石墨烯双曲超材料的宽带吸收特性研究

Home Search Collections Journals About Contact us My IOPscienceWideband absorption in fibonacci quasi-periodic graphene-based hyperbolic metamaterialsThis content has been downloaded from IOPscience. Please scroll down to see the full text.2014 J. Opt. 16 125108(/2040-8986/16/12/125108)View the table of contents for this issue, or go to the journal homepage for moreDownload details:IP Address: 202.119.79.14This content was downloaded on 14/12/2014 at 11:28Please note that terms and conditions apply.Wideband absorption infibonacci quasi-periodic graphene-based hyperbolic metamaterialsRenxia Ning1,2,Shaobin Liu2,Haifeng Zhang2,Xiangkun Kong2,Borui Bian2and Jie Bao11College of Information Engineering,Huangshan University,Huangshan,245041,People’s Republic ofChina2Key Laboratory of Radar Imaging and Microwave Photonics(Nanjing Univ.Aeronaut.Astronaut.),Mini-stry of Education,College of Electronic and Information Engineering,Nanjing University ofAeronautics and Astronautics,Nanjing,210016,People’s Republic of ChinaE-mail:plrg@Received10August2014,revised14October2014Accepted for publication17October2014Published27November2014AbstractA heterostructure containing a Fibonacci quasi-periodic layer and a resonant metal back reflectoris proposed,which can realize wideband absorption.The Fibonacci layer is composed ofgraphene-based hyperbolic metamaterials and isotropic media to obtain wideband absorption.Toenhance absorption,an impedance-matching layer is put on top of the Fibonacci layer.It isshown to absorb roughly90%of all available electromagnetic waves in an11terahertzabsorption bandwidth for a transverse magnetic mode at normal angle incidence.The absorptionbandwidth is affected by the reflection band pared with some previous designs,ourproposed structure has a larger absorption bandwidth and higher absorption in the mid-infraredrange.The results should be valuable in the design of infrared stealth and broadbandoptoelectronic devices.Keywords:wideband absorption,fibonacci quasi-periodic,graphene-based hyperbolicmetamaterials(Somefigures may appear in colour only in the online journal)1.IntroductionGraphene has emerged as an outstanding material for optoe-lectronic applications due to its high electronic mobility and unique doping capabilities[1].However,because of its short interaction length,a monolayer of graphene absorbs onlyπα(2.3%)of the incident light,whereα=e2/(ħc)is the quantum electrodynamicsfine structure constant[2,3].The low absorptivity,which indicates important applications for gra-phene as a transparent conductivefilm,can be derived from the frequency-independent sheet conductivity under condi-tions of negligible impurity and substrate scattering[4].Many papers on the linear and nonlinear effects of graphene[5,6], have focused on its absorption properties[7–10].Recently, more and more interest has centered on enhancing the absorption of graphene in the terahertz(THz)and mid-infrared frequency ranges[11–13].Sukosin et al[13]found that a single sheet of doped graphene,patterned into a peri-odic array of nanodisks,exhibits perfect light absorption. Woo et al[14]demonstrated a graphene-based Salisbury screen absorber operating in the THz regime,and showed that excellent absorbance values of0.95and0.97at0.5and 1.5THz,respectively,can be attained.However,these results demonstrate that the absorption band is very narrow. Experiments on graphene as a saturable absorber in micro-wave and visible frequency ranges have been reported[15]. Microwave absorbance of graphene always decreases with increasing power,though it is independent of the incident frequency.A hyperbolic metamaterial(HMM)[16]is a kind of anisotropic medium with a hyperbolic dispersion relation,and is of interest for its potential applications innegative J.Opt.16(2014)125108(7pp)doi:10.1088/2040-8978/16/12/125108refraction,optical waveguides and imaging hyperlens.A novel implementation of HMMs in the far-infrared frequency range is composed of stacked graphene sheets separated by thin dielectric layers [17],which can be used as a super absorber in the near-field.An HMM can also be designed as an ef ficient and innovative absorber to enhance the decay rate of emitters near its surface [18].These characteristics can be applied to obtain a very broad range of relative wavenumber [12].However,to the author ’s knowledge,there has been very little research on wideband absorption of graphene-based hyperbolic metamaterials (GHMMs).In