Analytical model for rare-earth-doped fiber amplifiers and lasers

An analytical model for two-, three-, and four-level system rare-earth-doped fiber amplifiers and lasers is presented. The theory is applicable to dopants such as erbium, neodymium, thulium; praseodymium, and ytterbium. Fiber-amplifier gain is expressed in terms of attenuation coefficients, intrinsic saturation powers, and cross-saturation powers at the pump and signal wavelengths. These parameters can be directly determined from one- and two-beam fiber-transmission measurements. System-independent formulas are given for the slopes and thresholds of ring and linear fiber lasers. Good agreement between theory and experiment has been shown for erbium-doped fiber amplifiers and lasers and thulium-doped fiber lasers. Because of the finite-pump-level lifetime, three- and four-level models predict a flattening of the fiber laser slope at higher pumping powers when the fiber is shorter than the optimum length. Approximate system-independent solutions are also given for fiber amplifiers with excited-state absorption at either the pump or signal wavelengths. A novel technique, requiring only one tunable light source, is proposed for finding the best pump wavelength when pump ESA is present. The two-level analytical model recently developed for erbium-doped fibers is a special case of this theory