Investigation of the graphene based planar plasmonic filtersHong-Ju Li, Ling-Ling Wang, Jian-Qiang Liu, Zhen-Rong Huang, Bin Sun, and Xiang Zhai Citation: Applied Physics Letters 103, 211104 (2013); doi: 10.1063/1.4831741 View online: http://dx.doi.org/10.1063/1.4831741 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/103/21?ver=pdfcov Published by the AIP Publishing

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Investigation of the graphene based planar plasmonic filters

Hong-Ju Li,1 Ling-Ling Wang,1,a) Jian-Qiang Liu,2 Zhen-Rong Huang,1 Bin Sun,1

and Xiang Zhai11School of Physics and Microelectronic and Key Laboratory for Micro-Nano Physics and Technologyof Hunan Province, Hunan University, Changsha 410082, China2School of Science, Jiujiang University, Jiujiang 332005, China

(Received 20 September 2013; accepted 31 October 2013; published online 18 November 2013)

We investigate numerically the edge modes supported by graphene ribbons and the planar band-stop

filter consisting of a graphene ribbon lateral coupled a graphene ring resonator by using the finite-

difference time-domain method. Simulation results reveal that the edge modes can enhance the

electromagnetic coupling between objects indeed and this structure realizes perfect, tunable filtering

effect. Successively, the channel-drop filter is constructed. Especially, the proposed structures can

be designed and the size of the ring is changed by creating non-uniform conductivity patterns on

monolayer graphene. Our studies will benefit the fabrication of the planar, ultra-compact devices in

the mid-infrared region. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4831741]

Surface plasmon polaritons (SPPs)1 are localized surface

electromagnetic (EM) waves, which propagate along the

interface between metals and dielectric materials.2 Owing to

their ability of overcoming the traditional diffraction limit, a

great diversity of plasmonic devices based on noble metals

have been discussed in the past decades. For example, optical

amplifiers, Y-shaped combiners,3 slow-light waveguides,4

and the unidirectional couplers,5,6 which are based on metal-

insulator-metal plasmonic waveguides,7,8 have been reported.

Despite of these extensive applications in designing optical

structures for engineering and transforming light, the per-

formance of noble metals is hampered by the difficulty in tun-

ing their permittivity functions and the existence of optical

losses. Certainly, these drawbacks degrade the functionality

of some metallic plasmonic devices, especially in the infrared

region. More recently, graphene,9–11 one of the promising

candidates for new-generation plasmonic material, with only

one atomic thin, has attracted tremendous interests from

researchers due to its extraordinary electronic and optical

properties including extreme confinement, dynamic tunabil-

ity,12 low losses,13 and crystallinity.14 Because of these ad-

vantageous features compared to conventional noble metals,

a growing number of research foci are pointed to constructing

and studying plasmonic devices based on graphene.15 To

date, the symmetric and anti-symmetric modes14,16,17 sup-

ported on double-layer graphene have been investigated theo-

retically and numerically. The optical splitters, spatial

switches, and Mach-Zehender interferometers18 based on

multilayer graphene19 have also been demonstrated in detail.

Remarkably, the waveguide patterns can be formed on a sin-

gle graphene layer20 by using different values of gate voltage

at different locations and the way of gate voltage21,22 to

change the conductivity of graphene has been achieved in

experiment.23,24 Thus, it is feasible to create certain desired

devices in monolayer graphene. On the other hand, it has also

been reported that graphene nano-ribbons25 support one sig-

nificant edge mode26 that the field is concentrated on the rims

of the ribbons. It may be capable of enhancing the EM cou-

pling between objects.

Taking the two noticeable facts mentioned above which

yield a viable way to construct plasmonic devices on a single

flake of graphene into consideration, we propose an original

planar band-stop filter structure consisting of one narrow gra-

phene ribbon lateral coupled with a graphene ring resona-

tor,27 which can be devised on monolayer graphene by

creating non-uniform conductivity patterns. By using the

finite-difference time-domain (FDTD) method, we find that

this structure realizes perfect filtering effect, due to the exis-

tence of the edge modes which can enhance the EM coupling

between objects indeed. The size of the ring is changed by

manipulating the locations of the non-uniform conductivity

patterns on monolayer graphene for modifying the transmis-

sion spectrum. This way exhibits more advantageous tunabil-

ity than that of constructing a new structure used usually in

metallic devices. As an application, the channel drop filter,

one typical wavelength division multiplexing optical com-

munication system, is further fabricated. The proposed devi-

ces exhibit outstanding characteristics and will benefit the

fabrication of ultra-compact, versatile, planar integrated cir-

cuits in the mid-infrared region for optical communication

and processing.

