Self-adaptive waveguide boundary for wideband multi-mode four-wave mixing

We propose a new approach to provide wideband multi-mode four-wave mixing, independent of the intrinsic waveguide dispersion. We adopt concepts from quantum mechanics and sub-wavelength engineering to design an effective photon well, with a graded potential along the waveguide cross section, that provides flexible control over the mode confinement. The self-adaptive nature of the waveguide boundary allows different spatial modes with equi-spaced frequencies and shared propagation wavevector, automatically fulfilling both, energy conservation and wavevector phase matching conditions. Capitalizing on this concept, we show phase-matching among modes separated by 400 nm (bridging from telecom wavelengths to almost 2{\mu}m), with less than 5% deviation in a remarkably large bandwidth exceeding 300 nm. Furthermore, we also show the flexibility of the proposed approach that can be seamlessly adapted to different technology platforms with the same or different waveguide thicknesses. This strategy opens a new design space for versatile nonlinear applications in which the manipulation of energy spacing and phase matching is pivotal, e.g. all-optical signal processing with four-wave mixing, mid-infrared light generation, Brillouin scattering with selectable phonon energy, etc.