Capacitor-Loaded Spoof Surface Plasmon (SSP) for Flexible Dispersion Control and High-Selectivity Filtering

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by  Xiaolan Tang

1
Capacitor-Loaded Spoof Surface Plasmon (SSP)
for Flexible Dispersion Control and
High-Selectivity Filtering
Xiao-Lan Tang, Qingfeng Zhang, Senior Member, IEEE, Sanming Hu, Senior Member, IEEE, Abhishek Kandwal,
Tongfeng Guo, Student Member, IEEE, and Yifan Chen, Senior Member, IEEE,
x
7 Abstract—This letter proposes a new spoof surface plasmon
1 transmission line (SSP-TL) using capacitor loading techniques. y
0 This new SSP-TL features flexible and reconfigurable disper- Unit Cell Circuit Model z
2 sion control and highly selective filtering performance without a C2 C1 C2
resorting to configuration change. Moreover, it requires much
n
a sameaxltlreermleinlyeswloiwdthwathvean(otrhae hcoignhvleyntcioonnfianleSdSfiPe-TldL),swfohricahcihsieqvuinitge w h L3 L1 L1 L3
J
useful for a compact system. To illustrate the design principle, In L2 Out
6 C3 C3
several examples are designed within the frequency range of d
1 2−8 GHz. Both numerical and experimental results are given (a)

incomparison withtheconventional SSP-TL.Itisdemonstrated New Cell ∆C
]
h that the proposed technique provides a better performance in ∆C
size reduction and dispersion reconfigurability.
p
- Index Terms—Spoof surface plasmon (SSP), capacitor-loaded,
s
s dispersion curve, reconfigurability, selective filtering.
a In Out
l
c I. INTRODUCTION
. (b)
s Surfaceplasmons,originallyproposedandappliedinoptics,
c
i arepropagatingwavesalongtheinterfacebetweenametaland Fig.1. SSP-TLusingsurfacecorrugation:(a)conventionalone,(b)proposed
s capacitor-loaded one.
a dielectric medium [1]. These waves, decayingexponentially
y
h inthedirectionperpendiculartotheinterface,exhibitahighly
p confined and localized field near the surface. In 2004, Pendry TLs, typically used for high-density transmission lines with
[ et al. has demonstrated that a similar surface plasmonic low crosstalk, would lose its benefit on compactness. To

1 phenomenon, known as spoof surface plasmon (SSP), can be overcomethis drawback, we propose a capacitor-loadedSSP-
v observedatmicrowavefrequenciesbyperforatingtheconduc- TL. Itfeaturesa smallline width butwith a stronglyconfined
7 tivesurfaceusingparametricalholes[2].Since then,SSPs are field,whichsignificantlyreducesthesizeofthewholesystem.
9
widely explored in low-crosstalk transmission lines [3]–[6], Moreover, this new SSP-TL exhibits the benefits on flexible
1
4 filters[7],leaky-waveantennas[8],[9]andso on,duetotheir control of the dispersion curve without resorting to changing
0 potentialapplicationsinmillimeter-waveandterahertzcircuits. the geometrical configurations. It can be potentially extended
. It has been demonstrated in the recent work [3] that to reconfigurable SSP-TLs by replacing the static capacitors
1
0 the dispersion properties of SSP transmission line (SSP-TL) with tunable ones. Typical applications may include highly
7 can be adjusted by modifying the geometrical dimensions selective filters with reconfigurable cutoff frequencies.
1 and/or dielectric material parameters. The working principle
v: lies in that the surface corrugation and dielectric parameters II. PRINCIPLE
Xi determine the effective capacitance along the surface and Conventional SSP-TL is realized by corrugating a metallic
hencethe electricalfield confinementanddispersionproperty.
stripwith subwavelengthperiodicslots, asshowninFig. 1(a),
r However, a highly confined field usually requires a high-
a where the parametersd, h, a and w denotethe periodicpitch,
depth corrugation and hence a large line width. Such SSP-
the slot depth, the slot width and the line width, respectively.
The corrugationprovides a capacitive loading along the strip,
This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may and hence supports a bounded mode confined to the surface,
nolongerbeaccessible. allowing to manipulate electromagnetic waves at subwave-
X.-L. Tang, Q. Zhang, A. Kandwal, T. Guo and Y. Chen are with the
length regime. The unit cell of SSP-TL is modeled by an
Department of Electrical and Electronic Engineering, South University of
ScienceandTechnologyofChina,Guangdong518055,China.X.-L.Tangis equivalent circuit, as shown on the right side of Fig. 1(a) [3],
alsowiththeStateKeyLaboratoryofMillimeterWaves,SoutheastUniversity, where L1, L2 and L3 are attributed to the magnetic field
Nanjing 210096,China.(e-mail: [email protected]).
