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.
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