Investigation On The Nonlinear Surface Plasmon Polaritons Of Graphene And Its Heterojunction

Graphene,as a new type of 2D material with monolayer carbon atom,has attracted great attention since it was discovered.Compared with traditional material,graphene has many advantages,such as ultra high nonlinear index of absorption and refraction,ultra fast response time and high modulation rate,large operating bandwidth,strong interaction between light and graphene and convenient controlling means,which makes graphene have great application potential in optoelectronics.Now the researches on graphene are in full swing,and surface plasmon polaritons(SPPs)on graphene have become a hot spot recently which have many advantages compared with SPPs on metal.The losses of SPPs on graphene are lower than SPPs on metal which means that propagation length of SPPs on graphene are longer than that on metal.And the localization of light field for SPPs on graphene is higher than that on metal,which makes the electromagnetic field are confined tightly near the interface.What’s more,the conductivity of graphene can be controlled conveniently by chemical doping or applied electrostatic field which makes graphene a good candidate for nano photonic devices.Our research works are carried on about the properties of SPPs on graphene,and the research results are listed as follows:1.The properties of SPPs in the structure of anisotropic dielectric between two graphenes are investigated.We find that the influence on odd and even modes is different when the orientations of optical axis are different.For odd mode,the effective index for the optical axis parallel to the graphene is the highest,while the effective index for the optical axis perpendicular to the graphene is the lowest.The propagation length of SPPs is the longest for the optical axis parallel to the interface when the separation of two graphenes is over a threshold.The properties of even mode are contrary to those of odd mode.And the intrinsic physical reasons are revealed through the distribution of magnetic field in the direction perpendicular to graphene.The influence of the position of the anisotropic dielectric has also been discussed.2.We have investigated theoretically the properties of hybrid nonlinear surface-phonon-plasmon-polaritons(SP3)at the interface of graphene-covered hexagonal boron nitride(hBN)and nonlinear medium.It is demonstrated that the hybrid nonlinear SP3 can be tuned by controlling the chemical potential,layer number and relaxation time of graphene.Moreover,we show that the nonlinear dielectric permittivity has great effect on the propagation constant.The real part of the propagation constant increases with positive nonlinear dielectric permittivity at different frequency for low frequency mode;while the imaginary part of the propagation constant decreases in the upper Reststrahlen band of hBN,and keeps nearly constant in the lower band,and increases outside the Reststrahlen band with positive nonlinear dielectric permittivity for low frequency mode.The results here are helpful for the application of graphene-hBN heterostructure.3.The transverse electric(TE)SPPs on a graphene parallel plate waveguide bounded by Kerr-type nonlinear media in the mid-infrared and terahertz frequencies are investigated.Through theoretical analysis of the exact dispersion relations,we reveal the existence conditions of the even mode and odd mode of nonlinear TE SPPs in this system.When the permittivity of the core is smaller than the linear permittivity of the nonlinear cladding,the even mode and two branches of the dispersion curve can exist.However,when the permittivity of the core is larger than the linear permittivity of the nonlinear cladding,both even and odd modes can be supported.The odd mode of TE SPPs can’t be found in the similar structure of metal.Moreover,it is found that the propagation constant of even and odd modes decreases with the increasing Fermi energy of graphene.The influence of the loss and nonlinearity of graphene on the property of the TE SPPs is also discussed.4.We have designed a bistable system based on graphenes-dielectric-graphenes which can be tuned by bias voltage conveniently,and low threshold power can be obtained in the system.The reflection coefficient is obtained by transfer matrix method,and the angle corresponding to attenuated total reflection(ATR)can be found.It can be found that the angle of ATR and the with of the dip of ATR decrease,and the optimal separation between the prism and the graphene increases with the Fermi energy of graphene increasing.The angle of ATR and the with of the dip of ATR increase,and the optimal separation between the prism and the graphene decreases at first then increases with the separation between the graphenes increasing.The system parameters have been optimized,and we find that the threshold power of the structure decreases with the separation between the graphenes decreasing,but the threshold power changes a little when the separation smaller than 300 nm.What’s more,the threshold power decreases with the Fermi energy,or the relaxation time,or the layer number of the graphenes increasing.Finally,the threshold power in the structure we designed with double multilayer-graphenes is four orders of magnitude lower than that with monolayer graphene.