Recent theoretical studies on exciton absorption in carbon nanotubes in an effective-mass approximation are
reviewed. It is clarified that one-dimensional character plays important roles in optical properties of carbon
nanotubes. For semiconducting tubes, exciton effects for polarization perpendicular to the tube axis cause
prominent peaks in optical absorption spectra in spite of the depolarization effect. Calculated excited exciton
energies for parallel polarization well reproduce measured energies for one- and two-photon absorption. Excitons
can also exist in metallic carbon nanotubes.
A brief review is given of electronic and optical properties of carbon nanotubes mainly from a theoretical point of view. The topics cover an effective-mass description of electronic states, Aharonov-Bohm effects, and optical absorption including interaction effects on the band structure gap and excitonic effects.