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.
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