  The phonon dispersions of monolayer and few-layer graphene (AB bilayer, ABA
and ABC trilayers) are investigated using the density-functional perturbation
theory (DFPT). Compared with the monolayer, the optical phonon $E_{2g}$ mode at
$\Gamma$ splits into two and three doubly degenerate branches for bilayer and
trilayer graphene, respectively, due to the weak interlayer coupling. These
modes are of various symmetry and exhibit different sensitivity to either Raman
or infrared (IR) measurements (or both). The splitting is found to be 5
cm$^{-1}$ for bilayer and 2 to 5 cm$^{-1}$ for trilayer graphene. The
interlayer coupling is estimated to be about 2 cm$^{-1}$. We found that the
highest optical modes at K move up by about 12 cm$^{-1}$ for bilayer and 18
cm$^{-1}$ for trilayer relative to monolayer graphene. The atomic displacements
of these optical eigenmodes are analyzed.
