Abstract

Calculation of the gain of erbium-doped fiber amplifiers (EDFAs) generally uses numerical integration of coupled, nonlinear, differential equations and requires knowledge of parameters such as the erbium atom density, spontaneous lifetimes, and the fiber active area, as well as the absorption cross-section, emission cross-section, and confinement factor for each wavelength involved [1], [2]. We derive analytic expressions from which the gain can be calculated by solving one transcendental equation. We show that a complete understanding of the input-output characteristics of a fiber amplifier of any length can be obtained from simple absorption measurements. This remarkable result is valid provided excited-state absorption [2], [3] and gain saturation due to amplified spontaneous-emission noise can be neglected. Measurements of saturated and unsaturated gain agree to better than 0.5 dB with gains predicted from absorption data.

© 1990 Optical Society of America