Analytical Model for Broadband Thulium-Bismuth-Doped Fiber Amplifier

Due to the tremendous growth in applications for fiber laser in medical science, sensor solution, and light detection and ranging system at 1.8 to 2-
$\mu{\rm m}$
region, more research efforts have been directed toward developing highly efficient broadband fiber amplifiers in this range. In order to amplify this region, Thulium-Bismuth-doped fiber amplifier (TBDFA) is proposed in conjunction with 800-nm pumping. Optimal Thulium ion concentration of 4.17
$\,\times 10^{26}~{\rm ion}/{\rm m}^{3}$
and Bismuth ion concentration of 2.08
$\,\times 10^{26}~{\rm ion}/{\rm m}^{3}$
together with low phonon energy of germanate glass lead to the highest energy transfer rates. Effective energy transfer mechanism from Bismuth to Thulium in addition to the cross relaxation process between Thulium ions results in higher amplification, efficiency, and super broadband amplification in TBDFA. We analytically solve the rate equations of TBDFA including the effect of energy transfer in order to calculate the broadband amplifier gain.