  We analyze optical absorption by atomically doped carbon nanotubes with a
special focus on the frequency range close to the atomic transition frequency.
We derive the optical absorbtion line-shape function and, having analyzed
particular achiral nanotubes of different diameters, predict the effect of
absorbtion line splitting due to strong atom-vacuum-field coupling in
small-diameter nanotubes. We expect this effect to stimulate relevant
experimental efforts and thus to open a path to new device applications of
atomically doped carbon nanotubes in modern nanotechnologies.
