Abstract
An exact analytical formulism obtained directly by solving a system of rate and propagation equations
in the presence of pump excited-state absorption is presented on the basis of four-band transition scheme in radially
symmetric and longitudinally uniform monomode erbium doped silica fiber lasers. The exact analytical expressions are
determined for overall gain, small-signal gain, pump intensity threshold, lasing threshold condition, and optimal
fiber length in terms of alleviative measurable quantities of photon intensities, transition rates, absorption and
emission cross sections, and reflectivity of mirrors. Mutatis mutandis, the
formulas bear a verisimilitude to analytical expressions appearing in the literature for these parameters.
© 2013 IEEE
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