Nonlinear pulse propagation in a fiber Bragg grating is investigated numerically by solving coupled-mode equations including the generation of stimulated Brillouin scattering (SBS) in a time region shorter than the phonon lifetime. It is found that the Brillouin threshold is substantially reduced compared with that in an optical fiber with no gratings. Nonlinear pulse propagation is investigated for two device operations whose driving point (i.e., frequency) lies outside the stop band and at the center of the stop band (zero detuning). In general, the generation of a single pulse or a pulse train that is due to modulational instability is spoiled by the pump depletion owing to SBS for incident pulses longer than 1 ns. In the interaction between SBS and nonlinear grating dynamics, there is a distinct difference between two device operations. This reflects the difference in the fields within the grating. Especially the pulse generation from an instability of gap solitons excited at the stop-band frequency is affected by SBS even if the pulse width is less than 1 ns.
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