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 $({\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}),$ via the parameters fitting from time series. The technique consists of minimizing a ${\chi }^2$ function which is constructed by transforming the original rate-equation system into its standard form. The value obtained for ${\sigma }_a,$ $(2.5\mathrm{}\pm 0.3)\times {10}^{-18}{\mathrm{cm}}^2,$ is consistent with previously reported results that had dispersion of more than one order of magnitude.