Analytic modeling of erbium-doped fiber amplifiers on the basis of intensity-dependent overlapping factors

Rate equations based on intensity-dependent overlapping factors are integrated to obtain analytic solutions for pump, signal, and amplified spontaneous emission (ASE), even when the coupled signal varies with time. The equations can be applied without the imposition of any restraints on the values of the pump, signal, and ASE powers, the excited-state-absorption cross section, the erbium-density distribution, or other parameters that characterize the fiber. The methods used to calculate pump, signal, and ASE powers are discussed. Experimental techniques to characterize the doped fiber that were based on these analytic expressions are introduced.