On the normalisation of the observed spectral gain line profile with increasing optical thickness of a substance layer

It is shown that a spectral gain line narrows down and its profile is normalised with increasing optical thickness of a layer of the amplifying medium. As a result, the gain line profile always becomes Gaussian, independently of the true form factor of the line, when the thickness of the active medium layer is sufficiently large. The normalisation of the line profile is demonstrated for the lines with Lorentzian, Gaussian, and ‘time-of-flight’ profiles.