Amplified spontaneous emission and maximum gain-length product revised forgeneral line shapes

The theory of amplified spontaneous emission (ASE) and the gain-length prod uct at saturation is revised. Formulas valid for both peak and integrated l ines are given. In the latter case the solution for a general Voigt stimula ted-emission line shape is presented, whereas in the two Limiting cases of Gaussian and Lorentzian Line shapes an approximation better than the one ob tained by the steepest-descent method is successfully achieved. Various par ameters that take into account the ratio of spontaneous to stimulated linew idths, 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 t he ASE photon flux and the gain-length product. (C) 1999 Optical Society of America [S0740-3224(99)01904-9] OCIS codes: 140.3430, 140.3280.