We have carried out a first principles calculation on the electronic structure, dielectric function and energy loss spectra of single-walled carbon nanotubes (SWCNTs). Calculations of optical spectra have been performed under electric fields polarized both parallel and perpendicular with respect to the nanotube axis. Our results show that the dielectric function is strongly anisotropic and much larger for the applied electric field parallel than perpendicular to the tube axis. We have calculated first, second, and third optical transitions in several SWCNTs with different chiralities, diameters and lengths. It is revealed that the absorption spectra of 4 Å single-walled carbon nanotubes depend strongly on their chiralities, while the absorption spectra of nanotubes with large diameter hardly show any chirality dependence. The results show that unlike the optical absorption, the energy loss function of SWCNTs does not significantly depend on chirality and show weak anisotropy. It is also found that the energy loss function peaks for electric fields polarized both parallel and perpendicular to the tube axis happen almost at the same energies, but with rather difference amplitudes.

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