Upconversion pumping of lasers via excited-state absorption: an analytical rate-equation formulation

Coupled power-gain equations were used to model lasers where optical pumping occurs as a result of a weak ground-state absorption followed by strong pump excited-state absorption (ESA). Inspired by the gain dynamics and energy-level structure of upconversion-pumped 2.3 µm T m 3 + lasers and 3.4 µm E r 3 + lasers, the model assumes that population in the lower laser level relaxes via a fast nonradiative decay to an intermediate storage level, which typically has a considerably slower decay rate than that of the upper laser level. After obtaining a description of the rate equation model, the continuous-wave regime was investigated by deriving analytical expressions for the power-dependent absorption, threshold pump power for lasing, output laser power, and laser slope efficiency. Results indicate that a slow decay rate of the lower level is necessary, so that sufficient population buildup can lead to enhanced nonlinear absorption via ESA. Furthermore, the asymptotic slope efficiency of the ESA pumped laser is similar to that of the ideal four-level laser, where the linear absorption is replaced by the effective nonlinear absorption.