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Erbium-doped fiber amplifiers are modeled using the propagation and rate equations of a homogeneous, two-level laser medium. Numerical methods are used to analyze the effects of optical modes and erbium confinement on amplifier performance, and to calculate both the gain and ASE spectra. Fibers with confined erbium doping are completely characterized from easily measured parameters: the ratio of the linear ion density to fluorescence lifetime, and the absorption of gain spectra. Then analytical techniques allow accurate evaluation of gain, saturation, and noise in low-gain amplifiers ( G s 20 dB).

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Traveling-wave amplification of a lambda = 1.53 microm signal with +22-dB gain is achieved at 295 K in an Er(3+)-doped single-mode fiber using a lambda = 514.5 nm pump source. The optimum fiber length for maximum gain is determined experimentally. A limit in signal-to-noise ratio that is due to concurrent amplification of spontaneous emission is observed. By cooling the fiber to 77 K, the amplifier gain is increased to +29 dB as a result of depopulation of the lower laser level.