Waveform-selective metasurfaces with normal waves at the same frequency

0.99 MB·English

by  Hiroki Wakatsuchi

Waveform-selective metasurfaces
with normal waves
at the same frequency
5 HirokiWakatsuchi1,2,∗
1 1CenterforInnovativeYoungResearchers,
0 NagoyaInstituteofTechnology,Nagoya,Aichi,466-8555,Japan
2 2DepartmentofElectricalandElectronicEngineering,
NagoyaInstituteofTechnology,Nagoya,Aichi,466-8555,Japan
n
∗[email protected]
a
J

2
1 Abstract: Waveform-selective metasurfaces, reported by Wakatsuchi et
al. in 2014, have enabled us to distinguish differentsurface waves even at

] the same frequency in accordance with their waveforms or pulse widths.
s
c In this study we demonstrate that such new characteristics are applicable
i
t to controlling not only surface waves but also free-space waves normal
p
to metasurfaces. Both simulation and measurement results show selective
o
absorption or transmission for specific pulses at the same frequency.
.
s
Thus the waveform selectivity is expected to create a wider range of
c
i new applications, for instance, waveform-selective antennas and wireless
s
communications.
y
h
© 2015 OpticalSocietyofAmerica
p
[ OCIScodes:(160.3918)Metamaterials;(350.4010)microwaves

