A comprehensive model of erbium-doped fiber amplifiers (EDFA) is propo
sed in this paper, taking exited-state absorption (ESA), amplified spo
ntaneous emission (ASE), background absorption, mode field, and Erbium
ion radial distribution into account. Computer programs capable of ha
ndling forward, backward, and different wavelength bidirectional pumpi
ng are developed. Among other things, it is found that under typical c
onditions, Gaussian field approximations may cause considerable errors
. The optimum V-value for small signal gain is much smaller than that
for minimum Gaussian or Desurvire spot size; ASE propagating opposite
to the pump beam can be several times higher than at propagating along
the pump beam, resulting in a faster-than-linear decrease of the pump
power at its beginning portion. Experimental results of domestic-made
erbium-doped fibers pumped by 980 nm and 1480 nm laser diodes are als
o given.