  Wave phenomena can be artificially engineered by scattering from
metasurfaces, which aids in the design of radio-frequency and optical devices
for wireless communication, sensing, imaging, wireless power transfer and
bio/medical applications. Scattering responses vary with changing frequency;
conversely, they remain unchanged at a constant frequency, which has been a
long-standing limitation in the design of devices leveraging wave scattering
phenomena. Here, we present metasurfaces that can scatter incident waves
according to two variables - the frequency and pulse width - in multiple bands.
Significantly, these scattering profiles are characterized by how the
frequencies are used in different time windows due to transient circuits. In
particular, with coupled transient circuits, we demonstrate variable scattering
profiles in response to unique frequency sequences, which can markedly increase
the available frequency channels in accordance with a factorial function. Our
proposed concept, which is analogous to frequency hopping in wireless
communication, advances wave engineering in electromagnetics and related
fields.
