Dependence of partially saturated polarization spectroscopy signals on pump intensity and collision rate

Understanding the saturation behavior of polarization-spectroscopy signals is a vital task for the development of this method as a versatile tool for quantitative detection of trace species. Recent progress in the theoretical treatment of the polarization-spectroscopy process offers the opportunity of studying its saturation behavior thoroughly. This theoretical treatment, referred to as direct numerical integration (DNI) calculations, is based on numerically demanding calculations; that is why we present a simple model that describes the curve shape of polarization spectroscopy power-dependence scans in both the saturated and the unsaturated regime. Polarization-spectroscopy-saturation curves in the copropagating beam geometry from the excitation of OH A²Σ⁺--X²Π(0,0) at the Q₂(8) line in a low-pressure flame were compared to both results from the DNI calculations and to our proposed analytical equation. Our simple model provides excellent fits to polarization-spectroscopy-saturation curves for absorption lines dominated by homogeneous broadening and for narrow-bandwidth excitation sources. The model does not give a good agreement with experiment for lines dominated by inhomogeneous broadening. For this case an empirical equation is proposed and investigated. Our proposed model offers a starting point for a simplification of the underlying polarization-spectroscopy theory, the complexity of which has been a major obstacle to the further development of this theory.