Amplified spontaneous emission (ASE) models and approximations for thin-disk laser modeling

Abstract

It is well–known that amplified spontaneous emission (ASE) can be a major source of upper laser level loss in high gain pulsed or steady–state solid state lasers. This paper briefly reviews the theory of ASE and, using a simple rate equation model of the upper laser level, a geometric, radiative transport equation to describe the ASE intensity, and the perturbation method of multiple time scales, demonstrates that the loss rate of the upper laser level due to ASE adiabatically follows the spontaneous emission source term. This result which includes gain saturation is applicable to both quasi–three level and four level lasers and rigorously justifies formally using the steady–state expression derived heuristically by Lowenthal and Eggleston 1 to model ASE loss in pulsed laser media. Then, it is shown that the frequency integral occurring in the ASE loss term can be evaluated analytically for both a broad “flat–top” and a Lorentzian stimulated emission lineshape but must be evaluated numerically or using an approximation due to Tommasini and Balmer 2 for a Gaussian stimulated emission lineshape. It is shown that at high gain loss due to ASE is mitigated by ASE line narrowing. For a thin disk laser an approximate expression for the rate of ASE loss (or ASE lifetime) can be obtained by evaluating the remaining volume integral using either the method of Speiser 3 or of Vretenar et al 4 . A new approximate expression for the ASE loss rate is obtained which, unlike Speiser’s 3 expression, accounts for ASE line narrowing and, unlike Vretenar et al’s 4 expression, correctly scales with the cylindrical volume of the disk. Application to both 1D and 3D laser modeling is briefly discussed.