Table Of ContentBistatic scattering characterization of a three-dimensional broadband cloaking
structure
PekkaAlitalo1,2,AliE.Culhaoglu2,AndreyV.Osipov2,StefanThurner2,ErichKemptner2,andSergeiA.Tretyakov1
1 Department of Radio Science and Engineering / SMARAD Centre of Excellence,
Aalto University, P.O. Box 13000,
FI-00076 Aalto, Finland
E-mail: pekka.alitalo@aalto.fi
2 Microwaves and Radar Institute,
German Aerospace Center DLR,
82234 Wessling, Germany
2
1
0
2 (Dated: October18, 2011)
n Here we present the results of full experimental characterization of broadband cloaking of a
a
finite-sized metallic cylinder at X-band. The cloaking effect is characterized by measuring the
J
bistatic scattering patterns of uncloaked and cloaked objects in free space and then comparing
4 these with each other. The results of the measurements demonstrate a broadband cloaking effect
and are in good agreement with numerical predictions.
]
h
p
-
s
s I. INTRODUCTION scattered in the forward direction. It is shown that the
a
both approaches agree well with the numerical results.
l
c It should be noted that the previous experimental
. The concept of electromagnetic cloaking has been
s demonstrations of reduction of total scattering widths
c found by many as an exciting example of the power of by cloaking devices5,6 have been obtained by emulating
i artificialelectromagneticmaterials(metamaterials). The
s infinitely long structures, since in both cases the mea-
y concepts of transformation optics1,2 and scattering can-
surements were carried out in a parallel-plate waveguide
h cellation3,4 describe different ways of making scattering
instead of free space. Here we carry out the measure-
p objects invisible, that is, reducing the total scattering
[ cross section of an object ideally to zero. First experi- ments in free space conditions, using two antennas to
measure the scattered fields produced by finite-sized ob-
2 mental proofs of reduction of the total scattering from
jects. In addition to measurements we also present the
v specific objects with these techniques have been pro-
corresponding numerical results for the total scattering
0 videdbymeasuringthemicrowavefielddistributionsnear
widthsandbistaticscatteringpatternsthatareobtained
5 cloaked and uncloaked objects.5,6
1 withthecommercialnumericalsoftwareANSYSHFSS.13
Recently, some alternative ways of achieving electro-
6
. magnetic cloaking by employing waveguiding structures
9 instead of complex materials have been proposed.7,8 II. GEOMETRY AND DIMENSIONS OF THE
0
These structures are composed of simple transmission CLOAK STRUCTURE
1
1 lines or specifically shaped metallic structures that en-
: able the electromagnetic wave either to go through the ThecloakgeometryisthesameaspresentedinRef.11,
v
object9 ortogoaroundtheobject.10,11 Boththesecloak-
i see Fig. 1. The conical metal plates, realized from and
X ing methods have been already studied numerically and
modelled as copper, form a periodic structure that sur-
r experimentally. However, the experimental results for roundsametalcylinderwhichistheobjecttobecloaked.
a these structures were obtained in a rectangular waveg-
The plates form a set of waveguides into which the elec-
uide setup,whichdoesnotallowthe analysisofthe total
tromagnetic wave with the electric field parallel to the
scattering cross sections or total scattering widths.
axis of the cylinder can couple to. The wave travels in-
In this paper we describe microwave measurements at sidethestructure,withveryweakreflections,aroundthe
X-bandofthebistaticscatteringpatternsofafinite-sized cylinderplacedinthecenter. Essentiallythiscloakingde-
waveguiding cloak structure composed of stacked coni- vice is designed to work for objects that are electrically
cal metal plates (therefore also called the “metal-plate small since the wave inside the cloak must travel a dis-
cloak”).10,11 The cloaking effect is experimentally char- tancelargerthanthewavethattravelsinfreespacealong
acterized by measuring the bistatic scattering patterns a straight line. However, it has been shown11 that the
and comparing the total scattering widths of both un- diameterofthecloakedcylindercanbe aslargeasabout
cloakedandcloakedobjects. Inadditiontobistaticmea- one wavelength without much compromising the cloak-
surements, we employ the forward scattering theorem12 ing effect. Therefore we use the structure and dimen-
toevaluatethetotalscatteringwidthusingonlythefields sionspresentedinRef.11todemonstratethe cloakingof
2
FIG.2. (Coloronline)Photographofthemeasurementsetup
at DLR, including the scatterer to be measured (in the cen-
ter). The inset shows a magnification of a part of thecloak.
receiving antenna is swept from φ = 22◦ to φ = 180◦.
