  Nonlinear optics, especially frequency mixing, underpins modern optical
technology and scientific exploration in quantum optics, materials and life
sciences, and optical communications. Since nonlinear effects are weak,
efficient frequency mixing must accumulate over large interaction lengths
restricting the integration of nonlinear photonics with electronics and
establishing limitations on mixing processes due to the requirement of phase
matching. In this work we report efficient four-wave mixing over micron-scale
interaction lengths at telecoms wavelengths. We use an integrated plasmonic gap
waveguide on silicon that strongly confines light within a nonlinear organic
polymer in the gap. Our approach is so effective because the gap waveguide
intensifies light by efficiently nanofocusing it to a mode cross-section of a
few tens of nanometres, generating a nonlinear response so strong that
efficient four-wave mixing accumulates in just a micron. This is significant as
our technique opens up nonlinear optics to a regime where phase matching and
dispersion considerations are relaxed, giving rise to the possibility of
compact, broadband, and efficient frequency mixing on a platform that can be
integrated with silicon photonics.
