Investigation Of The Graphene-based Plasmonic Crystals

Photonic crystals(PhCs),optical microstructure of periodically arranged dielectric functions,have been paid great attentions due to their unprecedented ability for wave manipulation and applications in optical communication and sensing.Recently,the exploration of topology on band structures has revolutionized our understanding of PhCs,leading to the achievements of quantum Hall effect(QHE),quantum spin Hall effect(QSHE)and topological insulator(TI)in photonics.However,the conventional dielectric-based Ph Cs are diffraction limited,and further size reduction is difficult to obtain,which hampered the further development of conventional photonic technology.It has been well established that the diffraction limitation could be circumvented by the use of the surface plasmon polaritons(SPPs).The light field can be confined to deep nanoscale,realizing efficient on-chip integration of optical components.Compared with conventional plasmonic materials(such as Au,Ag et al.),graphene-supported SPPs exhibit relative low Ohmic loss,tight field confinement and flexible tunability.In this paper,two-dimensional(2-D)plamonic crystals of different lattices,constructed by graphene,are used to realize Dirac,Dirac-like and double Dirac cone dispersions.The band topology and zero-refractive-index characteristic of the graphene plasmonic crystals(GPCs)are discussed in detail.The main research work and results are as follows:1.We constructed 2-D GPCs of honeycomb lattice.The band structures,calculated by finite-element method,exhibited double degenerated Dirac cones at the Brillouin zone(BZ)corner K points in mid-infrared frequency regime.By breaking the spatial inversion symmetry(a.tuning the chemical potential of graphene nanodisks,b.tuning the radii of graphene nanodisks),the Dirac cone was opened and a topological band gap of 3.2 THz was obtained.Two valley chiral states of opposite polarization directions(left-handed circular polarized and right-handed circular polarized)emerged at K points after the splitting of Dirac cone.We numerically simulated the selective excitation of the valley chiral states by using in-plane magnetic field of circular polarization,realized the topological valley edge transport within the band gap.2.We constructed 2-D GPCs of honeycomb lattice.By employing zone folding mechanism,the Dirac cones at the BZ corners are folded to a four-fold degenerated double Dirac cone at the BZ center.The topological trivial/nontrivial band gaps can be obtained by shrinking or expanding the graphene nanodisks.By using the interface constructed by the trivial and nontrivial plasmonic crystals,we realized pseudospin dependent unidirectional transmission of edge states in mid-infrared frequency regime.3.We constructed 2-D GPCs of triangular lattice.According to the band structures,calculated by finite-element method,we analyzed the modal properties.By tuning the radius of graphene nanodisk,a three-fold accidental degenerated Dirac-like cone was achieved at the BZ center ? point in mid-infrared frequency regime.The effective permittivity and permeability around the Dirac-like point were evaluated by using the method of average field of Bloch modes.Further numerical simulations including cloaking,focusing and unidirectional transmission were implemented to demonstrate the zero-refractive-index characteristic around the Dirac-like point.