To start, the characteristics of the SPPs propagating along

a graphene nano-ribbon embedded in air are investigated

numerically by using the FDTD method. As shown in the

inset (a) of Fig. 1, the graphene nano-ribbon with a narrow

width W is modeled as an ultra-thin film with a thickness of

D. The surface conductivity (rg) of the graphene is governed

by Kubo formula,28,29 which depends on the momentum

relaxation time s, temperature T, chemical potential lc, and

incident wavelength k (frequency x). At room temperature,

the Kubo equation is reduced to rg ¼ ie2lc

p�h2 xþis�1ð Þ,18 where the

intraband transition dominates. The equivalent permittivity of

graphene follows the equation: eeq ¼ 1þ irgg0= k0Dð Þ,20

where g0(�377 X) is the intrinsic impedance of air and

k0 ¼ 2p=k. The D is assumed to be 1 nm in our calculations,

although other extremely small values lead to similar results

because the eeq is thickness dependent. In terms of the single

a)Author to whom correspondence should be addressed. Electronic mail:

llwang@hnu.edu.cn

0003-6951/2013/103(21)/211104/4/$30.00 VC 2013 AIP Publishing LLC103, 211104-1

APPLIED PHYSICS LETTERS 103, 211104 (2013)

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graphene nano-ribbon, it is well known that it supports two

types of SPP modes; one is the waveguide modes that the field

is concentrated along the whole area of the ribbon (in the ydirection), and the other is the edge modes that the field is

concentrated on the rims of the ribbon.14,26 The waveguide

modes are mainly used for information transmission and the

edge modes may be more conducive to enhance the EM cou-

pling between objects. However, when the width W is

ultra-thin only dozens of nanometers, the graphene ribbon

only supports fundamental edge modes in the mid-infrared

region. In the inset (a) of the Fig. 1, the microscopic details of

the edges of the graphene ribbon are ignored. The value of Wis assumed to be 10 nm and other parameters of s and lc,

which directly affect the surface conductivity of graphene, are

chosen to be 0.5 ps, 0.3 eV, respectively. The SPP wave is

excited by a dipole point source placed 2 nm over the ribbon

in z direction and it will have the form ~E r;x;tð Þ ¼ ~E y;zð Þexp ikx xð Þx� ixtð Þ, where kx xð Þ is the wave vector in the

propagation direction x. The corresponding effective refrac-

tive indices are illustrated in Fig. 1. At the same time, it is

revealed clearly from the contour profiles of jEj2 in y-zcross-section that the most field energy is concentrated on the

rims of the graphene ribbon, demonstrated in the inset (b)

where the incident wavelength k is 10 lm. Thus, the

ultra-narrow graphene ribbon with W¼ 10 nm only supports

the fundamental edge modes indeed, which is in accordance

with the above theoretical analyses.

Now that the ultra-narrow graphene ribbons only sup-

port edge modes and it may benefit the EM coupling between

objects, we shall make full use of this feature to fabricate a

filter structure: one graphene nano-ribbon lateral coupled a

graphene ring resonator. Certainly, it also can be designed

on a single flake of graphene by creating non-uniform con-

ductivity patterns. As is displayed in Fig. 2, only the red

zones are manipulated to support SPPs and others behaving

as dielectric do not support the SPPs. The width of the gra-

phene waveguide is W, which is same as the width of the gra-

phene ring resonator. The outer radius of the graphene ring

resonator is R and the coupling length between the wave-

guide and the ring resonator is h. In addition, some ways to

realize inhomogeneous conductivity patterns across a single

graphene layer have also been achieved, which include a

split gate device to apply different bias voltages to different

locations, an uneven ground plane holding the monolayer

graphene, and non-uniform permittivity distribution under-

neath the graphene sheet.

By using the 3D FDTD method with perfectly matched

layer absorbing boundary conditions, the properties of the

proposed structure are investigated. For simplicity, in the

implementation, the graphene nano-ribbon lateral coupled a

graphene ring resonator embedded in air is considered. We

use non-uniform mesh, and the minimum mesh size inside

the graphene layer equals 0.1 nm and gradually increases

outside the graphene sheet, for saving storage space and

computing time. Similarly, one dipole point source is used to

excite the SPP wave. Two monitors are, respectively, put at

the points of P1 and P2 in order to detect the incident power

Pin and transmitted power Pout. The transmission is defined

to be T¼Pout/Pin. The material parameters are unchanged

and the main structure parameters W, h, R, are assumed to be

10 nm, 3 nm, and 25 nm, respectively. Simulation results cor-

responding to different incident wavelengths are tidied

clearly in Fig. 3.

