Dispersion Engineering at Ultrathin Thicknesses: Arbitrarily-Broadband Quadratic Phase Manipulations with Multiresonant Metasurfaces

We propose multiresonant metasurfaces that exhibit a broadband and purely-quadratic spectral phase to be utilized for dispersion compensation and in general any application requiring temporal pulse shaping of broadband signals. The proposed metasurfaces can be fundamentally ultrathin; they exchange propagating phase accumulation with resonant phase delay and require implementing a specific combination of Lorentzian resonances in the electric and magnetic surface conductivities (i.e., a specifically-resonant surface replaces a bulk volume). The required sheet conductivities are rigorously derived taking care to satisfy fundamental physical constraints. Our approach overcomes the fundamental limitations of both conventional, non-resonant approaches (too bulky), as well as modern, singly-resonant metasurfaces (too narrowband) and aspires to bring broadband dispersion engineering at ultrathin physical scales.