## Abstract

Analytical and numerical study of graphene ribbons has become a prime focus of recent research due to their potential applications in tunable absorption, wavefront manipulation, polarization conversion, and so on. In this paper, an accurate analysis of a perfect electric conductor (PEC)–backed array of graphene ribbons (PAGR) is presented based on the well-known electromagnetic (EM) image theorem, where the induced currents are theoretically derived under a transverse-magnetic-polarized incident wave. For the first time, the proposed analysis rigorously incorporates the EM coupling effects between the PEC back plate and the subwavelength array of graphene ribbons. It is proved that the strong interaction between the PEC back plate and graphene ribbons drastically affects the results, especially in ultra-thin PAGR structures, whereas it was neglected in the previous works. As a proof of principle, an ultra-thin graphene-assisted absorber ($=0.05{\lambda}_{0}$) exhibiting tunable absorption at the terahertz regime is theoretically designed to verify the proposed analytical scheme. Unlike the previous studies, this paper reveals a more general, valid, and reliable analysis of PEC-backed graphene ribbons and can be simply extended to 2D geometries of PEC-backed graphene metasurfaces.

© 2018 Optical Society of America

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