Threshold characteristics of linear cavity Yb3+-doped double-clad fiber laser

Analytical solutions to rate equations including losses describing threshold pumped fiber lasers

“…At present, the rate equations (REs) are still the most widely used and powerful tool to theoretically predict the laser characteristics [6][7][8][9]. It is desirable if analytical solutions may be obtained for the REs.…”

“…From the previous reports, it can be realized that neglect of the loss coefficient (a s ) of the laser radiation is a precondition for obtaining approximated analytical results [8][9][10][11][12][13][14]. Another key point is either neglecting the background loss (a p ) of the pump wave [8,10,11] or making known the evolution of the pump radiation along the fiber [9,13,14].…”

“…Another key point is either neglecting the background loss (a p ) of the pump wave [8,10,11] or making known the evolution of the pump radiation along the fiber [9,13,14]. Chen et al [10,11] have derived some analytical results from the REs after neglecting a s and a p .…”

“…Considering the fact that the upper-level population N is negligibly small, Kelson et al [13,14] and Xiao et al [9] have extracted certain analytical expressions from the REs describing a double-clad RDFL. Hu et al [8] have obtained the expression for the threshold pump power of a double-clad fiber laser by solving REs without a s and a p , and compared the theoretical predictions with the experimental results. In typical double-clad RDFLs, a p is usually larger than the gain provided by the re-emission arising from the interaction between the pump photons and upper-level ions, and the assumptions taken in [9] and [13] are justified.…”

“…Under these circumstances, neglecting the quantity a p may be a better approximation. It is conceivable that neglecting a p and a s [8,10,11], or a s and N [13,14], definitely resulted in an underestimation of the threshold pump power and overestimation of the laser output power. In fact, Hu et al [8] have indicated that the threshold predicted by the approximated theory is slightly smaller than the measured result.…”