Weak modulation of a quasi-phase-matching (QPM) grating opens possibilities for engineering both the average quadratic nonlinearity and the incoherent average cubic nonlinearity induced by QPM. The relative strength of the average quadratic and effective (intrinsic plus induced) cubic nonlinearity is studied for LiNbO(3) . We show how the induced average cubic nonlinearity can be engineered to dominate the intrinsic material cubic nonlinearity and how doing so will allow the intensity at which the quadratic and cubic nonlinearities balance and thus compete to be decreased to a few gigawatts per square centimeter.

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We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.

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We show that a variety of quasi-phase-matched structures with engineered patterns can potentially be used for soliton control in quadratic nonlinear media. We study geometries with dislocations, tilts, and wells and predict spatial switching between different output soliton states. Experimental implementation conditions are discussed.