We report a unique assignment of the chiral index (n1,n2) of carbon nanotubes to their optical transition energies and radial-breathing-mode frequencies. Our results provide a fast and easy method to assign nanotubes in an unknown sample by Raman spectroscopy using only one or a few excitation energies. Given the assignment, we can analyze how the optical and vibrational properties of carbon nanotubes depend on the chirality. We observe systematic dependences of the Raman scattering cross section on the chiral angle, indicating that the Raman and fluorescence intensity is not solely correlated to the chirality distribution.
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