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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.

We present a first-principles calculation of two second-order optical response functions as well as the dielectric function for GaAs and GaP. Specifically, we evaluate the dielectric function ⑀() and the secondharmonic generation response coefficient (2) (Ϫ2;,) over a large frequency range. The electronic linear electro-optic susceptibility (2) (Ϫ;,0) is also evaluated below the band gap. These results are based on a series of self-consistent LDA calculations using the full-potential linearized augmented plane wave method. Self-energy corrections are included at the level of the ''scissors'' approximation, which corrects for the underestimation of the local density approximation band gap and produces a change in the velocity matrix elements. The analytic expressions for the second-order response functions are free of the unphysically divergent terms at zero frequency that have previously plagued such calculations. Results for (2) (Ϫ;,0) are in good agreement with experiment below the band gap and those for (2) (Ϫ2;,) are compared with experimental data where available. We note that despite the equivalence of both of these second-order response functions at zero frequency, there seems to be some discrepancy between the experimental results for these functions in this regime.

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