Amplitude-only,passive,broadband,opticalspatial - PDF document

Amplitude-only,passive,broadband,opticalspatial cloakingofverylargeobjects JohnC.Howell, 1, *J.BenjaminHowell, 2 andJosephS.Choi 3 1 DepartmentofPhysicsandAstronomy,UniversityofRochester,Rochester,NewYork14627,USA 2 TCMS,Rochester,NewYork14618,USA 3 TheInstituteofOptics,UniversityofRochester,Rochester,NewYork14627,USA *Correspondingauthor:howell@pas.rochester.edu Received26December2013;accepted5February2014; posted6February2014(Doc.ID203722);published20March2014 Wedemonstratethreeamplitudecloaksthatcanhideverylargespatialobjectsovertheentirevisible spectrumusingonlypassive,off-the-shelfoptics.Thecloakedregionforallofthedevicesexceeds 10 6 mm 3 ,withthelargestexceeding 10 8 mm 3 .Althoughunidirectional,thesecloakscanhidethecloaked object,eveniftheobjectistransverselyilluminatedorself-illuminated.Duetothesmallusablesolid angle,butsimplescaling,thesecloaksmaybeofvalueinhidingsmallfield-of-viewobjectssuchas mid-tohigh-earthorbitsatellitesfromearth-basedobservation.Activephasefrontmanipulationcan alsomakethesecloaksinvisibletosomeformsofimagehomodyning.©2014OpticalSocietyofAmerica OCIScodes: (230.3205)Invisibilitycloaks;(110.3010)Imagereconstructiontechniques;(350.4600) Opticalengineering;(220.2740)Geometricopticaldesign. http://dx.doi.org/10.1364/AO.53.001958 1.Introduction Theintriguingandexcitingpossibilitiesofoptical spatialcloakinghaveattractedboththepopularcul- tureandthescientificcommunity[ 1 – 14 ].Great strideshavebeentakentoachievethe “ HolyGrail ” ofopticalcloaking:broadbandopticalinvisibilityin boththephaseandamplitudeofthefield,omnidir- ectionality,theabilitytocloakmacroscopicobjects andbeinvisible.Manyoftheinitialdevelopments inexperimentalopticalcloakingwerebasedon transformationoptics[ 1 – 3 ]andstudiedinmetama- terials[ 1 , 4 – 10 ]andinpatterneddielectrics[ 11 , 12 ] withtheuseofquasi-conformalmapping.Whilere- markableprogresshasbeenmade,muchworkre- mainsintermsofachievingthecloakingatoptical wavelengths,increasingthebandwidthoverwhich thecloakworks,andscalingtolargedimensions. Towardthesegoals,arecentclassicalopticsmethod usingbirefringentcalcitecrystals[ 14 ]achieveda polarization-dependent,broadband,visible,unidi- rectionalcloakofasmallinclinewithapeakheight of2mm.Anotherintriguingadvancewastherecent demonstrationoftemporalcloaking(hidingatempo- ralevent)work[ 15 ]basedonsplittemporallensing anddispersivepropagationinfibers. Onecanconsidercloakingtobeanopticalinvisibil- ityillusion.Cloaksbasedontransformationoptics havetheillusionofhidingobjectssuchthatboththe phaseandamplitudeofafieldareundisturbed[ 16 ]. Thephaseandamplituderequirementalsomakes themdifficulttoachieve.Withouttherequirement ofphasepreservation,onecanmakeverysimple cloaksbasedonpassivelinearrefractiveandreflec- tiveelements.However,wavefrontsensing,suchas imagehomodyning,canrevealthepresenceof “ am- plitude-only ” cloaksbyfindingphasediscontinuities. Here,wereporton “ amplitude ” cloakingdevices basedonoff-the-shelfopticsthatcanachievebroad- bandinvisibilityandarbitraryspatialscalingandbe hiddenthemselves.Wedemonstratecloakingover 1559-128X/14/091958-06$15.00/0 ©2014OpticalSocietyofAmerica 1958APPLIEDOPTICS/Vol.53,No.9/20March2014 thevisiblespectrumwithcloakingregionsexceeding 10 6 mm 3 ,withthelargestexceeding 10 8 mm 3 .Atits mostbasiclevel,theopticalillusionistosimply guidelightaroundanobjectasiftheobjectisn ’ t