Research ArticleExperimental Realization of anExtreme-Parameter Omnidirectional Cloak

Bin Zheng12 Yihao Yang123 Zheping Shao12 Qinghui Yan12Nian-Hai Shen3 Lian Shen12 Huaping Wang4 Erping Li1Costas M Soukoulis35 and Hongsheng Chen12

1Key Lab of Advanced MicroNano Electronic Devices amp Smart Systems of ZhejiangCollege of Information Science and Electronic Engineering Zhejiang University Hangzhou 310027 China2State Key Laboratory of Modern Optical Instrumentation andThe Electromagnetics Academy at Zhejiang UniversityZhejiang University Hangzhou 310027 China3Department of Physics and Astronomy and Ames Laboratory-US DOE Iowa State University Ames IA 50011 USA4Institute of Marine Electronics Engineering Zhejiang University Hangzhou 310058 China5Institute of Electronic Structure and Laser FORTH 71110 Heraklion Crete Greece

Correspondence should be addressed to Yihao Yang yangyihaooozjueducn and Hongsheng Chen hansomchenzjueducn

Received 14 May 2019 Accepted 15 July 2019 Published 18 August 2019

Copyright copy 2019 Bin Zheng et al Exclusive Licensee Science and Technology Review Publishing House Distributed under aCreative Commons Attribution License (CC BY 40)

An ideal transformation-based omnidirectional cloak always relies on metamaterials with extreme parameters which werepreviously thought to be too difficult to realize For such a reason in previous experimental proposals of invisibility cloaksthe extreme parameters requirements are usually abandoned leading to inherent scattering Here we report on the firstexperimental demonstration of an omnidirectional cloak that satisfies the extreme parameters requirement which can hideobjects in a homogenous background Instead of using resonant metamaterials that usually involve unavoidable absorptive lossthe extreme parameters are achieved using a nonresonant metamaterial comprising arrays of subwavelength metallic channelsmanufactured with 3D metal printing technology A high level transmission of electromagnetic wave propagating throughthe present omnidirectional cloak as well as significant reduction of scattering field is demonstrated both numerically andexperimentally Our work may also inspire experimental realizations of the other full-parameter omnidirectional optical devicessuch as concentrator rotators and optical illusion apparatuses

1 Introduction

Various design concepts of invisibility cloaks have beenrecently realized thanks to the pioneering works in meta-materials and transformation optics Designs of invisibilitycloaks based on other methods have also been reported [1ndash3] From the viewpoint of transformation optics a concealedregion is mapped from a point in virtual space Despite theelegance of the proposed general transformation optics cloak-ing theory [4 5] it is tremendously difficult to implementthe required extreme parameters and this is why previousimplementations have relied on approximations [6ndash8] Theseapproximations degrade the performance of the cloak dueto considerable reflections Another way to eliminate the

extreme parameters is to transform the hidden object intoa line instead of a point the idea behind carpet cloaks [9ndash16] and unidirectional cloaks [17ndash19] However the carpetcloaks should work on a conducting ground plane and theunidirectional cloaks suffer from narrow viewing angles Inshort an omnidirectional cloak with perfect performancerequires extreme parameters but still remains elusive

All of these difficulties stem from the need to create ahidden region inside the cloak that does not exist before thetransformation The hidden region has a finite dimensionbut it is mapped from a point with an infinitesimal sizeThe light rays must therefore propagate around the innerboundary of the cloak with an infinite speed and theconstitutive parameters need to be of extreme values eg

AAASResearchVolume 2019 Article ID 8282641 8 pageshttpsdoiorg103413320198282641

2 Research

120576120588(120583120588) = 0 and 120576120579(120583120579) = infin (the so-called singularity) fortransverse magnetic TM (transverse electric TE) waves at theinner boundary of the cylindrical cloaks [20] These extremeparameters cannot be avoided for an ideal omnidirectionalcloak with perfect performance independently of the choiceof coordinate transformation equationsThe designs of meta-materials with permeability (TE wave case) or permittivity(TM wave case) ranging from zero to infinity are verychallenging in general Resonantmetamaterials such as SRRs[21] usually suffer frommaterial absorptions that prevent thepermeability from reaching an infinite value Therefore theextreme parameters requirement is one of themain challengethat hinders the realization of omnidirectional cloaks withperfect performance

Here we successfully achieved the first practical real-ization of an omnidirectional cloak with extreme param-eters that can hide an object in a homogenous isotropicbackground We subtly design a metamaterial to fulfill theextreme parameters requirement by taking advantage of thenature of the conductive metals at low frequencies Instead ofusing resonant metamaterials we realize all the constitutiveparameters with non-resonant metamaterials that displaylower material absorptions As a demonstration we fabricate(with the aid of three-dimensional (3D) metal printingtechnology) and experimentally characterize a metamaterialcloak sample

2 Results and Discussion

Figure 1(a) shows the schematic view of the proposed omni-directional cloak with extreme parameters In a cylindricalcloak a point in the virtual space is transformed into acircle in the physical space and different circles have differ-ent tension or compression ratios that lead to constitutiveparameters of the cloak spatially distributed along the radialdirection In the present work instead of using an inhomo-geneous transformation in a cylindrical cloak we dividedthe cloak shell into eight regions and used a homogeneoustransformation [22] to design a square cloak as shown inFigure 1(b) The space between a square of side 1198872 and asmaller square of side 119886 in the virtual space is transformedinto the space between a square of side 1198872 and a smaller squareof side 1198871 in the physical space Here we set 119886 = 0 iethe square in the virtual space with zero cross section and1198872 = 21198871 For the TM wave case and embedding the cloakin a homogenous background with 120576119887119892 = 1 and 120583119887119892 = 1 byusing transformation optics (see Supplementary Information(available here)) we obtain the constitutive parameters (forsimplification we use superscript u v w instead of u1015840 v1015840w1015840 in physical space) 120576119906119886 = 05 120576

V119886 = 2 120583

119908119886 = 2 in Region

I1015840 and 120576119906119887 = infin 120576V119887 = 0 120583

119908119887 = 0 in Region II1015840 an object

in Region III1015840 becomes completely invisible from all of theview angles It is worth noting that region II1015840 in physicalspace is now an optical nihilitymedium [23ndash25] with extremeanisotropic parameters which is mapped from a volumelessline in the virtual space The region I1015840 is with regularanisotropicmediumwhile the region III1015840 is the hidden regionfor arbitrary objects In this cloak while zero and infinite

values are still present the large values close to the singularityvanish This will facilitate the experimental implementationbut without losing any performance Note that the proposedcloak preserves both the phase and amplitude of the lightwhich is different from the cloak designed with geometricaloptics [26]

The key point for realizing this cloak lies on how todesign an appropriate metamaterial [27 28] to provide theconstitutive parameters of Region II1015840 that include bothzero and infinite values Previous work has shown thatone dimensional metallic silt array can find equivalency tothis nihility medium right at the Fabry-Perot (FP) resonantfrequency [25 29] However this FP resonant frequency willbe related with the propagation length in the u1015840 directionsmaking it not suitable for the realization of the Region II1015840In order to do this we should first understand the physicalnature of this medium It is obvious that in Region II1015840electromagnetic (EM) waves cannot propagate along the v1015840direction because 120576119906119887 = infin and the material behaves like aperfect electric conductor (PEC) However since 120576V119887 = 0 120583

119908119887 =

0EMwaves can propagate along the u1015840 direction with infinitephase velocity or zero phase delay The Region II1015840 mediumbehaves like a sampler that samples the phase and amplitudeof EMwaves along one boundary (eg the white linemarked 1in Figure 1(c)) and then transfers this information includingphase and amplitude to the other boundary (eg the whiteline marked 2 in Figure 1(c)) or vice versa In fact the wholesquare of side 1198872 in the virtual space is transformed into I1015840-type regions in the physical space The II1015840-type regions arenihility spaces that play the role of connecting each I1015840-typeregion

With this profound physical understanding in mind wesuccessfully design a metamaterial composed of metallicchannel and slits arrays that exhibit the same behavior ofthe II1015840-type medium (see Figure 2(b)) In this metamaterialthe effective relative permittivity is 120576V119887 = 1198990

2 minus 1198882(41198912ℎ2)where 1198990 is the refraction index of air 119888 is the speed oflight in the free space 119891 is the frequency and ℎ is theheight of the metal channel [27] Therefore at the cut-offfrequency of the metallic channels 120576V119887 = 0 If the width ofthe channels is sufficiently narrow the EM waves can tunnelthrough the waveguide with almost total transmission andzero phase delay behaving exactly like the epsilon-mu-near-zero medium [30ndash32] We apply a well-established retrievalprocess [33] to obtain the effective constitutive parametersshowing that around 100GHz both 120576V119887 and 120583

119908119887 are exactly

zero This metallic channel array metamaterial automaticallyfulfills the requirement of 120576119906119887 = infin because EM waves areprevented to propagate along the v1015840 direction by the PECwallsTherefore we achieve the singular parameter by simplymaking themost of the nature of the conductivemetals at lowfrequency

In order to destroy the spoof surface plasmon polaritonsinduced by the metallic channel arrays [34ndash36] we add somesplits along the v1015840 direction on the surface of Region II1015840 (seethe inset of Figure 2(a)) From a metamaterial perspectivethis slit array has a macroscopic effective EM responsenamely 120576119906119887 = 119886119908 120583

119908119887 = 119908119886 where 119886 and 119908 are respectively

Research 3

`

Virtual space

Physical space

(a) (b)

b1

b2

ubvb

ua

va

III

II

I

aua

ubvb

I

II

IIIa

1

2

Figure 1 (a) Schematic view of the proposed omnidirectional cloak with extreme parameters (b) Designing an omnidirectional cloak basedon transformation optics The space between the big square and the small one in virtual space is transformed into corresponding regions inphysical spaceThese regions are divided into eight triangular segments that can be grouped into two groups Region I (I1015840) and Region II (II1015840)The green lines represent trajectories of rays The blue square is the hidden area

the period and width of the slits When 119908 ≪ 119886 ≪ 1205820 then120576119906119887 997888rarr infin and 120583119908119887 997888rarr 0 therefore this structure fulfillsexactly the parameter requirements in Region II1015840 In thisexperimental realization we choose 119886=235mm 119908=05mmand 119897=100mmThese self-supportingmetallic channel arraysis fabricated by a standard commercial 3D printing using analuminum alloy

The constitutive parameters of medium for Region I1015840is finite ie 120576119906119886 = 05 120576

V119886 = 2 and 120583

119908119886 = 2 For easy

of realization we use an ultrathin cut-wire metamaterial toconstruct this medium as shown in Figure 2(c) The cutwires are print on an ultrathin printed circuit board (PCB)(01mm Teflon woven glass fabric copper-clad laminate witha permittivity of 25 and tg120575 lt 0001 at 10GHz) Then weattach them on polymer foam sheets (106mmRohacell 71HFwith a permittivity of 11 and tg120575 lt 00016 at 100GHz) andstack them layer-by-layer constructing a bulky metamaterialThe retrieved effective constitutive parameters at 100GHz120576119906119886 = 1 120576

V119886 = 4 120583

119908119886 = 1 fulfilling the parameters requirement

for Region I1015840 Physically at frequencies much lower than theresonance frequency the cut-wire metamaterial provides aparaelectric response along the cut wires (120576V119886 gt 1) and theinteraction with the electric field perpendicular to the cutwires is very weak (120576119906119886 = 1) In addition as the cut wirescreate only an electric response the effective permeability

remains almost unity (120583119908119886 = 1) We can obtain the desiredEM responses by tuning the geometries of the cut wires ie1199011 1199012 and 1198971

