  In this letter, we propose a magnet-less non-reciprocal isolating system
based on time-varying metasurfaces. Two parallel time-varying metasurfaces, one
for frequency up-conversion and one for down-conversion by the same amount, are
used for realizing a region of space where incident waves from opposite
directions experience an opposite Doppler frequency shift. As a result, any
device within this region becomes sensitive to the illumination direction,
exhibiting a different scattering response from opposite directions and thus
breaking reciprocity. Very importantly, thanks to the opposite frequency shift
of the metasurfaces, the frequency of the transmitted electromagnetic field is
the same as for the incident one. Here, we demonstrate this general approach by
using a Bragg grating as the device between the time-varying metasurfaces. The
combined structure of the metasurfaces and the grating exhibits different
transmission and reflection properties for opposite illumination direction,
thereby realizing an isolator. More broadly, this letter presents a strategy
for converting any conventional electromagnetic device to a non-reciprocal one
by placing it between two time-varying metasurfaces. This approach opens the
door to several new non-reciprocal components based on thin and lightweight
metasurfaces, which are simpler to realize compared to their volumetric
counterparts.
