question archive Absorption linewidth for an absorbing atomic transition

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Absorption linewidth for an absorbing atomic transition. Consider the curves of power transmission T(w) = exp[-20m (w)L] through an atomic medium with a lorentzian resonant transition, plotted versus normalized frequency detuning (w - Wa)/Awa for various values of the midband absorption factor 2am (Wa) L, as shown in this section. Suppose an "absorption linewidth" Awabs is defined as the full width of the power transmission profile T(w) at a level halfway down into the dip, i.e., halfway between the midband value T(wa) and the far-off-resonance value T = 1. Derive an expression for this linewidth Awabs as a function of the midband absorption 20m (Wa)L, and examine its limiting values for very small and very large absorptions.