this paper,we theo-retically investigated the wideband absorption properties of a Fibonacci quasi-periodic GHMM in the mid-infrared range,but ignore the nonlinear effect of graphene.The paper is organized as follows.In section 2,we analyze the group and phase indices of GHMMs.A Fibonacci quasi-periodic structure composed of the GHMM and dielectric has been studied by the transfer matrix method (TMM).In section 3,we discuss absorption bandwidth.Finally,we conclude in section 4.2.Theoretical model and numerical method2.1.The electrical properties of grapheneFor a graphene sheet,the electromagnetic properties are described in terms of the surface conductivity σ.Inter-band and intra-band transitions can be described by Kubo model [19,20].The conductivity σis given by ⎜⎟⎛⎝⎜⎛⎝⎞⎠σπωτμπμωτμωτ=ℏ++++ℏ−ℏ++ℏ+μ−e k T i k Te e i i i ()2ln 1i 4ln 2()2(),(1)B B k T 222B where,ωis radian frequency,ħis the reduced Planck con-stant,κB is the Boltzman constant,e is the charge of the electron,T is the temperature,μdenotes the chemical potential,and τis electron –phonon relaxation time,respec-tively.We assume that the electronic band structure of a graphene sheet is unaffected by the neighboring sheets,so the effective permittivity εG of graphene can be written as [21]εσωε=+id 1,(2)G G 0where d G is the thickness of graphene sheet,and ε0is the permittivity in the vacuum.2.2.Effective permittivity of GHMMFor our multilayer design,we may use the effective medium theory to study electromagnetic wave propagation in the GHMM,which is an anisotropic medium with the followingapproximate uniaxial dielectric tensor components [22]:⎛⎝⎜⎜⎞⎠⎟⎟εεεε=,(3)xx yy zz where εxx =εyy =ε‖,εzz =ε⊥,ε‖and ε⊥are the parallel andvertical components of the relative permittivity,respectively.We also haveεεε=++∥d d d d ,(4)G G C CG C εεεεε=++⊥()d d d d ,(5)G C G C G C C Gwhere,εC and d C are dielectric permittivity and dielectricthickness,respectively.ε⊥≈εC ,ε‖=εC +i σ/ε0ωd C ,while d C ≫d G .For transverse magnetic (TM)wave propagation in our structure,the spatial dispersive curve can be derived as k z 2/εxx +k 02k x 2/εzz =,if εxx εzz <0,the dispersive curve is hyperbolic and εxx εzz >0,is elliptical [23,24].2.3.Absorption of fibonacci quasi-periodic GHMMA schematic view of an obliquely incident electromagnetic wave on a one-dimensional (1D)Fibonacci quasi-periodic structure composed of two-type dielectric and GHMM is plotted in figure 1.Cell structures based on the Fibonacci sequence in the periodic structure have been studied [25,26].In this paper,we assume that the first two layers of the Fibonacci sequence are S(1)={AB}and S(2)={Q},where A,B and Q,represent a loss dielectric,conventional material layer and GHMM,with thicknesses of d A ,d B ,d Q (d Q =dC +d G ),respectively,as marked in figure 1(a).Figure 1(b)depicts a GHMM unit cell consisting of dielectric C (cesium lead chloride:CsPbCl 3)and graphene.We then calculate absorption as a function of frequency and incident angle for TM wave in a half-in finite slab of material.The TMM has been given in previous papers [27–29].The absorption can be calculated from A =1-|r |2-|t |2,where r and t are re flection and transmission coef ficients,respectively.Figure 1.(a)Schematic diagram of 4th order 1D Fibonacci quasi-periodic GHMM composed of dielectric A,B and Q at incident angle (θ).(b)Front view of GHMM.3.Numerical results and discussionIn this section,we investigate the properties of the relative permittivity of GHMM and absorption of1D Fibonacci quasi-periodic GHMM in the mid-infrared regime,and subse-quently study the effect of the graphene,structure parameters and incident angle on the absorption bandwidth.We choose the structure parameters as follows:εA=2.8+0.09i[30,31],μA=1,d A=5.5μm,εB=1.21,μB=1,d B=1μm,εC=14.3 [32],μC=1,d G=0.335nm,[33]μG=1.3.1.The group index of refraction for GHMMThe relative permittivity of monolayer GHMM isfirst cal-culated and plotted infigures2–3.Infigure2,we show Re (ε‖)(the real part ofε‖)for monolayer GHMM withFigure2.Real part ofε‖versus frequency for different(a)μ,(b)T,(c)d C and(d)τ. Figure3.Imaginary part ofε‖versus frequency for different(a)μ,(b)T,(c)d C and(d)τ.different graphene and dielectric parameters.When the chemical potential or the electron-phonon relaxation time is increased,or the thickness of dielectric in the GHMM is decreased,then Re(ε‖)decreases.When Re(ε‖)is smaller than zero,a hyperbolic type is observed.Figure3shows Im (ε‖)(the imaginary part ofε‖)for