“…In the early days of nonlinear optics, the motivation to study this kind of parametric interactions was to explore various possibilities for the simultaneous generation of several harmonics in a single nonlinear crystal (see, e.g., Akhmanov and Khokhlov [1964,1972]) as well as to use the cascading of several parametric processes for measuring higher-order susceptibilities in nonlinear optical crystals (see, e.g., Yablonovitch, Flytzanis, and Bloembergen [1972]; Akhmanov, Dubovik, Saltiel, Tomov, and Tunkin [1974]; Akhmanov [1977]; Kildal and Iseler [1979]; Bloembergen [1982]). More recently, these processes were proved to be efficient for the higher-order harmonic generation, for building reliable standards for the third-order nonlinear susceptibility measurements (see, e.g., Bosshard, Gubler, Kaatz, Mazerant, and Meier [2000] and references therein), and also for generating multi-color optical solitons. Additionally, it is expected that the multistep parametric processes and multistep cascading will find their applications in optical communication devices, for wavelength shifting and all-optical switching (see discussions below).…”