Modelling spontaneous four-wave mixing in periodically tapered waveguides

A periodically tapered waveguides technique is an emerging potential route to establish quasi-phase-matching schemes in third-order nonlinear materials for efficient ondemand parametric interactions. In this paper, I investigate this method in enhancing spontaneous photon-pair emission in microstructured fibres and planar waveguides with sinusoidally varying cross sections. To study this process for continuous and pulsed-pump excitations, I have developed a general robust quantum model that takes into account self- and cross-phase modulations. The model shows a great enhancement in photon-pair generation in waveguides with a small number of tapering periods that are feasible via the current fabrication technologies. I envisage that this work will open a new area of research to investigate how the tapering patterns can be fully optimised to tailor the spectral properties of the output photons in nonlinear guided structures. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement