  The evolution of light pulses and beams in a quasi-phase-matched (QPM)
quadratic medium is usually described by considering only the spatial harmonic
of the QPM grating that minimizes the residual phase-mismatch. I show that, for
strongly phase-mismatched interactions (the cascading regime), several
harmonics need to be accounted for in order to obtain the correct value of the
effective cubic nonlinearity, of which I find a simple analytical expression. I
discuss the effects of the higher order harmonics of the grating on solitary
wave propagation.
