  Saturation effects affecting absorption and fluorescence spectra of an atomic
vapor confined in an Extremely Thin Cell (cell thickness $L < 1 \mu m$) are
investigated experimentally and theoretically. The study is performed on the
$D_{2}$ line ($\lambda ~= ~852 nm)$ of $Cs$ and concentrates on the two
situations $L = \lambda /2$ and $L =\lambda$, the most contrasted ones with
respect to the length dependence of the coherent Dicke narrowing. For $L =
\lambda /2$, the Dicke-narrowed absorption profile simply broadens and
saturates in amplitude when increasing the light intensity, while for $L
=\lambda$, sub-Doppler dips of reduced absorption at line-center appear on the
broad absorption profile. For a fluorescence detection at $L =\lambda$,
saturation induces narrow dips, but only for hyperfine components undergoing a
population loss through optical pumping. These experimental results are
interpreted with the help of the various existing models, and are compared with
numerical calculations based upon a two-level modelling that considers both a
closed and an open system.
