Theoretical Modelling Of Optical Properties Of Periodic Graphene Structures

Surface plasmon polaritons(SPPs),are surface collective charge oscillations that occur at the interface bewtwen conductors and dielectrics,which are bounded to and propagate along conductor-dielectric interfaces.SPPs hold a series of novel optical properties,such as subwavelength mode confinement,giant local field enhancement,anomalous reflection and transmission,and strong optical absorption.SPPs have already shown lots of fascinating applications,for instance molecule sensors,highefficiency solar cells,and photonic integrated circuits and so on.The previous studies mostly focus on SPPs in gold and silver,which have relatively large Ohm loss in the optical regime.However,as one of two-dimensional(2D)materials,graphene has been demonstrated to be an appropriate candidate as a plasmonic material.Graphene,hexagonal carbon crystal,is a semi-metal with the conduction band and the valence band touching at Dirac points.Comparing to plasmons in noble metals,graphene plasmons resonance frequency can be actively tuned,and have the higher carrier mobility and the local field enhancement.These properties make graphene plasmons play an important role in plasmonic applications,for example photoelectric modulation,optical signal processing,and tunable Terahertz metamaterial,to name a few.However in practice,it is still quite time-and resource-consuming to compute the electromagnetic scattering in complex graphene nanostructured systems.It is very worth to propose an efficient computing method especially for periodic or layered structures.In this manuscript,we present a theoretical model that can be implemented to study the electromagnetic scattering problem in graphene structure arrays efficiently.Our work is mainly divided into the following three parts:(1)Calculation of equivalent surface conductivity of graphene metasurface.The graphene structure arrays are treated as a uniform two-dimensional sheet,and accordingly the optical response is characterized by an equivalent surface conductivity.In the homogenization procedure,the surface conductivity of an infinite graphene sheet are used to depict the local resonances,and the interaction between structures is described by the depolarization factor.(2)Theoretical model verification based on single-layer and double-layer graphene structure.The method can be easily extended to investigate the optical properties of multilayer graphene structures by combining the transfer matrix method(TMM),in which the full wave simulations(such as finite element method)are very time-and resource-consuming.We compared the numerical calculation results and simulation results in the single-layer and double-layer graphene structures,and verified that the theoretical model has certain reliability in calculating the multi-layer graphene structures.(3)Calculation and analysis of the multilayer graphene structures based on the theoretical model.We have proposed an efficient theoretical calculation model and verified the accuracy of the calculation results in the simulation structure.Then,by this method,we discussed the periodicity,the dielectric layer and the number of layers dependence of absorption in the multi-layer graphene structure.Under the premise of high light absorption,we have found that different systems have the best unit structure period size and the optimized thickness of the dielectric layer,and the more graphene layers,the more favorable the high light absorption.Our work not only provides an alternative solution to optoelectronic devices design based on layered graphene structures,but also provides an effective reference basis for the design of graphene plasma components.