  We present an \textit{ab initio} study based on density-functional theory of
first- and second-order Raman spectra of graphene-based materials with
different stacking arrangements and numbers of layers. Going from monolayer and
bilayer graphene to periodic graphitic structures, we investigate the behavior
of the first-order G-band and of the second-order 2D-band excited by the same
set of photon energies. The former turns out to be very similar in all
considered graphene-based materials, while in the latter we find the signatures
of individual structures. With a systematic analysis of the second-order Raman
spectra at varying frenquency of the incident radiation, we monitor the Raman
signal and identify the contributions from different phonon modes that are
characteristic of each specific arrangement. Supported by good agreement with
experimental findings and with previous theoretical studies based on
alternative approaches, our results propose an effective tool to probe and
analyze the fingerprints of graphene-based and other low-dimensional materials.