Both antennas are operating with the vertical polariza-
tion(electric field parallelto the z-axis). See Fig.2 for a
photograph of the setup. The transmitted and received
signalsaremeasuredwithavectornetworkanalyzer(Ag-
FIG. 1. (Color online) Geometry of the cloak enclosing the
cloaked object. The cloaked object is a solid cylinder with ilent HP 8719D) in the band 8.2 GHz-12.4 GHz with
diameter D. One half of a single unit cell of the cloak, cut 401 frequency points. Both antennas are equipped with
along thexz-plane,is shown. microwave lenses that focus the antenna beams exactly
on the object that is measured. The beam’s half-power
widthatthefocusisapproximately45mmandthemea-
TABLE I. Dimensions of the cloak operating at around sured structures are made considerably higher than the
10 GHz11.
beamwidth to avoid any scattering effects caused by the
D H h L1 L2 t w finite height. The cloak to be measured is made of 20
30 mm 9.2 mm 6 mm 61 mm 32 mm 0.1 mm 2 mm unitcellsshowninFig.1,i.e.,thecloak(andthecloaked
cylinder) has the height 184 mm.
Undertheseconditionsthebarecylinderandthecloak
ametal(brass)cylinderhavingthediameterof30mmat
scattermostlyinthexy-planeandthereforewecanchar-
X-band (specifically, in the band 8.2 GHz – 12.4 GHz).
acterize the cloaking effect using the total scattering
The optimized dimensions for cloaking at frequencies
width instead of the total scattering cross section. We
around 10 GHz are shown in Table I. A dielectric sup-
measure the scattering pattern of the cloaked/uncloaked
portofheighthandthicknessw hasbeenaddedbetween
◦ ◦
object for angles 22 −180 since the scattering struc-
two adjacent metal plates to enable practical realization
of the structure. This dielectric is Rohacell(cid:13)R 51 HF14 tures are symmetrical with respect to the xz-plane and
◦ ◦
themeasurementofangles0 −22 isnotpossibledueto
and is numerically modelled as having the relative per-
the finite size of the antennas. However,the lack of data
mittivity of ǫ = 1.07 and loss tangent of tanδ = 0.003.
r ◦ ◦
for angles 0 −22 will not be problematic since most
These material properties are so close to the free space
of the scattering occurs in the forward direction (close
valuesthatthelayersdonotpracticallyaffectthecloak’s
to φ =180◦), and we can compare our measured results
operation,ascanbeconcludedbycomparingthenumer-
withnumericalresultsinthesameangularrange. Allthe
ical results shown later in this paper with the results
measurements presented in this paper have been carried
presented in Ref. 11.
out with an angular step of 0.5◦.
For every angle we measure the complex scatter-
III. EXPERIMENTAL SETUP FOR ing parameter of the studied object (S ). In addi-
21,O
MEASURING THE BISTATIC SCATTERING
tion, the measurement is repeated without the scatterer
(S , i.e., transmission in free space) to account for
21,FS
We usea bistaticmeasurementsetupcomposedoftwo the crosstalkbetween the transmitting andreceiving an-
antennas to measure the fields scattered by uncloaked tennas. A value directly proportional to the scattered
andcloakedobjectsinvariousdirectionsinthexy-plane. electric field is then obtained from these two measure-
The transmitting antenna is fixed at φ = 0◦ while the ments with
3
1
E (f,φ)=S (f,φ)−S (f,φ), (1) 0.9 10mm/15mm, analytical (integration, angles 0 to 180)
sca,O 21,O 21,FS 10mm/15mm, analytical(integration, angles 22 to 180)
10mm/15mm, experimental (integration, angles22 to 180)
where f is the frequency and φ is the angle in the xy- h0.8 10mm/15mm, experimental (FW sca. theorem)
dt
plane. g wi0.7
One of the most practicalwaysto characterizea cloak n
eri
andtodeterminetheefficiencyofcloakingistostudythe att0.6
c
tboytatlhsecattottearlinsgcawttiedrtihngofwtihdethclooafktehdeoubnjecclota,kneodrmoabljiezcetd. otal s0.5
d t
ThesameanalysishasbeenusedinRef.5. Thescattered ze0.4
field intensities areintegratedoverthe xy-plane for both mali
objects. Thenormalizedtotalscatteringwidth(σW,norm, Nor0.3
i.e., the total scattering width of object 1 normalized by
0.2 5mm/15mm, analytical (integration, angles 0 to 180)
the total scattering width of object 2) is therefore
5mm/15mm, analytical(integration, angles 22 to 180)
