Energy transfer processes in rare-earth-doped glass fiber

In the development of fiber sources emitting in the mid-infrared, the primary light emitter is typically a rare-earth ion that is doped into an optical fiber composed of soft glass. For a number of transitions, the most important to date being the 3 µm transitions of Er³⁺ and Ho³⁺, it has been found necessary to either codope with another rare-earth ion to quench the lower laser level, or involve high rare-earth ion concentrations so that favorable energy transfer processes can increase the optical gain. For these cases, the transfer of energy between the rare-earth ions takes place resulting in a redistribution of the populated electronic states of the ions. In this chapter, we will introduce the basic concepts and theory of energy transfer between excited and ground states of the rare-earth ions. In the modeling of mid-infrared photonic systems, a rate equation approach is typically used. The understanding of energy transfer and the quantization of the energy transfer parameters is needed so that the transfer parameters (e.g., in units of s^-1) can be used in numerical modeling of mid-infrared fiber light source systems. Numerical modeling of fiber lasers employing codoping is particularly important and in conjunction with spectroscopic measurements, understanding and optimization of the overall system can result. Since the concentration of rare-earth ions used for mid-infrared fiber photonics is never greater than 10mol%, we will not be discussing the exchange interaction. We also examine the temporal behavior derived from experimental measurements from a number of rare-earth ions that exhibit mid-infrared emission and demonstrate the essential characteristics of the various types of energy transfer.