  The nature of the primary photoexcitations in semiconducting single-walled
carbon nanotubes (S-SWCNTs) is of strong current interest. We have studied the
emission spectra of S-SWCNTs and two different $\pi$-conjugated polymers in
solutions and films, and have also performed ultrafast pump-probe spectroscopy
on these systems. The emission spectra relative to the absorption bands are
very similar in S-SWCNTs and polymers, with redshifted photoluminescence in
films showing exciton migration. The transient photoinduced absorptions (PAs)
in SWCNTs and $\pi$-conjugated polymers are also remarkably similar, with a low
energy PA$_1$ and a higher energy PA$_2$ in all cases. Theoretical calculations
of excited state absorptions within a correlated $\pi$-electron Hamiltonian
find the same excitonic energy spectrum for S-SWCNTs and $\pi$-conjugated
polymers, illustrating the universal features of quasi-one-dimensional excitons
in carbon-based $\pi$-conjugated systems. In both cases PA$_1$ is an excited
state absorption from the optically allowed exciton to a two-photon exciton
that occurs below the continuum band threshold. PA$_1$ therefore gives the
lower limit of the binding energy of the lowest optical exciton. The binding
energy of lowest exciton belonging to the widest S-SWCNTs with diameters $\geq$
1 nm in films is 0.3--0.4 eV, as determined by both experimental and
theoretical methods.
