Saturation Broadening of Homogeneous Line Profiles

The power absorbed per unit volume on the transition l) — 2) by atoms with the population densities N, N2 in a radiation field with a broad spectral profile with spectral energy density p is according to (2.15) and (3.79) 

Since the absorption profile a(w) of a homogeneously broadened line is Lo-rentzian, see (3.36b), the induced absorption probability of a monochromatic wave with frequency w follows a Lorentzian line profile Bi2p(w)L(w-Wo). We can therefore introduce a frequency-dependent spectral saturation parameter for the transition -+ E2, 

We can assume that the mean relaxation rate (R) is independent of w within the frequency range of the line profile. With the definition (3.36b) of the Lorentzian profile L(w-wo), we obtain for the spectral saturation parameter 

Substituting (3.85) into (3.83) yields the frequency dependence of the absorbed radiation power per unit frequency interval dw = 1 Hz 

This a Lorentzian profile with the increased half width 

The halfwidth ys = 8ms of the saturation-broadened line increases with the saturation parameter Sb at the lin center mo. If the induced transition rate at equals the total relaxation rate R, the saturation parameter So = [Bi2p coo)]/R becomes -So = 1, which increases the linewidth by a factor /2, compared to the imsaturated linewidth 8mo for weak radiation fields (p 0). 

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Figure 3.23 Saturation broadening of a homogeneous line profile...

In Sect.2.8, we saw that a sufficiently strong radiation field can significantly change the population densities and N2 of an atomic system by induced absorption and emission. This saturation of the population densities also causes additional line broadening. The spectral line profiles of such partially saturated transitions are different for homogeneously and for in-homogeneously broadened lines [3.19]. We treat first the homogeneous case. 

In Vol. 1, Sect. 3.6 we saw that the saturation of homogeneously broadened transitions with Lorentzian line profiles results again in a Lorentzian profile with the... 

However, when the frequency is coincident with the center frequency of the Doppler profile, the weak probe wave interacts with molecules whose absorption has already been reduced by the strong counterrunning wave. Consequently, the absorption of the probe wave has a resonant minimum equal in width to the homogeneous width and centered exactly on the Doppler-broadened absorption line. This method has been demonstrated in experiments using a CO2 laser operating at 10/um and SFe molecules (Basov et al. 1969), and now it is universally accepted in laser saturation spectroscopy. 

Fig.3.19a-c. Saturation by a monochromatic standing wave, (a) Population distribution n(v ) for 03 coq. (b) Absorption coefficient a(o3) of an in-homogeneously broadened line, as obtained when tuning the frequency U3 of the standing wave across the line profile, (c) Saturation of a homogeneous absorption profile... 

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