  Metasurfaces have emerged as a promising technology for the manipulation of
electromagnetic waves within a thin layer. In planar ultrathin metasurfaces,
there exist rigorous narrowband design methods, based on the equivalent surface
impedance of patterned metallic layers on dielectric substrates. In this work,
we derive a limit on bandwidth achievable in these metasurfaces, based on
constraints that their meta-atoms should be passive, causal and lossless, and
that they should obey the time-bandwidth product rules of a single resonance
structure. The results show that in addition to elementary design parameters
involving variation of the surface impedance, the bandwidth is critically
limited by the dielectric substrate thickness and permittivity. We then propose
a synthesis method for broadband ultrathin metasurfaces, based on an LC
resonance fit of the required surface impedance, and experimentally verify a
broadband dispersive structure at millimeter-wave frequencies. This results in
a bandwidth enhancement of over 90%, relative to a reference metasurface
created with the narrowband design process.
