  We demonstrate a simple and scalable approach to increase conversion
efficiencies of nonlinear metasurfaces by incorporating them into multipass
cells and by letting the pump beam to interact with the metasurfaces multiple
times. We experimentally show that by metasurface design, the associated
phase-matching criteria can be fulfilled. As a proof of principle, we achieve
phase matching of second-harmonic generation (SHG) using a metasurface
consisting of aluminium nanoparticles deposited on a glass substrate. The
phase-matching condition is verified to be achieved by measuring superlinear
dependence of the detected SHG as a function of number of passes. We measure an
order of magnitude enhancement in the SHG signal when the incident pump
traverses the metasurface up to 9 passes. Results are found to agree well with
a simple model developed to estimate the generated SHG signals. We also discuss
strategies to further scale-up the nonlinear signal generation. Our approach
provides a clear pathway to enhance nonlinear optical responses of
metasurface-based devices. The generic nature of our approach holds promise for
diverse applications in nonlinear optics and photonics.
