Optical characterizations of densely doped Tm$^{3+}$: KYW crystals at low temperatures

We investigate the optical lifetime, decay characteristics, spectral linewidth and energy level properties of thulium ions doped in a KY(WO$_{\text{4}}$)$_{\text{2}}$ crystal at 4K temperature. High doping concentration of thulium ions with inhomogeneous broadening allow us to study nonradiative behaviors, instantaneous spectral diffusion, and spectral power broadening in this solid-state material. The theoretical consideration of ion-ion interactions is shown to accurately characterize the absorption, decay and other spectral behaviors of Tm$^{\text{3+}}$ ions. We observe more than ten-fold reduction in the decay time of $^3$H$_4$ state and about three-fold reduction in the spectral-hole lifetime as we approach the center of the inhomogeneous broadening, corresponding to higher optical densities.