Due to their unique optical properties, carbon nanotubes have been widely investigated for use in photonic and optoelectronic devices and optical absorption and emission with nanotubes have been achieved in experiments. On the other hand, the structural characteristics of nanotubes, e.g. the chirality, diameter, and length, as well as other factors such as the polarization of the incident light, presence of a magnetic field and mechanical deformation can significantly affect the optical properties of these structures. Some of these effects have been theoretically studied at the tight-binding approximation level. However, a systematic first-principles-based study of nanotubes that addresses these effects did not exist in the literature prior to the present work. This thesis aims at performing such a fundamental study.

We first describe a method for calculating the dipole moments and transition rates in nanotubes. This also enables the study of selection rules, based on which a modified set of rules is defined. The probability of absorption is studied in the full range of infrared-visible-ultraviolet. We show that π-σ*, σ-π*, and σ-σ* transitions that are neglected in previous works are allowed and can lead to high probabilities of transition. We then investigate several effects caused by the curvature of the nanotube sidewall and their impacts on the optical properties. The overall effect is shown to not only depend on the diameter, but also on the chirality of the nanotube. Through the study of the light polarization effect, we show that the overall transition rate spectrum of the perpendicularly polarized light is suppressed for smaller-diameter nanotubes in the IR/VIS range. In the UV region, however, perpendicular polarization is generally absorbed at a higher rate compared to parallel polarization. Finally, we show how the absorption spectra of short nanotube segments can be different from those of long nanotubes. We examine the effect of length on individual absorption peaks and also investigate the effect of spin on the optical properties of nanotube segments. The calculation method described in this thesis and the results can be used to estimate the effects of structural and environmental factors on the optical absorption properties of nanotubes.