  Photoluminescence excitation measurements in semi-conducting carbon nanotubes
show a systematic non-resonant contribution between the well known excitonic
resonances. Using a global analysis method, we were able to delineate the
contribution of each chiral species including its tiny non-resonant component.
By comparison with the recently reported excitonic absorption cross-section on
the $S_{22}$ resonance, we found a universal non-resonant absorbance which
turns out to be of the order of one half of that of an equivalent graphene
sheet. This value as well as the absorption line-shape in the non-resonant
window is in excellent agreement with microscopic calculations based on the
density matrix formalism. This non-resonant absorption of semi-conducting
nanotubes is essentially frequency independent over 0.5~eV wide windows and
reaches approximately the same value betweeen the $S_{11}$ and $S_{22}$
resonances or between the $S_{22}$ and $S_{33}$ resonances. In addition, the
non-resonant absorption cross- section turns out to be the same for all the
chiral species we measured in this study. From a practical point of view, this
study puts firm basis on the sample content analysis based on photoluminescence
studies by targeting specific excitation wavelengths that lead to almost
uniform excitation of all the chiral species of a sample within a given
diameter range.
