energies remaining in the THz range but
exceeding two band gap energies it is reduced by three orders of magnitude),
and thereafter it starts to increase proportionally to the photon frequency. A
similar effect occurs in an armchair carbon nanotube with a band gap opened and
controlled by a magnetic field applied along the nanotube axis. There is a
direct correspondence between armchair graphene nanoribbons and single-walled
zigzag carbon nanotubes. The described sharp photon-energy dependence of the
transition matrix element together with the van Hove singularity at the band
gap edge of the considered quasi-one-dimensional systems make them promising
candidates for active elements of coherent THz radiation emitters. The effect
of Pauli blocking of low-energy interband transitions caused by residual doping
can be suppressed by creating a population inversion using high-frequency
(optical) excitation.
