Vol.:(0123456789) 1 3 Appl. Phys. B (2017) 123:91 DOI 10.1007/s00340-017-6651-9 Trapped modes and resonances in gyrotropic graphene stacks Faroq Razzaz 1  · Majeed A. S. Alkanhal 1   Received: 7 June 2016 / Accepted: 20 January 2017 © Springer-Verlag Berlin Heidelberg 2017 Graphene has several EM and optically unique proper- ties such as high charge carrier mobility, electronic energy spectrum without a gap between the valence and conduc- tion bands, and frequency-independent absorption of EM radiation [6–8]. Recently, signifcant attention has been focused on EM analysis and characterization of graphene [9–11]. Sev- eral investigations were carried out on the interaction of EM felds with graphene. EM absorbance and refectance properties of graphene composites for diferent applica- tions [12], EM wave absorption properties of graphene modifed with carbon nanotube composites [13], and EM interference shielding of fexible graphene/polymer com- posite flms in sandwiched structures [14] have been pre- sented recently in the literature. Other studies demonstrated that both polarized plasmons (TE/TM) can be supported in graphene [15, 16]. The giant Faraday rotation infuence on graphene coupled to metallic nanoparticles was theoreti- cally investigated in [17]. The propagation of surface plas- mon polaritons (SPP) in a graphene-based resonator-cou- pled waveguide system was numerically and theoretically investigated in [18]. Analytical models based on transfor- mation optics for subwavelength gratings coupled into the plasmons of graphene were presented in [19]. Refection, transmission, and absorption of EM waves by a super lat- tice graphene layer in the presence of an external magnetic feld were investigated in [20]. Hyperbolic wavevector dis- persions at mid- and far-infrared frequencies in multilayer graphene-dielectric stacks were studied in [21]. Waveguide modes in multilayer graphene-dielectric structures and the efective medium theory of graphene structures in the infra- red band were presented in [22]. The conditions of large wavevector propagating EM waves in a subwavelength periodic multilayer graphene structure was theoretically investigated in [23]. Abstract This paper examines the anomalous electro- magnetic wave interactions with gyrotropic graphene-die- lectric stacks and characterizes their perturbed wave reso- nances. Expressions for the dispersion relations, trapped mode condition, and the propagating and evanescent modes in the gyrotropic graphene stack have been derived and numerically quantifed. The evanescent modes supported in the ambient medium couple as propagating modes in the gyrotropic graphene-dielectric stack at the discrete frequen- cies of the trapped modes. Valuation of the resonances in the material tensor and the resonances around the trapped modes that result in transmission anomalies (total trans- mission and total refection) and feld amplifcations in the gyrotropic graphene is described. The efects of the chemi- cal potential and the external magnetic feld on the number of discrete trapped modes and subsequently on the trans- mission resonances are numerically assessed. 1 Introduction Material technology is evolving rapidly toward creating new materials with particular electromagnetic (EM) and optical properties that do not exist in natural materials. One of the frontiers at which great conquests are being made is graphene formations. Since it was frst synthesized in 2004 [1], graphene has been used in numerous applications in electronics [2, 3], optoelectronics [3], and photonics [4] and in the development of bioelectric sensory devices [5]. * Majeed A. S. Alkanhal majeed@ksu.edu.sa 1 Department of Electrical Engineering, King Saud University, 800, Riyadh 11421, Saudi Arabia