S. Hu is with the State Key Laboratory of Millimeter Waves, Southeast excitedbythecurrentsalongthestripunits,C2 andC3models
University, Nanjing210096,China. the electric field pointing to the infinity (in x direction), and
2
15
CST:h=3mm CST:h=8mm CPW-to-SSP Capacitor-Loaded SSP
Transition
CST:h=5mm CST:h=11mm
12
ChipCapacitor
z) AirLine (a)
H 9
G CPW-to-SSP Conventional SSP
(
y Transition
c
n
ue 6
eq x
Fr
(b) z y
3
E.C:∆C=0pF E.C:∆C=0.2pF
E.C:∆C=0.1pF E.C:∆C=0.5pF Fig. 3. Fabricated prototypes of the capacitor-loaded SSP-TL and conven-
tional SSP-TL.
0
0 0.2 0.4 0.6 0.8 1
βd/π
plasmonsinoptics,isinverselyproportionaltothecorrugation
Fig. 2. Dispersion Curves of (a) conventional SSP-TL and (b) capacitor-
depth h. Also, the group velocity around this frequency is
loaded SSP-TL.(E.C:Equivalent Circuit)
extremelysmall, whichgivesrisetoa stronglylocalizedwave
inanalogytothestronglight-electroninteractioninoptics.The
C1 represents the local electric field excited between the gap smallgroupvelocityalsoleadstoasharpmagnituderesponse,
(mostly in y direction). which is very useful in high-selectivity filters.
To analyze the unit cell of Fig. 1(a), one adds a periodic Although a high corrugation depth h is good for field
boundary condition on both sides of the unit cell, and subse- confinement,itinevitablyincreasesthelinewidthwthatisnot
quentlycomputesthedispersioncurveusingthesoftwareCST preferred in a compact system. To overcome this drawback,
Microwave Studio. One may consider an example, in which we propose the capacitor-loaded SSP-TL in Fig. 1(b). The
the substrate is Rogers 4003C (ǫr = 3.38, tanδ = 0.0027) additional loaded capacitors along the surface brings in an
with thickness of 1.52 mm, and the strip dimensions in extra capacitance, in equivalence to the extra capacitance
Fig.1(a)area=1mm,w =5mm,d=5mmandh=3mm. brought by the increased corrugation depth in conventional
The calculated dispersion curve is shown as the blue squares SSP-TLs. Therefore, the proposed SSP-TL increases the field
in Fig. 2. Note that it exhibits a typical SSP response, which confinement capability and meanwhile maintains a small line
stays close to the air line at low frequencies but goes away width. The capacitor-loaded unit cell can be modeled by
at high frequencies. The circuit parameters of Fig. 1(a) are adding the extra capacitance ∆C to the original circuit, as
calculated as L1 = 0.8 nH, L2 = 0.14 nH, L3 = 0.2 nH, shown in Fig. 1(b). One may use this circuit model to
C1 = 22.5 fF, C2 = 161 fF and C3 = 178 fF, by using obtain the dispersion curves in Fig. 2. Note that, the SSP-TL
the approach provided in [3]. One may further calculate the loaded with different capacitances achieves almost the same
dispersion curveof the equivalentcircuit to verify its validity. dispersion curves as the conventional SSP-TL with different
One firstly computes the scattering parameters (S11 and S21) depths.
of the circuit model, and subsequently obtains the dispersion
relation by
III. EXPERIMENTAL VALIDATION
β =ℑ 1cosh−1 1−S121+S221 , (1) To validate the proposed capacitor-loaded SSP-TL, we ex-
(cid:20)d (cid:18) 2S21 (cid:19)(cid:21) perimentallyimplementtheonewith∆Cof0.2pFona1.52-
whereℑ[.] denotesthe operationoftakingthe imaginarypart. mm-thickRogers4003Csubstrate,incorrespondencewiththe
It should be noted that the above equation is obtained under purple-linedispersioncurveof Fig. 2. In comparison,we also
theconditionofsymmetry(S11 =S22)andreciprocity(S21 = implement the conventionalSSP-TL with a corrugationdepth
S12), and hence valid for symmetrical and reciprocal cases h = 8 mm, exhibiting a similar dispersion curve to the pro-
only. The computed dispersion curve using (1) is displayed posed SSP-TL. Fig. 3 shows the fabricated prototypes of the
as the blue dotted line in Fig. 2, which well follows the one twoSSP-TLs.Taperedlinesareemployedforasmoothtransi-
obtained by CST full-wave simulation. tion and modeconversionbetween the 50Ω-CPWline (width:
Toincreasethefieldconfinementorlocalization,oneshould 12 mm, gap: 0.5 mm) and SSP [4]. As shown in the zoomed
further bend the dispersion curve away from the air line. One figureofFig.3(a),theproposedSSP-TLisloadedwith0.2pF
way to achieve this is to increase the corrugation depth h, chip capacitors (Murata GJM1555C1HR20WB01D). The line
which is well validated by the dispersion curves of Fig. 2. parameters are w = 5 mm, h = 3 mm, a = 1 mm, and
When h increases from 3 mm to 11 mm, the dispersion d=5 mm. In contrast, the conventional SSP-TL has a much
curves gradually bend away from the air line, giving rise to wider line width (i.e. w = 10 mm), due to the increased
a much slower trapped wave. Note that, in the case of a high corrugationdepthh=8mm.Thus,thecapacitor-loadedSSP-
corrugation depth (e.g. h = 11 mm), the dispersion curve TL reduces the line width by half.
