Propagation of Low-Frequency Spoof

Surface Plasmon Polaritons in a Bilateral

DOI: 10.1109/JPHOT.2015.2392382
1943-0655 2015 IEEE

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

Propagation of Low-Frequency Spoof

Department of Electrical Engineering, Chung Hua University, Hsinchu 30012, Taiwan

DOI: 10.1109/JPHOT.2015.2392382
1943-0655 2015 IEEE. Translations and content mining are permitted for academic research only.
Personal use is also permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received November 5, 2014; revised December 26, 2014; accepted January 9, 2015.
Date of publication January 14, 2015; date of current version February 10, 2015. This work was supported by the Ministry of Science and Technology of China under Grant MOST 103-2221-E-216-001.
Corresponding author: J. J. Wu (e-mail: jjwu@chu.edu.tw).

Abstract: In this work, spoof surface plasmon polaritons in a novel subwavelength periodic bilateral cross-metal diaphragm channel waveguide are theoretically and experimentally investigated. It is found that the propagation frequency range can be broadened due
to the absence of the bandgap between the fundamental band and the second guiding
band by tuning the geometric parameters. In addition, the dispersion curve of the second
band can pass through the light line and then enter into the radiation region, leading to a
frequency-based beam steering radiation. We also find that, below the light line, there
exists an anomalous linear dispersion such that the guiding mode propagation length can
be extended up to around 200
. Good agreement has been achieved between experimental and numerical results.
Index Terms: Bandgap, spoof surface plasmon polaritons (SSPPs), channel waveguides.

1. Introduction
Surface plasmon polaritons (SPPs), which are electromagnetic (EM) waves propagating and
strongly confined at the metal-dielectric interface, can enhance and guide light in subwavelength
scale [1], [2]. This feature opens up previously inaccessible length-scale for integrated optics [3].
Today, there have been several optical circuits proposed based on subwavelength EM confinement [4], [5]. To generate a highly confined EM field at low frequencies such as microwave
or terahertz (THz), Pendry et al. proposed a new concept of metamaterial to mimic the SPPs
[6], [7]. To engineer the low-frequency surface plasmon, a new structure geometry-controlled
SPPs was proposed by cutting periodic subwavelength structure in metal surface and its physical mechanism is called spoof SPPs (SSPPs) [8]. With the concept of SSPPs, a subwavelength
periodic corrugated metal wire at THz has been used to study field distributions and dispersion
properties [9]. The study of transmission loss and transmission length of the above metal wire is
also available [10]. In addition, some new kinds of waveguides based on the use of Domino or

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

Fig. 1. Geometric parameters for the designed structures. (a) The UMD SSPPs waveguide. h
23 mm, w 10 mm, d 9 mm, w1 5 mm, h1 5 mm, w2 w1 =2, and a 6:75 mm. The metal
slices are arranged unilaterally on one side. (b) The BMD SSPPs waveguide. The metal slices are
arranged with equal spacing alternately and bilaterally on the two sides of the channel. (c) The inner
structure of the UMD waveguide in detail. (d) The inner structure of the BMD waveguide in detail.

wedge structure are proposed for the THz integrated circuit [11][13]. Subwavelength periodic
structures supported SSPPs in the THz regime have been experimentally verified thus far [14],
[15]. All the aforementioned waveguides, however, have a large bend loss. Later, a waveguide
with V shaped groove based on SSPPs with low bend loss is proposed [16]. A waveguide
based on periodically unilateral diaphragm is also available [17]. Transmission properties in a
U-shaped subwavelength corrugated waveguide with SSPPs have been reported [18]. Furthermore, studies of SSPPs waveguide at microwave are obtainable [19][21]. Additionally, to overcome the problem of crosstalk in high speed circuit, the SSPPs-based microstrip line has been
used to suppress the mutual coupling between adjacent microstrip lines [22][24]. Very recently,
a deep-subwavelength negative-index waveguiding is studied in [25] using coupled conformal
surface plasmons [26].
In this work, based on the principle of SSPPs, we first present a new microwave subwavelength metallic waveguide consisting of periodic unilateral metal diaphragm channel structure,
which has modal field with high confinement in the waveguide. Adjusting the spatial period and
geometric parameters enables us to control the transmission efficiency and the bandwidth. Second, if we change unilateral metal diaphragm (UMD) to bilateral metal diaphragm (BMD) structure, we find that a band can change into two bands, that is, the original fundamental band
changes into a fundamental band (first band) and an additional guiding band (second band).
The bandgap between these two bands can be absent by tuning the geometric parameters.
Thus, the supporting transmission bandwidth can be effectively enhanced in the absence of
bandgap. This absence also gives rise to a linear dispersion appearing below the light line,
which is an anomalous dispersion in a one-dimensional periodic structure. Furthermore, the dispersion curve of the second band with negative group velocity can pass the light line and then
enter into the radiation region, leading to a possible leaky-wave antenna. Theoretical and experimental results suggest that such SSPPs structure can be applied to the waveguide and
frequency-based beam steering radiations at microwave or THz frequencies.