different parameters.In contrast to Re(ε‖),Im(ε‖)is positive,which indicates that GHMM is a dissipative medium.The smaller chemical potential,the shorter electron–phonon relaxation time is; likewise,the larger d C is,the larger Im(ε‖)is.The results show thatε‖can be changed slightly when the temperature varies from250–350K,as shown infigures2(b)and3(b). Thus,the influence of temperature can be insignificant in general[19].3.2.The absorption band for fibonacci quasi-periodic GHMM We now discuss the absorption band of Fibonacci quasi-periodic GHMM.In order to realize wideband absorption,we design a periodic structure(ABQ)N,where N is the periodic number and the following parameters are chosen:d C=15nm,τ=20fs,μ=0.3eV,T=300K,N=12.The reflection,trans-mission and absorption are presented infigure4(a).The absorption is less than0.75due to the larger transmission. Depending on the relationship between the absorption, reflection and transmission,we should reduce the transmis-sion and reflection to attain a larger absorption.By employing an(ABQ)N Ag structure,we may obtain larger absorption with decreasing transmission.Silverfilm is used as a resonant metal back reflector[28,34],with its parameter selected according to Ref.[35–36].We can also choose other metals such as gold or aluminum,without affecting the results[35].The absorption,transmission and reflection of(ABQ)N Ag are plotted infigure4(b),where we can see that the transmission is zero because of the Ag reflector.The absorption of(ABQ)N Ag is larger than that of (ABQ)N,and approaches1at27THz and0.6at16THz. However,reflectionfluctuations due to an impedance mis-match,cause the absorptionfluctuations.We now consider improving the impedance matching to reduce the reflection.In a previous design,we showed that a Fibonacci quasi-periodic structure can enhance photonic band gaps[25],with energy localized within the band gap.After multiple resonances,energy is nearly completely absorbed; thus,wideband absorption can be attained.For the M(FS)s Ag structure illustrated infigure5(inset),M,FS(with a Fibo-nacci sequence order numbers of s=7)and Ag denote the impedance-matching layer,Fibonacci quasi-periodic GHMM and reflector,respectively.We choose the parameters of the dielectric M to beεM=1.4and d M=3μm.The calculated wideband absorption from15.5to26.5THz is shown in figure5.3.3.Effects of the GHMMNext,we examine how absorption is affected by the graphene parameters of a GHMM,with the results shown infigure6. As we can see,the absorption bandwidth is hardly affected by the parametersτ,μ,T and s,but the absorption value can be tuned by these parameters.Infigure6,whenτis20fs,the absorption is larger than whenτis200or2fs because Im(ε‖) is a maximum asτ=20fs,as revealed before infigure3(d).InFigure4.The reflection,transmission and absorption of(a)(ABQ)N and(b)(ABQ)N Ag withτ=20fs,μ=0.3eV,d C=15nm,T=300K.Figure5.The reflection and absorption of M(FS)s Ag atτ=20fs,μ=0.3eV,εC=14.3,d C=15nm,T=300K,(inset)M,FS(s=7)and Ag denote the impedance matching layer,Fibonacci quasi-periodic GHMM and sliver as resonant metal back reflector,respectively.figures 6(b)and (d),it is observed that the absorption can be increased by increasing μand s .In figure 6(c),we can see that the absorption is unaffected by different temperatures because ε‖only changes slightly with temperatures over the range 250–350K.To study the GHMM in fluence on absorption,we plot the relation between the absorption of M(FS)s Ag and thickness of dielectric C of GHMM in figure 7.As shown in figure 7(a),absorption is nearly 1when the value of εC is 15or so;however,when d C is 10nm,the absorption fluctuates in the low frequency range,and as d C increase,fluctuations appear in the high frequency regime.The above discussions are only valid for the M(FS)s Ag structure.In general,the absorption bandwidth depends on τ,μ,εC ,and s ,but is independent of T .3.4.Wideband absorptionThe incident angle of the electromagnetic wave also affects absorption.We find that the absorption bandwidth is 11THz (from 15.5to 26.5THz)at normal incidence.In figure 8(a),the absorption as a function of incident angle is plotted for frequencies of 17,19,21,23and 25THz,respectively.The results show that for M(FS)s Ag,the absorption is almost 1when the incident angle is between −75°and 75°for fre-quencies between 19and 25THz.Figure 8(b)shows the results as the incidence angle chan-ges from 0°to 89°.We see that for a TM mode,the absorption band