Reductive perturbation analysis of short pulse propagation in a nonlinear dielectric slab: the role of material dispersion in bright-to-dark solution transitions

The pulse propagation in a lossless nonlinear dielectric slab of parabolic index profile with material dispersion is analyzed with the reductive perturbation method. The cases of temporally and spatially short optical pulses, with respect to the respective effectiveness of the nonlinearity are both considered. The evolution equations are given explicitly for the practical single mode case. Envelope solitons are obtained through the nonlinear Schroedinger equation which results in the third order of the perturbation scheme. The lower-order soliton solutions are derived analytically along with the conditions for sustaining bright or dark solitons (the latter cannot be excited if resonance effects in the material dispersion are absent)