Investigation of the graphene based planar plasmonic filters Hong-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 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 93.180.53.211 On: Wed, 19 Feb 2014 05:13:45
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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
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
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
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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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Highlight
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.
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