It is interesting to notice that both of the conjoint meta-materials are non-resonant whose benefits are threefoldFirst as the EM responses of the metamaterials are far belowresonance the losses are inherently low Second the sizesof the unit cells can be as small as needed ie we canshrink the sizes of unit cells proportionally in the 119906V-planeand the constitutive parameters at 100GHz wonrsquot changeThus if the unit cells are small enough at the intersection ofdifferent regions all of the boundaries can match very wellwith negligible voids in the implementation Last but notleast while resonant metamaterials are generally sensitive tosmall fabrication imperfections thatmay dramatically changetheir EM properties nonresonant metamaterials [37] arereliably robust to parametric uncertainties

The fabricated cloak sample (shown in Figure 3) is 80mmby 80mm with eight unit cells (the height of each unit cellis 17mm) in the z-direction With a preliminary simulation(see Supplementary Information) we find that the cloak canbe very robust with only a few unit cells in the z-direction Onthe one hand as the metallic channel metamaterial confinesthe energy inside the couplings between neighboring chan-nels in the z-direction are quite weak On the other hand the

4 Research

HEk

Hidden region

(a)

(b)

minus2

4

0

2

minus4 0

2

4

6

(c)

l1

h1h1

p2

p1

wb

wb

vb

vb

ub

wa

va

ua

wa

va

ua

ub

uavawa

vbwb

h

bw1

w

l

a

90 10095 100 105 110Frequency (GHz)Frequency (GHz)

Figure 2 Unit cell designs of the omnidirectional metamaterial cloak (a) Designed metamaterial cloak (b) Unit cell and the correspondingeffective constitutive parameters of the extreme metamaterial Here ℎ=150mm ℎ1=160mm 119887=50mm and the width of the slits is1199081=025mm (c) Unit cell and the corresponding effective constitutive parameters of the non-extreme metamaterial Here 1199011= 60mm1199012=235mm and 1198971=50mm

cut-wire metamaterial is also not sensitive to the variances inthe z-direction

The proposed cloak works for a background with 120576119887119892 = 2and 120583119887119892 = 05 ie a refractive index of n=1 the same asthat in air In the measurement for simplicity we replacethe background with air causing some minor reflections atthe outer boundary of the omnidirectional cloak withoutaltering the extreme parameters requirement in the omnidi-rectional cloak These reflections due to the mismatch of theimpedance at the outer boundary can be technically solvedby adding an isotropic gradient metamaterial layer aroundthe cloak whose refraction index stays unity and impedancechanges slowly from that of air to that of the metamaterial ofthe cloak (a detailed design of this gradually changing meta-material layer is included in the Supplementary Information)In fact this method has been applied in some other cloakingdesigns such as the full-parameter unidirectional cloak inwhich a taper structure with gradually changing impedanceis used to couple the EMwaves from the air to the cloak region[19]

We set up an experimental system to measure the 119867119911-field distributions around the cloak in a fully anechoicchamber as shown in Figure 3(c) An open X-band rect-angular waveguide with z-polarized magnetic field locatedat a distance of 50mm away from the cloak is used as

a source A loop antenna with a radius of 4mm is usedas the receiving antenna Both transmitting and receivingantennas are connected to a vector network analyzer (VNA)to obtain the amplitude and phase of the measured field Themeasuring loop antenna is attached to a mechanical arm of a3D measurement platform and can be controlled to move inthe xy planes to point-to-point probe the magnetic field Thescan region (the light-blue rectangle) is 300mm by 236mmwith a resolution of 4mm

In the experiments we measure three cases which arewith an incidence angle of 0∘ (Figures 4(a)ndash4(c)) 225∘(Figures 4(d)ndash4(f)) and 45∘ (Figures 4(g)ndash4(i)) respectivelyThe optimum cloaking frequency of the metamaterial cloakslightly shifts from 100GHz to 98GHz in the implementa-tion From the measured results one can see that placing abared PEC bump in the free space causes strong reflections(backward scattering) and forms a shadow behind the bump(forward scattering) (Figures 4(b) 4(e) and 4(h)) Theforward and backward scatterings are strongly suppressedby covering the bump with a cloak ((Figures 4(c) 4(f)and 4(i)) where both the phase and amplitude of the EMwave are well reconstructed As we get rid of the back-ground some reflections reasonably occur resulting from theimpedance mismatching Note that the bold solid squaresin Figures 4(c) 4(f) and 4(i) represent the unmeasured

Research 5

(b)(a)

Hidden region

(c)

z

yx

3D metal printing

PCB +Foam

80 mm 80 mm

Figure 3 Photographs of the fabricated cloak and scheme of the experiment setup (a) Top view of the metamaterial cloak The extrememetamaterial is realized with the standard commercial 3Dmetal printing technology and the non-extreme one is implemented with the PCB-Foam layered structures (b) Perspective view of the metamaterial cloak with 8 unit cells in the 119911 direction (c) Scheme of the experimentsetup An open X-band rectangular waveguide with z-polarized magnetic field located at a distance of 50mm away from the cloak is usedas a source A loop antenna with a radius of 4mm is used as the receiving antenna Both transmitting and receiving antennas are connectedto a VNA to obtain the amplitude and phase of the measured field The measuring loop antenna is attached to a mechanical arm of a 3Dmeasurement platform and can be controlled to move in the xy planes to point-to-point probe the magnetic field The scan region (thelight-blue rectangle) is 300mm by 236mm with a resolution of 4mm

regions To get complete information in these regions we fillthe unmeasured regions with the simulated magnetic fielddistributions The simulated and experimental results are inexcellent agreement From the results we can exactly see thatthe EM waves are first separated into two beams that passthrough Region I1015840 with a compressed wavelength and tunnelthrough the metallic rectangular waveguide with zero-phasedelay (see the insets) then rejoin again with the same phaseand amplitude as if they had passed directly through theair As the effective singular parameter of 120576V119887 = 0 occurs atcut-off frequency the cloak still works at single frequency

Nevertheless it will be the first step to achieve extremeparameter cloak with omnidirectional cloaking performancerobustly because both Region I1015840 and II1015840 are realized with non-resonant homogeneous metamaterials with pretty simplestructures and the absorptions of these metamaterials areweak

3 Conclusions and Outlook

In summary we design fabricate and experimentally char-acterize the first extreme-parameter omnidirectional cloak

6 Research

(f)

-Max

0

MaxFree space

(a)

(g)

(d)

Bared bump

(b)

(h)

(e)

Cloaked bump

(c)

(i)

45∘

0∘

225

∘

Figure 4 Measured 119867119911 magnetic field distributions near the metamaterial cloak at the optimum cloaking frequency of 98 GHz Fielddistributions for free space bared aluminum cylinder and cloaked aluminum cylinder respectively when EM waves are incident with anangle of 0∘ [(a)ndash(c)] 225∘ [(d)ndash(f)] and 45∘ [(g)ndash(i)] respectively The black-line squares and the gray areas in (b) (e) and (h) represent theunmeasured region and the aluminum cylinder respectively The black arrows in (a) (d) and (g) indicate the incidence of the point sourceof EM waves The bold black line squares and the blue squares in (c) (f) and (i) represent the unmeasured and hidden regions respectivelyThe unmeasured areas are filled with simulated119867119911-field distributions Insets the enlarged image of119867119911-field distributions in the cloak

with non-resonant metamaterials Both of the numerical andexperimental results clearly show the excellent performanceof omnidirectional invisibility of the present cloak verifyingthe rightness of our design The present work providesan important guidance toward the realization of complexfunctionalities with metamaterials and will motivate varioustransformation optics based devices for practical applica-tions such as concentrators [38 39] rotators [40] and opticalillusion [41] apparatuses

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Bin Zheng and Yihao Yang contributed equally to this work

Acknowledgments

The authors thank P Rebusco at Massachusetts Institute ofTechnology for critical reading and editing of themanuscriptWork in Zhejiang University was sponsored by the NationalNatural Science Foundation of China under Grants no61625502 no 61574127 no 61601408 no 61775193 and no11704332 the ZJNSF under Granta no LY17F010008 andno LY19F010015 the Top-Notch Young Talents Program of

China the Fundamental Research Funds for the Central Uni-versities and the Innovation Joint ResearchCenter for Cyber-Physical-Society Work at Ames Laboratory was partiallysupported by the US Department of Energy Office of BasicEnergy Science Division ofMaterials Sciences and Engineer-ing (Ames Laboratory is operated for the US Departmentof Energy by Iowa State University under Contract no DE-AC02-07CH11358) The European Research Council underERCAdvanced Grant no 320081 (PHOTOMETA) supportedwork at FORTH

Supplementary Materials

Figure S1 Full-wave simulation of the full-parameter omni-directional cloak with practical structures (a)-(d) Magneticfield distributions near the present cloak when a point sourceemits EM wave along the side (a) the diagonal (b) anda nonsymmetry plane (c) of the cloak and the side of a10-wavelength-size cloak (d) respectively The blue squaresrepresent the hidden regions (e)-(h)119867119911-field patterns whenboth the PEC object and the cloak are removed from thehomogenous background (i)-(l)119867119911-field patterns when onlythe PEC object is present without the cloakThe gray squaresrepresent the PEC objects (m)-(o) Differential RCS of thepresent cloak (the red line) and bared PEC objects (the blueline) at 100GHz when the EM wave is incident at an angleof 0∘ 45∘ and 225∘ respectively The reduced total RCS of

Research 7

the three cases are 00829 00717 and 00743 respectively(p) Reduced total RCS as a function of frequency at theincidence angle of 45∘ Figure S2 (a)-(b) A mismatched-impedancematerial (120576119887 = 2 120583119887 = 05) covered with the GML(c)-(d) A bared mismatched-impedance material (e)-(f) Amismatched-impedance material (120576119887 = 2120583119887 = 05) coveredwith the discretized GML (g)-(h)The omnidirectional cloakcovered with the GML Figure S3 (a)-(b) A mismatched-impedance material (120576119887 = 2120583119887 = 05) covered withthe discrete GML composed of practical structures (c)-(d)Without the discrete GML (e) Metamaterial unit cell It isa rectangular metallic waveguide loaded with a dielectricmaterial (120576119897 = 25) The period of the unit cell is 119901 andbetween each unit cell is air (f) Geometries (the unit is mm)targeted relative permittivity (120576) and permeability (120583) andeffective relative permittivity (1205761015840) and permeability (1205831015840) ofeach unit cell Here ℎ1=16mm 119886=3mm and 119901=4mm arefixed for all unit cells (Supplementary Materials)

References

[1] AGreenleafM Lassas andGUhlmann ldquoAnisotropic conduc-tivities that cannot be detected by EITrdquo Physiological Measure-ment vol 24 no 2 pp 413ndash419 2003

[2] AAlu andN Engheta ldquoAchieving transparencywith plasmonicand metamaterial coatingsrdquo Physical Review E vol 72 ArticleID 016623 2005

[3] U Leonhardt ldquoOptical conformal mappingrdquo Science vol 312no 5781 pp 1777ndash1780 2006

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] J B Pendry Y Luo and R Zhao ldquoTransforming the opticallandscaperdquo Science vol 348 no 6234 pp 521ndash524 2015

[6] B Kante D Germain and A de Lustrac ldquoExperimen-tal demonstration of a nonmagnetic metamaterial cloak atmicrowave frequenciesrdquo Physical Review B vol 80 Article ID201104 2009

[7] D Schurig J J Mock B J Justice et al ldquoMetamaterialelectromagnetic cloak at microwave frequenciesrdquo Science vol314 no 5801 pp 977ndash980 2006

