Broadband Frequency-Selective Spoof Surface Plasmon Polaritons on Ultrathin Metallic Structure

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We propose an ultrathin metallic structure to produce frequency-selective spoof surface plasmon polaritons (SPPs) in the microwave and terahertz frequencies. Designed on a thin dielectric substrate, the ultrathin metallic structure is composed of two oppositely oriented single-side corrugated strips, which are coupled to two double-side corrugated strips. The structure is fed by a traditional coplanar waveguide (CPW). To make a smooth conversion between the spatial modes in CPW and SPP modes, two transition sections are also designed. We fabricate and measure the frequency-selective spoof SPP structure in microwave frequencies. The measurement results show that the reflection coefficient is less than -10 dB with the transmission loss around 1.5 dB in the selective frequency band from 7 to 10 GHz, which are in good agreements with numerical simulations. The proposed structure can be used as an SPP filter with good performance of low loss, high transmission and wide bandwidth in the selective frequency band.

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Received
15 October 2014

Accepted
7 January 2015

Published
2 February 2015

Correspondence and

requests for materials

should be addressed to

[T.J.C. (tjcui@seu.edu.](mailto:tjcui@seu.edu.cn)

[cn)](mailto:tjcui@seu.edu.cn)

## Broadband Frequency-Selective Spoof Surface Plasmon Polaritons on Ultrathin Metallic Structure

Jia Yuan Yin 1, Jian Ren 2, Hao Chi Zhang 1, Bai Cao Pan 1 & Tie Jun Cui 1,3

1State Key Laboratory of Millimeter Waves, School of Information Science and Engineering, Southeast University, Nanjing 210096,
China, 2 Science and Technology on Antenna and Microwave Laboratory, Xidian University, Xi’an 710071, China, 3 Cooperative
Innovation Center of Terahertz Science, University of Electronic Science and Technology, Chengdu 611731, China.

We propose an ultrathin metallic structure to produce frequency-selective spoof surface plasmon polaritons
(SPPs) in the microwave and terahertz frequencies. Designed on a thin dielectric substrate, the ultrathin
metallic structure is composed of two oppositely oriented single-side corrugated strips, which are coupled to
two double-side corrugated strips. The structure is fed by a traditional coplanar waveguide (CPW). To make
a smooth conversion between the spatial modes in CPW and SPP modes, two transition sections are also
designed. We fabricate and measure the frequency-selective spoof SPP structure in microwave frequencies.
The measurement results show that the reflection coefficient is less than -10 dB with the transmission loss
around 1.5 dB in the selective frequency band from 7 to 10 GHz, which are in good agreements with
numerical simulations. The proposed structure can be used as an SPP filter with good performance of low
loss, high transmission, and wide bandwidth in the selective frequency band.

ecause of the negative permittivity behavior of metals at visible frequencies, surface plasmon polaritons
(SPPs) are propagating on the interface of metal and dielectric with exponential decay in the direction
vertical to the interface 1,2 . However, the metals will behave like perfectly electric conductors (PECs) instead
# B
of plasmas with negative permittivity when the frequency is reduced to the terahertz and microwave bands, which
do not support the existence of SPPs. In order to realize SPPs in such lower frequencies, plasmonic metamaterials
have been proposed to produce the so-called spoof SPPs 3–14 . The plasmonic metamaterials are usually formed by
one- or two-dimensional periodical textures on metal surfaces. Among them, there had been some valuable works
on subwavelength corrugated structures which can be used to transmit spoof SPPs 9,10–13 . Ref. 9 showed how the
dispersion relation of SPPs propagating along a perfectly conducting wire can be tailored by corrugating its
surface with a periodic array of radial grooves. With this method, highly localized SPPs can be sustained in the
terahertz region of the electromagnetic spectrum. The realization of planar plasmonic terahertz guided-wave
devices using periodically performed metal films was described 11 . The experimental results showed that the
propagating terahertz radiation was well confined in both the in-plane and out-of-plane axes. The other way
of guiding terahertz waves along corrugated V-grooves was proposed in Ref. 12. This kind of structure presents
longer propagation lengths and lower bending losses, making it the excellent candidate for guiding terahertz
waves on planar surfaces. The corrugated metallic wedges can also route the terahertz waves, which featured the
subwavelength confinement in the transverse plane 13 . Based on the proposed wedge waveguides, the frequency
selective focusing and slow terahertz radiation have also been demonstrated 13 . More recently, an ultrathin
corrugated metallic strip with subwavelength width has been proposed using a competitive structure, which
can support and propagate conformal SPPs on arbitrarily curved surfaces 14 . As the plasmonic metamaterials are
advancing at a rapid pace, they are considered as a solid avenue for real applications.

