Broadband metasurfaces enabling arbitrarily large delay-bandwidth products

Metasurfaces allow for advanced manipulation of optical signals by imposing phase discontinuities across flat interfaces. Unfortunately, these phase shifts remain restricted to values between 0 and 2 π , limiting the delay-bandwidth product of such sheets. Here, we develop an analytical tool to design metasurfaces that mimic three-dimensional materials of arbitrary thickness. In this way, we demonstrate how large phase discontinuities can be realized by combining several subwavelength Lorentzian resonances in the unit cell of the surface. Our methods open up the temporal response of metasurfaces and may lead to the construction of metasurfaces with a plethora of new optical functions.