Tailored Spontaneous Four-Wave Mixing in Sinusoidally-Tapered Fibres

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 [1]. 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 [2]. In this work, I have developed a rigorous quantum model to investigate spontaneous four-wave mixing (SFWM) inside these tapered waveguides [3]. The right combinations between the modulation amplitude Δd and tapering period ΛT that enhances the expected number of photons (Ns) at the targeted wavelengths are portrayed in Fig. 1(a), for fibres with same number of periods M. The values of (Ns) are normalised to the case when Δd = 0, to quantify the enhancement in photon-pairs generation using the PTW-technique in comparison to uniform fibres. For only M = 50, (NVs) is remarkably enhanced by 35 dB. The output spectrum of the photon-pairs is featured as a narrow sinc-function with very weak sidelobes that are significantly diminished for large number of periods, as depicted in Fig. 1(b). The 2D representation of the spectrum as a function of the photon-pairs wavelengths (λs, λi) is shown in panel (c). In this plot, the pump is assumed to be a monochromatic at a frequency satisfies the energy conservation. The corresponding (Ns) for a Gaussian-pulse pump source with an input energy 1 nJ and a full-width-half-maximum 4 ps is portrayed in Fig. 1(d). Using the Schmidt decomposition analysis, the spectral-purity is 0.74. This shows the ability of the PTW-technique in producing highly-efficient relatively-pure single photons at any on-demand frequencies without applying any bandpass filters. This work will also open a new direction 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.