We report the first experimental observation of nonlinear propagation effects in fiber Bragg gratings, resulting in nonlinear optical pulse compression and soliton propagation. The solitons occur at frequencies near the photonic band gap of the grating; they are due to a combination of the negative dispersion of the grating, which dominates the material dispersion, and self-phase modulation. The solitons propagate at velocities well below the speed of light in the uniform medium.

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