Multistep cascading and fourth-harmonic generation

A concept of multistep cascading is applied to the problem of fourth-harmonic generation (FHG) in a single quadratic crystal, and a new model of parametric wave mixing is analyzed in detail. Important applications to the optical frequency division and efficient FHG as well as the realization of the double-phase-matching multistep cascading processes in engineered QPM structures with phase-reversal sequences are also suggested.  2001 Elsevier Science B.V. All rights reserved. OCIS: 190.4410; 190.5530; 190.2620; 190.4160 Cascading effects in optical materials with quadratic (second-order or χ(2)) nonlinear response provide an efficient way to lower the critical power of all-optical switching devices [1]. The concept of multistep cascading [2] brings new ideas into this field, leading to the possibility of an enhanced nonlinearity-induced phase shift and generation of multicolor parametric spatial solitons. In particular, multistep cascading can be achieved by two nearly phase-matched secondorder nonlinear processes, second-harmonic generation (SHG) and sum-frequency mixing (SFM), involving the third-harmonic wave [3,4]. In this Letter, we extend the concept of multistep cascading to the processes involving the fourthharmonic generation (FHG) in a single noncentrosymmetric crystal, and analyze a new model of multi* Corresponding author. E-mail address: [email protected] (Yu.S. Kivshar). step cascading and its stationary solutions for normal modes — plane waves and spatial solitons. Our study provides the first analysis of the problem of FHG via a pure cascade process, observed experimentally more than 25 years ago [5] and later studied in a special limit only [6]. Additionally, we demonstrate that engineered QPM structures with phase-reversal sequences can provide an effective mean to verify experimentally many of the multistep cascading effects. We consider the FHG via two second-order parametric processes: ω + ω = 2ω and 2ω + 2ω = 4ω, where ω is the frequency of the fundamental wave. In the approximation of slowly varying envelopes with the assumption of zero absorption of all interacting waves, we obtain