0.1 5mm/15mm, experimental (integration, angles22 to 180)
5mm/15mm, experimental (FW sca. theorem)
|E (f,φ)|2dφ
sca,O1 0
σW,norm(f)= R |Esca,O2(f,φ)|2dφ, (2) 8.5 9 9.5 10f [GH1z0].5 11 11.5 12
R
where “O1” stands for object 1 and “O2” for object 2. FIG.3. (Coloronline)Analyticalandexperimentalresultsfor
All our scattering objects are cylindrically symmetric, normalizedtotalscatteringwidths. Totalscatteringwidthsof
so it wouldbe enoughin (2) to integrate only from0◦ to cylinders with radii 5 mm and 10 mm are normalized to the
180◦,butsincewearelimitedintheangularrangeofthe totalscatteringwidthofacylinderhavingtheradius15mm.
measurement setup, we have to approximate (2) by in-
◦ ◦
tegrating from 22 to 180 . However, the backscattered
field at φ = 0◦ can be determined by measuring the re-
only over the limited range of angles. We measure three
flectioncoefficient(S )ofthe transmitting antenna and
11 different metal cylinders with radii 5 mm, 10 mm, and
equating it to the scattered field. We are not using this
15mm(theheightofallcylindersequals184mm). Then
valueofthe scatteredfieldintheintegration,but wecan
we use (1) for the scattered fields and (2) to obtain the
use it for making surethat the scatteringobjects behave
normalized total scattering widths using the integration
as expected also in the back direction.
method. We alsoemploy the forwardscattering theorem
The forward scattering (or optical) theorem12 states
(3), where we use the cylinder with radius 10 mm as the
that the total scattering width (or cross section) is di-
calibrationobject. Fig. 3 presents analytical and experi-
rectly related to the complex field scattered in the for-
mentalresults for the normalizedtotalscattering widths
ward direction. This theorem offers a convenient way to
of various cylinders. The measured results agree well
estimatethetotalscatteringwidthsoftheobjectsstudied
with the analytical ones, although a little bit of fluctua-
heresinceonlythescatteredfieldsatφ=180◦needtobe
tionisnaturallyseeninthemeasuredvalues. Itshouldbe
considered. To employ the theorem, we need to find the
noted that two analytical results are shown for compari-
far-field scattering coefficients12 of the studied objects.
son: the exact solution of (2), and one obtained by inte-
These are found by using a calibrationscatterer,such as ◦ ◦
grating in (2) from 22 to 180 . These analytical curves
a metal cylinder. Specifically, the total scattering width
overlap and with the scaling in the plot it is impossible
of an object is found with
to distinguish these results from each other. This is ex-
pected since the approximation done in the integration
4 E (f,φ=180) disregardsonlyasmallportionoftheangularrange,and
σ (f)=− Re P sca,O , (3)
W,FW k (cid:26) calE (f,φ=180)(cid:27) moreover, the objects scatter much more in the forward
sca,cal
direction than in the back direction. One important fac-
where k is the wavenumber, P is the analytically tor is also that close to the back direction(in 0◦ to 22◦),
cal
known12 far-field scattering coefficient of the calibration the scattering cross section is stable with respect to the
object, and E , E are the measured scattered angle. Also the forward scattering theorem gives a rea-
sca,O sca,cal
electric fields of the studied object and calibration ob- sonable result, although we can conclude that the inte-
ject, respectively. The normalized total scattering width grationmethodgivesamoreaccurateresult. The reason
is obtainedby taking the ratioof σ oftwo different for this is that the scattered field in the forward direc-
W,FW
objects. tion (φ = 180◦) has larger measurement error than the
Wefirstverifytheoperationofthemeasurementsetup scattered fields in other directions. This is very much
by measuring metal cylinders of different diameters so expected since for small scatterers and for angles close
thatwecancomparethemeasuredscatteringwidthswith to 180◦, the parameters S (f,φ) and S (f,φ) are
21,O 21,FS
the known analytical results. In this way we can esti- at maximum and close to each other which leads to the
mate the error which is introduced by integrating in (2) larger error.