there.Onemightarguethatanendoscope,anindex- guidingfibersystemusedtoimageholloworgansin thehumanbody,achievesthisend.Theetymologyof “ smokeandmirrors ” impliestheuseofdistraction andopticalillusionthroughthecarefulguidingof light.Suchillusionshavebeenaroundforalmost twocenturies[ 17 ].Itshouldnotcomeasasurprise thatreflectiveandrefractiveopticscanbeusedto cloakverylargeoptics.Todemonstratethispoint, webuiltandreportonthreecloakingdevices.Impor- tantly,eachdevicecanbeeasilyscaledtomuch largersystems.Itshouldbenotedfromtheoutset thatthepurposeofthispaperistodemonstrate thesimplicityofamplitudecloaking. Thefirstdeviceisbasedonthebendingoflightata dielectricinterface.Wedemonstratearealizationof thedeviceusingtwoL-shapedwater-filledtanks. Theseconddeviceusesquadraticphaseelements, suchaslenses,anddoesn ’ tsufferfromtheedgeeffect problemsofthefirstdevice(thisisthespatialequiv- alentofthetemporalcloak[ 15 ]).Thethirddevice simplyusesmirrorstoguidelightaroundtheobject. Thelattercloak,whilenotnew[ 17 – 19 ],isintended todemonstratetheeaseofscalingofthesesystems. 2.CloakingwithSnell ’ sLaw Theexperimentalsetupofthefirstdeviceisshownin Fig. 1 .Thecloakisbasedontheideathatlightis transverselyshiftedbuthasthesamedirectionafter passingthroughatiltedmedium(havingadifferent indexofrefraction)withtwostraightparallelfaces. Thesetupusestwowater-filledtankstobendlight aroundacloakingregion.Thefirsttankcausesall theraysbelowtheopticalaxistobeshifteddown- wardandtheraysabovetheopticalaxistobeshifted upward.Aftertheraysexitthesecondwallofthe firsttank,theyareparalleltotheopticalaxisbut haveadisplacementrelativetotheiroriginaltrajec- tory.Thedisplacementhidesanyobjectinthe middle.Thesecondtankundoestheeffectsofthe firsttanksothattheraysareonceagainparallel withthedisplacementundone.Thediameterof thecloakingregioncanbefoundfromSnell ’ slawand thewidthofthetank.FromFig. 2 ,wecancompute thesizeofthecloakingregion.WeuseSnell ’ slaw n a sin

a  n w sin

w  ,where n a  1 ( n w  1 . 33 ) istheindexofrefractionofair(water)and
a (
w )is theangleoftherayrelativetothenormalinair (water).Usingstraightforwardtrigonometry,wefind thatthedistance d betweentheincidentrayand therayafterpropagatingthroughthemediumis givenby d  x sin

a  arcsin
n  1 w sin

a  cos
arcsin
n  1 w sin

a  : (1) Thetankshaveawidthof x
200 mm,andtheinci- dentlightrayshaveanangleof   4 ,yieldingacloak- ingregionof 2 d  105 mm,ingoodagreementwith theobservedsize. Analternativeperspectivetothefunctionalityof thiscloakisthattheeffectoftheL-shapedtanks istocreateasplitlinearphaserampacrossthefront oftheelectricfield.Thesplitlinearphaseramp causesparallelraystobedeflectedinoppositedirec- tionsaboutthecloakingregion.Thisisaunidirec- tionalcloakingdevice,becausesomeraysnot paralleltotheopticalaxiscanpenetratethecloaking region[seeFig. 1(b) ].Inaddition,thenonparallel raystraversedifferentlengthsofwaterandhave differentincidentanglesinthetwotanks,causing distortiontothebackground.Thetransversedis- placementsoftheraysnotparalleltotheopticalaxis Fig.1.CloakingdevicebasedonSnell ’ slaw.TwoL-shapedwater- filledtanksbendlightaroundacloakingregion.(a)Raysparallel totheopticalaxis:atthefirstinterface,lightbendsawayfromthe opticalaxisduetotheinterfacewithwater.Thelightthenbends backinthesamedirectionatthesecondinterface.Thesecondtank bringsthelightbackwithboththesamedirectionandnotrans- versedisplacement.