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1. Introduction
In general electromagnetic propertiesare determined by the composition of each material as
well as by the frequency of an incoming wave. For example, the former includes molecules
that behave differently in response to incoming waves. However, their scales are orders of
angstrom and thus it is difficult to controltheir behaviorsin an artificial manner. The advent
ofartificialmaterials,ortheso-calledmetamaterialsandmetasurfaces[1,2,3],enabledusto
controlelectromagneticpropertiesdependingnotonlyoncompositemoleculesbutalsoonthe
resonanceof subwavelength-scaleperiodicstructures,which can arbitrarilybe designedeven
tocreatenewkindsofapplicationssuchasdiffraction-limitlesslenses[4,5],cloaking[6,7,8],
extremelythin absorbers[9, 10, 11, 12, 13, 14], etc. However,still the resonanceof artificial
materials is strongly influenced by the incoming frequency componentso that even artificial
materials behave differently in accordance with the frequency. This in turns indicates that if
thefrequencyisfixed,alwayseachmaterialbehavesinthesamemanner.Althoughnonlinear
artificialmaterialscanvarytheirelectromagneticpropertiesdependingonthemagnitudeofthe
incomingwave or externalbias [15, 16, 17], it is still difficultto manipulateelectromagnetic
responsesatthesamefrequencywiththesamepowerlevel.
Recently, Wakatsuchi et al. demonstrateda new techniqueto controlabsorptionand trans-
missionofsurfacewavesthroughuseofcircuit-basedmetasurfacesthatconsistedofschottky
diodesandothercircuitcomponentssuchascapacitors,inductors,andresistors[18,19,20,21].
Fig.1.(Coloronline)Imageofwaveformselectivity.Conventional materialsarecapable
of sensingdifferent wavesandabsorbing specificsignalsifthefrequencies aredifferent.
Waveform-selectivemetasurfacesallowustodistinguishdifferentwavesevenatthesame
frequencydependingonthewaveformsorpulsewidths.
Inthesestructures,firstlyanincomingwaveinducedelectricchargesonperiodicallymetalized
patches,generatingstrongelectricfieldacrossthegaps.Withinthegapsdiodesrectifiedthein-
comingsignalandconvertedthefrequencycomponenttozerofrequency.Therectifiedenergy
wasthencontrolledbythetimeconstantsofothercircuitcomponents,i.e.RC andL/Rwhere
R,L,andCrepresentresistance,inductance,andcapacitance,respectively.Asaresult,theab-
sorbingperformancesofthecircuit-basedmetasurfacesvarieddependingonthepulsewidthof
theincomingwave(Fig.1).
In the previous study, however, such waveform selectivities were demonstrated only with
surfacewaves,althoughthesamephenomenaareexpectedtobeachievedwithfree-spacewaves
impinging the surfaces at a normal angle, since the structures can still resonate in response
to normal waves, which can potentially broaden the range of the applications of waveform-
selectivemetasurfaces.Therefore,inthispaperweinvestigatetheperformancesofwaveform-
selective metasurfaces with normal waves both numerically and experimentally for the first
time.
2. Simulationmethod
Simulationswerecarriedoutbyaco-simulationmethod[14,18,19],whichintegratedanelec-
tromagneticsimulatorHFSS(version15.0)withacircuitsimulatorDesigner(version8.0).In
this methodmetasurfaceswere modeledin the EM simulator with lumpedports,which were
laterreplacedwithcircuitcomponentsinthecircuitsimulator,whereallofthesimulationre-
sults wereobtained.Comparedto anconventionalsimulationmethodperformedsolelybyan
electromagnetic simulator, this co-simulation analysis allowed us to significantly reduce the
simulationtime,thuscontributingtoreadilychangingcircuitparameters,dimensionsofmeta-
surfaces, etc. In these simulationsabsorbingperformancewas evaluatedfromabsorptanceA,
whichwascalculatedfromA=1−S2 ,whereS wasthereflectioncoefficient.
11 11
Fig. 2. (Color online) (a) Simulation model surrounded by periodic boundaries. Patches
wereplacedonadielectricsubstrate(Rogers3003).(b)Betweenpatchessomecircuitcom-
ponents were deployed. Each dimension was given from cx =7.6, cy =1.7, dx =1.3,
dy =0.5, g=1.0, l=2.4, p=18.0, rx =1.0, ry=2.0,tp=0.017, andts=1.524 (all
inmm).(c)and(d)pairsofaparallelcapacitorandresistorwereusedascapacitor-based
metasurfaces, while pairs of a series inductor and resistor were used as inductor-based
metasurfaces.(e)and(f)Thesetwocircuitconfigurationswerecombinedeitherinparallel
orinseries,respectively,asparallel-typemetasurfacesorseries-typemetasurfaces.
Fig.2showsthebasicconfigurationofthemetasurfacessimulated.Fig.2(a)illustratesthat
aperiodicunitofametasurfacewassurroundedbyperiodicboundariessothataninfinitearray
of themetasurfacewaseffectivelymodeled.As seenin thisfigure,theperiodicstructurewas
composedofconductingpatchesandgroundplaneaswellasadielectricspacer(Rogers3003)
in between. Four diodes were deployed in a gap (Fig. 2(b)) to play a role of a diode bridge,
whichmoreeffectivelyconvertedanincomingwavetozerofrequencycomponent,comparedto
halfwaverectificationobtainedbyasinglediode[14](i.e.considerFouriertransformsoffull-
wave rectification |cos| and half-wave rectification (cos+|cos|)/2). Within the diode bridge
someothercircuitcomponentsweredeployed,whichdeterminedthetypeandbehaviorofthe
waveform-selectivemetasurface.Althoughdetailsarefullydescribedinotherpublications[18],
in shortuse ofa capacitorinparallelwith a resistor leadsto absorptionofa shortpulse(Fig.
2(c)), while use of an inductor in series with a resistor results in absorption of a long pulse
(Fig. 2(d)). In addition, combinationsof these circuit configurationsin parallel/series lead to
selectivetransmission/absorptionofsomemiddlepulsesinbetween(Fig.2(e)and(f)).These
areallunderstandableif theimpedancesofacapacitorandinductor(namely1/jw C and jw L
where j2 =−1 andw is an angularfrequency)are associated with the frequencycomponent
convertedfrom f tozerofrequency,where f denotestheincomingfrequencycomponent.De-
Table1.Circuitparametersusedforwaveform-selectivemetasurfaces
Circuitcomponent Value Resonantfrequency
Capacitor-based Capacitor 1nF 300MHz
