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Abstmc-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. I. INTRODUCI-IONINCE the first rare-earth-doped fiber lasers were built S over 20 years ago [l], many experimental and theoretical results on silica-and fluoride-doped fiber amplifiers and lasers with various rare-earth dopants have been reported. Commercially available erbium-doped fiber amplifiers (EDFA's) have already established their key role for 1.55 p m optical communication networks [21. Research is now rapidly advancing on praseodymium-and neodymium-doped fiber amplifiers for the 1.3 p m window [3], [4]. In active fibers the single mode maintains high pump and signal intensities over long interaction lengths resulting in the favorable combination of low loss and high gain from low-input pump power. This allows diode pumping and results in fiber lasers with high slope efficiencies and low threshold powers even when intracavity losses are high. Many doped fiber lasers have been reported with lasing wavelengths from 0.55 to 2.9 p m based on erbium (Er3+ ), neodymium (Nd3+), ytterbium (Yb3+ ),holmium (Ho3+ 1, thulium (Tm3+ 1, praseodymium (Pr3+ 1, and samarium (Sm3+) 121. The broadened linewidths of rare-earth ions in glass also enable wide tuning ranges [51 and are suitable for short-pulse mode locking [6]. Narrow linewidths and Q-switching have also been demonstrated 171, [81.Ongoing development of fiber lasers and amplifiers requires accurate and simple theoretical modeling. The theory of amplification and lasing in fibers differs from traditional laser models in two important aspects. First, the guiding property of single-mode fibers simplifies the analysis since transverse beam and ion profiles can be assumed to be constant along the fiber. Second, the active medium is confined to the central part of the beam profi...

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Stable and efficient self-mode locking in a Q-switched highly doped erbium fiber laser has been demonstrated. The proposed mechanism of the pulse formation based on self-phase modulation agrees well with the observed pulse characteristics.

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The dynamics of the green (2H11/12, 4S3/2) and red (4F9/2) upconversion emission excited by 15 ns pulses from an Er:fibre laser at 1500 nm are presented and analyzed. The upconversion process is found to fit a kinetic model, which includes both cross relaxation and energy transfer.