Langevin Treatment of Atomic Coherence Effect on Hybrid Erbium-doped Fiber Amplification

The effects of atomic coherence on hybrid erbium-doped fiber amplifier (HEDFA) pumped simultaneously by two diode lasers with different frequencies are studied by using Langevin quantum theory. The expressions of coherence and incoherence gain are derived. The theoretical results show that HEDFA has a near flat bandwidth response from 1531 to 1568 nm and large coherence gain under the conditions of low temperature and small detuning.