Transverse Electric Mode Excitation in Graphene-Based Multilayers Through Attenuated Total Reflection Technique

Graphene monolayer can support transverse electric plasmonic modes where in-plane current oscillations are present and parallel to electric field vector. These modes, as recently shown, can be excited by Attenuated Total Reflection (ATR) Technique where mode coupling is obtained above a cutoff distance between prism and graphene. In this work, we extend this analysis by considering a graphene (equally doped)/dielectric stack as supporting element. We show that Surface Plasmonic (SP) modes are excited through this technique showing smaller cutoff distances than those reported for monolayer graphene. We found that cutoff distance, d_c, decreases as the number of stacked layers grows following the rule d_c=α/(2n), where α is the decaying length and n is the number of graphene layers. We prove surface plasmon excitation, corresponding to minima in the ATR, by numerical calculation of dispersion relations of SPs for two, three and four graphene layers in the stacking.