Considering the structure, it is well known that if the

incident wavelengths satisfy the resonance condition of the

graphene ring resonator, the SPPs will be effectively con-

fined in the resonator because of the edge modes’ high-

efficiency coupling feature, and there will be a low transmis-

sion at P2 output. Therefore, one can find obviously that two

pronounced transmission dips corresponding to the wave-

lengths k¼ 6.88 lm and k¼ 5.40 lm appear in the transmis-

sion spectrum, exhibiting evident filtering property shown in

Fig. 3(a). Moreover, the Figs. 3(b) and 3(c) display the

FIG. 1. Effective refractive indices of the SPP modes supported by a free-

standing graphene ribbon as a function of incident wavelengths k. Inset (a)

demonstrates the graphene nano-ribbon waveguide with width W¼ 10 nm,

where the SPPs propagate along x direction; (b) and (c) show the field distri-

butions of the SPPs relating to graphene ribbons’ y-z cross-section at

k¼ 10 lm.

FIG. 2. Schematic diagram of the band-stop filter structure consisting of a

graphene waveguide lateral coupled with a graphene ring resonator, which is

constructed on a single flake of graphene where only the red areas support

SPPs and the others do not.

FIG. 3. (a) The transmission spectrum of the proposed structure. The con-

tour profiles of field Hz of the filter structure at different incident wave-

lengths of (b) k¼ 6.88 lm, (c) k¼ 5.40 lm.

211104-2 Li et al. Appl. Phys. Lett. 103, 211104 (2013)

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contour profiles of Hz for incident wavelengths k¼ 6.88 lm,

5.40 lm, respectively, which relate to the transmission dips

in Fig. 3(a). Clearly, the second-order resonance is formed in

the graphene ring resonator at k¼ 6.88 lm and third-order

resonance is formed at k¼ 5.40 lm.

Successively, we would like to investigate the influence

of the outer radius R of the graphene ring on the wave-

lengths of the transmission dips. The size of the ring is

changed on a single graphene layer by the same principle

shown in Fig. 2. The locations of the red zones are manipu-

lated for tuning the outer radius. This way is unlike the con-

ventional metallic filters where the transmission spectrum is

modified by constructing a new structure directly.

Simulation results are presented in Fig. 4. The transmission

spectrum plotted in blue, green, and red lines correspond to

the graphene rings with outer radii of 20 nm, 25 nm, and

30 nm, respectively. To compare the curves shown in Fig. 4,

the transmission dips with same order tend to red shift as

the outer radius increases and the whole transmission spec-

tra exhibit an obvious tunability. The relationship between

the wavelengths of the transmission dips and the outer radii

of the graphene rings relates approximately to the standing

wave equation 2pnef f Ref f ¼ mk0(m¼ 1, 2, 3,…), where neff

is the effective refraction index of the graphene ring,

Reff�R-W/2 is the effective radius of the ring resonator,

and the k0 is the resonance wavelength. According to this

standing wave equation, with the increase of the graphene

ring’s outer radius the resonance wavelengths tend to red

shift, which is in accordance with the FDTD results shown

in Fig. 4. Hence, utilizing the edge modes the perfect filter-

ing effect is realized by the proposed structure which can be

constructed on a single flake of graphene. The transmission

spectrum can be tuned dynamically by changing the outer

radius of the graphene ring. Especially, the size of the

graphene ring can be tuned by non-uniform conductivity

patterns on a single graphene layer. It exhibits more advan-

tageous tunability than the conventional ways.

As an application, a channel-drop filter is further fabri-

cated, shown in the inset of Fig. 5(a). It is a typical wave-

length demultiplexing structure, consisting of two graphene

ribbons with a graphene ring resonator assumed to be em-

bedded in air. In order to investigate its characteristics, only

the outer radius of the ring is changed to be 18 nm and other

parameters are identical to above. The edge modes are

excited by one dipole point source at P1 port. On the one

hand, the SPP waves couple into the ring resonator and then

travel clockwise and anticlockwise simultaneously in the

graphene ring, and finally pass different outputs under the

condition of different incident wavelengths. As shown in

Fig. 5(a) where the incident wavelength is 5.23 lm, the SPP

waves can pass through outputs P2, P3, and P4 simultane-

ously. When the incident wavelength increases to be

5.51 lm, the structure behaves as a perfect optical splitter

that the SPPs only transmit to P2 and P3 ports, as seen in

Fig. 5(b). In Fig. 5(c), the incident wavelength k¼ 8.10 lm

is dropped into P4 output completely, achieving the intrinsic

function of the channel-drop filter. On the other hand, if the

incident wavelengths do not satisfy the resonance conditions

of the graphene ring mentioned above, the SPPs will pass

through the P2 port directly shown in Fig. 5(d). Therefore,

such a structure is a multi-functional plasmonic device and

will plays substantial roles in highly integrated circuits for

wavelength demultiplexing.