(b)CODEVsimulationofrayfans(solid/red arrows)displacedfromtheopticalaxis.Dashedlinesindicate wheretherayswouldgowithoutthedevice.Thefinalrayshave thesameangles.However,theraysnotparalleltotheaxisare displaced,resultinginashiftintheperceivedobjectposition. Fig.2.Distance d betweenanunalteredrayandthepathofthe rayafterexitingthewatercanbefoundfromSnell ’ slawandthe widthofthetank L . 20March2014/Vol.53,No.9/APPLIEDOPTICS1959 canbeseenintheCODEVsimulationinFig. 1(b) .As expected,sincenoopticalpowerispresentinthis device,theanglesremainunchanged.However,the finalraysthatanobserversees(solid/redlines)have anarrowerrangeofanglesthanwhatwouldhappen withoutthecloakingdevice.Thismeansthattheob- jectswillappearcloserthanwheretheyareactually located. Unlikeothercloaksandtheseconddevicedis- cussedlater,thereisn ’ taneffectivecompressionof thefield.Thislackoffieldcompressionleadstoedge effects.Thisfirstdevicewillsufferfromedgeeffects attheextremewingsofthedevice.Duetothedeflec- tionwithoutcompressionoftheraysatthefirst interface,thesecondinterfaceofthetankhastopro- trudefartherthanthefirstinterface.So,unlessthe tanksareinfiniteinextent,theedgeswillhavesome problems.Itshouldalsobenotedthattransverseil- luminationorself-illuminationofthecloakedobject cannotbeobservedinthecloakeddirection,sincethe tankswilldeflectthelightawayfromtheobserver. TheactualexperimentalsetupisshowninFig. 3 . Anaerialviewofthesetupshowsahelicopterinthe cloakingregionbetweenthetwowatertanks.The cloakingabilityofthefirstcloakingdeviceisshown inFig. 4 .Belowthewaterlineinthepicture,theheli- coptercannotbeseenandthetruckappearsinits place.However,abovethewaterline,thehelicopter isvisibleandinfrontofthetruck.Thebendingof thelightcausesthelighttopassaroundthebottom ofthehelicopterandbendbacksothatthetruckcan beviewedinitsplace.Thetransversewidthofthe helicopterisapproximately125mm,beingapproxi- mately20mmlargerthanthecloakingdiameter.A smallwhitebrightlylitpieceofthehelicopteratits widestpointcanbeseen.Itshouldbenotedthatthe helicopterisilluminateddirectlyfromaboveandre- mainsinvisible.Thus,thetransverseilluminationof thecloakedobjectdoesnotrevealitspresence,asone wouldexpectfromacloakingdevice. Whilethefirstcloakingdeviceisstraightforward toimplement,thescalingtoverylargeobjectsbe- comesratherimpracticalunlessonewishestocarry aroundverylargetanksofwater.Ageneralizationof thisdeviceistohaveadevicethatcausesasplit linearphaseramp.Thiscanbeachievedwithaholo- gram,aspatiallightmodulator,andalargepieceof glasswithlongprism-likewedges(equivalenttoa Fresnellensbutwithlinearratherthanquadratic etching). 3.CloakingwithLenses ThesecondschemeisshowninFig. 5 .Thisscheme canbeconsideredasthespatialequivalentofthe temporalcloakusedin[ 15 ].Lensesareusedtoguide lightaroundthecloakingregion.Fresnellensesare usedattheinterfacesofthecloakingdevice,because oftheirlowmass,scalability,andrectangularshape. Unfortunately,passingthroughafocusinvertsthe backgroundbehindtheobject.Inthisspatialcloak, diverginglensesbetweentheFresnellensesprevent thelightfrompassingthroughafocus,whichmeans Fig.3.Aerialviewofthefirstcloakingdevice.Ahelicopteris showninsidethecloakingregionofthefirstdevice.Atruckis shownontheothersideoftheviewingregion.Thetruckwill appearinthehelicopter ’ splacewhenwaterisinsidethetanks andviewedalongtheopticalaxis. Fig.4.Belowthewaterline,thehelicopteriscloakedandthe truckappearsinitsplace.Thelightcomingfromthetruckpasses aroundthehelicopterviathewatertanksandisthenseeninplace ofthehelicopter.Abovethewaterline,thehelicopterisshownin frontofthetruck. Fig.5.Experimentalcloakingschematicoftheseconddevice. Converginganddiverginglensesareusedtomaplightaround thecloakingregion. 