2nd-Order Debye relaxation in electromagnetic metasurfaces for wideband dispersion engineering

-order Debye relaxation under the two resonances, although they are typically Lorentzian. More importantly, the two resonances can be tailored to form a 2nd-order Debye relaxation process so as to achieve smooth phase variations in between them, which lays a solid foundation for wideband dispersion engineering. As proof of concept, we propose a quad-elliptical-arc (QEA) structure as the meta-atom, whose dispersion can be customized by tailoring the 2nd-order Debye relaxation. With this meta-atom, we demonstrated two metasurface prototypes that can achieve chromatic and achromatic focusing, respectively, in the entire X band (8.0-12.0 GHz), showcasing the powerful capacity of wideband dispersion engineering. This work digs out relaxation processes in metamaterials and opens up new territories for metamaterial research, which may find wide applications in wideband devices and systems.