Theoretical Model of a Thulium-Doped Fiber Amplifier Pumped at 1570 nm and 793 nm in the Presence of Cross Relaxation

The static behavior of a thulium-doped fiber amplifier (TDFA) operating around 2 μm region at different pump wavelengths is investigated in this paper. A theoretical model is built up by solving a set of rate and propagation equations with considering the effect of cross relaxation mechanism. The developed model provides the influences of the amplified spontaneous emission noise, seed wavelength, and the thulium-doped fiber length into the TDFA performance. Simulation results indicate that the TDFA performance with pump at 1570 nm is more efficient than pump at 793 nm for core pumped thulium-doped silica fiber. Our findings show that the maximum gain reaches up to 30 dB with a 27 dBm pump power when a -10 dBm seed wavelength at 1840 nm is used. In contrast to indirect pumping at 793 nm, only 22 dB maximum gain is achieved under the same conditions. The model is also validated with previous experimental work. Our simulations are consistent with the experimental findings with small variations.