[8] W Cai U K Chettiar A V Kildishev and V M ShalaevldquoOptical cloaking with metamaterialsrdquo Nature Photonics vol 1no 4 pp 224ndash227 2007

[9] J Li and J B Pendry ldquoHiding under the carpet a new strategyfor cloakingrdquo Physical Review Letters vol 101 no 20 Article ID203901 2008

[10] X Chen Y Luo J Zhang K Jiang J B Pendry and S ZhangldquoMacroscopic invisibility cloaking of visible lightrdquoNature Com-munications vol 2 article no 176 2011

[11] R Liu C Ji J J Mock J Y Chin T J Cui and D R SmithldquoBroadband ground-plane cloakrdquo Science vol 323 no 5912 pp366ndash369 2009

[12] J Valentine J Li T Zentgraf G Bartal and X Zhang ldquoAnoptical cloak made of dielectricsrdquoNature Materials vol 8 no 7pp 568ndash571 2009

[13] L H Gabrielli J Cardenas C B Poitras and M LipsonldquoSilicon nanostructure cloak operating at optical frequenciesrdquoNature Photonics vol 3 no 8 pp 461ndash463 2009

[14] T Ergin N Stenger P Brenner J B Pendry and M WegenerldquoThree-dimensional invisibility cloak at optical wavelengthsrdquoScience vol 328 no 5976 pp 337ndash339 2010

[15] H F Ma and T J Cui ldquoThree-dimensional broadband ground-plane cloak made of metamaterialsrdquo Nature Communicationsvol 1 article no 21 2010

[16] B Zhang Y Luo X Liu and G Barbastathis ldquoMacroscopicinvisibility cloak for visible lightrdquo Physical Review Letters vol106 Article ID 033901 2011

[17] X Sheng H S Chen B I Wu and J A Kong ldquoOne-directional perfect cloak created with homogeneous materialrdquoIEEEMicrowave andWireless Components Letters vol 19 articleno 131 2009

[18] Y Luo J Zhang H Chen L Lixin Ran B IWu and J A KongldquoA rigorous analysis of plane-transformed invisibility cloaksrdquoIEEE Transactions on Antennas and Propagation vol 57 no 12pp 3926ndash3933 2009

[19] N Landy and D R Smith ldquoA full-parameter unidirectionalmetamaterial cloak for microwavesrdquo Nature Materials vol 12no 1 pp 25ndash28 2013

[20] B Zhang H Chen B I Wu Y Luo L Ran and J A KongldquoResponse of a cylindrical invisibility cloak to electromagneticwavesrdquo Physical Review B vol 76 Article ID 121101 2007

[21] J B Pendry A J Holden D J Robbins andW J Stewart ldquoMag-netism from conductors and enhanced nonlinear phenomenardquoIEEE Transactions onMicrowaveTheory and Techniques vol 47no 11 pp 2075ndash2084 1999

[22] H Chen and B Zheng ldquoBroadband polygonal invisibility cloakfor visible lightrdquo Scientific Reports vol 2 article no 255 2012

[23] W Yan M Yan and M Qiu ldquoGeneralized nihility media fromtransformation opticsrdquo Journal of Optics vol 13 Article ID024005 2010

[24] Q He S Xiao X Li and L Zhou ldquoOptic-null mediumrealization and applicationsrdquo Optics Express vol 21 Article ID28948 2013

[25] L Xu Q Wu Y Zhou and H Chen ldquoTransformation deviceswith optical nihility media and reduced realizationsrdquo Frontiersof Physics vol 14 Article ID 42501 2019

[26] J C Howell J B Howell and J S Choi ldquoAmplitude-only pas-sive broadband optical spatial cloaking of very large objectsrdquoApplied Optics vol 53 no 9 p 1958 2014

[27] Y Liu and X Zhang ldquoMetamaterials a new frontier of scienceand technologyrdquo Chemical Society Reviews vol 40 no 5 pp2494ndash2507 2011

[28] CM Soukoulis andMWegener ldquoPast achievements and futurechallenges in the development of three-dimensional photonicmetamaterialsrdquoNature Photonics vol 5 no 9 pp 523ndash530 2011

[29] M M Sadeghi S Li L Xu B Hou and H Chen ldquoTransforma-tion optics with Fabry-Perot resonancesrdquo Scientific Reports vol5 Article ID 8680 2015

[30] B Edwards A Alu M E Young M Silveirinha and NEngheta ldquoExperimental verification of epsilon-near-zerometa-material coupling and energy squeezing using a microwavewaveguiderdquo Physical Review Letters vol 100 no 3 Article ID033903 2008

[31] R Liu Q Cheng T Hand et al ldquoExperimental demonstra-tion of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequenciesrdquo Physical ReviewLetters vol 100 no 2 Article ID 023903 2008

Research 3

`

Virtual space

Physical space

(a) (b)

b1

b2

ubvb

ua

va

III

II

I

aua

ubvb

I

II

IIIa

1

2

Figure 1 (a) Schematic view of the proposed omnidirectional cloak with extreme parameters (b) Designing an omnidirectional cloak basedon transformation optics The space between the big square and the small one in virtual space is transformed into corresponding regions inphysical spaceThese regions are divided into eight triangular segments that can be grouped into two groups Region I (I1015840) and Region II (II1015840)The green lines represent trajectories of rays The blue square is the hidden area

the period and width of the slits When 119908 ≪ 119886 ≪ 1205820 then120576119906119887 997888rarr infin and 120583119908119887 997888rarr 0 therefore this structure fulfillsexactly the parameter requirements in Region II1015840 In thisexperimental realization we choose 119886=235mm 119908=05mmand 119897=100mmThese self-supportingmetallic channel arraysis fabricated by a standard commercial 3D printing using analuminum alloy

The constitutive parameters of medium for Region I1015840is finite ie 120576119906119886 = 05 120576

V119886 = 2 and 120583

119908119886 = 2 For easy

of realization we use an ultrathin cut-wire metamaterial toconstruct this medium as shown in Figure 2(c) The cutwires are print on an ultrathin printed circuit board (PCB)(01mm Teflon woven glass fabric copper-clad laminate witha permittivity of 25 and tg120575 lt 0001 at 10GHz) Then weattach them on polymer foam sheets (106mmRohacell 71HFwith a permittivity of 11 and tg120575 lt 00016 at 100GHz) andstack them layer-by-layer constructing a bulky metamaterialThe retrieved effective constitutive parameters at 100GHz120576119906119886 = 1 120576

V119886 = 4 120583

119908119886 = 1 fulfilling the parameters requirement

for Region I1015840 Physically at frequencies much lower than theresonance frequency the cut-wire metamaterial provides aparaelectric response along the cut wires (120576V119886 gt 1) and theinteraction with the electric field perpendicular to the cutwires is very weak (120576119906119886 = 1) In addition as the cut wirescreate only an electric response the effective permeability

remains almost unity (120583119908119886 = 1) We can obtain the desiredEM responses by tuning the geometries of the cut wires ie1199011 1199012 and 1198971

It is interesting to notice that both of the conjoint meta-materials are non-resonant whose benefits are threefoldFirst as the EM responses of the metamaterials are far belowresonance the losses are inherently low Second the sizesof the unit cells can be as small as needed ie we canshrink the sizes of unit cells proportionally in the 119906V-planeand the constitutive parameters at 100GHz wonrsquot changeThus if the unit cells are small enough at the intersection ofdifferent regions all of the boundaries can match very wellwith negligible voids in the implementation Last but notleast while resonant metamaterials are generally sensitive tosmall fabrication imperfections thatmay dramatically changetheir EM properties nonresonant metamaterials [37] arereliably robust to parametric uncertainties

The fabricated cloak sample (shown in Figure 3) is 80mmby 80mm with eight unit cells (the height of each unit cellis 17mm) in the z-direction With a preliminary simulation(see Supplementary Information) we find that the cloak canbe very robust with only a few unit cells in the z-direction Onthe one hand as the metallic channel metamaterial confinesthe energy inside the couplings between neighboring chan-nels in the z-direction are quite weak On the other hand the

4 Research

HEk

Hidden region

(a)

(b)

minus2

4

0

2

minus4 0

2

4

6

(c)

l1

h1h1

p2

p1

wb

wb

vb

vb

ub

wa

va

ua

wa

va

ua

ub

uavawa

vbwb

h

bw1

w

l

a

90 10095 100 105 110Frequency (GHz)Frequency (GHz)

Figure 2 Unit cell designs of the omnidirectional metamaterial cloak (a) Designed metamaterial cloak (b) Unit cell and the correspondingeffective constitutive parameters of the extreme metamaterial Here ℎ=150mm ℎ1=160mm 119887=50mm and the width of the slits is1199081=025mm (c) Unit cell and the corresponding effective constitutive parameters of the non-extreme metamaterial Here 1199011= 60mm1199012=235mm and 1198971=50mm

cut-wire metamaterial is also not sensitive to the variances inthe z-direction

The proposed cloak works for a background with 120576119887119892 = 2and 120583119887119892 = 05 ie a refractive index of n=1 the same asthat in air In the measurement for simplicity we replacethe background with air causing some minor reflections atthe outer boundary of the omnidirectional cloak withoutaltering the extreme parameters requirement in the omnidi-rectional cloak These reflections due to the mismatch of theimpedance at the outer boundary can be technically solvedby adding an isotropic gradient metamaterial layer aroundthe cloak whose refraction index stays unity and impedancechanges slowly from that of air to that of the metamaterial ofthe cloak (a detailed design of this gradually changing meta-material layer is included in the Supplementary Information)In fact this method has been applied in some other cloakingdesigns such as the full-parameter unidirectional cloak inwhich a taper structure with gradually changing impedanceis used to couple the EMwaves from the air to the cloak region[19]

We set up an experimental system to measure the 119867119911-field distributions around the cloak in a fully anechoicchamber as shown in Figure 3(c) An open X-band rect-angular waveguide with z-polarized magnetic field locatedat a distance of 50mm away from the cloak is used as

a source A loop antenna with a radius of 4mm is usedas the receiving antenna Both transmitting and receivingantennas are connected to a vector network analyzer (VNA)to obtain the amplitude and phase of the measured field Themeasuring loop antenna is attached to a mechanical arm of a3D measurement platform and can be controlled to move inthe xy planes to point-to-point probe the magnetic field Thescan region (the light-blue rectangle) is 300mm by 236mmwith a resolution of 4mm

In the experiments we measure three cases which arewith an incidence angle of 0∘ (Figures 4(a)ndash4(c)) 225∘(Figures 4(d)ndash4(f)) and 45∘ (Figures 4(g)ndash4(i)) respectivelyThe optimum cloaking frequency of the metamaterial cloakslightly shifts from 100GHz to 98GHz in the implementa-tion From the measured results one can see that placing abared PEC bump in the free space causes strong reflections(backward scattering) and forms a shadow behind the bump(forward scattering) (Figures 4(b) 4(e) and 4(h)) Theforward and backward scatterings are strongly suppressedby covering the bump with a cloak ((Figures 4(c) 4(f)and 4(i)) where both the phase and amplitude of the EMwave are well reconstructed As we get rid of the back-ground some reflections reasonably occur resulting from theimpedance mismatching Note that the bold solid squaresin Figures 4(c) 4(f) and 4(i) represent the unmeasured

Research 5

(b)(a)

