In summary, overtones and combination modes have been identified in the second-order spectra for the two dominant features in the first-order spectra (the radial breathing mode and the tangential mode) that are associated with the resonant Raman enhancement process arising from the 1D electronic density of states. Just as for the ease of the first-order spectra, the resonant contributions to the second-order spectra also involve a different set of (n, m) nanotubes at each laser excitation energy E{sub}(laser). A second-order analog is observed for the broad spectral band identified with contributions from metallic nanotubes to the first-order tangential mode spectra. The unique feature of the second-order tangential overtone band shows a larger E{sub}(laser) range over which the metallic nanotubes contribute, and this effect is attributed to the large (hω{sub}(phonon)～0.4eV) energy of these phonons. Combination modes associated with (ω{sub}(tang) + ω{sub}(RBM)) and (ω{sub}(tang) + 2ω{sub}(RBM)) have been identified. These combination modes show behaviors as a function of E{sub}(laser) that are consistent with the behavior of their first-order constituents, namely that different nanotubes contribute to the spectra at each value of E{sub}(laser). The behavior of the 'D-band' and G'-band features show a very large phonon frequency dependence on E{sub}(laser), and show a resonant 2D behavior when the electron and phonon wave vectors coincide, as also occurs in other sp{sup}2 carbons. Future Raman studies are likely to explore the relation between the Stokes and the anti-Stokes spectra as a function of E{sub}(laser). Surface-enhanced Raman scattering (SERS) is likely to be explored as a method for achieving much higher sensitivity, allowing exploration of the vibrational spectra of a small number of nanotubes and perhaps even eventually the Raman spectrum of a single nanotube.
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