Homogeneous line broadening transition probabilities

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... 

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,... 

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