  Known coherent metasurfaces control interference of waves of a given
frequency with other coherent waves at the same frequency, either illuminating
from a different direction or created as intermodulation products. In this
paper, we introduce a class of metasurfaces that are modulated in time
coherently with the illuminating radiation. Importantly, such modulation opens
a possibility to control reflection, absorption, and transmission at multiple
frequencies, including illuminations by two or more incoherent waves. In
particular, we study dynamic resistive layers and show how to use them to
design thin multi-frequency perfect absorbers that overcome the bandwidth limit
for static linear absorbers. Furthermore, we demonstrate possibilities of
remote tuning of the absorption level. We hope that this work opens up novel
avenues in wave engineering using coherent modulation of metasurface
parameters.
