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.
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