Researches On The Graphene-based Long Range Surface Plasmon Polaritons Waveguide

Mid-infrared electromagnetic(EM)waves have attracted intensive research interest because of their wide application in the fields of communication,biomedicine,spectroscopy,homeland security,etc.To achieve the transmission of mid-infrared EM waves in the future photonic integrated circuits with high-integration densities,it is essential to develop an optical waveguide with strong sub-wavelength confinement and a long propagation distance.Graphene-based surface plasmon polaritons(SPPs)waveguide is a promising candidate for achieving this objective.But,the propagation length of the graphene-based waveguide is still relatively small,which greatly limit their practical applications.To improve the propagation length significantly,we proposed and investigated several graphene-based waveguides with larger propgation distance by using the finite-difference time-domain method,based on a thorough analysis of the various kinds of the garaphene-based and the metal-based SPP waveguide.Moreover,we investigated the coupling features of the graphene-based and the metal-based SPP waveguides.The main contents and conclusion of this paper are summarized as follows.(1)We proposed a graphene-based cylindrical hybrid waveguide,which is composed of a cylindrical silicon nanowire core,a silica layer and then a graphene layer from inside to out.First,we derive the EM field expression of the waveguide by solving the Helmholtz equation,and then analyze the waveguide's mode features based on the analytical solutions of the EM field and the numerical simulation.These derivations demonstrate that the waveguide has the ability to achieve an larger propagation length compared with that of the graphene-coated nanowire waveguide.Next,utilizing the perturbation theory of coupled mode,we show that the symmetric coupling mode(SCM)and the anti-symmetric coupling mode(ASCM)originate from the coupling of two waveguide with identical mode.Thus,the six lowest-order coupling modes originate from the coupling of three lowest-order single-waveguide modes.We demonstrate that the m =1 order yy-coupling mode has a maximum coupling length and a minimum crosstalk.(2)We investigated a graphene-based rectangular long range SPP(LRSPP)waveguide,which is composed of two identical outer graphene nanoribbons and two identical inner silica layers symmetrically placed on both sides of a silicon layer.Based on the coupled-mode perturbation theory,we demonstrate that the LRSPP and short range SPP(SRSPP)modes originate from the coupling of the same modes of the two graphene nanoribbons.Moreover,the LRSPP fundamental mode of this waveguide is capable of achieving an ultra-long propagation length(?10 ?m).Further,for this waveguide,in ultra-deep sub-Savelength confinement(?10-7 A0,where A0 is the diffraction-limited mode area)similar to that of other conventional graphene-based hybrid waveguides is maintained.(3)We researched a graphene-based cylindrical waveguide,which is composed of a cylindrical silicon nanowire core surrounded by an inner graphene layer,a silica layer,and an outer graphene layer from inside to out.First,we derive the EM field equation and the dispersion equation of this waveguide.Then,through a numerical simulation using the finite-difference time-domain method,we demonstrate that,when two graphene layers couple with each other,the LRSPP and short-range SPP(SRSPP)modes exhibit different EM field distributions and propagation properties because of the difference of boundary conditions between them.For the fundamental LRSPP mode,a larger propagation length(?10 ?m)and a comparable mode area(?10-5 A0)can be simultaneously achieved.Moreover,the coupling effective of the proposed waveguide is dramatically improved because of its closed structure.Thus,its long propagation length can be maintained even if the coupling distance becomes larger.(4)We investigated the coupling feature of the graphene-based SPP waveguide and the metal-based SPP waveguide.There are different SPP waveguide with different SPP material in the future photonic integrated circuits.Thus,it is very actual value to achieve the exchange of information for different waveguides.However,for the graphene-based SPP waveguide,the real part of the effective index,nr,is much larger than that of the metal-based SPP waveguide.This result in that the coupling and the information exchange cannot be achieved between the two types of waveguides.Therefore,we proposed a cylindrical LRSPP waveguide with multi-layer graphene.The study shows that the nr of the LRSPP fundamental mode for this waveguide can be reduced evidently by increasing the layers of graphene and the radius of the silicon nanowire.Next,we researched a metal-based cylindrical hybrid waveguide,which is composed a cylindrical silver nanowire surrounded a silica layer and then a silicon layer from inside to out.We found that the nr value of this waveguide can be increased by decreasing the radius of the silver nanowire and increasing the thickness of silicon layer.Thus,we can obtain the identical nr value and wave vector by selecting the appropriate parameters for the two types of waveguide.Then,the effective coupling can be achieved between them.