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Small Signal Analysis of Modulation Instability in Erbium-doped Fiber Amplifier

A new approach is given which utilizes small signal analysis to solve the nonlinear Schrodinger equation (NLSE) for erbium-doped fiber amplifier. Based on the result of small signal analysis, the whole characteristic of modulation instability (MI) induced by cross-phase modulation (XPM) in erbium-doped fiber amplifier (EDFA) can be discussed. The gain spectrum becomes flatten with the increasing of the fiber length. A big signal power and gain make the onset of the modulation instability rather easy. The dispersion coefficient has no connection with the onset of modulation instability and has little effect on the value of gain induced by modulation instability.