Hidden region

(c)

z

yx

3D metal printing

PCB +Foam

80 mm 80 mm

Figure 3 Photographs of the fabricated cloak and scheme of the experiment setup (a) Top view of the metamaterial cloak The extrememetamaterial is realized with the standard commercial 3Dmetal printing technology and the non-extreme one is implemented with the PCB-Foam layered structures (b) Perspective view of the metamaterial cloak with 8 unit cells in the 119911 direction (c) Scheme of the experimentsetup An open X-band rectangular waveguide with z-polarized magnetic field located at a distance of 50mm away from the cloak is usedas a source A loop antenna with a radius of 4mm is used as the receiving antenna Both transmitting and receiving antennas are connectedto a VNA to obtain the amplitude and phase of the measured field The measuring loop antenna is attached to a mechanical arm of a 3Dmeasurement platform and can be controlled to move in the xy planes to point-to-point probe the magnetic field The scan region (thelight-blue rectangle) is 300mm by 236mm with a resolution of 4mm

regions To get complete information in these regions we fillthe unmeasured regions with the simulated magnetic fielddistributions The simulated and experimental results are inexcellent agreement From the results we can exactly see thatthe EM waves are first separated into two beams that passthrough Region I1015840 with a compressed wavelength and tunnelthrough the metallic rectangular waveguide with zero-phasedelay (see the insets) then rejoin again with the same phaseand amplitude as if they had passed directly through theair As the effective singular parameter of 120576V119887 = 0 occurs atcut-off frequency the cloak still works at single frequency

Nevertheless it will be the first step to achieve extremeparameter cloak with omnidirectional cloaking performancerobustly because both Region I1015840 and II1015840 are realized with non-resonant homogeneous metamaterials with pretty simplestructures and the absorptions of these metamaterials areweak

3 Conclusions and Outlook

In summary we design fabricate and experimentally char-acterize the first extreme-parameter omnidirectional cloak

6 Research

(f)

-Max

0

MaxFree space

(a)

(g)

(d)

Bared bump

(b)

(h)

(e)

Cloaked bump

(c)

(i)

45∘

0∘

225

∘

Figure 4 Measured 119867119911 magnetic field distributions near the metamaterial cloak at the optimum cloaking frequency of 98 GHz Fielddistributions for free space bared aluminum cylinder and cloaked aluminum cylinder respectively when EM waves are incident with anangle of 0∘ [(a)ndash(c)] 225∘ [(d)ndash(f)] and 45∘ [(g)ndash(i)] respectively The black-line squares and the gray areas in (b) (e) and (h) represent theunmeasured region and the aluminum cylinder respectively The black arrows in (a) (d) and (g) indicate the incidence of the point sourceof EM waves The bold black line squares and the blue squares in (c) (f) and (i) represent the unmeasured and hidden regions respectivelyThe unmeasured areas are filled with simulated119867119911-field distributions Insets the enlarged image of119867119911-field distributions in the cloak

with non-resonant metamaterials Both of the numerical andexperimental results clearly show the excellent performanceof omnidirectional invisibility of the present cloak verifyingthe rightness of our design The present work providesan important guidance toward the realization of complexfunctionalities with metamaterials and will motivate varioustransformation optics based devices for practical applica-tions such as concentrators [38 39] rotators [40] and opticalillusion [41] apparatuses

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Bin Zheng and Yihao Yang contributed equally to this work

Acknowledgments

The authors thank P Rebusco at Massachusetts Institute ofTechnology for critical reading and editing of themanuscriptWork in Zhejiang University was sponsored by the NationalNatural Science Foundation of China under Grants no61625502 no 61574127 no 61601408 no 61775193 and no11704332 the ZJNSF under Granta no LY17F010008 andno LY19F010015 the Top-Notch Young Talents Program of

China the Fundamental Research Funds for the Central Uni-versities and the Innovation Joint ResearchCenter for Cyber-Physical-Society Work at Ames Laboratory was partiallysupported by the US Department of Energy Office of BasicEnergy Science Division ofMaterials Sciences and Engineer-ing (Ames Laboratory is operated for the US Departmentof Energy by Iowa State University under Contract no DE-AC02-07CH11358) The European Research Council underERCAdvanced Grant no 320081 (PHOTOMETA) supportedwork at FORTH

Supplementary Materials

Figure S1 Full-wave simulation of the full-parameter omni-directional cloak with practical structures (a)-(d) Magneticfield distributions near the present cloak when a point sourceemits EM wave along the side (a) the diagonal (b) anda nonsymmetry plane (c) of the cloak and the side of a10-wavelength-size cloak (d) respectively The blue squaresrepresent the hidden regions (e)-(h)119867119911-field patterns whenboth the PEC object and the cloak are removed from thehomogenous background (i)-(l)119867119911-field patterns when onlythe PEC object is present without the cloakThe gray squaresrepresent the PEC objects (m)-(o) Differential RCS of thepresent cloak (the red line) and bared PEC objects (the blueline) at 100GHz when the EM wave is incident at an angleof 0∘ 45∘ and 225∘ respectively The reduced total RCS of

Research 7

the three cases are 00829 00717 and 00743 respectively(p) Reduced total RCS as a function of frequency at theincidence angle of 45∘ Figure S2 (a)-(b) A mismatched-impedancematerial (120576119887 = 2 120583119887 = 05) covered with the GML(c)-(d) A bared mismatched-impedance material (e)-(f) Amismatched-impedance material (120576119887 = 2120583119887 = 05) coveredwith the discretized GML (g)-(h)The omnidirectional cloakcovered with the GML Figure S3 (a)-(b) A mismatched-impedance material (120576119887 = 2120583119887 = 05) covered withthe discrete GML composed of practical structures (c)-(d)Without the discrete GML (e) Metamaterial unit cell It isa rectangular metallic waveguide loaded with a dielectricmaterial (120576119897 = 25) The period of the unit cell is 119901 andbetween each unit cell is air (f) Geometries (the unit is mm)targeted relative permittivity (120576) and permeability (120583) andeffective relative permittivity (1205761015840) and permeability (1205831015840) ofeach unit cell Here ℎ1=16mm 119886=3mm and 119901=4mm arefixed for all unit cells (Supplementary Materials)

References

[1] AGreenleafM Lassas andGUhlmann ldquoAnisotropic conduc-tivities that cannot be detected by EITrdquo Physiological Measure-ment vol 24 no 2 pp 413ndash419 2003

[2] AAlu andN Engheta ldquoAchieving transparencywith plasmonicand metamaterial coatingsrdquo Physical Review E vol 72 ArticleID 016623 2005

[3] U Leonhardt ldquoOptical conformal mappingrdquo Science vol 312no 5781 pp 1777ndash1780 2006

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] J B Pendry Y Luo and R Zhao ldquoTransforming the opticallandscaperdquo Science vol 348 no 6234 pp 521ndash524 2015

[6] B Kante D Germain and A de Lustrac ldquoExperimen-tal demonstration of a nonmagnetic metamaterial cloak atmicrowave frequenciesrdquo Physical Review B vol 80 Article ID201104 2009

[7] D Schurig J J Mock B J Justice et al ldquoMetamaterialelectromagnetic cloak at microwave frequenciesrdquo Science vol314 no 5801 pp 977ndash980 2006

[8] W Cai U K Chettiar A V Kildishev and V M ShalaevldquoOptical cloaking with metamaterialsrdquo Nature Photonics vol 1no 4 pp 224ndash227 2007

[9] J Li and J B Pendry ldquoHiding under the carpet a new strategyfor cloakingrdquo Physical Review Letters vol 101 no 20 Article ID203901 2008

[10] X Chen Y Luo J Zhang K Jiang J B Pendry and S ZhangldquoMacroscopic invisibility cloaking of visible lightrdquoNature Com-munications vol 2 article no 176 2011

[11] R Liu C Ji J J Mock J Y Chin T J Cui and D R SmithldquoBroadband ground-plane cloakrdquo Science vol 323 no 5912 pp366ndash369 2009

[12] J Valentine J Li T Zentgraf G Bartal and X Zhang ldquoAnoptical cloak made of dielectricsrdquoNature Materials vol 8 no 7pp 568ndash571 2009

[13] L H Gabrielli J Cardenas C B Poitras and M LipsonldquoSilicon nanostructure cloak operating at optical frequenciesrdquoNature Photonics vol 3 no 8 pp 461ndash463 2009

[14] T Ergin N Stenger P Brenner J B Pendry and M WegenerldquoThree-dimensional invisibility cloak at optical wavelengthsrdquoScience vol 328 no 5976 pp 337ndash339 2010

[15] H F Ma and T J Cui ldquoThree-dimensional broadband ground-plane cloak made of metamaterialsrdquo Nature Communicationsvol 1 article no 21 2010

[16] B Zhang Y Luo X Liu and G Barbastathis ldquoMacroscopicinvisibility cloak for visible lightrdquo Physical Review Letters vol106 Article ID 033901 2011

[17] X Sheng H S Chen B I Wu and J A Kong ldquoOne-directional perfect cloak created with homogeneous materialrdquoIEEEMicrowave andWireless Components Letters vol 19 articleno 131 2009

[18] Y Luo J Zhang H Chen L Lixin Ran B IWu and J A KongldquoA rigorous analysis of plane-transformed invisibility cloaksrdquoIEEE Transactions on Antennas and Propagation vol 57 no 12pp 3926ndash3933 2009

[19] N Landy and D R Smith ldquoA full-parameter unidirectionalmetamaterial cloak for microwavesrdquo Nature Materials vol 12no 1 pp 25ndash28 2013

[20] B Zhang H Chen B I Wu Y Luo L Ran and J A KongldquoResponse of a cylindrical invisibility cloak to electromagneticwavesrdquo Physical Review B vol 76 Article ID 121101 2007

[21] J B Pendry A J Holden D J Robbins andW J Stewart ldquoMag-netism from conductors and enhanced nonlinear phenomenardquoIEEE Transactions onMicrowaveTheory and Techniques vol 47no 11 pp 2075ndash2084 1999

[22] H Chen and B Zheng ldquoBroadband polygonal invisibility cloakfor visible lightrdquo Scientific Reports vol 2 article no 255 2012

[23] W Yan M Yan and M Qiu ldquoGeneralized nihility media fromtransformation opticsrdquo Journal of Optics vol 13 Article ID024005 2010

[24] Q He S Xiao X Li and L Zhou ldquoOptic-null mediumrealization and applicationsrdquo Optics Express vol 21 Article ID28948 2013

[25] L Xu Q Wu Y Zhou and H Chen ldquoTransformation deviceswith optical nihility media and reduced realizationsrdquo Frontiersof Physics vol 14 Article ID 42501 2019

[26] J C Howell J B Howell and J S Choi ldquoAmplitude-only pas-sive broadband optical spatial cloaking of very large objectsrdquoApplied Optics vol 53 no 9 p 1958 2014

[27] Y Liu and X Zhang ldquoMetamaterials a new frontier of scienceand technologyrdquo Chemical Society Reviews vol 40 no 5 pp2494ndash2507 2011

[28] CM Soukoulis andMWegener ldquoPast achievements and futurechallenges in the development of three-dimensional photonicmetamaterialsrdquoNature Photonics vol 5 no 9 pp 523ndash530 2011

[29] M M Sadeghi S Li L Xu B Hou and H Chen ldquoTransforma-tion optics with Fabry-Perot resonancesrdquo Scientific Reports vol5 Article ID 8680 2015

[30] B Edwards A Alu M E Young M Silveirinha and NEngheta ldquoExperimental verification of epsilon-near-zerometa-material coupling and energy squeezing using a microwavewaveguiderdquo Physical Review Letters vol 100 no 3 Article ID033903 2008

[31] R Liu Q Cheng T Hand et al ldquoExperimental demonstra-tion of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequenciesrdquo Physical ReviewLetters vol 100 no 2 Article ID 023903 2008

