A detailed analysis of theexcited state absorption (ESA) transition ⁴ I _13/2 → ⁴ I _9/2 which occurs in erbium (Er) doped ZBLAN fiber lasers is performed through numerical modeling. It is found that the ESA plays a significant role in enhancing the 2.8 μ m lasing of Er ³⁺ ions. The ESA promotes the ions residing in ⁴ I _13/2 (the lower state of the 2.8 μ m laser) to ⁴ I _9/2 , where the ions subsequently decay to ⁴ I _11/2 (the upper state of the 2.8 μ m laser) rapidly. An energy recycling is consequently realized via the ESA. The ESA can be activated in cascaded 2.8 μ m/1.6 μ m Er-doped ZBLAN fiber lasers by absorbing the 1.6 μ m signal. Through numerical simulation it is found that in cascaded lasers the slope efficiency of the 2.8 μ m laser can be elevated to ∼48% with the assistance of the ESA, a value that surpasses the Stokes limit (∼35%) substantially and agrees well with the experimental results previously reported. It is also found that the ESA-induced energy recycling is exothermic, an effect that is non-ignorable in the high-power circumstance. Moreover, the injection of an additional 1.6 μ m pump for directly exploiting the ⁴ I _13/2 → ⁴ I _9/2 ESA is simulated using the model. It is found that as the second pump is introduced, the 2.8 μ m lasing almost entirely relies on the ESA-induced energy recycling, and hence, the laser is capable of operating under very low 976 nm pump power. The simulation results indicate that the 2.8 μ m lasing in Er-doped ZBLAN fiber lasers can even be realized using a single 1.6 μ m pump, via a combination of the ⁴ I _15/2 → ⁴ I _13/2 and ⁴ I _13/2 → ⁴ I _9/2 transition. The outcomes of this work can inspire the development of novel, high-performance 2.8 μ m Er-doped ZBLAN fiber lasers.

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1	Engineering	3	3	88
2	Natural Sciences	1	1	26
3	Applied Physics	1	1	26
4	Computer Science	1	1	22
5	Physics	1	1	26

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