Abstract

Reference 1 derives the two-photon probe-absorption coefficient for a homogeneously broadened medium subjected to an arbitrarily intense saturator wave. We have generalized this theory to allow for Doppler broadening with a counterrunning probe and saturator waves. We have carried out integrals over a Lorentzian Doppler distribution analytically and have specialized to a number of limits, such as extreme Doppler broadening. In this limit, we find the simple probe absorption coefficient ${\alpha }_1\simeq 2{\alpha }_0\left(\text{γ}{\mathcal{D}}_1{I}_2-i{\text{ω}}_s{T}_1\right)$, where α₀ is the unsaturated two-photon absorption coefficient, I₂ is the saturator intensity, γ is the two-photon coherence decay rate constant, ω_s is the Stark shift parameter, T₁ is the population difference decay time, and ${\mathcal{D}}_1=1/\left[\text{γ+}i\left({\text{ω+ω}}_s{I}_2-{\nu }_2-{\nu }_1\right)\right]$. For vanishing Stark shifts (ω_s = 0), this is the standard two-photon probe absorption coefficient, but for large ω_s, the complex Lorentzian ${\mathcal{D}}_1$ becomes detuned. In the homogeneously broadened limit, the absorption spectrum resembles the one-photon case. In this paper we show the transition between these two limits.

© 1985 Optical Society of America