  We calculate the optical properties of carbon nanotubes in an external static
electric field directed along the tube axis. We predict strong Franz-Keldysh
oscillations in the first and second band-to-band absorption peaks, quadratic
Stark effect of the first two excitons, and the field dependence of the bound
exciton ionization rate for a wide range of tube chiralities. We find that the
phonon assisted mechanism dominates the dissociation rate in electro-optical
devices due to the hot optical phonons. We predict a quadratic dependence of
the Sommerfeld factor on the electric field and its increase up to 2000% at the
critical field of the full exciton dissociation.