2. Theoretical Analysis
The proposed two waveguides shown in Fig. 1 are constructed by U-shaped metallic groove
with periodic subwavelength metallic slices. In Fig. 1(a), we have a UMD waveguide, where the

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

groove height h is 23 mm, the width w is 10 mm, the lattice constant d is 9 mm, the metal slice
width w1 is 5 mm, a notch of w2  h1 is at the top of the metal slice with the dimension h1
5 mm and w2 w1 =2, and the interval a between adjacent metal slices is 6.75 mm. In Fig. 1(b),
we have a BMD waveguide with the same parameters as in Fig. 1(a). In addition, the metal
slices are alternately and bilaterally arranged with equal spacing on two sides of the channel.
The transmission properties of these two waveguides will be studied from the dispersion curves
calculated using commercial finite element method software (COMSOL Multiphysics). In the following simulations, the metal is assumed to be a perfect electric conductor (PEC).
The dispersion curves in the first Brillouin zone for two waveguides are shown in Fig. 2(a)
and (b), respectively. For the UMD SSPPs waveguide, there are two guided SSPPs modes. The
cutoff and asymptotic frequencies of the first mode are fuc1 6:19 GHz and fus1 10:65 GHz,
respectively. For the second mode, the cutoff and asymptotic frequencies are fuc2 14:05 GHz
and fus2 14:512 GHz, respectively. The bandwidth for the first mode is 4.46 GHz. By using the
phase measurement technique [18], we experimentally obtained the dispersion relation [black
triangles in Fig. 2(a) and (b)], which fits with the numerical results very well. The field distributions for the two modes at zone boundary  0:5 are shown on the right of Fig. 2(a), in which
we can see that the modal fields are tightly confined in the groove with asymmetric field distributions. Thus, this structure clearly can provide a guiding mode in a different frequency regime
compared to the U-V shaped SSPPs waveguide with d 9 mm [18]. In fact, the transmission
band can be adjusted by changing the geometric dimensions of the periodic structure.
For the BMD SSPPs waveguide, the dispersion curves together with four marked points are
shown in Fig. 2(b). A, B, C, and D are the first band at  0:5, the intersection of the second
band and the light line, the second band at  0:1, and the third band at zone boundary  0:5,
respectively. The corresponding model field distributions for these four points are shown on the
right. It is found that the first band and the second band have nearly the same modal field distributions. It is of interest to note that the bandgap between the first and second band is nearly absent. The absence of bandgap at zone boundary  0:5 is ascribed to the cancellation (a phase
difference of 180 ) between the two reflected waves from the metal slices on the two sides. As
the metal slices are arranged with equal spacing, the two reflected waves from the adjacent
metal slices at  0:5 have a phase difference of 180 and thus cancel each other totally. If the
spacing between the metal slices in the BMD waveguide is unequal, there will be a bandgap between the first and the second band. The similar result has also been observed in other SSPPs
waveguide and explained by using the glide-reflection symmetry operation [25]. Since the first
and the second bands are continuous at point A for BMD waveguide, the transmission bandwidth
of the waveguide can be enhanced. For the first band, the cutoff frequency is fbc1 4:696 GHz
whereas the asymptotic frequency is fbs1 10:39 GHz. The second band will start at fbs1 and
then intersects with the light line at fcp 12:163 GHz. Thus, the total bandwidth of the guiding
bands 1 and 2 can be enhanced to 7.467 GHz fcp  fbc1 , which has a 67% increase compared
to the UMD waveguide. In addition, the BMD waveguide also has a much wider bandwidth than
the V-shape and U-shape SSPPs waveguide reported in [18], whose bandwidth is below 4 GHz.
After the band 2 crosses the light line, it will enter the radiation zone and stops at the zone
center at which fsr 14:905 GHz. Although the field distributions of A (BMD 1st) and C (BMD
2nd) in Fig. 2(b) are similar, their characteristics are different. The mode at A is a guiding mode
whereas the mode at C is a leaky mode. The similarity in the field distribution implies that the
leaky mode could propagate some distance and radiate gradually, which is very essential to obtain the directive radiation. In the radiation zone, the dispersion curve shows negative group velocity and the propagation constant becomes complex, i.e., kz  j, where  Pr =Pf =
2d , where Pf is the total power of the mode and Pr is the transverse radiated power. The supported leaky mode has a pencil-like steering radiation at different frequencies. The value of 
for the leaky wave is shown in Fig. 2(c), in which  increases from 2.81 m1 at fcp to 75.78 m1
at fsr , that is, the leaky efficiency becomes large as the frequency increases. This kind of SSPPs
also has the third and the forth higher order guiding bands. For the third band, the cutoff and
asymptotic frequencies are 13.183 GHz and 14.471 GHz, respectively.

