  We analyze optical soliton propagation in the presence of weak absorption
lines with much narrower linewidths as compared to the soliton spectrum width
using the novel perturbation analysis technique based on an integral
representation in the spectral domain. The stable soliton acquires spectral
modulation that follows the associated index of refraction of the absorber. The
model can be applied to ordinary soliton propagation and to an absorber inside
a passively modelocked laser. In the latter case, a comparison with water vapor
absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with
experiment. Compared to the conventional absorption measurement in a cell of
the same length, the signal is increased by an order of magnitude. The obtained
analytical expressions allow further improving of the sensitivity and
spectroscopic accuracy making the soliton absorption spectroscopy a promising
novel measurement technique.