One of the advantages of plasmonic metamaterials is the simple structure, which offers convenience for
fabrications. Many efforts have been made to generate highly confined spoof SPP waves 3–14 and design functional
devices 3–14 in the microwave and terahertz frequencies. However, a problem has emerged as the plasmonic
metamaterials are developed: the SPP functional components and circuits need to be connected to the conventional microwave and terahertz circuits, which are commonly composed of two-conductor transmission lines like
microstrips and coplanar waveguides (CPWs). That is to say, it is very important to convert the spatial waves
supported by the traditional transmission lines to SPP modes supported by the plasmonic structures with high
efficiency. In the past, the conversion between single- and two-conductor transmission lines has been studied 15–18 .

Figure 1 | Schematic picture of the ultrathin metallic frequency-selective
structure, in which the yellow part is metal (modeled as copper) and the
dark gray part is thin dielectric substrate. The length of each part is
l1510 mm, l2560 mm, and l35123 mm.

Recently, a broadband and efficient conversion from spatially guided
waves to SPPs in the microwave frequency has been proposed 19, in
which gradient corrugation grooves and flaring ground are presented
to match both the momentum and impedance. In Ref. 20, the broadband transition between microstrip line and conformal surface plasmon waveguide was also presented.

Based on the successful developments of mode conversions,
plasmonic functional devices catch more and more attentions. As
a key component, the filter plays a very important role in the
wireless communication, radar, and other systems. To design an
SPP filter, a bulky structure was presented using periodic subwavelength metallic Domino array 21 . Recently a method to control the
rejections of SPPs has been proposed using metamaterial particles 22 . Meanwhile, a double-grating plasmonic waveguide and
band-pass filter have been proposed in Ref. 23, employing a
stepped slot line to couple electromagnetic energies from the
microstrip. However, the above SPP filters are either bulky or
performance limited.

In this article, we propose an ultrathin metallic structure
printed on a thin dielectric substrate to produce the frequencyselective spoof SPPs in the microwave and terahertz frequencies,
which is composed of two oppositely oriented single-side corrugated strips coupled to two double-side corrugated strips. In order
to feed the structure and extract the transmitted SPPs by traditional CPWs, two transition sections are also designed for
smooth conversion between spatial modes in CPWs and SPPs.
This compact structure can be used as a good SPP filter. We
fabricate and measure the SPP filter in the microwave frequency,
and the measurement results show that the reflection coefficient is
less than -10 dB and the transmission loss is around 1.5 dB in the
selective frequency range from 7 to 10 GHz. Hence the proposed
SPP filter is compact but has good performance of low loss, high
transmission, and wide band, which is important to produce the
plasmonic integrated circuits in microwave and terahertz frequencies in the near future.

Results
As shown in Fig. 1, the proposed frequency-selective spoof SPP
structure is designed using ultrathin metallic strips, which are
printed on a thin and flexible dielectric film. In the current design
in the microwave frequency, the thickness of metal (copper) film is
0.018 mm, while the thickness of dielectric substrate is d50.05 mm,
which correspond to 6/10000 and 17/10000 wavelengths at 10 GHz,
respectively. For designs and theoretical characterizations, the parameters of this particular structure are accurately retrieved as:
l1510 mm, l2560 mm, and l35123 mm. As demonstrated in
Fig. 1, the proposed structure is connected to two CPW sections with
50-V impedance to feed energies and receive the transmitted SPP
signals.

The whole structure of the SPP frequency-selective filter is composed of three parts, as illustrated in Fig. 2. The first part is CPW (see
Fig. 2(a)) for the purposes to feed or receive electromagnetic fields.
To achieve the 50-V impedance, the CPW parameters are chosen as
w515 mm, g50.55 mm, and H510 mm. The second part is a transition section between CPW and the SPP waveguide, a double-side
corrugated metallic strip. The details of the transition design have
been demonstrated in Ref. 19, according to which the transition
structure consists of a flaring ground and gradient grooves, as shown
in Fig. 2(b). The flaring ground is designed to match the impedance
between CPW and SPP waveguide, while the gradient grooves are
used to match the momentum. The designed dimensions of the
transition part are given as: h150.5 mm, h251 mm, h351.5 mm,
h452 mm, h552.5 mm, h653 mm, h753.5 mm, and h854 mm.
The curvature of the flaring ground is k50.2. The third part is the
main structure constructed by a double-side corrugated strip and two
single-side corrugated strips, as illustrated in Fig. 2(c), in which the
period, width, and depth of metallic grooves are chosen as p55 mm,
a53 mm, and h54 mm. The two coupled single-side corrugated
strips with opposite orientation directions are aimed to realize the
frequency-selective characteristics.

