Estimating the Raman Cross Sections of Single Carbon Nanotubes

The order of magnitude of Raman differential cross sections of radial breathing modes (RBMs) of individual carbon nanotubes is measured for 633 and 785 nm laser excitations. This is shown by both a calibration applied to previously published data from other authors at 785 nm and our own measurements of individual nanotubes at 633 nm excitation. We find typical values of differential cross sections of RBMs to be on the order of ∼10<sup>−22</sup> cm<sup>2</sup>/sr for resonant nanotubes on a silicon substrate. This study therefore provides a rigorous quantification of the accepted view that Raman cross sections of carbon nanotubes are “huge”.