  We show that ultrathin metasurfaces with a specific multiresonant response
can enable simultaneously arbitrarily-strong and arbitrarily-broadband
dispersion compensation, pulse (de-)chirping and compression or broadening.
This breakthrough overcomes the fundamental limitations of both conventional
non-resonant approaches (bulky) and modern singly-resonant metasurfaces
(narrowband) for quadratic phase manipulations of electromagnetic signals. The
required non-uniform trains of resonances in the electric and magnetic sheet
conductivities that completely control phase delay, group delay, and chirp, are
rigorously derived and the limitations imposed by fundamental physical
constraints are thoroughly discussed. Subsequently, a practical, truncated
approximation by finite sequences of physically-realizable linear resonances is
constructed and the associated error is quantified. By appropriate spectral
ordering of the resonances, operation can be achieved either in transmission or
reflection mode, enabling full space coverage. The proposed concept is not
limited to dispersion compensation, but introduces a generic and powerful
ultrathin platform for the spatio-temporal control of broadband real-world
signals with a myriad of applications in modern optics, microwave photonics,
radar and communication systems.