4 Research

HEk

Hidden region

(a)

(b)

minus2

4

0

2

minus4 0

2

4

6

(c)

l1

h1h1

p2

p1

wb

wb

vb

vb

ub

wa

va

ua

wa

va

ua

ub

uavawa

vbwb

h

bw1

w

l

a

90 10095 100 105 110Frequency (GHz)Frequency (GHz)

Figure 2 Unit cell designs of the omnidirectional metamaterial cloak (a) Designed metamaterial cloak (b) Unit cell and the correspondingeffective constitutive parameters of the extreme metamaterial Here ℎ=150mm ℎ1=160mm 119887=50mm and the width of the slits is1199081=025mm (c) Unit cell and the corresponding effective constitutive parameters of the non-extreme metamaterial Here 1199011= 60mm1199012=235mm and 1198971=50mm

cut-wire metamaterial is also not sensitive to the variances inthe z-direction

The proposed cloak works for a background with 120576119887119892 = 2and 120583119887119892 = 05 ie a refractive index of n=1 the same asthat in air In the measurement for simplicity we replacethe background with air causing some minor reflections atthe outer boundary of the omnidirectional cloak withoutaltering the extreme parameters requirement in the omnidi-rectional cloak These reflections due to the mismatch of theimpedance at the outer boundary can be technically solvedby adding an isotropic gradient metamaterial layer aroundthe cloak whose refraction index stays unity and impedancechanges slowly from that of air to that of the metamaterial ofthe cloak (a detailed design of this gradually changing meta-material layer is included in the Supplementary Information)In fact this method has been applied in some other cloakingdesigns such as the full-parameter unidirectional cloak inwhich a taper structure with gradually changing impedanceis used to couple the EMwaves from the air to the cloak region[19]

We set up an experimental system to measure the 119867119911-field distributions around the cloak in a fully anechoicchamber as shown in Figure 3(c) An open X-band rect-angular waveguide with z-polarized magnetic field locatedat a distance of 50mm away from the cloak is used as

a source A loop antenna with a radius of 4mm is usedas the receiving antenna Both transmitting and receivingantennas are connected to a vector network analyzer (VNA)to obtain the amplitude and phase of the measured field Themeasuring loop antenna is attached to a mechanical arm of a3D measurement platform and can be controlled to move inthe xy planes to point-to-point probe the magnetic field Thescan region (the light-blue rectangle) is 300mm by 236mmwith a resolution of 4mm

In the experiments we measure three cases which arewith an incidence angle of 0∘ (Figures 4(a)ndash4(c)) 225∘(Figures 4(d)ndash4(f)) and 45∘ (Figures 4(g)ndash4(i)) respectivelyThe optimum cloaking frequency of the metamaterial cloakslightly shifts from 100GHz to 98GHz in the implementa-tion From the measured results one can see that placing abared PEC bump in the free space causes strong reflections(backward scattering) and forms a shadow behind the bump(forward scattering) (Figures 4(b) 4(e) and 4(h)) Theforward and backward scatterings are strongly suppressedby covering the bump with a cloak ((Figures 4(c) 4(f)and 4(i)) where both the phase and amplitude of the EMwave are well reconstructed As we get rid of the back-ground some reflections reasonably occur resulting from theimpedance mismatching Note that the bold solid squaresin Figures 4(c) 4(f) and 4(i) represent the unmeasured

Research 5

(b)(a)

Hidden region

(c)

z

yx

3D metal printing

PCB +Foam

80 mm 80 mm

Figure 3 Photographs of the fabricated cloak and scheme of the experiment setup (a) Top view of the metamaterial cloak The extrememetamaterial is realized with the standard commercial 3Dmetal printing technology and the non-extreme one is implemented with the PCB-Foam layered structures (b) Perspective view of the metamaterial cloak with 8 unit cells in the 119911 direction (c) Scheme of the experimentsetup An open X-band rectangular waveguide with z-polarized magnetic field located at a distance of 50mm away from the cloak is usedas a source A loop antenna with a radius of 4mm is used as the receiving antenna Both transmitting and receiving antennas are connectedto a VNA to obtain the amplitude and phase of the measured field The measuring loop antenna is attached to a mechanical arm of a 3Dmeasurement platform and can be controlled to move in the xy planes to point-to-point probe the magnetic field The scan region (thelight-blue rectangle) is 300mm by 236mm with a resolution of 4mm

regions To get complete information in these regions we fillthe unmeasured regions with the simulated magnetic fielddistributions The simulated and experimental results are inexcellent agreement From the results we can exactly see thatthe EM waves are first separated into two beams that passthrough Region I1015840 with a compressed wavelength and tunnelthrough the metallic rectangular waveguide with zero-phasedelay (see the insets) then rejoin again with the same phaseand amplitude as if they had passed directly through theair As the effective singular parameter of 120576V119887 = 0 occurs atcut-off frequency the cloak still works at single frequency

Nevertheless it will be the first step to achieve extremeparameter cloak with omnidirectional cloaking performancerobustly because both Region I1015840 and II1015840 are realized with non-resonant homogeneous metamaterials with pretty simplestructures and the absorptions of these metamaterials areweak

3 Conclusions and Outlook

In summary we design fabricate and experimentally char-acterize the first extreme-parameter omnidirectional cloak

6 Research

(f)

-Max

0

MaxFree space

(a)

(g)

(d)

Bared bump

(b)

(h)

(e)

Cloaked bump

(c)

(i)

45∘

0∘

225

∘

Figure 4 Measured 119867119911 magnetic field distributions near the metamaterial cloak at the optimum cloaking frequency of 98 GHz Fielddistributions for free space bared aluminum cylinder and cloaked aluminum cylinder respectively when EM waves are incident with anangle of 0∘ [(a)ndash(c)] 225∘ [(d)ndash(f)] and 45∘ [(g)ndash(i)] respectively The black-line squares and the gray areas in (b) (e) and (h) represent theunmeasured region and the aluminum cylinder respectively The black arrows in (a) (d) and (g) indicate the incidence of the point sourceof EM waves The bold black line squares and the blue squares in (c) (f) and (i) represent the unmeasured and hidden regions respectivelyThe unmeasured areas are filled with simulated119867119911-field distributions Insets the enlarged image of119867119911-field distributions in the cloak

with non-resonant metamaterials Both of the numerical andexperimental results clearly show the excellent performanceof omnidirectional invisibility of the present cloak verifyingthe rightness of our design The present work providesan important guidance toward the realization of complexfunctionalities with metamaterials and will motivate varioustransformation optics based devices for practical applica-tions such as concentrators [38 39] rotators [40] and opticalillusion [41] apparatuses

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Bin Zheng and Yihao Yang contributed equally to this work

Acknowledgments

The authors thank P Rebusco at Massachusetts Institute ofTechnology for critical reading and editing of themanuscriptWork in Zhejiang University was sponsored by the NationalNatural Science Foundation of China under Grants no61625502 no 61574127 no 61601408 no 61775193 and no11704332 the ZJNSF under Granta no LY17F010008 andno LY19F010015 the Top-Notch Young Talents Program of

China the Fundamental Research Funds for the Central Uni-versities and the Innovation Joint ResearchCenter for Cyber-Physical-Society Work at Ames Laboratory was partiallysupported by the US Department of Energy Office of BasicEnergy Science Division ofMaterials Sciences and Engineer-ing (Ames Laboratory is operated for the US Departmentof Energy by Iowa State University under Contract no DE-AC02-07CH11358) The European Research Council underERCAdvanced Grant no 320081 (PHOTOMETA) supportedwork at FORTH

Supplementary Materials

Figure S1 Full-wave simulation of the full-parameter omni-directional cloak with practical structures (a)-(d) Magneticfield distributions near the present cloak when a point sourceemits EM wave along the side (a) the diagonal (b) anda nonsymmetry plane (c) of the cloak and the side of a10-wavelength-size cloak (d) respectively The blue squaresrepresent the hidden regions (e)-(h)119867119911-field patterns whenboth the PEC object and the cloak are removed from thehomogenous background (i)-(l)119867119911-field patterns when onlythe PEC object is present without the cloakThe gray squaresrepresent the PEC objects (m)-(o) Differential RCS of thepresent cloak (the red line) and bared PEC objects (the blueline) at 100GHz when the EM wave is incident at an angleof 0∘ 45∘ and 225∘ respectively The reduced total RCS of

Research 7

the three cases are 00829 00717 and 00743 respectively(p) Reduced total RCS as a function of frequency at theincidence angle of 45∘ Figure S2 (a)-(b) A mismatched-impedancematerial (120576119887 = 2 120583119887 = 05) covered with the GML(c)-(d) A bared mismatched-impedance material (e)-(f) Amismatched-impedance material (120576119887 = 2120583119887 = 05) coveredwith the discretized GML (g)-(h)The omnidirectional cloakcovered with the GML Figure S3 (a)-(b) A mismatched-impedance material (120576119887 = 2120583119887 = 05) covered withthe discrete GML composed of practical structures (c)-(d)Without the discrete GML (e) Metamaterial unit cell It isa rectangular metallic waveguide loaded with a dielectricmaterial (120576119897 = 25) The period of the unit cell is 119901 andbetween each unit cell is air (f) Geometries (the unit is mm)targeted relative permittivity (120576) and permeability (120583) andeffective relative permittivity (1205761015840) and permeability (1205831015840) ofeach unit cell Here ℎ1=16mm 119886=3mm and 119901=4mm arefixed for all unit cells (Supplementary Materials)

References

[1] AGreenleafM Lassas andGUhlmann ldquoAnisotropic conduc-tivities that cannot be detected by EITrdquo Physiological Measure-ment vol 24 no 2 pp 413ndash419 2003

[2] AAlu andN Engheta ldquoAchieving transparencywith plasmonicand metamaterial coatingsrdquo Physical Review E vol 72 ArticleID 016623 2005

[3] U Leonhardt ldquoOptical conformal mappingrdquo Science vol 312no 5781 pp 1777ndash1780 2006

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] J B Pendry Y Luo and R Zhao ldquoTransforming the opticallandscaperdquo Science vol 348 no 6234 pp 521ndash524 2015

[6] B Kante D Germain and A de Lustrac ldquoExperimen-tal demonstration of a nonmagnetic metamaterial cloak atmicrowave frequenciesrdquo Physical Review B vol 80 Article ID201104 2009

[7] D Schurig J J Mock B J Justice et al ldquoMetamaterialelectromagnetic cloak at microwave frequenciesrdquo Science vol314 no 5801 pp 977ndash980 2006

[8] W Cai U K Chettiar A V Kildishev and V M ShalaevldquoOptical cloaking with metamaterialsrdquo Nature Photonics vol 1no 4 pp 224ndash227 2007

[9] J Li and J B Pendry ldquoHiding under the carpet a new strategyfor cloakingrdquo Physical Review Letters vol 101 no 20 Article ID203901 2008

[10] X Chen Y Luo J Zhang K Jiang J B Pendry and S ZhangldquoMacroscopic invisibility cloaking of visible lightrdquoNature Com-munications vol 2 article no 176 2011

[11] R Liu C Ji J J Mock J Y Chin T J Cui and D R SmithldquoBroadband ground-plane cloakrdquo Science vol 323 no 5912 pp366ndash369 2009

[12] J Valentine J Li T Zentgraf G Bartal and X Zhang ldquoAnoptical cloak made of dielectricsrdquoNature Materials vol 8 no 7pp 568ndash571 2009

