Quantitative information from time series: Cr : yttrium-aluminum-garnet cross-section measurement

Ln this paper we show how to use the richness of the dynamic responses of a physical system to perform a nontrivial measurement. In particular, we hav e calculated the Cr:YAG (YAG denotes yttrium aluminum garnet) absorption cr oss section in an optical system, namely, a solid-state laser (Nd:YAG) with a saturable absorber (Cr4+:YAG), via the parameters fitting from time seri es. The technique consists of minimizing a chi(2) function which is constru cted by transforming the original rate-equation system into its standard fo rm. The value obtained for sigma(a), (2.5 +/- 0.3) x 10(-18) cm(2), is cons istent with previously reported results that had dispersion of more than on e order of magnitude.