becomes almost flat when it is close to the cutoff frequency. The two fabricated prototypes are measured using an Ag-
This frequency,in analogyto the plasma frequencyof surface ilent PNA network analyzer (E5071C) within the frequency
3
0 45 1
Wide Stop Band Proposed[Fig.3(a)] Conventional [Fig.3(b)]
30 0.8
−20 15
|S21|ofFig.3(a) mm) 0 0.6
dB)−40 |S21|ofFig.3(b) 0 |S x (-15 0.4
( 1
|1 |1 -30 0.2
|S2−60 −10(dB) -45-4 5 -30 -15 0 15 30 45 -45 -30 -15 0 15 30 45 0
z (mm) z (mm)
−80 |S11|ofFig.3(a) −20 1 x=−6mm ∆z=10.9mm x=−11mm ∆z=16.7mm
d0.8
|S11|ofFig.3(b) d Fiel0.6
2 3 4 5 6 7 8 9 10 e
z
Frequency (GHz) ali0.4
m
or ∆z ∆z
N0.2
Fig. 4. The measured scattering parameters of the two fabricated SSP-TL
0
prototypes inFig.3. -45 -30 -15 0 15 30 45-45 -30 -15 0 15 30 45
z (mm) z (mm)
(a) (b)
range 2−10 GHz. The measured responses of the scattering
Fig.5. Cross-sectiondistribution oftheelectric fieldoftheSSP-TLsin(a)
parametersareshowninFig.4.Notethatthecapacitor-loaded Fig.3(a)and(b)Fig.3(b)at4GHz.
SSP-TLhasasimilarresponseastheconventionalSSP-TL,in
spite of a slight discrepancy in the cutoff frequency, possibly 0
due to the tolerances brought by PCB fabrication and the
commercial chip capacitors (±0.05 pF). Also note that, the Reconfigurable
Operation Band
proposedSSP-TLhasaverysharpmagnituderesponsearound
5.8 GHz, which exhibitsa highly selective filtering feature. It −20
also exhibits a wide stop band from 5.8 GHz to 10 GHz. B)
d
To compare the field confinement capability of the two (
|1
SSP-TLs, their normalized electric fields in the cross section S2
|
(x−z plane) at 4 GHz are plotted in Fig. 5. Note from the −40 ∆C=0.1pF
2D distributions that the proposed SSP-TL has a better field ∆C=0.2pF
confinement.Toquantifythisimprovement,weplotthe1Dz- ∆C=0.3pF
distribution across the maximum point. Then one may define ∆C=0.5pF
−60
theconfinedregionusingthewidthwhenthefielddropsto0.3 2 3 4 5 6 7 8
(about−10dB)ofthemaximumstrength.Notethatthiswidth Frequency (GHz)
is 10.9 mm in the proposed SSP-TL, and is 16.7 mm in the
Fig.6. MeasuredmagnituderesponsesofthefabricatedprototypeofFig.3(a)
conventional one. Thus, the confinement capability, inversely
withdifferent loadingcapacitances.
proportional to the confined region, is improved by 53%.
TheproposedSSP-TLloadedwithdifferentcapacitancesare
also fabricated and measured. The scattering parameters are [2] J. B. Pendry, L. Martn-Moreno, and F. J. Garcia-Vidal, “Mimicking
shown in Fig. 6. Note that the cutoff frequency (in analogy surface plasmons with structured surfaces.” Science, vol.305, no. 5685,
pp.847–8,2004.
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June2015.
the operation band. The static capacitors may be replaced by
[4] H.F.Ma,X.Shen,Q.Cheng,W.X.Jiang,andT.J.Cui,“Broadbandand
tunable capacitors to make it truly reconfigurable, which will high-efficiency conversion fromguided waves tospoofsurface plasmon
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IV. CONCLUSION
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SSP-TL.Theprinciplewasillustratedandseveralexperimental surface plasmonic filterinmicrowave frequency,” Appl.Phys.Lett.,vol.
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[8] A. Kianinejad, Z. N. Chen, L. Zhang, and W. Liu, “Spoof plasmon-
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