An increasing theoretical understanding of the cascaded quadratic nonlinearity and a growing number of numerical simulations of interesting and potential applications has led during the last six years to the performance of a series of experiments which have confirmed the theoretical expectations very well. The first experiments in bulk and waveguide structures investigated mainly the basic physics involved. Intensity-dependent phase shifts were measured. Soliton formation in temporal and spatial dimensions and all-optical switching based on the cascaded nonlinearity were observed. In contrast to the electronic third-order nonlinearity (which supports similar all-optical effects) the quadratic cascaded nonlinearity has the advantage of being more flexible, that it can easily be "engineered", and that it provides new effects like stable two dimensional solitons. Cascading is based on a nonlinear coupling between different travelling waves and can be influenced and adjusted by simple adjustment of the linear wave propagation characteristics of the involved waves. The resulting possibility to adjust the strength and even the sign of the cascaded nonlinearity with temperature or electro-optically was confirmed and characterized in detail experimentally.
In view to applications of cascading the fast development of the technology of quasi-phasematching (QPM) for quadratic nonlinearly coupled waves during the last years has been very important. In lithium niobate for example, the power level for the observation of all-optical effects was reduced from a few thousand to a few ten Watts by replacing birefringent phase-matching with QPM. Furthermore, the possible implementation of spatial inhomogeneous QPM gratings opens a wide range for an optimization of the cascaded nonlinearity in a particular application. For example, the nonlinear loss due to frequency conversion has been minimized with a non-uniform phase-mismatch along the propagation.
Beside being a versatile laboratory for the investigation of nonlinear wave-propagation and dynamics the cascaded nonlinearity has some potential for applications in optical communication systems. Under this point of view, till now, the probably most important experiment demonstrates high-quality multiple-channel wavelength conversion in engineered QPM lithium niobate waveguides. In other very close-to-application experiments the nonlinear phase shifts in cascading were applied for Kerr-lens mode locking and pulse compression. All-optical transistor and diode action based on cascading have been demonstrated. Also quadratic spatial solitons (light-induced waveguides) have an exciting potential for all-optical beam steering and signal routing as well as for beam cleaning. Theory and corresponding soliton interaction experiments have shown that the soliton propagation direction is sensitive to intensity or can be shifted in the interaction with another soliton. A further interesting experimental field is the investigation of modulational instabilities of beams in one or two dimensions for the generation of soliton "arrays". Finally, the very stable and reproducable all-optical switching experiments in directional couplers are worth to be extended. In arrays of coupled waveguides discrete solitons could be used for all-optical and fast signal routing and distribution.
In contrast to a widely spread opinion, recent experiments on mode locking, pulse compression and coupler switching using femtosecond laser pulses have shown that cascading is not inherently limited to narrow bandwidth signals, as it is the generation of new frequencies due to phase-matching constraints. More experimental investigations of the potential of cascading for sub-picosecond data processing are on the way.