  We study theoretically the interactions of excitonic states with surface
electromagnetic modes of small-diameter (~1 nm) semiconducting single-walled
carbon nanotubes. We show that these interactions can result in strong
exciton-surface-plasmon coupling. The exciton absorption lineshapes exhibit the
line (Rabi) splitting $~0.1-0.3$ eV as the exciton energy is tuned to the
nearest interband surface plasmon resonance of the nanotube. We expect this
effect to open a path to new optoelectronic device applications of
semiconducting carbon nanotubes.
