  The phase-matching condition is a key aspect in nonlinear wavelength
conversion processes, which requires the momenta of the photons involved in the
processes to be conserved. Conventionally, nonlinear phase matching is achieved
using either birefringent or periodically poled nonlinear crystals, which
requires careful dispersion engineering and are usually narrowband. In recent
years, metasurfaces consisting of densely packed arrays of optical antennas
have been demonstrated to provide an effective optical momentum to bend light
in arbitrary ways. Here, we demonstrate that gradient metasurface structures
consisting of phased array antennas are able to circumvent the phase-matching
requirement in on-chip nonlinear wavelength conversion. We experimentally
demonstrate phase-matching-free second harmonic generation over many coherent
lengths in thin film lithium niobate waveguides patterned with the gradient
metasurfaces. Efficient second-harmonic generation (1660% W-1cm-2) in the
metasurface-based devices was observed over a wide range of pump wavelengths
(1580-1650 nm).