[13] L H Gabrielli J Cardenas C B Poitras and M LipsonldquoSilicon nanostructure cloak operating at optical frequenciesrdquoNature Photonics vol 3 no 8 pp 461ndash463 2009

[14] T Ergin N Stenger P Brenner J B Pendry and M WegenerldquoThree-dimensional invisibility cloak at optical wavelengthsrdquoScience vol 328 no 5976 pp 337ndash339 2010

[15] H F Ma and T J Cui ldquoThree-dimensional broadband ground-plane cloak made of metamaterialsrdquo Nature Communicationsvol 1 article no 21 2010

[16] B Zhang Y Luo X Liu and G Barbastathis ldquoMacroscopicinvisibility cloak for visible lightrdquo Physical Review Letters vol106 Article ID 033901 2011

[17] X Sheng H S Chen B I Wu and J A Kong ldquoOne-directional perfect cloak created with homogeneous materialrdquoIEEEMicrowave andWireless Components Letters vol 19 articleno 131 2009

[18] Y Luo J Zhang H Chen L Lixin Ran B IWu and J A KongldquoA rigorous analysis of plane-transformed invisibility cloaksrdquoIEEE Transactions on Antennas and Propagation vol 57 no 12pp 3926ndash3933 2009

[19] N Landy and D R Smith ldquoA full-parameter unidirectionalmetamaterial cloak for microwavesrdquo Nature Materials vol 12no 1 pp 25ndash28 2013

[20] B Zhang H Chen B I Wu Y Luo L Ran and J A KongldquoResponse of a cylindrical invisibility cloak to electromagneticwavesrdquo Physical Review B vol 76 Article ID 121101 2007

[21] J B Pendry A J Holden D J Robbins andW J Stewart ldquoMag-netism from conductors and enhanced nonlinear phenomenardquoIEEE Transactions onMicrowaveTheory and Techniques vol 47no 11 pp 2075ndash2084 1999

[22] H Chen and B Zheng ldquoBroadband polygonal invisibility cloakfor visible lightrdquo Scientific Reports vol 2 article no 255 2012

[23] W Yan M Yan and M Qiu ldquoGeneralized nihility media fromtransformation opticsrdquo Journal of Optics vol 13 Article ID024005 2010

[24] Q He S Xiao X Li and L Zhou ldquoOptic-null mediumrealization and applicationsrdquo Optics Express vol 21 Article ID28948 2013

[25] L Xu Q Wu Y Zhou and H Chen ldquoTransformation deviceswith optical nihility media and reduced realizationsrdquo Frontiersof Physics vol 14 Article ID 42501 2019

[26] J C Howell J B Howell and J S Choi ldquoAmplitude-only pas-sive broadband optical spatial cloaking of very large objectsrdquoApplied Optics vol 53 no 9 p 1958 2014

[27] Y Liu and X Zhang ldquoMetamaterials a new frontier of scienceand technologyrdquo Chemical Society Reviews vol 40 no 5 pp2494ndash2507 2011

[28] CM Soukoulis andMWegener ldquoPast achievements and futurechallenges in the development of three-dimensional photonicmetamaterialsrdquoNature Photonics vol 5 no 9 pp 523ndash530 2011

[29] M M Sadeghi S Li L Xu B Hou and H Chen ldquoTransforma-tion optics with Fabry-Perot resonancesrdquo Scientific Reports vol5 Article ID 8680 2015

[30] B Edwards A Alu M E Young M Silveirinha and NEngheta ldquoExperimental verification of epsilon-near-zerometa-material coupling and energy squeezing using a microwavewaveguiderdquo Physical Review Letters vol 100 no 3 Article ID033903 2008

[31] R Liu Q Cheng T Hand et al ldquoExperimental demonstra-tion of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequenciesrdquo Physical ReviewLetters vol 100 no 2 Article ID 023903 2008

Research 5

(b)(a)

Hidden region

(c)

z

yx

3D metal printing

PCB +Foam

80 mm 80 mm

Figure 3 Photographs of the fabricated cloak and scheme of the experiment setup (a) Top view of the metamaterial cloak The extrememetamaterial is realized with the standard commercial 3Dmetal printing technology and the non-extreme one is implemented with the PCB-Foam layered structures (b) Perspective view of the metamaterial cloak with 8 unit cells in the 119911 direction (c) Scheme of the experimentsetup An open X-band rectangular waveguide with z-polarized magnetic field located at a distance of 50mm away from the cloak is usedas a source A loop antenna with a radius of 4mm is used as the receiving antenna Both transmitting and receiving antennas are connectedto a VNA to obtain the amplitude and phase of the measured field The measuring loop antenna is attached to a mechanical arm of a 3Dmeasurement platform and can be controlled to move in the xy planes to point-to-point probe the magnetic field The scan region (thelight-blue rectangle) is 300mm by 236mm with a resolution of 4mm

regions To get complete information in these regions we fillthe unmeasured regions with the simulated magnetic fielddistributions The simulated and experimental results are inexcellent agreement From the results we can exactly see thatthe EM waves are first separated into two beams that passthrough Region I1015840 with a compressed wavelength and tunnelthrough the metallic rectangular waveguide with zero-phasedelay (see the insets) then rejoin again with the same phaseand amplitude as if they had passed directly through theair As the effective singular parameter of 120576V119887 = 0 occurs atcut-off frequency the cloak still works at single frequency

Nevertheless it will be the first step to achieve extremeparameter cloak with omnidirectional cloaking performancerobustly because both Region I1015840 and II1015840 are realized with non-resonant homogeneous metamaterials with pretty simplestructures and the absorptions of these metamaterials areweak

3 Conclusions and Outlook

In summary we design fabricate and experimentally char-acterize the first extreme-parameter omnidirectional cloak

6 Research

(f)

-Max

0

MaxFree space

(a)

(g)

(d)

Bared bump

(b)

(h)

(e)

Cloaked bump

(c)

(i)

45∘

0∘

225

∘

Figure 4 Measured 119867119911 magnetic field distributions near the metamaterial cloak at the optimum cloaking frequency of 98 GHz Fielddistributions for free space bared aluminum cylinder and cloaked aluminum cylinder respectively when EM waves are incident with anangle of 0∘ [(a)ndash(c)] 225∘ [(d)ndash(f)] and 45∘ [(g)ndash(i)] respectively The black-line squares and the gray areas in (b) (e) and (h) represent theunmeasured region and the aluminum cylinder respectively The black arrows in (a) (d) and (g) indicate the incidence of the point sourceof EM waves The bold black line squares and the blue squares in (c) (f) and (i) represent the unmeasured and hidden regions respectivelyThe unmeasured areas are filled with simulated119867119911-field distributions Insets the enlarged image of119867119911-field distributions in the cloak

with non-resonant metamaterials Both of the numerical andexperimental results clearly show the excellent performanceof omnidirectional invisibility of the present cloak verifyingthe rightness of our design The present work providesan important guidance toward the realization of complexfunctionalities with metamaterials and will motivate varioustransformation optics based devices for practical applica-tions such as concentrators [38 39] rotators [40] and opticalillusion [41] apparatuses

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Bin Zheng and Yihao Yang contributed equally to this work

Acknowledgments

The authors thank P Rebusco at Massachusetts Institute ofTechnology for critical reading and editing of themanuscriptWork in Zhejiang University was sponsored by the NationalNatural Science Foundation of China under Grants no61625502 no 61574127 no 61601408 no 61775193 and no11704332 the ZJNSF under Granta no LY17F010008 andno LY19F010015 the Top-Notch Young Talents Program of

China the Fundamental Research Funds for the Central Uni-versities and the Innovation Joint ResearchCenter for Cyber-Physical-Society Work at Ames Laboratory was partiallysupported by the US Department of Energy Office of BasicEnergy Science Division ofMaterials Sciences and Engineer-ing (Ames Laboratory is operated for the US Departmentof Energy by Iowa State University under Contract no DE-AC02-07CH11358) The European Research Council underERCAdvanced Grant no 320081 (PHOTOMETA) supportedwork at FORTH

Supplementary Materials

Figure S1 Full-wave simulation of the full-parameter omni-directional cloak with practical structures (a)-(d) Magneticfield distributions near the present cloak when a point sourceemits EM wave along the side (a) the diagonal (b) anda nonsymmetry plane (c) of the cloak and the side of a10-wavelength-size cloak (d) respectively The blue squaresrepresent the hidden regions (e)-(h)119867119911-field patterns whenboth the PEC object and the cloak are removed from thehomogenous background (i)-(l)119867119911-field patterns when onlythe PEC object is present without the cloakThe gray squaresrepresent the PEC objects (m)-(o) Differential RCS of thepresent cloak (the red line) and bared PEC objects (the blueline) at 100GHz when the EM wave is incident at an angleof 0∘ 45∘ and 225∘ respectively The reduced total RCS of

Research 7

the three cases are 00829 00717 and 00743 respectively(p) Reduced total RCS as a function of frequency at theincidence angle of 45∘ Figure S2 (a)-(b) A mismatched-impedancematerial (120576119887 = 2 120583119887 = 05) covered with the GML(c)-(d) A bared mismatched-impedance material (e)-(f) Amismatched-impedance material (120576119887 = 2120583119887 = 05) coveredwith the discretized GML (g)-(h)The omnidirectional cloakcovered with the GML Figure S3 (a)-(b) A mismatched-impedance material (120576119887 = 2120583119887 = 05) covered withthe discrete GML composed of practical structures (c)-(d)Without the discrete GML (e) Metamaterial unit cell It isa rectangular metallic waveguide loaded with a dielectricmaterial (120576119897 = 25) The period of the unit cell is 119901 andbetween each unit cell is air (f) Geometries (the unit is mm)targeted relative permittivity (120576) and permeability (120583) andeffective relative permittivity (1205761015840) and permeability (1205831015840) ofeach unit cell Here ℎ1=16mm 119886=3mm and 119901=4mm arefixed for all unit cells (Supplementary Materials)

References

[1] AGreenleafM Lassas andGUhlmann ldquoAnisotropic conduc-tivities that cannot be detected by EITrdquo Physiological Measure-ment vol 24 no 2 pp 413ndash419 2003

[2] AAlu andN Engheta ldquoAchieving transparencywith plasmonicand metamaterial coatingsrdquo Physical Review E vol 72 ArticleID 016623 2005

[3] U Leonhardt ldquoOptical conformal mappingrdquo Science vol 312no 5781 pp 1777ndash1780 2006

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] J B Pendry Y Luo and R Zhao ldquoTransforming the opticallandscaperdquo Science vol 348 no 6234 pp 521ndash524 2015

[6] B Kante D Germain and A de Lustrac ldquoExperimen-tal demonstration of a nonmagnetic metamaterial cloak atmicrowave frequenciesrdquo Physical Review B vol 80 Article ID201104 2009

[7] D Schurig J J Mock B J Justice et al ldquoMetamaterialelectromagnetic cloak at microwave frequenciesrdquo Science vol314 no 5801 pp 977ndash980 2006

[8] W Cai U K Chettiar A V Kildishev and V M ShalaevldquoOptical cloaking with metamaterialsrdquo Nature Photonics vol 1no 4 pp 224ndash227 2007

[9] J Li and J B Pendry ldquoHiding under the carpet a new strategyfor cloakingrdquo Physical Review Letters vol 101 no 20 Article ID203901 2008

[10] X Chen Y Luo J Zhang K Jiang J B Pendry and S ZhangldquoMacroscopic invisibility cloaking of visible lightrdquoNature Com-munications vol 2 article no 176 2011

[11] R Liu C Ji J J Mock J Y Chin T J Cui and D R SmithldquoBroadband ground-plane cloakrdquo Science vol 323 no 5912 pp366ndash369 2009

