Andryieuski, Andrei

Khromova, I.

Lavrinenko, Andrei

We study terahertz to infrared electromagnetic properties of multilayer graphene/dielectric artificial medium and present a novel concept of terahertz modulation at midinfrared wavelengths. This approach allows the realization of high-speed electrically controllable terahertz modulators based on hollow waveguide sections filled with multilayer graphene

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Multilayer Graphene for Waveguide Terahertz ModulatorKhromova, I.; Andryieuski, Andrei; Lavrinenko, AndreiPublished in:Proceedings of META 2014Publication date:2014Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Khromova, I., Andryieuski, A., & Lavrinenko, A. (2014). Multilayer Graphene for Waveguide Terahertz Modulator.In Proceedings of META 2014META 2014 CONFERENCE, 20 – 23 MAY 2014, SINGAPOREMultilayer Graphene for Waveguide Terahertz ModulatorIrina Khromova1, Andrei Andryieuski2, Andrei Lavrinenko21Department of Electrical and Electronic Engineering, Public University of Navarra, Pamplona, Spain2Department of Photonics Engineering, Denmark University of Technology, Lyngby, Denmark*corresponding author, E-mail: irina.khromova@unavarra.esAbstractWe study terahertz to infrared electromagnetic proper-ties of multilayer graphene/dielectric artificial medium andpresent a novel concept of terahertz modulation at mid-infrared wavelengths. This approach allows the realizationof high-speed electrically controllable terahertz modulatorsbased on hollow waveguide sections filled with multilayergraphene.1. IntroductionActive developement of terahertz/infrared science and en-gineering has created a growing demand for new electronicand quasi-optical devices. In the absence of mature tech-nologies aplicable to this frequency region, a huge effortis being made to investigate the opportunities offered bynovel materials, such as graphene [1] and artificially cre-ated metamaterials on its base.Due to extrodinarily high carrier mobility [2] andpicosecond-scale photocarrier generation and relaxation[3], graphene has been actively studied as a solution forhigh-speed modulators at different frequency ranges [4]-[6].In this work, we investigate dielectric properties of mul-tilayer graphene as an artificial medium and present a novelconcept of a terahertz modulator based on a hollow waveg-uide filled with graphene/dielectric composite.2. Multilayer Graphene/Dielectric MediumWe investigate the properties of a composite shown inFig. 1: graphene sheets are interlayed by a dielectric ma-terial of thickness d and a dielectric permittivity "M . Wesuppose that each pair of graphene sheets is gated by ap-plied voltage, thus, providing the tunability of the elec-tromagnetic parameters of the structure. Despite implyinga technological challenge, such a composite was recentlysuccessfully fabricated using 100 nm-thick PMMA layersbetween graphene sheets [7].Supposing d to be much smaller than the wavelengthof the terahertz/infrared radiation, we can characterize thestructure by an effective dielectric permittivity:"eff ("M ; !; d; Ef ; ) = "M + i(Ef ; )!"Md; (1)Figure 1: Tunable multilayer graphene controlled by ap-plied gate voltage.where ! is the angular frequency, Ef is the Fermy energyof the graphene sheets (in this work, we neglect the ef-fects of the substrates and consider the Fermy energy of allgraphene layers to be equal),  is the graphene scatteringrate set as 1012s 1.Graphene conductivity  is calculated by the Kubo for-mula [8] taking the both the intraband and interband termsinto account: = intra + inter;intra =2e2kBT~2Ln(2Cosh(Ef2kBT))i! + i(2)inter =e24~(H(!2) +i4!Z 10H() H(!2 )!2   42 d)where e is the electron charge, ~ is the Plank constant, kBis the Boltzman constant, T is the temperature consideredto be equal to 300K, and H(x) is a function determined asin [8].In contrast to the submillimetre band, at high terahertzfrequencies graphene exhibits high conductivity and lowlosses. When the interband transitions kick in, the imagi-nary part of graphene conductivity becomes negative whileits real part starts to grow. In a graphene/dielectric medium,this effect can be seen as a metal to dielectric transition fol-lowed by low-loss dielectric to high-loss dielectric transi-tion (Fig. 2). In the vicinity of this peculiar frequency re-gion, the real part of the effective dielectric permittivity of20 30 40 50f,THz-1123e'10 20 30 40 50f,THz0.51.01.52.0e''fEeV03.0 eV08.0eV06.0eV04.0 eV07.0eV05.0fEeV03.0eV08.0eV06.0eV04.0eV07.0eV05.0Figure 2: Real ("0) and imaginary ("00) parts of the dielectricpermittivity of the multilayer graphene medium with d =50nm and ("M = 2:25) at different Fermy energy levels.the structure exceeds the host medium permittivity "M . Asthe frequency increases, the medium becomes lossier andless optically dense.The frequency at which this spectrally narrow change inmacroscopic electromagnetic properties takes place is ex-tremely sensitive towards changes in the concentration ofcharge carriers in graphene layers. The latter is governedby gate voltage.In this paper, we suggest using this phenomenonto achieve electrically controllable modulation in hollowwaveguides filled with graphene/dielectric medium.3. Hollow waveguide filled withgraphene/dielectric compositeAt mid-infrared wavelengths, where both ohmic and dielec-tris losses are present, hollow waveguides are considered asthe