The reflection spectrum of Brillouin dynamic grating is calculated by a numerical method called piecewise approach. A sawtooth frequency modulation is proposed to be used in Brillouin dynamic grating localization along the fiber. It is shown that the reflection spectrum has a flat band where its linewidth depends on the amplitude of frequency modulation. The maximum reflection of dynamic grating can be adjusted by the amplitude of modulation and the power of pump waves, which generates the grating. This grating can be useful as a fiber laser cavity mirror.
