Lorentzian broadened absorption line profile

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

There are some further steps, which should also be included, and are quite straightforward in practice. The true profiles of the absorption lines are not Lorentzian, as assumed in the simple theory above, but are broadened by the Maxwellian velocity distribution ... 

V sinO < y/k, the molecule after the collision is still in resonance with the standing light wave inside the laser resonator. Such soft collisions with deflection angles 0 < therefore do not appreciably change the absorption probability of a molecule. Because of their statistical phase jumps (Vol. 1, Sect. 3.3) they do, however, contribute to the linewidth. The line profile of the Lamb dip broadened by soft collisions remains Lorentzian. 

Since the absorption profile a(co) of a homogeneously broadened line is Lorentzian, see (3.36b), the induced absorption probability of a monochromatic wave with frequency o) follows a Lorentzian line profile B[2p(co) L co — coo). We can therefore introduce a frequency-dependent spectral saturation parameter 5 for the transition E E2,... 

If the probability Tik(co) of absorption or emission of radiation with frequency a> causing a transition Ek is equal for all the molecules of a sample that are in the same level i ,, we call the spectral line profile of this transition homogeneously broadened. Natural line broadening is an example that yields a homogeneous line profile. In this case, the probability for emission of light with frequency u> on a transition with the normalized Lorentzian profile L (o—u>o) and central frequency coq is given by... 

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