To analyze the saturating process of $Cr^{4+}:YAG$ crystal and plastic organic dye as the saturable absorber, we have measured the residual optical losses between a free running and a passive Q-switching mode for various optical densities. The undepleted ground state population density and the saturated transmission of the saturable absorber have been evaluated by the additional optical losses with the increased threshold pump energies between two resonators. ill the passive Q-switching mode, the saturable transmission of saturable absorber is less than the maxrnium saturable transmission due to the undepleted ground state population density. nsity.