Amplified spontaneous emission and maximum gain–length product revised for general line shapes

The theory of amplified spontaneous emission (ASE) and the gain–length product at saturation is revised. Formulas valid for both peak and integrated lines are given. In the latter case the solution for a general Voigt stimulated-emission line shape is presented, whereas in the two limiting cases of Gaussian and Lorentzian line shapes an approximation better than the one obtained by the steepest-descent method is successfully achieved. Various parameters that take into account the ratio of spontaneous to stimulated linewidths, the form factor depending on the linewidths of the inhomogeneous and homogeneous convoluted line shapes, and the population inversion fraction arise from the theory, giving the complete functional dependence for both the ASE photon flux and the gain–length product.