Theory of Spatial Coherence in Near-Field Raman Scattering

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A theoretical study describing the coherence properties of near-field Raman scattering in two-and onedimensional 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 nonpropagating) 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 the correlation length L c of optical phonons from experimentally recorded near-field Raman measurements.The coherence properties of optical phonons have been broadly explored in the time and frequency domains, and the spatially resolved approach presented here provides a complementary methodology for the study of local material properties at the nanoscale.