[12] J Valentine J Li T Zentgraf G Bartal and X Zhang ldquoAnoptical cloak made of dielectricsrdquoNature Materials vol 8 no 7pp 568ndash571 2009

[13] L H Gabrielli J Cardenas C B Poitras and M LipsonldquoSilicon nanostructure cloak operating at optical frequenciesrdquoNature Photonics vol 3 no 8 pp 461ndash463 2009

[14] T Ergin N Stenger P Brenner J B Pendry and M WegenerldquoThree-dimensional invisibility cloak at optical wavelengthsrdquoScience vol 328 no 5976 pp 337ndash339 2010

[15] H F Ma and T J Cui ldquoThree-dimensional broadband ground-plane cloak made of metamaterialsrdquo Nature Communicationsvol 1 article no 21 2010

[16] B Zhang Y Luo X Liu and G Barbastathis ldquoMacroscopicinvisibility cloak for visible lightrdquo Physical Review Letters vol106 Article ID 033901 2011

[17] X Sheng H S Chen B I Wu and J A Kong ldquoOne-directional perfect cloak created with homogeneous materialrdquoIEEEMicrowave andWireless Components Letters vol 19 articleno 131 2009

[18] Y Luo J Zhang H Chen L Lixin Ran B IWu and J A KongldquoA rigorous analysis of plane-transformed invisibility cloaksrdquoIEEE Transactions on Antennas and Propagation vol 57 no 12pp 3926ndash3933 2009

[19] N Landy and D R Smith ldquoA full-parameter unidirectionalmetamaterial cloak for microwavesrdquo Nature Materials vol 12no 1 pp 25ndash28 2013

[20] B Zhang H Chen B I Wu Y Luo L Ran and J A KongldquoResponse of a cylindrical invisibility cloak to electromagneticwavesrdquo Physical Review B vol 76 Article ID 121101 2007

[21] J B Pendry A J Holden D J Robbins andW J Stewart ldquoMag-netism from conductors and enhanced nonlinear phenomenardquoIEEE Transactions onMicrowaveTheory and Techniques vol 47no 11 pp 2075ndash2084 1999

[22] H Chen and B Zheng ldquoBroadband polygonal invisibility cloakfor visible lightrdquo Scientific Reports vol 2 article no 255 2012

[23] W Yan M Yan and M Qiu ldquoGeneralized nihility media fromtransformation opticsrdquo Journal of Optics vol 13 Article ID024005 2010

[24] Q He S Xiao X Li and L Zhou ldquoOptic-null mediumrealization and applicationsrdquo Optics Express vol 21 Article ID28948 2013

[25] L Xu Q Wu Y Zhou and H Chen ldquoTransformation deviceswith optical nihility media and reduced realizationsrdquo Frontiersof Physics vol 14 Article ID 42501 2019

[26] J C Howell J B Howell and J S Choi ldquoAmplitude-only pas-sive broadband optical spatial cloaking of very large objectsrdquoApplied Optics vol 53 no 9 p 1958 2014

[27] Y Liu and X Zhang ldquoMetamaterials a new frontier of scienceand technologyrdquo Chemical Society Reviews vol 40 no 5 pp2494ndash2507 2011

[28] CM Soukoulis andMWegener ldquoPast achievements and futurechallenges in the development of three-dimensional photonicmetamaterialsrdquoNature Photonics vol 5 no 9 pp 523ndash530 2011

[29] M M Sadeghi S Li L Xu B Hou and H Chen ldquoTransforma-tion optics with Fabry-Perot resonancesrdquo Scientific Reports vol5 Article ID 8680 2015

[30] B Edwards A Alu M E Young M Silveirinha and NEngheta ldquoExperimental verification of epsilon-near-zerometa-material coupling and energy squeezing using a microwavewaveguiderdquo Physical Review Letters vol 100 no 3 Article ID033903 2008

[31] R Liu Q Cheng T Hand et al ldquoExperimental demonstra-tion of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequenciesrdquo Physical ReviewLetters vol 100 no 2 Article ID 023903 2008

6 Research

(f)

-Max

0

MaxFree space

(a)

(g)

(d)

Bared bump

(b)

(h)

(e)

Cloaked bump

(c)

(i)

45∘

0∘

225

∘

Figure 4 Measured 119867119911 magnetic field distributions near the metamaterial cloak at the optimum cloaking frequency of 98 GHz Fielddistributions for free space bared aluminum cylinder and cloaked aluminum cylinder respectively when EM waves are incident with anangle of 0∘ [(a)ndash(c)] 225∘ [(d)ndash(f)] and 45∘ [(g)ndash(i)] respectively The black-line squares and the gray areas in (b) (e) and (h) represent theunmeasured region and the aluminum cylinder respectively The black arrows in (a) (d) and (g) indicate the incidence of the point sourceof EM waves The bold black line squares and the blue squares in (c) (f) and (i) represent the unmeasured and hidden regions respectivelyThe unmeasured areas are filled with simulated119867119911-field distributions Insets the enlarged image of119867119911-field distributions in the cloak

with non-resonant metamaterials Both of the numerical andexperimental results clearly show the excellent performanceof omnidirectional invisibility of the present cloak verifyingthe rightness of our design The present work providesan important guidance toward the realization of complexfunctionalities with metamaterials and will motivate varioustransformation optics based devices for practical applica-tions such as concentrators [38 39] rotators [40] and opticalillusion [41] apparatuses

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Bin Zheng and Yihao Yang contributed equally to this work

Acknowledgments

The authors thank P Rebusco at Massachusetts Institute ofTechnology for critical reading and editing of themanuscriptWork in Zhejiang University was sponsored by the NationalNatural Science Foundation of China under Grants no61625502 no 61574127 no 61601408 no 61775193 and no11704332 the ZJNSF under Granta no LY17F010008 andno LY19F010015 the Top-Notch Young Talents Program of

China the Fundamental Research Funds for the Central Uni-versities and the Innovation Joint ResearchCenter for Cyber-Physical-Society Work at Ames Laboratory was partiallysupported by the US Department of Energy Office of BasicEnergy Science Division ofMaterials Sciences and Engineer-ing (Ames Laboratory is operated for the US Departmentof Energy by Iowa State University under Contract no DE-AC02-07CH11358) The European Research Council underERCAdvanced Grant no 320081 (PHOTOMETA) supportedwork at FORTH

Supplementary Materials

Figure S1 Full-wave simulation of the full-parameter omni-directional cloak with practical structures (a)-(d) Magneticfield distributions near the present cloak when a point sourceemits EM wave along the side (a) the diagonal (b) anda nonsymmetry plane (c) of the cloak and the side of a10-wavelength-size cloak (d) respectively The blue squaresrepresent the hidden regions (e)-(h)119867119911-field patterns whenboth the PEC object and the cloak are removed from thehomogenous background (i)-(l)119867119911-field patterns when onlythe PEC object is present without the cloakThe gray squaresrepresent the PEC objects (m)-(o) Differential RCS of thepresent cloak (the red line) and bared PEC objects (the blueline) at 100GHz when the EM wave is incident at an angleof 0∘ 45∘ and 225∘ respectively The reduced total RCS of

Research 7

the three cases are 00829 00717 and 00743 respectively(p) Reduced total RCS as a function of frequency at theincidence angle of 45∘ Figure S2 (a)-(b) A mismatched-impedancematerial (120576119887 = 2 120583119887 = 05) covered with the GML(c)-(d) A bared mismatched-impedance material (e)-(f) Amismatched-impedance material (120576119887 = 2120583119887 = 05) coveredwith the discretized GML (g)-(h)The omnidirectional cloakcovered with the GML Figure S3 (a)-(b) A mismatched-impedance material (120576119887 = 2120583119887 = 05) covered withthe discrete GML composed of practical structures (c)-(d)Without the discrete GML (e) Metamaterial unit cell It isa rectangular metallic waveguide loaded with a dielectricmaterial (120576119897 = 25) The period of the unit cell is 119901 andbetween each unit cell is air (f) Geometries (the unit is mm)targeted relative permittivity (120576) and permeability (120583) andeffective relative permittivity (1205761015840) and permeability (1205831015840) ofeach unit cell Here ℎ1=16mm 119886=3mm and 119901=4mm arefixed for all unit cells (Supplementary Materials)

References

[1] AGreenleafM Lassas andGUhlmann ldquoAnisotropic conduc-tivities that cannot be detected by EITrdquo Physiological Measure-ment vol 24 no 2 pp 413ndash419 2003

[2] AAlu andN Engheta ldquoAchieving transparencywith plasmonicand metamaterial coatingsrdquo Physical Review E vol 72 ArticleID 016623 2005

[3] U Leonhardt ldquoOptical conformal mappingrdquo Science vol 312no 5781 pp 1777ndash1780 2006

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] J B Pendry Y Luo and R Zhao ldquoTransforming the opticallandscaperdquo Science vol 348 no 6234 pp 521ndash524 2015

[6] B Kante D Germain and A de Lustrac ldquoExperimen-tal demonstration of a nonmagnetic metamaterial cloak atmicrowave frequenciesrdquo Physical Review B vol 80 Article ID201104 2009

[7] D Schurig J J Mock B J Justice et al ldquoMetamaterialelectromagnetic cloak at microwave frequenciesrdquo Science vol314 no 5801 pp 977ndash980 2006

[8] W Cai U K Chettiar A V Kildishev and V M ShalaevldquoOptical cloaking with metamaterialsrdquo Nature Photonics vol 1no 4 pp 224ndash227 2007

[9] J Li and J B Pendry ldquoHiding under the carpet a new strategyfor cloakingrdquo Physical Review Letters vol 101 no 20 Article ID203901 2008

[10] X Chen Y Luo J Zhang K Jiang J B Pendry and S ZhangldquoMacroscopic invisibility cloaking of visible lightrdquoNature Com-munications vol 2 article no 176 2011

[11] R Liu C Ji J J Mock J Y Chin T J Cui and D R SmithldquoBroadband ground-plane cloakrdquo Science vol 323 no 5912 pp366ndash369 2009

[12] J Valentine J Li T Zentgraf G Bartal and X Zhang ldquoAnoptical cloak made of dielectricsrdquoNature Materials vol 8 no 7pp 568ndash571 2009

[13] L H Gabrielli J Cardenas C B Poitras and M LipsonldquoSilicon nanostructure cloak operating at optical frequenciesrdquoNature Photonics vol 3 no 8 pp 461ndash463 2009

[14] T Ergin N Stenger P Brenner J B Pendry and M WegenerldquoThree-dimensional invisibility cloak at optical wavelengthsrdquoScience vol 328 no 5976 pp 337ndash339 2010

[15] H F Ma and T J Cui ldquoThree-dimensional broadband ground-plane cloak made of metamaterialsrdquo Nature Communicationsvol 1 article no 21 2010

[16] B Zhang Y Luo X Liu and G Barbastathis ldquoMacroscopicinvisibility cloak for visible lightrdquo Physical Review Letters vol106 Article ID 033901 2011

[17] X Sheng H S Chen B I Wu and J A Kong ldquoOne-directional perfect cloak created with homogeneous materialrdquoIEEEMicrowave andWireless Components Letters vol 19 articleno 131 2009

[18] Y Luo J Zhang H Chen L Lixin Ran B IWu and J A KongldquoA rigorous analysis of plane-transformed invisibility cloaksrdquoIEEE Transactions on Antennas and Propagation vol 57 no 12pp 3926ndash3933 2009

[19] N Landy and D R Smith ldquoA full-parameter unidirectionalmetamaterial cloak for microwavesrdquo Nature Materials vol 12no 1 pp 25ndash28 2013

