Abstract
Unlike regular three-dimensional solids two of a nanotube dimensions are confined and quantized. Bulk samples consist of irregular networks of merging and splitting bundles of parallel tubes. On a local scale, nanotubes are at the same time one-dimensional crystals and two-dimensional quantum rings. They have attracted extensive studies on individual aspects in their electronic and optical properties [1]. The current contribution aims at bridging the fundamental physical concepts behind carbon nanotubes to their unique spectroscopic signatures in optical absorption, luminescence, Raman and electron energy loss spectroscopy. The aim is not to compete with the local depth of a focused review, but to briefly convey the physical concept and related spectroscopic signatures of one-dimensionality. Indirect signatures are the manifold appearances of van Hove singularities in their optical transitions. Direct probes of one-dimensionality unveil the confined momentum space, which manifests in the distinction of localized and propagating excitations.