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 line shape exhibits Rabi splitting ∼ 0.1 eV as the exciton energy is tuned to the nearest interband surface plasmon resonance of the nanotube. We also show that the quantum confined Stark effect may be used as a tool to control the exciton binding energy and the nanotube band gap in carbon nanotubes in order, e. g., to bring the exciton total energy in resonance with the nearest interband plasmon mode. The exciton-plasmon Rabi splitting we predict here for an individual carbon nanotube is close in its magnitude to that previously reported for hybrid plasmonic nanostructures artificially fabricated of organic semiconductors on metallic films. We expect this effect to open up paths to new tunable optoelectronic device applications of semiconducting carbon nanotubes.

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The zero-point electromagnetic ͑Casimir͒ energy of an infinitely long cylindrical layer of finite thickness is calculated. The dielectric and magnetic properties of the layer and those of the surrounding medium are assumed to be described by real constant dielectric permittivities and magnetic permeabilities satisfying the relationship of constant speed of light across the interfaces. We use the mode summation technique together with the Riemann-function regularization procedure to remove the occurring divergences from the Casimir energy. We present analytical expressions and numerical calculations for various limiting cases in terms of the radial dimension, curvature, and material composition of the cylindrical layer.