  Emerging photonic functionalities are mostly governed by the fundamental
principle of Lorentz reciprocity. Lifting the constraints imposed by this
principle could circumvent deleterious effects that limit the performance of
photonic systems. A variety of approaches have recently been explored to break
reciprocity, yet most efforts have been limited to confined photonic systems.
Here, we propose and experimentally demonstrate a spatio-temporally modulated
metasurface capable of extreme breakdown of Lorentz reciprocity. Through
tailoring the momentum and frequency harmonic contents of the scattered waves,
we achieve dynamical beam steering, reconfigurable focusing, and giant
free-space optical isolation exemplifying the flexibility of our platform. We
develop a generalized Bloch-Floquet theory which offers physical insights into
the demonstrated extreme nonreciprocity, and its predictions are in excellent
agreement with experiments. Our work opens exciting opportunities in
applications where free-space nonreciprocal wave propagation is desired,
including wireless communications and radiative energy transfer.
