Modulation instability (MI) in a fiber Bragg grating (FBG) is investigated and reviewed analytically. The dispersion relation equation of MI obtained from the coupled-mode equation is solved exactly. The closed-form expressions of the gain of MI and the threshold condition in the normal dispersion regime are derived. The results from the closed-form expressions are well consistent with those from numerical simulations and previous literature. Based on the analytical investigation, the characteristics of MI in an FBG are analyzed.
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