Quasi-phase-matching periodically-tapered waveguides (PTWs) can enable efficient on-demand third-order parametric interactions using right combinations of the tapering period and modulation amplitude . Similar to periodically-poled ferroelectric crystals, this new technique eliminates the stringent constraints imposed by conventional methods on the frequencies, mode profiles, and polarisations of the interacting photons. An example of PTWs is the sinusoidally-tapered fibres that have been exploited in manuiplating supercontinuum generation and modulation instability . In this work, I have developed a rigorous quantum model to investigate spontaneous four-wave mixing (SFWM) inside these tapered waveguides .
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