  We use the macroscopic quantum electrodynamics approach suitable for
absorbing and dispersing media to study the properties and role of collective
surface excitations --- excitons and plasmons --- in single-wall and
double-wall carbon nanotubes. We show that the interactions of excitonic states
with surface electromagnetic modes in individual small-diameter (<~1 nm)
single-walled carbon nanotubes can result in strong exciton-surface-plasmon
coupling. Optical response of individual nanotubes exhibits Rabi splitting ~0.1
eV, both in the linear excitation regime and in the non-linear excitation
regime with the photoinduced biexcitonic states formation, as the exciton
energy is tuned to the nearest interband surface plasmon resonance of the
nanotube. An electrostatic field applied perpendicular to the nanotube axis can
be used to control the exciton-plasmon coupling. For double-wall carbon
nanotubes, we show that at tube separations similar to their equilibrium
distances interband surface plasmons have a profound effect on the inter-tube
Casimir force. Strong overlapping plasmon resonances from both tubes warrant
their stronger attraction. Nanotube chiralities possessing such collective
excitation features will result in forming the most favorable inner-outer tube
combination in double-wall carbon nanotubes. These results pave the way for the
development of new generation of tunable optoelectronic and
nano-electromechanical device applications with carbon nanotubes.
