  Nonlinear metasurfaces have recently been established as a new platform for
generating photon pairs via spontaneous parametric down-conversion. While for
classical harmonic generation in metasurfaces a high level of control over all
degrees of freedom of light has been reached, this capability is yet to be
developed for photon pair generation. In this work, we theoretically and
experimentally demonstrate for the first time precise control of the emission
angle of photon pairs generated from a nonlinear metasurface. Our measurements
show angularly tunable pair-generation with high coincidence-to-accidental
ratio for both co- and counter-propagating emission. The underlying principle
is the transverse phase-matching of guided-mode resonances with strong angular
dispersion in a nonlinear lithium niobate metagrating. We provide a
straightforward design strategy for photon pair generation in such a device and
find very good agreement between the calculations and experimental results.
Here we use all-optical emission angle tuning by means of the pump wavelength,
however the principle could be extended to modulation via the electro-optic
effect in lithium niobate. In sum, this work provides an important addition to
the toolset of sub-wavelength thickness photon pair sources.
