  Doppler-free spectroscopy using two counter-propagating dual-frequency laser
beams in alkali vapor cells has been demonstrated recently, providing the
detection of high-contrast sign-reversed natural-linewidth sub-Doppler
resonances. However, to date, only a qualitative theory based on a simplified
$\Lambda$-scheme model has been reported to explain underlying physics of this
phenomenon. In this work, we develop a general and extended theoretical model
of dual-frequency sub-Doppler spectroscopy (DF SDS) for Cs D1 line. The latter
considers the real atomic energy structure, main relaxation processes and
various nonlinear effects including optical pumping, optical transition
saturation, Zeeman and hyperfine coherent population trapping (CPT) states.
This model allows to describe quantitatively the respective contributions of
involved physical processes and consequently to estimate main properties
(height and linewidth) of detected sub-Doppler resonances. Experimental results
performed with a Cs vapor micro-fabricated cell are reported and explained by
theoretical predictions. Spatial oscillations of the sub-Doppler resonance
amplitude with translation of the reflection mirror are highlighted. Reported
results show that DF SDS could be a promising approach for the development of a
fully-miniaturized and high-performance optical frequency reference, with
applications in various compact quantum devices.