[20] B Zhang H Chen B I Wu Y Luo L Ran and J A KongldquoResponse of a cylindrical invisibility cloak to electromagneticwavesrdquo Physical Review B vol 76 Article ID 121101 2007

[21] J B Pendry A J Holden D J Robbins andW J Stewart ldquoMag-netism from conductors and enhanced nonlinear phenomenardquoIEEE Transactions onMicrowaveTheory and Techniques vol 47no 11 pp 2075ndash2084 1999

[22] H Chen and B Zheng ldquoBroadband polygonal invisibility cloakfor visible lightrdquo Scientific Reports vol 2 article no 255 2012

[23] W Yan M Yan and M Qiu ldquoGeneralized nihility media fromtransformation opticsrdquo Journal of Optics vol 13 Article ID024005 2010

[24] Q He S Xiao X Li and L Zhou ldquoOptic-null mediumrealization and applicationsrdquo Optics Express vol 21 Article ID28948 2013

[25] L Xu Q Wu Y Zhou and H Chen ldquoTransformation deviceswith optical nihility media and reduced realizationsrdquo Frontiersof Physics vol 14 Article ID 42501 2019

[26] J C Howell J B Howell and J S Choi ldquoAmplitude-only pas-sive broadband optical spatial cloaking of very large objectsrdquoApplied Optics vol 53 no 9 p 1958 2014

[27] Y Liu and X Zhang ldquoMetamaterials a new frontier of scienceand technologyrdquo Chemical Society Reviews vol 40 no 5 pp2494ndash2507 2011

[28] CM Soukoulis andMWegener ldquoPast achievements and futurechallenges in the development of three-dimensional photonicmetamaterialsrdquoNature Photonics vol 5 no 9 pp 523ndash530 2011

[29] M M Sadeghi S Li L Xu B Hou and H Chen ldquoTransforma-tion optics with Fabry-Perot resonancesrdquo Scientific Reports vol5 Article ID 8680 2015

[30] B Edwards A Alu M E Young M Silveirinha and NEngheta ldquoExperimental verification of epsilon-near-zerometa-material coupling and energy squeezing using a microwavewaveguiderdquo Physical Review Letters vol 100 no 3 Article ID033903 2008

[31] R Liu Q Cheng T Hand et al ldquoExperimental demonstra-tion of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequenciesrdquo Physical ReviewLetters vol 100 no 2 Article ID 023903 2008

Research 7

the three cases are 00829 00717 and 00743 respectively(p) Reduced total RCS as a function of frequency at theincidence angle of 45∘ Figure S2 (a)-(b) A mismatched-impedancematerial (120576119887 = 2 120583119887 = 05) covered with the GML(c)-(d) A bared mismatched-impedance material (e)-(f) Amismatched-impedance material (120576119887 = 2120583119887 = 05) coveredwith the discretized GML (g)-(h)The omnidirectional cloakcovered with the GML Figure S3 (a)-(b) A mismatched-impedance material (120576119887 = 2120583119887 = 05) covered withthe discrete GML composed of practical structures (c)-(d)Without the discrete GML (e) Metamaterial unit cell It isa rectangular metallic waveguide loaded with a dielectricmaterial (120576119897 = 25) The period of the unit cell is 119901 andbetween each unit cell is air (f) Geometries (the unit is mm)targeted relative permittivity (120576) and permeability (120583) andeffective relative permittivity (1205761015840) and permeability (1205831015840) ofeach unit cell Here ℎ1=16mm 119886=3mm and 119901=4mm arefixed for all unit cells (Supplementary Materials)

References

[1] AGreenleafM Lassas andGUhlmann ldquoAnisotropic conduc-tivities that cannot be detected by EITrdquo Physiological Measure-ment vol 24 no 2 pp 413ndash419 2003

[2] AAlu andN Engheta ldquoAchieving transparencywith plasmonicand metamaterial coatingsrdquo Physical Review E vol 72 ArticleID 016623 2005

[3] U Leonhardt ldquoOptical conformal mappingrdquo Science vol 312no 5781 pp 1777ndash1780 2006

[4] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo Science vol 312 no 5781 pp 1780ndash1782 2006

[5] J B Pendry Y Luo and R Zhao ldquoTransforming the opticallandscaperdquo Science vol 348 no 6234 pp 521ndash524 2015

[6] B Kante D Germain and A de Lustrac ldquoExperimen-tal demonstration of a nonmagnetic metamaterial cloak atmicrowave frequenciesrdquo Physical Review B vol 80 Article ID201104 2009

[7] D Schurig J J Mock B J Justice et al ldquoMetamaterialelectromagnetic cloak at microwave frequenciesrdquo Science vol314 no 5801 pp 977ndash980 2006

[8] W Cai U K Chettiar A V Kildishev and V M ShalaevldquoOptical cloaking with metamaterialsrdquo Nature Photonics vol 1no 4 pp 224ndash227 2007

[9] J Li and J B Pendry ldquoHiding under the carpet a new strategyfor cloakingrdquo Physical Review Letters vol 101 no 20 Article ID203901 2008

[10] X Chen Y Luo J Zhang K Jiang J B Pendry and S ZhangldquoMacroscopic invisibility cloaking of visible lightrdquoNature Com-munications vol 2 article no 176 2011

[11] R Liu C Ji J J Mock J Y Chin T J Cui and D R SmithldquoBroadband ground-plane cloakrdquo Science vol 323 no 5912 pp366ndash369 2009

[12] J Valentine J Li T Zentgraf G Bartal and X Zhang ldquoAnoptical cloak made of dielectricsrdquoNature Materials vol 8 no 7pp 568ndash571 2009

[13] L H Gabrielli J Cardenas C B Poitras and M LipsonldquoSilicon nanostructure cloak operating at optical frequenciesrdquoNature Photonics vol 3 no 8 pp 461ndash463 2009

[14] T Ergin N Stenger P Brenner J B Pendry and M WegenerldquoThree-dimensional invisibility cloak at optical wavelengthsrdquoScience vol 328 no 5976 pp 337ndash339 2010

[15] H F Ma and T J Cui ldquoThree-dimensional broadband ground-plane cloak made of metamaterialsrdquo Nature Communicationsvol 1 article no 21 2010

[16] B Zhang Y Luo X Liu and G Barbastathis ldquoMacroscopicinvisibility cloak for visible lightrdquo Physical Review Letters vol106 Article ID 033901 2011

[17] X Sheng H S Chen B I Wu and J A Kong ldquoOne-directional perfect cloak created with homogeneous materialrdquoIEEEMicrowave andWireless Components Letters vol 19 articleno 131 2009

[18] Y Luo J Zhang H Chen L Lixin Ran B IWu and J A KongldquoA rigorous analysis of plane-transformed invisibility cloaksrdquoIEEE Transactions on Antennas and Propagation vol 57 no 12pp 3926ndash3933 2009

[19] N Landy and D R Smith ldquoA full-parameter unidirectionalmetamaterial cloak for microwavesrdquo Nature Materials vol 12no 1 pp 25ndash28 2013

[20] B Zhang H Chen B I Wu Y Luo L Ran and J A KongldquoResponse of a cylindrical invisibility cloak to electromagneticwavesrdquo Physical Review B vol 76 Article ID 121101 2007

[21] J B Pendry A J Holden D J Robbins andW J Stewart ldquoMag-netism from conductors and enhanced nonlinear phenomenardquoIEEE Transactions onMicrowaveTheory and Techniques vol 47no 11 pp 2075ndash2084 1999

[22] H Chen and B Zheng ldquoBroadband polygonal invisibility cloakfor visible lightrdquo Scientific Reports vol 2 article no 255 2012

[23] W Yan M Yan and M Qiu ldquoGeneralized nihility media fromtransformation opticsrdquo Journal of Optics vol 13 Article ID024005 2010

[24] Q He S Xiao X Li and L Zhou ldquoOptic-null mediumrealization and applicationsrdquo Optics Express vol 21 Article ID28948 2013

[25] L Xu Q Wu Y Zhou and H Chen ldquoTransformation deviceswith optical nihility media and reduced realizationsrdquo Frontiersof Physics vol 14 Article ID 42501 2019

[26] J C Howell J B Howell and J S Choi ldquoAmplitude-only pas-sive broadband optical spatial cloaking of very large objectsrdquoApplied Optics vol 53 no 9 p 1958 2014

[27] Y Liu and X Zhang ldquoMetamaterials a new frontier of scienceand technologyrdquo Chemical Society Reviews vol 40 no 5 pp2494ndash2507 2011

[28] CM Soukoulis andMWegener ldquoPast achievements and futurechallenges in the development of three-dimensional photonicmetamaterialsrdquoNature Photonics vol 5 no 9 pp 523ndash530 2011

[29] M M Sadeghi S Li L Xu B Hou and H Chen ldquoTransforma-tion optics with Fabry-Perot resonancesrdquo Scientific Reports vol5 Article ID 8680 2015

[30] B Edwards A Alu M E Young M Silveirinha and NEngheta ldquoExperimental verification of epsilon-near-zerometa-material coupling and energy squeezing using a microwavewaveguiderdquo Physical Review Letters vol 100 no 3 Article ID033903 2008

[31] R Liu Q Cheng T Hand et al ldquoExperimental demonstra-tion of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequenciesrdquo Physical ReviewLetters vol 100 no 2 Article ID 023903 2008

8 Research

[32] M Silveirinha and N Engheta ldquoTunneling of electromagneticenergy through subwavelength channels and bends using 120576-near-zero materialsrdquo Physical Review Letters vol 97 no 15Article ID 157403 2006

[33] X Chen T M Grzegorczyk B-I Wu J Pacheco Jr and JA Kong ldquoRobust method to retrieve the constitutive effectiveparameters of metamaterialsrdquo Physical Review E StatisticalNonlinear and Soft Matter Physics vol 70 Article ID 0166082004

[34] J B Pendry L Martın-Moreno and F J Garcia-Vidal ldquoMim-icking surface plasmons with structured surfacesrdquo Science vol305 no 5685 pp 847-848 2004

[35] F J Garcia-Vidal L Martın-Moreno and J B Pendry ldquoSurfaceswith holes in them new plasmonic metamaterialsrdquo Journal ofOptics A Pure and Applied Optics vol 7 no 2 pp S97ndashS1012005

[36] A P Hibbins B R Evans and J R Sambles ldquoPhysics experi-mental verification of designer surface plasmonsrdquo Science vol308 no 5722 pp 670ndash672 2005

[37] Y Yang L Jing B Zheng et al ldquoFull-polarization 3D meta-surface cloak with preserved amplitude and phaserdquo AdvancedMaterials vol 28 no 32 pp 6866ndash6871 2016

[38] H Chen C T Chan and P Sheng ldquoTransformation optics andmetamaterialsrdquoNatureMaterials vol 9 no 5 pp 387ndash396 2010

[39] Y Luo H Chen J Zhang L Ran and J A Kong ldquoDesignand analytical full-wave validation of the invisibility cloaksconcentrators and field rotators created with a general class oftransformationsrdquo Physical Review B vol 77 Article ID 1251272008

[40] H Chen B Hou S Chen X Ao W Wen and C T ChanldquoDesign and experimental realization of a broadband transfor-mation media field rotator at microwave frequenciesrdquo PhysicalReview Letters vol 102 no 18 Article ID 183903 2009

[41] Y Lai J Ng H Chen et al ldquoIllusion opticsThe optical transfor-mation of an object into another objectrdquoPhysical Review Lettersvol 102 no 25 Article ID 253902 2009