Exact Analytical Formulism for Erbium Doped Fiber Lasers

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.