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

Fig. 2. (a) Dispersion curves of UMD SSPPs waveguide for the simulated and experimental results
(black triangle) and its modal field distributions at zone boundary of  0:5. (b) Dispersion curves
of BMD SSPPs waveguide (experimental results with black triangle), in which there are four marked
points A, B, C, and D. The definitions of these four points are described in the text. Modal field distributions (right panel) at points A, B, C, and D are shown. (c) Imaginary part of propagation constant  of BMD SSPPs waveguide in leaky-wave frequency band. (d) Normalized propagation
lengths in guided band for UMD (solid) and BMD (dashed) waveguides.

As mentioned previously, the metal is modeled as a PEC at microwave and thus the sustained mode of the proposed waveguide is lossless. However, it is known that SSPPs with
strong EM field confinement suffer from a significant ohmic loss in a real metal. Therefore, for a
waveguide constructed by a real metal, the metallic loss should be taken into account at microwave. We now choose the metal as aluminum (Al) whose relative permittivity is described by
Drude model. In order to determine the propagation length based on the calculated absorption
loss of metal, a perturbation approach has been used [10]. The propagation length of the guiding mode is L 1=2 Imkz  Pf =Pd d , where Pd is loss power in one periodic cell, and Pf is

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

Fig. 3. Modal field distributions of UMD and BMD SSPPs waveguide. (a) UMD SSPPs waveguide
at 5.75 GHz  0:2. (b) BMD SSPPs waveguide at 5.63 GHz  0:2. (c) BMD SSPPs waveguide at 14.027 GHz (second band at  0:2).

total power of a mode. The normalized propagation length L=
is evaluated from the cutoff frequency to asymptotic frequency and then to the cross point of the second band with the light
line. The result is shown in Fig. 2(d). The solid line is for UMD waveguide and the dashed line is
for BMD waveguide. From Fig. 2(d), the propagation length decreases rapidly from 550
to zero
from fuc1 to fus1 for UMD waveguide due to the strong confinement of EM field on the bottom of
waveguide and slow light effect near fus1 . For BMD waveguide, the ohmic loss is larger than that
of UMD waveguide due to double metal diaphragm in BMD waveguide. Therefore, its propagation length is 267
smaller than that in UMD waveguide 516
at 8 GHz. However, it is surprising that both of the propagation lengths become the same around 10 GHz. A salient feature of
the BMD waveguide is that the propagation length 267
remains unchanged around 8 GHz and
then slowly decreases to the value around 208
near fcp . This feature is due to the linear dispersion relation below the light line which is an anomalous dispersion in one-dimensional periodic
structures. With such superior feature, it will enable the SSPPs wave (in the first and second
bands) to propagate smoothly through the waveguide at a relatively wide frequency range due
to the absence of bandgap.
We also simulate the propagating and radiating phenomena in these SSPPs waveguides.
Fig. 3(a) shows the field distributions of UMD waveguide at 5.756 GHz  0:2. It can be seen
from the figures that the field is efficiently confined inside the corrugation. Fig. 3(b) is the field
distributions of BMD waveguide at 5.63 GHz (first band at  0:2). It is seen that the modal
field can be confined more effectively due to the two-sided corrugation. Fig. 3(c) is the field distributions of BMD waveguide at 14.027 GHz (second band at  0:2). In this case, the fields
belong to the leaky band and thus lots of EM fields are expected to radiate from the waveguide.
We can further find the angle of the leaky-wave radiation direction (i.e. the main lobe) by making
use of the approximate expression,  sin1 =k0 [27]. Since the leaky-wave mode has a negative group velocity, our calculation shows  309:1 at f 13 GHz and  341:6 at
f 14:5 GHz, respectively.