gradually has a blue shift and a larger bandwidth with a smaller absorption.The wideband absorption region changes from 15.5to 26.5THz,and the frequency range is 11THz.Figure 6.The absorption of M (FS)s Ag for different (a)τ,(b)μ,(c)T and (d)s at normal incidence with TMmode.Figure 7.The absorption of M(FS)sAg for different (a)dielectric and (b)thickness with τ=20fs,μ=0.3eV,T =300.4.ConclusionIn summary,the wideband absorption of1D quasi-periodic structures composed of lossy dielectric,isotropic dielectric and GHMM,arranged according to a recursive Fibonacci sequence,has been investigated.The relative permittivity of GHMM and the absorption band of M(FS)s Ag,which can be tuned by the GHMM and incident angle.The results show that,when impedance matching and total reflection are employed,this new kind of ternary quasi-periodic structure has a wideband absorption,which is insensitive to the inci-dent angle of the electromagnetic wave.We conclude that wideband absorption can be attained by using a recursive Fibonacci sequence,and the absorption can be increased by pared with some previous conventional reso-nant absorbers[11,36],the structure that we propose has a larger bandwidth and absorption in the mid-infrared fre-quency range.Wideband absorption may have potential applications in infrared stealth and broadband photodetectors. It is noteworthy that the nonlinearity of GHMM is also very interesting,as we shall discuss in a future paper. AcknowledgementsThis work was supported by the Specialized Research Fund of China for the Doctoral Program of Higher Education(grant No.20123218110017),Jiangsu Province Science Foundation (Grant No.BK2011727),the Natural Science Foundation of China(Grant No.61307052),the Foundation of Aeronautical Science(No.20121852030),the Fundamental Research Funds for the Central Universities(2013302),Youth Funding for Science&Technology Innovation in NUAA (NS2014039),Open Research Program in Jiangsu Key Laboratory of Meteorological Observation and Information Processing(Grant No.KDXS1207),the Jiangsu Innovation Program for Graduate Education(CXZZ13_0166),Huang-shan University Program for Scientific Research (2010xkj006),the Anhui for Scientific Research (KJ2013B267).References[1]Fang Z et al2013ACS Nano72388–95[2]Furchi M et al2012Nano Lett.122773–7[3]Nair R R et al2008Science3201308[4]Bonaccorso F,Sun Z,Hasan T and Ferrari A C2010Nat.Photonics4611–22[5]Zhang H,Virally S,Bao Q,Kion Ping L,Massar S,Godbout N and Kockaert P2012Opt.Lett.371856–8 [6]Fang Z,Zhen Y,Fan L,Zhu X and Nordlaner P2012Phys.Rev.B85245401[7]Vincenti M A,de Ceglia D,Grande M,D’Orazio A andScalora M2013Opt.Lett.383550–3[8]Nikitin A Y et al2012Phys.Rev.B85081405[9]Alaee R,Farhat M,Rockstuhl C and Lederer F2012Opt.Exp.2028017–24[10]Andryieuski A and Lavrinenko A V2013Opt Exp.219144–55[11]Liu J T et al2013EPL(Europhys.Lett.)10457002[12]Nefedov I S,Valaginnopoulos C A and Melnikov L A2013J.Opt.15114003[13]Thongrattanasiri S,Koppens F H L and de Abajo F J G2012Phys.Rev.Lett.108047401[14]Min Woo J et al2014Appl.Phys.Lett.104081106[15]Zheng Z,Zhao C,Lu S,Chen Y,Li Y,Zhang H and Wen S2012Opt.Exp.2023201–14[16]Smith D R and Schurig D2003Phys.Rev.Lett.90077405[17]Othman M A K,Guclu C and Capolino F2013Opt.Exp.217614–32[18]Guclu C,Campione S and Capolino F2012Phys.Rev.B86205130[19]Falkovsky L A2008J.Phys.:Conf.Ser.129012004[20]Mikhailov S A and Ziegler K2007Phys.Rev.Lett.99016803[21]Vakil A and Engheta N2011Science3321291–4[22]DaSilva A M et al2013Phys.Rev.B88195411[23]Madani A,Zhong S,Tajalli H,Roshan Entezar S,Namdar A and Ma Y2013Prog.Electromagn.Res.143545–58[24]Xiang Y et al2014Sci.Rep.45483[25]Zhang H F,Zhen J P and He W P2013Optik—InternationalJournal for Light and Electron Optics1244182–7[26]Zhao P L and Chen X2011Appl.Phys.Lett.99182108[27]Ning R et al2014Eur.Phys.J.Appl.Phys.6820401[28]Sreekanth K V,De Luca A and Strangi G2013Appl.Phys.Lett.103023107[29]Zhang H F,Liu S B and Kong X K2013Phys.B:CondensedMatter410244–50[30]Tao H et al2008Phys.Rev.B78241103[31]Zhu W et al2014Appl.Phys.Lett.104051902Figure8.(a)Absorption versus incident angle for different frequencies from17to25THz.(b)Absorption versus incident angle and frequency.[32]Palik E D1985Handbook of Optical Constants of Solids(NewYork:Academic Press)pp350–7[33]Novoselov K S et al2004Science306666–9[34]Pu M et al2013Opt.Exp.2111618–27[35]Laman N and Grischkowsky D2008Appl.Phys.Lett.93051105[36]Zheng H,Vallée R,Almeida R M,Rivera T and Ravaine S2014Opt.Mater.Exp.41236–42。