To sum up, the planar filter consisting of a graphene rib-

bon lateral coupled a graphene ring resonator is proposed

and investigated numerically by using the FDTD method.

Simulation results reveal that edge modes can enhance the

EM coupling between objects indeed and this structure

exhibits perfect band-stop filtering effect. The wavelengths

of the transmission dips in the transmission spectrum tend to

red shift as the graphene ring’s outer radius increases, pre-

senting obvious tunability. This phenomenon is explained by

FIG. 4. The transmission spectra of the filter structure for different outer

radii of the graphene rings. The blue, green, and red lines correspond to the

outer radii of 20 nm, 25 nm, and 30 nm, respectively.

FIG. 5. The contour profiles of the

field jHzj2 of the channel drop filter

structure at different incident wave-

lengths of (a) k¼ 5.23 lm, (b)

k¼ 5.51 lm, (c) k¼ 8.10 lm, and (d)

k¼ 6.86 lm.

211104-3 Li et al. Appl. Phys. Lett. 103, 211104 (2013)

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a simple standing wave theory. As an application, the

channel-drop filter, one typical wavelength demultiplexing

structure, is demonstrated further. Especially, all proposed

structures can be designed on a single flake of graphene by

creating non-uniform conductivity patterns and the size of

the ring also can be changed by the same principle. This way

exhibits more advantageous tunability than that used in con-

ventional metallic devices. Undoubtedly, our studies of these

real planar filters will benefit the fabrication of versatile,

ultra-compact devices in the mid-infrared region for optical

communication and processing.

This work was supported by the National Natural

Science Foundation of China (Grant Nos. 11074069,

11264021, 61176116), the Specialized Research Fund for the

Doctoral Program of Higher Education of China (Grant No.

20120161130003), the Hunan Provincial Science and

Technology Project of China (Grant Nos. 2012FJ4121,

2013FJ4043), and Aid program for Science and Technology

Innovative Research Team in Higher Educational

Institutions of Hunan Province.

1W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).2X. He, Q. Wang, and S. F. Yu, IEEE J. Quantum Electron. 48, 1554

(2012).3H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H.

Yao, Opt. Express 13, 10795 (2005).4G. Wang, H. Lu, and X. Liu, Appl. Phys. Lett. 101, 013111 (2012).5Y. Gong, X. Liu, L. Wang, and Y. Zhang, Opt. Commun. 284, 795 (2011).6T. Xu, Y. Zhao, D. Gan, C. Wang, C. Du, and X. Luo, Appl. Phys. Lett.

92, 101501 (2008).7J. Q. Liu, L. L. Wang, M. D. He, W. Q. Huang, D. Wang, B. S. Zou, and

S. Wen, Opt. Express 16, 4888 (2008).

8L. Wang, L. L. Wang, Y. Zeng, D. Xiang, B. Meng, X. Zhai, and A. L.

Pan, Opt. Commun. 284, 153 (2011).9K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V.

Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).10F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, Nat. Photonics 4, 611

(2010).11A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 (2007).12Q. Bao and K. Loh, ACS Nano 6, 3677 (2012).13W. B. Lu, W. Zhu, H. J. Xu, Z. H. Ni, Z. G. Dong, and T. J. Cui, Opt.

Express 21, 10475 (2013).14J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and

F. J. Garc�ıa de Abajo, ACS Nano 6, 431 (2011).15X. He, J. Tao, and B. Meng, Nanotechnology 24, 345203 (2013).16G. W. Hanson, J. Appl. Phys. 104, 084314 (2008).17C. H. Gan, H. S. Chu, and E. P. Li, Phys. Rev. B 85, 125431 (2012).18B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111

(2012).19B. Wang, X. Zhang, F. J. Garc�ıa-Vidal, X. Yuan, and J. Teng, Phys. Rev.

Lett. 109, 073901 (2012).20A. Vakil and N. Engheta, Science 332, 1291 (2011).21V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys.: Condens.

Matter 19, 026222 (2007).22X. He and S. Kim, J. Opt. Soc. Am. B 30, 2461 (2013).23J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J.

Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z.

Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L.

Koppens, Nature 487, 77 (2012).24Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner,

L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H.

Castro Neto, C. N. Lau, K. F. Keilmann, and D. N. Basov, Nature 487, 82

(2012).25A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys.

Rev. B 85, 081405 (2012).26A. Y. Nikitin, F. Guinea, F. J. Garc�ıa-Vidal, and L. Mart�ın-Moreno, Phys.

Rev. B 84, 161407 (2011).27N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, and F. G. de Abajo,

Light: Sci. Appl. 2, e78 (2013).28P. Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).29G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).

211104-4 Li et al. Appl. Phys. Lett. 103, 211104 (2013)

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