  Metasurfaces have been rapidly advancing our command over the many degrees of
freedom of light within compact, lightweight devices. However, so far, they
have mostly been limited to manipulating light in free space. Grating couplers
provide the opportunity of bridging far-field optical radiation and in-plane
guided waves, and thus have become fundamental building blocks in photonic
integrated circuits. However, their operation and degree of light control is
much more limited than metasurfaces. Metasurfaces integrated on top of guided
wave photonic systems have been explored to control the scattering of light
off-chip with enhanced functionalities - namely, point-by-point manipulation of
amplitude, phase or polarization. However, these efforts have so far been
limited to controlling one or two optical degrees of freedom at best, and to
device configurations much more complex compared to conventional grating
couplers. Here, we introduce leaky-wave metasurfaces, which are based on
symmetry-broken photonic crystal slabs that support quasi-bound states in the
continuum. This platform has a compact form factor equivalent to the one of
conventional grating couplers, but it provides full command over amplitude,
phase and polarization (four optical degrees of freedom) across large
apertures. We present experimental demonstrations of various functionalities
for operation at wavelengths near 1.55 microns based on leaky-wave
metasurfaces, including devices for phase and amplitude control at a fixed
polarization state, and devices controlling all four optical degrees of
freedom. Our results merge the fields of guided and free-space optics under the
umbrella of metasurfaces, exploiting the hybrid nature of quasi-bound states in
the continuum, for opportunities to advance in disruptive ways imaging,
communications, augmented reality, quantum optics, LIDAR and integrated
photonic systems.
