  Electroabsorption spectroscopy of well-identified index-defined
semiconducting carbon nanotubes is reported. The measurement of high definition
electroabsorption spectra allows direct indexation with unique nanotube
chirality. Results show that at least for a limited range of diameters,
electroabsorption is directly proportional to the exciton binding energy of
nanotubes. Electroabsorption is a powerful technique which directly probes into
carbon nanotube excitonic states, and may become a useful tool for in situ
study of excitons in future nanotube-based photonic devices such as
electroabsorption modulators.
