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 erbiumdoped 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 erbiumdoped fibers is a special case of this theory.