  A theoretical study describing the coherence properties of near-field Raman
scattering in two- and one-dimensional systems is presented. The model is
applied to the Raman modes of pristine graphene and graphene edges. Our
analysis is based on the tip-enhanced Raman scheme, in which a sharp metal tip
located near the sample surface acts as a broadband optical antenna that
transfers the information contained in the spatially-correlated (but
non-propagating) near-field to the far-field. The dependence of the scattered
signal on the tip-sample separation is explored, and the theory predicts that
the signal enhancement depends on the particular symmetry of a vibrational
mode. The model can be applied to extract of the correlation length $L_{\rm c}$
of optical phonons from experimentally recorded near-field Raman measurements.
Although the coherence properties of optical phonons have been broadly explored
in the time and frequency domains, the spatially-resolved approach presented
here provides an alternative probe for the study of local material properties
at the nanoscale.