3. Experimental Results
So far, we have presented the simulated results. We shall now demonstrate the experimental
results for the SSPPs waveguide structures. The parameters of unit cell in our experiment are
the same as geometrical parameters in the previous calculations. The total lengths of the two

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

Fig. 4. (a) Fabricated Al-based UMD waveguide. (b) Measured transmission and reflection coefficients of UMD waveguide. (c) Fabricated Al-based BMD waveguide. (d) Measured transmission
and reflection coefficients of BMD waveguide.

Fig. 5. (a) Simulated far-field radiation of the BMD at 13.5 GHz. (b) Measured far-field radiation of the
BMD at 13 GHz (dashed line) and 14.5 GHz (solid line). (c) Radiation efficiency of UMD (solid line) and
BMD (dashed line) SSPPs waveguide.

waveguides are equal to 407 mm. At each input port of the waveguides, there exists a 50-mmlong transition region (i.e., the width of the metal slice grows gradually) to reduce the reflection
caused by the junction between the SSPPs waveguide and the input waveguide. Fig. 4(a) and
(c) are the pictures of real UMD and BMD aluminous waveguides, respectively. Fig. 4(b) illustrates the measured transmission properties of the UMD waveguide. The values of transmission

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

coefficient S21 are 0.85 at 8 GHz, 0.914 at 9.365 GHz, 0.777 at 10.4 GHz, and less than 0.016
above fus1 . The reflection coefficient S11 is smaller than 0.21 below 10 GHz, and quickly increases to 0.775 at 10.5 GHz. Similar results for BMD waveguide are in Fig. 4(d). The transmission coefficient S21 is 0.877 at 8 GHz, 0.751 at 12.11 GHz, and smaller than 0.558 above fcp . It
is seen that the BMD waveguide has a broader transmission bandwidth compared to the UMD
waveguide. The bandwidth of transmission is 810.5 GHz in Fig. 4(b), and is 812.2 GHz in
Fig. 4(d). It is worth noting that, for the BMD waveguide, the transmission drops sharply above
fcp 12:163 GHz but the reflection does not substantially increase, which means the imported
power leaks out from the waveguide instead of being guided or reflected by the waveguide. The
value of jS11 j jS21 j in the leaky band is much smaller than that in the guiding band. Fig. 5(a)
displays the simulated far-field radiation pattern from the BMD SSPPs waveguide at 13.5 GHz.
In Fig. 5(b), the measured radiation pattern points to 337 at 14.5 GHz (solid line), and points to
306 at 13.0 GHz (dashed line). The measured radiation direction has a small deviation from
the theoretical results partially due to the fabrication error. The scanning angle for a single
beam is 31 , which can be doubled with two beams by feeding from both ports. The radiation
efficiency, defined as 1  jS11 j2  jS21 j2 , is shown in Fig. 5(c) for both UMD and BMD waveguides. The radiation efficiency is as small as 0.2 for the UMD waveguide, while it is greater
than 0.9 above 12.55 GHz for the BMD waveguide. Conclusively, in addition to supporting a
wide bandwidth for the guided SSPPs, the BMD waveguide can also be designed to have a
narrow-band leaky-wave beam scanning antenna.

4. Conclusion
In conclusion, we have analyzed the guiding and radiation properties of UMD and BMD SSPPs
waveguide. Experimental results show that such waveguide structures have high confinement
of modal field and the transmission bandwidth can be controlled by geometrical parameters. For
the BMD waveguide, the absence of the bandgap has a merit of increasing transmission bandwidth and consequently a sufficiently long propagation length over wide frequency range can be
obtained. In addition, it can be used for designing a narrow-band leaky-wave beam scanning
antenna. With these excellent features in these waveguides, it is expected that they could have
a wide variety of potential applications at microwave and THz frequencies.