4
1
Uncloaked, HFSS
0.9 Cloaked, HFSS
Uncloaked, experimental
0.8 Cloaked, experimental
0.7
2E|sca0.6
ed | 0.5
z
ali
m 0.4
or
N
0.3
0.2
0.1
0
0 20 40 60 80 100 120 140 160 180
φ [deg]
(a)
FIG.4. (Coloronline)Experimentalandnumericalresultsfor
the total scattering width of the cloaked object, normalized 1
Uncloaked, HFSS
to thetotal scattering width of the uncloaked object. 0.9 Cloaked, HFSS
Uncloaked, experimental
0.8 Cloaked, experimental
0.7
2E|sca0.6
ed | 0.5
z
ali
m 0.4
or
N
IV. EXPERIMENTAL AND NUMERICAL 0.3
RESULTS OF CLOAKING
0.2
0.1
0
0 20 40 60 80 100 120 140 160 180
Acloakwith20unitcellsofFig.1wasassembledona φ [deg]
metal cylinder having the diameter 30 mm. The cloaked
(b)
anduncloakedcylinderswerethenmeasuredasdescribed
above. Fig. 4 presents the normalized total scattering
1
width for the cloak studied in this paper, demonstrat- Uncloaked, HFSS
ing that the cloak reduces the total scattering width 0.9 Cloaked, HFSS
Uncloaked, experimental
of the uncloaked metal cylinder by about 70% in max- 0.8 Cloaked, experimental
imum. The wide operation bandwidth is also demon-
0.7
staettrrivainetgefdrw,eqsidiuntechnecotyfhtebhacenlodcaywkliidnistdhsehroofbwyanbmtoouortree2dt0uh%cae.ntT5h0he%etoctienanltasecrraeotl--f 2zed |E|sca00..56
ali
the cloaking band is at around 10 GHz, as predicted by m 0.4
or
numericalresults. Itshouldbeemphasizedthatbasedon N 0.3
the results of Fig. 3, the integration method is expected
0.2
tobemoreaccuratethanthatbasedontheforwardscat-
0.1
teringtheorem. However,itis clearthatthe both curves
demonstrate the cloaking effect. 0
0 20 40 60 80 100 120 140 160 180
φ [deg]
Although the most important figure of merit for the (c)
cloakisthe normalizedtotalscatteringwidth, itisinter-
esting to look at the angular dependence of the bistatic FIG. 5. (Color online) Angular dependency of the scattered
scattering patterns at fixed frequencies. Fig. 5 presents fieldintensities,normalizedtothatoftheuncloakedobjectat
the normalizedscatteredfield intensities as a function of φ=180◦. (a) f =10 GHz,(b) f =11 GHz,(c) f =12 GHz.
φ for frequencies 10GHz, 11GHz, and12GHz. It is ob- The results of the monostatic measurements (φ = 0◦) are
viousthattheexperimentalresultsdiffersomewhatfrom shown as squares (cloaked) and circles (uncloaked).
the numerical ones, but the numerical and experimen-
tal results for the overallperformanceof the cloak are in
good agreement.
5
V. CONCLUSIONS agreementwitheachother. Thecloakhasbeenshownto
reducethetotalscatteringwidthofthecylinderbymore
Experimentalconfirmationofscatteringreductionbya than50%inarelativefrequencybandwidthofabout20%
finite-sizedmetal-platecloakoperatingintheX-bandhas around 10 GHz.
beenpresented. Abistaticfreespacemeasurementsetup This work has been partially funded by the Academy
has been established for this purpose. The efficiency of of Finland and Nokia through the center-of-excellence
thecloakhasbeendemonstratedbydeterminingthetotal program. The work of P. Alitalo has been supported by
scattering widths of an uncloaked and cloaked metallic the Academy of Finland through post-doctoral project
cylinder of finite height. Measurement results have been funding. P. Alitalo acknowledges the work of Mr. Eino
compared with numerical ones. The results are in good Kahra in helping in the manufacturing of the cloak.
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