Analytical method for gain in erbium doped fiber amplifier with pumb excited state absorption

Analytical solutions to rate and propagation equations describing gain in terms of photon intensities, transition rates, and absorption and emission cross-sections is determined in radially symmetric and longitudinally uniform monomode erbium doped silica fiber in presence of pump excited-state absorption effect for a pumping wavelength of 514.5 nm under the steady-state conditions with the help of a homogenous four-band transition scheme.

► A newly derived formalism for the gain in EDFA with ESA effect is presented here.
► The analytical expressions match well with previous results once ESA is ignored.
► Our results are comprehensive and can be applied to other amplifiers and lasers.