Figure 3 gives the dispersion curves of the single-side and doubleside corrugated metallic strips. We observe that the cut-off frequency
of the double-side is a little bit lower than that of single-side, at
around 11 GHz. Based on the concept of microwave network, the
coupling part can be described by a four-port network 24, as illustrated
in the central diagram in Fig. 4. Because of the symmetry of the
structure, the analysis of coupling is only taken half into account.
For the four ports 1, 2, 3, and 4 marked in Fig. 4, we get the following
relationships

0 cosðkzÞ {i sinðkzÞ 0

cosðkzÞ 0 0 {i sinðkzÞ
{i sinðkzÞ 0 0 cosðkzÞ
0 {i sinðkzÞ cosðkzÞ 0

6664

b1
b2
b3
b4

a1
a2
a3
a4

6664

77756664

7775~e{jbz

7775 ð1Þ

Figure 2 | The configuration of the frequency-selective SPP structure, which is composed of three parts. (a) The CPW section, in which w515 mm,
g50.55 mm, and H510 mm. (b) The transition with flaring ground and gradient grooves, in which h150.5 mm, h251 mm, h351.5 mm, h452 mm,
h552.5 mm, h653 mm, h753.5 mm, and h854 mm. The curvature of the flaring ground is k50.2. (c) The corrugated metallic strips, in which
p55 mm a53 mm h54 mm and g 51 mm

deduced as

cos 2 ðkzÞ { 2i sin ð kz Þe jbz
e 2jbz z sin 2 ðkzÞ e 2jbz z sin 2 ðkzÞ

ð3Þ
7775

6664

{ 2i sin ð kz Þe jbz

e 2jbz z sin 2 ðkzÞ

cos 2 ðkzÞ
e 2jbz z sin 2 ðkzÞ

Figure 3 | The dispersion curves of single-side and double-side
corrugated metallic strips.

- -
b2 ~E a2

From the S-parameter matrix, we notice that the transmission coefficient (S21) can be zero under specific circumstances, implying that
the SPP waves cannot propagate through the coupling part.

To study the control of frequency-selective bands by the two single-side corrugated metallic strips, two parameters are chosen to
investigate the influence of the coupling part using numerical simulations. One parameter is the gap g1 between two corrugated metallic
strips, while the other parameter is the length of the coupling strip.
Fig. 5(a) illustrates the total transmission coefficients (S21) of the
whole structure with different gaps, in which the dielectric constant
and tangent loss of the substrate are set as 2.65 and 0.01, respectively.
It is obvious that SPPs are only allowed propagations under certain
frequency bands. As the gap is smaller, the coupling strength
becomes larger with a slight redshift of bandwidth. The influence
of the coupling length is demonstrated in Fig. 5(b), in which different
numbers (n) of unit cells are used in the coupling part. We note that
the coupling length has significant impact on the selective frequency
bandwidth. For longer coupling length (n54), the selective frequency has a larger bandwidth from 7 to 10 GHz; for shorter coupling length (n52), the selective frequency has a smaller bandwidth
from 9.5 to 10.5 GHz. We observe that the black line in Fig. 5 drops

b2
b4

-
a2 ð2Þ

where k is the coupling coefficient, and z is the length of coupling
part. Then the S scattering parameter matrix of the coupling part is

Figure 4 | Schematic of the coupling part of the proposed frequency-selective structure.

Figure 5 | The simulated transmission coefficients (S21) with different strip gaps (g1) and numbers of coupling unit cells (n). (a) The black, red, and blue
lines correspond to g151 mm, 1.5 mm, and 2 mm, respectively, in which n54 is fixed. (b) The black, red, and blue lines correspond to n54, 3, and 2,
respectively in which g151 mm is fixed

Figure 6 | The photograph of the fabricated frequency-selective SPP
structure, which is printed on a flexible dielectric film.

quickly at about 10.8 GHz, which implies a transmission zero isolating the stop band from the operating band. Then the black line rises
again at about 11 GHz. This phenomenon can be explained by the
combined effect of resonance and cutoff frequency. Owing to the
transmission zero, the periodic frequency response curve is supposed
to appear with crest and trough alternately. When the cutoff frequency is between the crest and trough, the peak emerges. In fact,
the dispersion relation of the coupling part is relevant to the transmission spectrum. Since the dispersion curve characterizes the relation between the propagation constant and frequency, and the
coupling strength is also related to the frequency, we can tune the
dispersion relation of the coupling part through the coupling
strength, and furthermore tune the transmission spectrum.

