Quasi-phase-matched χ(3)-parametric interactions in sinusoidally tapered waveguides

In this article, I show how periodically tapered waveguides can be employed as efficient quasi-phase-matching schemes for four-wavemixing parametric processes in third-order nonlinear materials. As an example, a thorough study of enhancing third-harmonic generation in sinusoidally tapered fibers has been conducted. The quasi-phasematching condition has been obtained for nonlinear parametric interactions in these structures using Fourier-series analysis. The dependencies of the conversion efficiency of the third harmonic on the modulation amplitude, tapering period, longitudinal-propagation direction, and pump wavelength have been studied. In comparison to uniform waveguides, the conversion efficiency has been enhanced by orders of magnitudes. I envisage that this work will have a great impact in the field of guided nonlinear optics using centrosymmetric materials.