  We have measured the electric field modulated absorption of a sample of
single-walled nanotubes (SWNT) suspended in a solid polyvinyl alcohol matrix.
The electroabsorption (EA) spectrum roughly follows the first derivative of the
absorption with respect to photon energy, scales quadratically with the
electric field strength, and shows a pronounced anisotropy of light
polarization with respect to the applied electric field direction. These
findings indicate a quadratic Stark effect caused by a change in the
polarizability of the excited states, which is common to quasi-one dimensional
(1D) excitons in organic semiconductors. The EA spectrum is well described by
calculations involving electron-electron interaction in the model Hamiltonian
of both zigzag and chiral nanotubes. We have calculated the EA spectra for both
zigzag and chiral nanotubes within a model Hamiltonian that includes
electron-electron interactions. The calculations reproduce the observed
quadratic Stark shift of the lowest optical exciton, as well as the more
complicated behavior of the EA spectrum in the energy region that corresponds
to the next higher exciton. Our findings show that the low-lying absorption
bands in semiconducting SWNT are excitonic in origin, in agreement with
transient optical measurements that identify the primary photoexcitations in
SWNT as quasi-1D excitons with a substantial binding energy.