References
[1] H. Raether, Surface Plasmons. Berlin, Germany: Springer-Verlag, 1988.
[2] A. L. Stepanov et al., Quantitative analysis of surface plasmon interaction with silver nanoparticles, Opt. Lett., vol. 30,
no. 12, pp. 15241526, Jun. 2005.
[3] R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, Demonstration of integrated optics elements based on
long-ranging surface plasmon polaritons, Opt. Exp., vol. 13, no. 3, pp. 977984, Feb. 2005.
[4] W. L. Barnes, A. Dereux, and T. W. Ebbesen, Surface plasmon subwavelength optics, Nature, vol. 424, pp. 824
830, Aug. 2003.
[5] L. Liu, Z. Han, and S. He, Novel surface plasmon waveguide for high integration, Opt. Exp., vol. 13, no. 17,
pp. 66456650, Aug. 2005.
[6] J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Mimicking surface plasmons with structured surfaces,
Science, vol. 305, no. 5685, pp. 847848, Aug. 2004.
[7] F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Surfaces with holes in them: New plasmonic metamaterials,
J. Opt. A: Pure Appl. Opt., vol. 7, no. 2, pp. S97S101, Feb. 2005.
[8] F. J. Garcia de Abajo and J. J. Saenz, Electromagnetic surface modes in structured perfect-conductor surfaces,
Phys. Rev. Lett., vol. 95, Nov. 2005, Art. ID. 233901.
[9] S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires, Phys. Rev. Lett., vol. 97, Oct. 2006, Art. ID. 176805.
[10] J. A. Kong, Electromagnetic Wave and Theory. Cambridge, MA, USA: Cambridge Press, 2005.
[11] D. Martin-Cano et al., Domino plasmons for subwavelength terahertz circuitry, Opt. Exp., vol. 18, no. 2, pp. 754
764, Jan. 2010.
[12] A. I. Fernandez-Dominguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, Terahertz wedge plasmon
polaritons, Opt. Lett., vol. 34, no. 13, pp. 20632065, Jul. 2009.
[13] Z. Gao, X. Zhang, and L. Shen, Wedge mode of spoof surface plasmon polaritons at terahertz frequencies, J. Appl.
Phys., vol. 108, no. 11, Dec. 2010, Art. ID. 113104.
[14] C. R. Williams et al., Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,
Nature Photon., vol. 2, no. 3, pp. 175179, Mar. 2008.

Vol. 7, No. 1, February 2015

4800208

IEEE Photonics Journal

Propagation of SSPPs in a Channel Waveguide

[15] G. Kumar, S. Li, M. M. Jadidi, and T. E. Murphy, Terahertz surface plasmon waveguide based on a one-dimensional
array of silicon pillars, New J. Phys., vol. 15, pp. 85 03185 041, Aug. 2013.
[16] A. I. Fernandez-Dominguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, Guiding terahertz waves along
subwavelength channels, Phys. Rev. B, vol. 79, Jun. 2009, Art. ID. 233104.
[17] Z. Gao, L. Shen, and X. Zheng, Highly-confined guiding of terahertz waves along subwavelength grooves, IEEE
Photon. Technol. Lett., vol. 24, no. 15, pp. 13431345, Aug. 2012.
[18] T. Jiang et al., Realization of tightly confined channel plasmon polaritons at low frequencies, Appl. Phys. Lett.,
vol. 99, no. 26, Dec. 2011, Art. ID. 261103.
[19] J. J. Wu, T. J. Yang, and L. F. Shen, Subwavelength microwave guiding by a periodically corrugated metal wire,
J. Electromagn. Waves Appl., vol. 23, no. 1, pp. 1119, 2009.
[20] W. Zhao, O. M. Eldaiki, R. Yang, and Z. Lu, Deep subwavelength waveguiding and focusing based on designer
surface plasmons polaritons, Opt. Exp., vol. 18, no. 20, pp. 21 49821 503, Sep. 2010.
[21] J. J. Wu et al., Bandpass filter based on low frequency spoof surface plasmon polaritons, Electron. Lett., vol. 48,
no. 5, pp. 269270, Mar. 2012.
[22] J. J. Wu et al., Reduction of wide-band crosstalk for guiding microwave in corrugated metal strip lines with subwavelength periodic hairpin slits, IET Microw. Antennas Propag., vol. 6, no. 2, pp. 231237, Jan. 2012.
[23] J. J. Wu et al., Differential microstrip lines with reduced crosstalk and common mode effect based on spoof surface
plasmon polaritons, Opt. Exp., vol. 22, no. 22, pp. 26 77726 787, Nov. 2014.
[24] S. K. Koo, H. S. Lee, and Y. B. Park, Crosstalk reduction effect of asymmetry stub loaded lines, J. Electromagn.
Waves Appl., vol. 25, no. 8/9, pp. 11561167, 2011.
[25] R. Quesada, D. Martn-Cano, F. J. Garca-Vidal, and J. Bravo-Abad, Deep-subwavelength negative-index waveguiding enabled by coupled conformal surface plasmons, Opt. Lett., vol. 39, pp. 29902993, May 2014.
[26] X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, Conformal surface plasmons propagating on ultrathin
and flexible films, Proc. Nat. Acad. Sci. USA, vol. 110, no. 1, pp. 4045, 2013.
[27] F. K. Schwering and S. T. Peng, Design of dielectric grating antennas for millimeter-wave applications, IEEE Trans.
Microw. Theory Tech., vol. MTT-31, no. 2, pp. 199209, Feb. 1983.

Vol. 7, No. 1, February 2015

4800208