1960APPLIEDOPTICS/Vol.53,No.9/20March2014 thattheimagewillbeuprightratherthaninverted. Theyalsohavetheinterestingpropertythatthe separationbetweenlensescanbequitelargeafter theraysarecollimated,sothatthecloakingregion canbeextendedlongitudinally. Analternativebutslightlylargerdesignwasac- tuallyusedtodemonstratethecloaking.Thealterna- tivedesign,showninFig. 6 ,removesthetwo diverginglensesfromthesetup.However,withthe twodiverginglensesremoved,theimageoftheback- groundisinverted.Tomaketheimageupright,we useanothersetofFresnellensesalsoseparatedby 2 f 1 inserieswiththefirsttwolenses.Intheactual experiment,thetwomiddleFresnellenseswere mountedtogetherasiftheywereasinglelens.The designofthedeviceisshowninFig. 7 ,andthe cloakedhelicopterisshowninFig. 8 .Itcanbeseen thatthetailofthehelicopteriscloakedandthetruck behindthehelicopterappearsinitsplace.Onecan noticethatintheuncloakedregion,asmallportion ofthetruckinthebackgroundcanbeseenabovethe helicopter.Four 175 mm× 250 mmFresnellenses wereused,eachhavingafocallengthof200mm. Thetruckisplacedadistanceof750mmfromthe firstlens,anditisobservedwitha 21 ×magnification camera(thehighestmagnificationofthecamera)at
6 . 4 m(thelargestdistanceallowedbythephysical space)fromtherearlens.Theimagequalityis limitedbythequalityoftheFresnellenses. 4.CloakingwithMirrors Thelastcloakisthemostobviousdesignonewould usetomakelightpassaroundanobject.Thedesign ofthedeviceisshowninFig. 9 .Invisibilitywithmir- rorshasbeenpreviouslydone.Thepointwewishto emphasizeisnotthenoveltybuttheeaseofscalingto nearlyarbitrarysize.Thefirstmirrorreflectsthe lightawayfromthecloakingregion.Thelightthen bouncesoffofaretroreflectingmirrorpair(two mirrorsatrightangles),andthenitreflectsoffof themirrorbehindtheobject. Theretroreflectingmirrorsmakeitsothatrays leavingthecloak,evenoff-axisrays,leaveatthesame angle(magnificationis1),albeitwithtransverse shifts[seeCODEVsimulationshowninFig. 9(b) ]. Thetransverseshiftsmeanthatthisdeviceworks optimallyatinfinity(largedistancefromthe observer).Incontrasttothefirstcloakingdevicewith Fig.6.Alternativeschematicfortheseconddevice.FourFresnel lensesinseriesareused.TwosetsofFresnellenseswitheachset separatedbytwicethefocallengthmakeitsotheimageisnotin- verted.Thedistancebetweenlenspairscanbearbitrarilysmall.In theactualexperiment,theyweremountedtogetherasiftheywere asinglelens.(a)On-axismarginalraysforanobjectatinfinity. (b)CODEVsimulationofthesameraysasintheactualexperi- ment.Theobjectwasplaced750mmfromthefirstFresnellens. Thefigureisnottoscaleforeaseofviewing. Fig.7.Setupforthesecondcloakingdevice.Thetailofahelicop- terisatthefocusofaFresnellens(lightpassesaroundit).Four Fresnellenses(thetwointhemiddleareincontact)allowfora one-to-onenoninvertedimagingofthebackground.Thelenses havethedimensionsof 175 mm× 250 mmandhaveafocallength of200mm.Thetruckisplacedadistanceof750mmfromthelast lens. Fig.8.Viewingalongtheopticalaxis,weseethetruckappearing intheplaceofthetailofthehelicopter.Theobservationwasdone witha 21 ×magnificationcameraat6.4mfromthefirstlens. 