Variational dynamics of spatial solitons in quasi-phase-matched quadratic media

We consider the stability and dynamics of quasi-phase-matched (QPM) solitons which are generated in materials with cascaded quadratic nonlinearity. The use of a variational reduction in conjunction with a Poincare (periodic orbit) analysis gives a reduced differential equation model which captures the leading-order fast and slow behaviours of the pulse dynamics. This strengthens previous results pertaining to the existence of QPM solitons, and further suggests that they are robust under even large perturbations. However, the perturbed QPM solitons are shown to manifest a slow scale behaviour which persists even for large propagation distances. This slow scale behaviour is qualitatively described with our averaging methods and is to be expected in physically realizable systems.