Electromagnetic Scattering From Individual Crumpled Graphene Flakes: A Characteristic Modes Approach

Abstract

Graphene flakes (GFs) in real composites are rarely perfectly flat, and often exhibit complicated crumpled shapes. Therefore, the goal of this paper was to quantify the electromagnetic scattering characteristics of individual crumpled GFs with shapes resembling those found in real composites. The extinction cross sections of tens of GFs, with different sizes and various levels of crumpleness, were calculated using multiple independent solvers. The results show that resonances in the extinction cross section spectrum decrease in amplitude as the GFs become more crumpled. Moreover, some crumpled GFs exhibited a broader resonance than that of perfectly flat GFs. To explain these results, we used a characteristic mode analysis to decompose the graphene surface currents into a set of fundamental currents or modes. For perfectly flat square GFs, the vertical and horizontal modes were found to overlap and resonate at the same frequencies. However, as the GFs became more crumpled, the horizontal/vertical symmetry broke down causing the corresponding modes to separate and resonate at different frequencies leading to an overall broader bandwidth. These results attest to the importance of modeling the exact shape of GFs to accurately characterize their electromagnetic response.