20March2014/Vol.53,No.9/APPLIEDOPTICS1961 water,heretheoutputrayshaveawiderrangeofan- gles.Theresultisthattheobjectsinthemirrorare actuallycloserthantheyappear(ascanbeseenin Fig. 11 ).Thiscanbeunderstoodbyrealizingthat thecloakingdevicebendslightaroundthehiddenob- ject.Sotheoutputlighthasactuallytraveledfarther andexpandedmorethanonadirectpath.Hence,an observerwillperceivethelighttohavestartedfrom fartheraway.Inthefirstcloakingdevice,theindex ofrefractiondifferencescausedanoppositeeffect, butherelighttravelsonlyinair,soitsrateofexpan- sionremainsthesame.Theidealscenarioisthento havethedistancebetweenthemirrorsbesmall,com- paredtothedistanceofthebackgroundobjectsfrom themirrors.Thiscanalsooccurwhentheobserveris infinitelyfaraway,asmentioned. Welistsomeofthedownsidesforthiscloak.First, thereareedgeeffectsifonemovestotheside (unidirectional).Second,theretroreflectingmirror pairmakesthecloakvisibleunlessthemirrorsare placedbehindawallorsomelargeobjects.Third, whiletheraysleaveinthesamedirections,they leavewithatransversedisplacementthatispropor- tionaltotheincominganglerelativetotheoptical axis.However,evenwiththesedrawbacks,itis clearlyscalabletoverylargedimensions. TheactualexperimentisshowninFig. 10 .Two setsofmirrorsarejoinedatrightangles.Itisimpor- tanttoalignthemirrorssothatthefrontandrear mirrorsareperpendicular.Tominimizebackground distortion,carefulattentionwasgiventosecuring thejoinedmirrorsatrightanglesandtomaking themasverticalaspossible.InFig. 11 onecansee thatpartofthechairiscloakedandtherubbish caninthebackgroundappearsinitsplace.Theim- agewastakenapproximately25mfromthemirrors, thusensuringthatthecloakoccupiedasmallfield ofview(unidirectionality).Themirrorshavedimen- sionsof 600 mm× 900 mm,withatotalcloaking volumeof 1 . 6 × 10 8 mm 3 .Thisvolumeissufficient tocloakahuman,albeitwithnotasmuchconven- ienceasHarryPotter ’ scloak.Thesimplicityofthe devicemeansthatmuchlargercloakingdevicescan easilybebuilt. Wehaveconsideredpassiveamplitude-onlycloaks. However,makingthesecloaksactive,inthesense thatthephasemaybeadjustedbasedonfeedback, mayallowforphaseandamplitudeinvisibility.The phasediscontinuitiescausedbythecloakcanbe amelioratedunidirectionallyforsometypesofimage homodyningbyaddingafrequency-dependentphase shifttothefield.Ifthecloakisbeinginterrogated byanarrowbandcoherentfieldofaparticularfre- quency,amodulationofthecloaktomakethephase frontsmoothcanbemade.Thus,activephasefront manipulationcouldachievebothamplitudeand phasecloakinginthiscontext. 5.Conclusions Insummary,wehavedemonstratedthree “ ampli- tude-only ” opticalcloakingdevices.Thecloakswork overthevisiblespectrumandhavecloakingregions Fig.9.Schematicforthethirddevice.Mirrorsreflectlight aroundthecloakingregion.(a)On-axismarginalraysforanobject atinfinity.(b)CODEVsimulationofthesamemarginalraysforan objectabout1.5mfromthemirrors.Theanglesoftheraysdonot change,buttheobjectwillappeartobefartherawaythanits actuallocation. Fig.10.Setupforthethirddevice.Twosetsofrightanglemirrors guidelightaroundthecloakedregion. Fig.11.Chairiscloaked,andarubbishcanappearsinitsplace. 1962APPLIEDOPTICS/Vol.53,No.9/20March2014 exceeding 10 6 mm 3 ,andwithgoodcoatings,thesec- onddevicecanbemadenearlyinvisible.Thesecond devicedoesnotsufferfromedgeeffectsforstraight- onviewing.Thedownsideisthatallofthesedevices areunidirectional.Thedevicesmayhavevalue,for example,incloakingsatellitesinmid-tohigh-earth orbitsorforanysmallfield-of-viewcloaking.It shouldbepointedoutthattransverseillumination orself-illuminationofthecloakedobjectstillrenders theobjectinvisibletotheobserver.Whileithasbeen shownthatperfectinvisibilitycannotbeattained [ 20 ],anopenquestioniswhetherstandardoptics