Theoretical Study Of Non-hermitian Optical System Based On Graphene Nanoribbons

With the development of economy and society,the traditional electronic information technology can not satisfy the needs of modern society.People put forward new requirements for the development of information technology.Photonic devices become an ideal carrier for information transmission.But the diffraction limit of traditional photonic devices hinders the miniaturization and integration of photonic devices.The research of surface plasmons(SPs)provides a solution for overcoming the diffraction limit.The study found that surface plasmon polaritons(SPPs)have the advantages of overcoming diffraction limit,easy integration and light manipulation at the nanometer scales.These characteristics of SPPs provide the fundamental for exploring the interaction between waveguide and resonator.In recent years,with the in-depth research on graphene,it has been discovered that graphene can excite SPs in the mid-infrared region.Photonic devices based on graphene surface plasmons(GSPs)show superior performance and can be used to manufacture tunable photonic devices at nanometer scale.In this paper,Exceptional Points(EPs)are found in non-Hermitian optical systems by using numerical simulation and analytical calculations,and unidirectional reflectionlessness is achieved at EPs.Firstly,a non-Hermitian graphene surface plasmonic waveguide system is proposed in this paper.This system consisting of two wing-shaped resonators and a graphene waveguide.Based on the far-field coupling between two wing-shaped plasmonic resonators,the system achieves unidirectional reflectionless effect in the mid-infrared region.The results show that when the wave is incident from one side of the structure,the reflection is almost 0.While the reflection is 26.212%incident from the other side.Thus,an EP is generated.All the simulation results are conducted by FEM.In addition,the parameters of graphene are changed to study the influence to unidirectional reflectionlessness.Secondly,a non-Hermitian optical system consisting of three resonators to construct far-field coupling is designed in the paper,which can realize dual-frequency unidirectional reflectionlessness at EPs.The system is composed of three wing-shaped resonators,which are side-coupled to the graphene plasmonic ribbon waveguide.Based on the temporal coupled-mode theory(TCMT)and numerical simulation,the dual-frequency unidirectional reflectionless phenomenon is studied.The reflections for forward incidence are zero at 34.34THz and 35.83 THz,while the reflections for backward incidence are close to 33.13%and21.13%,respectively.The contrast ratio between the forward and backward reflections is almost 1.A non-Hermitian scattering matrix is proposed to verify the existence of double EPs.Furthermore,the position of EPs can be dynamically tunable by changing the E_f of graphene.However,the positions of EPs could be unchanged with relaxation time.Finally,the non-Hermitian waveguide-cavity system based on near-field coupling has been studied.The system is make up of a graphene ribbon waveguide and two graphene resonators.The results of TCMT and simulation show that dual-frequency unidirectional reflectionlessness is approached at two EPs in the mid-infrared region.When the frequency is24.418 THz(20.865 THz),the forward(backward)reflectivity is nearly 0 and the backward(forward)reflectivity is 24.71%(22.945%).In addition,the relationship between the Fermi energy of graphene and the position of EPs is studied in the paper through changing bias voltage.It can be found that EPs position blue shifts with increasing E_f.