In experiments in the microwave frequency, we fabricate a sample
of the frequency selective structure, in which the gap between two
adjacent corrugated strips is set as g151 mm, the number of coupling
units is chosen as n54, and the dielectric constant and loss tangent of
the substrate are the same as those in simulations, as illustrated in
Fig. 6. The measured and simulated results of the S parameters
(reflection coefficients S11 and transmission coefficients S21) are
shown in Fig. 7, which have good agreements to each other. We
notice that the reflection coefficients (S11) are less than -10 dB from
7 to 10 GHz, which verifies the good impedance and momentum
matching from CPW to SPP waveguide. As illustrated in Fig. 7(b),
the transmission coefficients indicate good frequency-selective property of the proposed structure. The transmission loss is only around
1.5 dB in the selective frequency band.
In order to demonstrate the frequency-selective characteristics
clearly, we also give the near-field distributions above the structure
at different frequencies. Figure 8 presents the simulated near electric
fields on an observation plane, which is 4 mm above the proposed
structure. At 6 GHz and 11 GHz, the electric-field distributions are
shown in Figs. 8(a) and 8(d), respectively. It is obviously that the
energy cannot propagate through the coupling structure since such
frequencies are beyond the selected frequency band. On the other
hand, at 7 GHz and 9 GHz, which are within the selected frequency
band, excellent mode conversions and energy propagations are

Figure 8 | The simulated near electric-field distributions. (a) The
frequency is 6 GHz, which is beyond the selected frequency band. (b) The
frequency is 7 GHz, which is within the selected frequency band. (c) The
frequency is 9 GHz, which is within the selected frequency band.
(d) The frequency is 11 GHz, which is beyond the selected frequency band.

clearly observed, as displayed in Figs. 8(b) and 8(c). Figure 9 provides the relevant measurement results of the near electric fields,
which are in very good agreements with the simulation results. As
discussed in Figs. 8 and 9, small reflections and high transmissions
of SPPs are realized in the selected frequency band using the proposed structure, which can be used as an SPP band-pass filter. The
good measurement results suggest that the proposed SPP filter
should be a promising device for the plasmonic integrated circuits
in the microwave frequencies.

Discussion
In this article, we have proposed a compact and ultrathin structure to
produce frequency selective spoof SPPs in the microwave frequencies. In particular, we presented four coupled corrugated metallic
strips to reach the frequency-selective properties. Besides the coupled
structure, we also proposed two transition sections to covert the SPP
modes to spatial transverse electromagnetic modes, so as to connect

Figure 7 | The simulation and measurement results of S parameters, in which the red lines are simulations and the black lines are measurements.
(a) The reflection coefficients (S11) (b) The transmission coefficients (S21)

Figure 9 | The measured near electric-field distributions. (a) The
frequency is 6 GHz, which is beyond the selected frequency band. (b) The
frequency is 7 GHz, which is within the selected frequency band. (c) The
frequency is 9 GHz, which is within the selected frequency band.
(d) The frequency is 11 GHz, which is beyond the selected frequency band.

with CPWs smoothly in feeding and receiving electromagnetic fields.
We made numerical simulations and experiments to validate our
design. Both the simulated and measured S parameters and nearelectric-field results demonstrate that the proposed structure has
high transmissions (with insertion loss of 1.5 dB) and low reflections
(below -10 dB) in the selected frequency band from 7 to 10 GHz.
Such performance makes the proposed structure be a good SPP
band-pass filter. The proposed filter may be further used in multilayer structures in the future for higher integrations. We remark that
the method can be extended to the terahertz frequencies to realize
plasmonic functional devices and integrated circuits.

Methods
Numerical simulations are performed by the commercial software, CST Microwave
Studio. The experimental structure is fabricated using a 0.05-mm thin dielectric film
with dielectric constant 2.65 and tangent loss 0.01, respectively. The thickness of
metal (copper) film is 0.018 mm. We use Agilent Vector Network Analyzer to
measure the S parameters (i.e., the reflection coefficients S11 and transmission coefficients S21) of the fabricated sample. The near electric-filed distributions are measured by a home-made near-field scanning system, in which the probe is set as 2 mm
above the fabricated sample.

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Acknowledgments
This work was supported in part by the National Science Foundation of China (60990320,
60990324, 61171024, 61171026, and 61138001), in part by the National High Tech (863)
Projects (2012AA030402 and 2011AA010202), and in part by the 111 Project (111-2-05).

Author contributions

J.Y.Y. and J.R. conceived the idea. J.Y.Y. did the simulations and optimization. H.C.Z. did
the theoretical analysis. J.Y.Y., J.R. and B.C.P performed the measurements. J.Y.Y. and
T.J.C. wrote the manuscript based on the input from all authors. All authors contributed to
the discussion.

Additional information
Competing financial interests: The authors declare no competing financial interests.

How to cite this article: Yin, J.Y., Ren, J., Zhang, H.C., Pan, B.C. & Cui, T.J. Broadband
Frequency-Selective Spoof Surface Plasmon Polaritons on Ultrathin Metallic Structure. Sci.
Rep. 5, 8165; DOI:10.1038/srep08165 (2015).

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