  Periodically-tapered-waveguides technique is an emerging potential route to
establish quasi-phase-matching schemes for efficient on-demand parametric
interactions in third-order nonlinear materials. In this paper, I investigate
this method in enhancing spontaneous photon-pairs emission in fibres and planar
waveguides with sinusoidally-varying cross sections. I have developed a general
robust quantum model to study this process under continuous or pulsed-pump
excitations. The model shows a great enhancement in photon-pairs 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
third-order nonlinear guided structures.
