Analytical method for diffraction analysis and design of perfect-electric-conductor backed graphene ribbon metagratings

Graphene-based gratings and metagratings have attracted great interest in the last few years because they could realize various multi-functional beam manipulation, such as beam splitting, focusing, and anomalous reflection in the terahertz (THz) regime. However, most of graphene-based metagratings are designed through numerical simulations, which are very time-consuming. In this paper, an accurate analytical method is proposed for diffraction analysis of a perfect electric conductor (PEC)-backed array of graphene ribbons. In contrast to previous analytical treatments, the proposed method can predict the electromagnetic performance of graphene ribbons not only in the subwavelength regime, but also for wavelengths shorter than the array constant. Results are obtained by first deriving the surface current density induced on graphene ribbons by an obliquely incident transverse-magnetic (TM) polarized plane wave. Closed-form expressions for reflection coefficients of diffracted orders are then obtained using the surface current distribution. We validate the proposed method through comparison with full-wave simulation results. Finally, a tunable beam splitter and a tunable retroreflector in the THz regime are designed using the method proposed. The designed structures have good power efficiency (80% for beam splitter and 90% for retroreflector). Moreover, their operating frequency and angle may be controlled by changing the bias voltage of graphene ribbons. The proposed method paves the path for analytical design of tunable metagratings with widespread potential for THz and optical beam-manipulation applications.