Multistep cascading and fourth-harmonic generation
  We apply the concept of multistep cascading to the problem of fourth-harmonic generation in a single quadratic crystal. We analyze a new model of parametric wave mixing and describe its stationary solutions for two- and three-color plane waves and spatial solitons. Some applications to the optical frequency division as well as the realization of the double-phase-matching processes in engineered QPM structures with phase reversal sequences are also discussed. 
Andrey A. Sukhorukov, Tristram J. Alexander, Yuri S. Kivshar, and   Solomon M. Saltiel