Investigation of Non-Linear Energy Transfer Dynamics of Erbium in Yttrium Aluminum Garnet

Yttrium Aluminum Garnet (YAG, Y_3 〖Al〗_5 O_12) crystals doped with Erbium have posed an interesting position in the field of rare earth solid state lasers as they possess the property of self-saturation, in which the upper energy level in a laser has a much shorter lifetime than that of the lower level. This is the case of the 2.94μm transition in Er:YAG. That property at first seems to make this material unfit for use as a laser gain medium, however further research into these classes of rare earth materials revealed interesting non-liner energy transfer mechanisms that allow it to be a useful mid wave infra-red (MWIR) coherent source in the continuous wave (CW) and pulsed regimes. This came to fruition due to decades of modeling and spectroscopic research investigating the non-linear energy transfer mechanisms of excited state absorption (ESA), energy transfer up-conversion (ETU), and cross relaxation (XR). These effects show up in the rise and fall times of the levels observed through fluorescence. Resulting in the non-exponential rise and fall characteristics and having a squared or even cubed relation to the population. The population evolution for each of the lasing levels is now affected by ions recycling energy and in turn cause the lifetimes of the levels to “effectively” change to a point where simple linear models do not adequately describe the system and its performance. The non-linear energy transfer dynamics of Er:YAG are modeled under high resonant pump conditions. By pumping with selective resonant pumps, the interaction dynamics of the (_ ^4)I_(11/2) and the (_ ^4)I_(13/2) levels in the Erbium ion reveal the contributions from generally ignored non-linear energy transfer mechanisms. Specifically, the multi-photon effect known as excited state absorption (ESA) is modeled by measuring and characterizing the cross section in single crystal Er:YAG samples utilizing a pump and probe technique coupled with transient fluorescence measurements. The measured ESA cross section is then included in the rate equation modeling