The saturation intensity, $I_{\text{s}}$, of alkali vapors is often quoted for their strongest closed, nondegenerate two-level transition. In realistic atomic systems, however, level degeneracy and optical pumping substantially modify the saturation behavior. This paper presents a robust technique for measuring the saturation intensity of alkali vapors under real experimental conditions. Central to this approach is the derivation of a generalized Maxwell-based Beer-Lambert equation and its implementation for a three-level system (an upper level, two lower levels). We apply this technique to natural rubidium vapor $(27.8\%{}^{87}\mathrm{Rb}+72.2\%{}^{85}\mathrm{Rb})$ and determine the saturation intensities of all Doppler-broadened ${\text{D}}_2$-line transitions, probed by a linearly polarized laser beam at vapor temperatures $25–33{}^{\circ }\text{C}$. We find that all transitions exhibit $I_{\text{s}}$ in the range $31–34\text{W}{\text{m}}^{-2}$, roughly twice the commonly cited value $16.70\text{W}{\text{m}}^{-2}$. This technique also yields the hyperfine optical pumping factor $\beta$, which ranges from 3.1 to 22 across the transitions and can depend on intensity, leading to accelerated saturation. Accurate determination of the $I_{\text{s}}$ and $\beta$ values under experimentally relevant conditions allows more precise modeling and quantitative exploitation of alkali-vapor nonlinearities.

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• Atom optics
• Electronic polarizability
• Electronic susceptibility
• Light-matter interaction
• Nonlinear optics
• Optical pumping
• Atomic systems
• Atoms