canachievegeometric(rayoptic)omnidirectional ormultidirectionalcloaking[ 2 ].Currenteffortsare exploringcloakswithsphericalsymmetry(muchlike retroreflectingspheresachievingmultidirectional reflection),whichmayachievemultidirectional cloaking. AftersubmissionofthispapertothearXiv[ 21 – 23 ], anotheramplitude-onlycloakingschemeappeared [ 24 ].Theirschemeusedpassiverefractiveelements tomimicmetamaterialcloaks. TheauthorswouldliketothankC.Levitforpoint- ingoutreference[ 17 ].J.C.Howellwouldliketo thankA.Aluforhelpfuldiscussions. References 1.J.B.Pendry,D.Schurig,andD.R.Smith, “ Controllingelectro- magneticfields, ” Science 312 ,1780 – 1782(2006). 2.U.Leonhardt, “ Opticalconformalmapping, ” Science 312 , 1777 – 1780(2006). 3.H.Chen,C.T.Chan,andP.Sheng, “ Transformationopticsand metamaterials, ” Nat.Mater. 9 ,387 – 396(2010). 4.D.Schurig,J.J.Mock,B.J.Justice,S.A.Cummer,J.B.Pendry, A.F.Starr,andD.R.Smith, “ Metamaterialelectromagnetic cloakatmicrowavefrequencies, ” Science 314 ,977 – 980(2006). 5.W.Cai,U.K.Chettiar,A.V.Kildishev,andV.M.Shalaev, “ Op- ticalcloakingwithmetamaterials, ” Nat.Photonics 1 ,224 – 227 (2007). 6.N.Liu,H.Guo,L.Fu,S.Kaiser,H.Schweizer,andH.Giessen, “ Three-dimensionalphotonicmetamaterialsatoptical frequencies, ” Nat.Mater. 7 ,31 – 37(2008). 7.I.I.Smolyaninov,Y.J.Hung,andC.C.Davis, “ Two- dimensionalmetamaterialstructureexhibitingreducedvis- ibilityat500nm, ” Opt.Lett. 33 ,1342 – 1344(2008). 8.I.I.Smolyaninov,V.N.Smolyaninova,A.V.Kildishev,and V.M.Shalaev, “ Anisotropicmetamaterialsemulatedby taperedwaveguides:applicationtoopticalcloaking, ” Phys. Rev.Lett. 102 ,213901(2009). 9.N.LandyandD.R.Smith, “ Afull-parameterunidirectional metamaterialcloakformicrowaves, ” Nat.Mater. 12 ,25 – 28 (2013). 10.R.Liu,C.Ji,J.J.Mock,J.Y.Chin,T.J.Cui,andD.R.Smith, “ Broadbandground-planecloak, ” Science 323 ,366 – 369 (2009). 11.J.Valentine,J.Li,T.Zentgraf,G.Bartal,andX.Zhang, “ An opticalcloakmadeofdielectrics, ” Nat.Mater. 8 ,568 – 571 (2009). 12.L.H.Gabrielli,J.Cardenas,C.B.Poitras,andM.Lipson, “ Sil- iconnanostructurecloakoperatingatopticalfrequencies, ” Nat.Photonics 3 ,461 – 463(2009). 13.U.LeonhardtandT.Tyc, “ Broadbandinvisibilitybynon- Euclideancloaking, ” Science 323 ,110 – 112(2009). 14.B.Zhang,Y.Luo,X.Liu,andG.Barbastathis, “ Macroscopic invisibilitycloakforvisiblelight, ” Phys.Rev.Lett. 106 , 033901(2011). 15.M.Fridman,A.Farsi,Y.Okawachi,andA.L.Gaeta, “ Demon- strationoftemporalcloaking, ” Nature 481 ,62 – 65(2012). 16.R.Fleury,J.Soric,andA.Alu, “ Physicalboundsonabsorption andscatteringforcloakedsensors, ” arXiv:1309.3619 (2013). 17.R.Houdin, TheSecretsofStageConjuring (Wildside,2008). 18. “ Invisibility, ” http://www.youtube.com/watch?v=RwgIr06OJLo . 19. “ MirrorsTricksofMagicShowsattheScienceandTechnology MuseumMadaTech — 12, ” http://www.youtube.com/watch? v=_hF8xuPShsM . 20.E.WolfandT.Habashy, “ Invisiblebodiesanduniquenessof theinversescatteringproblem, ” J.Mod.Opt. 40 ,785 – 792 (1993). 21.J.C.HowellandJ.B.Howell, “ Simple,broadband,optical spatialcloakingofverylargeobjects, ” Phys.Opt.,ar- Xiv:1306.0863(2013). 22. “ Human-scaleinvisibilitycloakunveiled, ” MITTechnology Review(June6,2013). 23.A.Boyle, “ This ‘ InvisibilityCloak ’ CouldConcealSatellitesor HideYourKids , ” (NBCNews,2013). 24.H.Chen,B.Zheng,L.Shen,H.Wang,X.Zhang,N.I.Zheludev, andB.Zhang, “ Ray-opticscloakingdevicesforlargeobjectsin incoherentnaturallight, ” Nat.Commun. 4 ,2652(2013). 20March2014/Vol.53,No.9/APPLIEDOPTICS1963