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

In dielectric physics, electromagnetic (EM) properties of dielectrics arise from several important polarization mechanisms that can be described by Debye, Drude or Lorentz models. Metamaterials, as well as their 2D counterparts-metasurfaces, can exhibit bizarre EM parameters such as negative permittivity, whereas polarization mechanisms leading to such have long been discussed in dielectric physics. Drude and Lorentz's models are usually used in metamaterial design, whereas the Debye model is almost absent, though it is so important in dielectric physics. This leaves an unreconciled gap between the dielectric physics and metamaterials. In this paper, we explore Debye relaxations in metasurfaces for the sake of wideband dispersion engineering. By analyzing two fundamental resonance modes of a typical meta-atom, we first show that the reflection phase experiences 1^st-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.