  Environmental dielectric screening effects on exciton transition energies in
single-walled carbon nanotubes (SWNTs) have been studied quantitatively in the
range of dielectric constants from 1.0 to 37 by immersing SWNTs bridged over
trenches in various organic solvents by means of photoluminescence and the
excitation spectroscopies. With increasing environmental dielectric constant
($\epsilon_{\rm env}$), both $E_{11}$ and $E_{22}$ exhibited a redshift by
several tens meV and a tendency to saturate at a $\epsilon_{\rm env} \sim 5$
without an indication of significant ($n$,$m$) dependence. The redshifts can be
explained by dielectric screening of the repulsive electron-electron
interaction. The $\epsilon_{\rm env}$ dependence of $E_{11}$ and $E_{22}$ can
be expressed by a simple empirical equation with a power law in $\epsilon_{\rm
env}$, $E_{\rm ii} = E_{\rm ii}^{\infty} + A\epsilon_{\rm env}^{-\alpha}$. We
also immersed a sample in sodium-dodecyl-sulfate (SDS) solution to investigate
the effects of wrapping SWNTs with surfactant. The resultant $E_{11}$ and
$E_{22}$, which agree well with Weisman's data [Nano Lett. {\bf 3}, 1235
(2003)], are close to those of $\epsilon_{\rm env}$ of 2. However, in addition
to the shift due to dielectric screening, another shift was observed so that
the ($2n+m$)-family patterns spread more widely, similar to that of the
uniaxial-stress-induced shift.
