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

In 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 have calculated the Cr:YAG (YAG denotes yttrium aluminum garnet) absorption cross section in an optical system, namely, a solid-state laser (Nd:YAG) with a saturable absorber (Cr⁴⁺:YAG), via the parameters fitting from time series. The technique consists of minimizing a χ² function which is constructed by transforming the original rate-equation system into its standard form. The value obtained for σ_a, (2.5±0.3)×10^-18 cm², is consistent with previously reported results that had dispersion of more than one order of magnitude.