χ(2) Solitary Waves in Graded-Index Slab Waveguides

Analytical approximate stationary solutions of solitary waves in a graded-index slab waveguide, are found for Type I second harmonic generation (SHG) processes, ignoring the usual assumptions that the linear and nonlinear effects occur separately in each transverse direction. We compare our results with those available in the literature and show how our model can depict accurately the influence of the nonlinearity on the phase constant. The analytical results are also validated by the numerical integration of the governing equations.