Optical transitions in carbon nanotubes

Analytical expressions for the optical matrix elements of semiconducting carbon nanotubes are obtained for different polarizations of the incident light. It is shown that, for the light polarized along the nanotube axis and transitions between the extrema of electronic subbands, the optical matrix element only weakly depends on the nanotube chirality and excitation energy. It is found that, for the light polarized in the plane perpendicular to the nanotube axis, both v²→c¹ and v¹→c² transitions are allowed.