optimal solution for transferring radiation [9, 10]. Weconsider a rectangular hollow waveguide filled with multi-layer graphene and demonstrate efficient electrically con-trollable modulation at frequencies around the CO2 laseremission line. For simplicity, ohmic losses in the waveg-uide are neglected. In the on-state, the modulating waveg-uide section transmits the fundamental mode, which is sup-pressed due to dielectric to metal transision at lower fre-quencies and dielectric losses at higher frequencies. AsFigure 3: Inverse attenuation coefficient,  1, of a TE10mode of a graphene-filled waveguide as a function of thewaveguide width a and graphene Fermi energyEf . The redcurve corresponds to the local minimum of  (on). Darkgrey and light grey curves denote the cut-off conditions ofthe TE10 and TE20 modes, respectively.discussed in the previous Section, modulation is achievedby changing the applied gate voltage.Fig. 3 shows the analytically calculated inverse atten-uation coefficient of a TE10 mode of a hollow rectangu-lar waveguide filled with multilayer graphene. For givenwaveguide dimensions, provided they fall between the TE10and TE20 cut-off conditions, the minimum of the attenua-tion coefficient determines the Fermi energy level at whichthe highest transmission is achieved. It can be seen that aslight variation of gate voltage can drammatically changethe dielectric properties of the waveguide core leading tostrong attenuation of the fundamental mode.Once the desired transmission parameter is defined, thelength of the waveguide modulator section is determinedas:L =   1 onTon (3)For instance, a 95% transmission in a 5  m waveg-uide can be achieved at L = 20:7m (meaning muchhigher transmission for shorter modulation sections). Thechange of the Fermy energy level required to achieve de-sired modulation depth is given in Table.1.The grapheneconductivity model used in this paper does not allow evalu-ating the modulator performance for Fermy energies belowEf0  0:03 eV.4. Modulator designKnowing the resulting refractive index of thegraphene/dielectric composite in the on-state, non,we can use the same filling for the input and outputmetallic waveguides to minimize the insertion loss. Ideally,non = 1 can be reached if we assume certain freedom of2Table 1: Example of modulation depth calculation forTon = 0:95, Ef = 0:1042 eV, a = 5 m.Fermy energy change normalized modulation depthEf , eV10Log(Ton=Toff )a; dB m 10.044 0.480.047 0.63>0.064 >0.71f0 = 30 THzON-state (Ef=0.1eV)f0 = 30 THzOFF-state (Ef=0.06eV)S12 = -0.2dBS12 < -36dBFigure 4: On- and off- state fields in a graphene-based mod-ulator.choice of dielectric material between graphene sheets.Fig. 4 shows the numerically obtained electric fieldspropagating between the input and output metallic waveg-uides through the modulator section filled with multilayergraphene. This example demonstrates the performance ofthe novel terahertz modulator - a 0:04 eV change of thegraphene Fermi energy leads to complete and quick switchbetween transmission and attenuation regimes.5. ConclusionsThe interplay between interband and intraband tran-sitions in graphene allows to convert a multilayergraphene/dielectric structure into a transparent and elec-tromagnetically dense artificial medium in a narrow mid-infrared wavelength range. Gate voltage can be usedto electrically control the concentration of carriers in thegraphene sheets and, thus, efficiently change the dispersionof the whole structure. Placed inside a hollow waveguide,multilayer graphene/dielectric composite provides high-speed modulation of radiation and offers a novel conceptof a terahertz modulator.References[1] K. Geim and K.S. Novoselov, The rise of grapheneNaure Mat., 6: 183–91, 2007.[2] X. Du, I. Skachko, A. Barker, E.Y. Andrei, Approach-ing ballistic transport in suspended graphene, NatureNanotechnol., 3: 491–495, 2008.[3] T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn,M. Wolf, Strongly coupled optical phonons in the ul-trafast dynamics of the electronic energy and currentrelaxation in graphite, Phys. Rev. Lett., 95: 187403,2005.[4] B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly,D. Jena, L. Liu, and H. (Grace) Xing, Uniqueprospects for graphene-based terahertz modulators,Appl. Phys. Lett., 99: 113104, 2011.[5] B. Sensale-Rodriguez, R. Yan, and M. Kelly, Broad-band graphene terahertz modulators enabled by intra-band transitions, Nature Comm., 3: 780–787, 2012.[6] S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu,X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, Switching terahertz waves withgate-controlled active graphene metamaterials, NatureMat., 11: 936–941, 2012.[7] Z. Xu, C. Chen, S. Q. Y. Wu, B. Wang, J. Teng, Ch.Zhang, Q. Bao, Graphene-polymer Multilayer Het-erostructure for Terahertz Metamaterials, Proc. SPIE8923: 89230C, 2013.[8] V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte,Magneto-optical conductivity in graphene, Journal ofPhysics: Condensed Matter, 19 (2): 026222, 2007.[9] J. Sanghera and I. Aggarwal, Infrared Fiber Optics,CRC Press, Boca Raton, FL, 1998.[10] J. A. Harrington, A Review of IR Transmitting, Hol-low Waveguides, Fiber Integrated Opt., 19: 211–219,2000.3

Multilayer Graphene for Waveguide Terahertz Modulator

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Multilayer Graphene for Waveguide Terahertz Modulator

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