metasurface Resistor 10kW N/A
Inductor-based Inductor 100m H 10MHz
metasurface Resistor 5.5W N/A
Capacitor 100pF 1.02GHz
Parallel-type Inductor 1mH 2.4MHz
metasurface Resistor(pairedwithcapacitor) 10kW N/A
Resistor(pairedwithinductor) 31.2W N/A
Capacitor 10nF 57.3MHz
Series-type Inductor 10m H 45MHz
metasurface Resistor(pairedwithcapacitor) 10kW N/A
Resistor(pairedwithinductor) 2W N/A
Table2.ParametersforSPICEmodelofdiodes
Parameter Value
B 7.0V
V
C 0.18pF
J0
E 0.69eV
G
I 1·10−5A
BV
I 5·10−8A
S
N 1.08
R 6.0W
S
P (VJ) 0.65V
B
P (XTI) 2
T
M 0.5
Fig. 3. (Color online) Simulationresults of infinitearrays of (left)capacitor- and (right)
inductor-basedmetasurfaces.Thesimulationswereperformedwith(a,b)CWsand(c,d)
50-nsshortpulses.
Fig.4.(Coloronline)Pulsewidthdependencesof(a)capacitor-andinductor-basedmeta-
surfacesand(b)parallel-andseries-typemetasurfaceswith0dBmpulsesat3.8GHz.
tailed dimensionsand moreinformationof the structure are givenin Fig. 2 andTables 1 and
2.
3. Simulationresults
Fig.3showssimulationresultsofthecapacitor-andinductor-basedmetasurfaceswithcontin-
uouswaves(CWs) andshortpulses(50nslong).AsseeninFigs.3(a)and(c),thecapacitor-
basedmetasurfaceeffectivelyreducedreflectionofshortpulsesandexhibitedstrongabsorption
around3.9GHz,althoughtheabsorbingperformanceforCWswaslimitedevenatthesamefre-
quency.Thisisbecausethecapacitorsusedinsidediodebridgesstoredtheincomingenergiesof
shortpulsesanddissipatedthemwithresistorslater,althoughCWsignalsfullychargedupthe
capacitorsto preventthisabsorbingmechanism.On the otherhand,the inductor-basedmeta-
surface showed strong absorption for CW signals, while short pulses were poorly absorbed.
This can be accounted for the electromotive force of inductors, which blocked an incoming
short pulse but was gradually reduced due to the presence of the zero frequencycomponent.
As a result, more energywas dissipated with the resistors deployed in series with the induc-
tors. Clear transitions between a short pulse and long pulse can be seen in Fig. 4(a). In this
figure, the incoming frequency and power were respectively set to 3.8 GHz and 0 dBm. As
aconsequence,thecapacitor-basedmetasurfacegraduallyreducedtheabsorbingperformance
asthe pulsewidthincreased,whilethe inductor-basedmetasurfaceenhanced.Notethatthese
absorptancecurvessaturatedaroundthetimeconstantsused(seeRCandL/RofTable1).
Additionally,Fig.4(b)showsthepulsewidthdependencesofmetasurfacescombiningthese
two circuitconfigurationsin either parallelor series, i.e. as parallel-typeor series-typemeta-
surfaces (see Figs. 2(e) and (f) for specific circuitconfigurations).In this case the circuit pa-
rameters of capacitors, inductors, and resistors were modified as those in Table 1 in order to
increase the contrast between a weaker level of absorptance and a stronger level within this
pulse widthrange.Asa result, thesetwo structuresrespectivelyexhibitedtemporalreduction
andenhancementoftheabsorbingperformanceatthesamefrequencyof3.8GHzasthepulse
width increased from 20 ns to 20 m s. Regarding the parallel-type metasurface, short pulses
wereeffectivelyabsorbedbythecapacitorpart,whilelongpulseswereabsorbedbytheinduc-
torpart.Forthisreasonbothshortandlongpulseswerestronglyabsorbed,althoughtherewas
still a region where both capacitor and inductor parts did not effectively absorb some pulses
inbetween.Ontheotherhand,theseries-typemetasurfaceexhibitedweakabsorptionforboth
short and long pulses due to the inductor part and capacitor part, respectively.However,still
bothcircuitpartsstronglyabsorbedincomingwavesaround500nspulsewidth,resultinginthe
temporalenhancementoftheabsorbingperformance.
Importantly,allthesetrendsagreedwithresultsofsurfacewavecasesdemonstratedbefore
[18].Oneoftheimportantdifferenceshereliesinthepowerlevelnecessaryforachievingthe
waveformselectivity,asthecrosssectionusedinthisstudyissmallerthanbefore.Additionally,
absorptance peaks were entirely shifted to lower frequencycompared to surface wave cases,
whichissupposedtobeduetoangulardependencesofthemetasurfacesasseeninotherkinds
ofmetasurfaces(e.g.[10,22]).
4. Measurementmethod
AsdrawninFig.5(a),measurementswereperformedwithaTE(TransverseElectric)waveg-
uide,ormorespecificallyWR284,asarealisticbutstillsimplemeasurementmethodtoevaluate
theperformancesofthewaveform-selectivemetasurfaces.Duetothefinitesizeofthecrosssec-
tionofthewaveguide,thenumbersoftheperiodicunitsweresettotwoandfour,respectively,
alongthedirectionoftheincidentelectricfieldandalonganotherdirectionofthecrosssection
(Fig.5(b)).Byreducingthe originalperiodicity18mmto17mm,eachmeasurementsample
fit into the cross section of the waveguide.To ensure that incomingwaves would notsignifi-
cantlyleak outofthe waveguide,coppertapewas attachedto the groundplanesofthemeta-
surfacesand waveguideas shownin Fig. 5(c).Anotherside of the waveguidewas connected
toanadapter,whichreceivedincomingsignalsfromanetworkanalyzer(KeysightTechnology
N5222A)viaacoaxialcable.Althoughourpreviousstudyusedadifferentmeasurementsetup
that consisted of a signal generator, power meters, power sensors, etc [14, 18, 19], this new
measurementsetupallowedustoreadilysweepfrequencysothatfinerfrequencystepscouldbe
used,whichwasusefultoseemoredetailsofthewaveformselectivity.Inthesemeasurements
calibrationwas performedwith an electroniccalibrationmodule(N4691-60006)betweenthe
Fig.5.(Coloronline)Measurementsetupandsample.(a)Themeasurementsetupwascom-
posedofanetworkanalyzer,coaxialcable,andTEwaveguide(WR284)wheremeasure-
mentsamplesweredeployed.(b)Eachsamplehadareducedperiodicity(p=17mm)and
2×4periodicunitstofitintothecrosssectionofthewaveguide.Diodeswerechosenfrom
commercial schottky diodes of Avago (HSMS-2863/2864). (c) To ensure that incoming
waveswouldnotsignificantlyleakoutofthewaveguide,coppertapewasattachedtothe
groundplanesofmeasurementsamplesandwaveguide.(d)Apairoftwo0.2pFcapacitors
wasdeployedineachgaptoshiftentirefeaturesofabsorbingperformancesofwaveform-
selectivemetasurfacesbelow4.16GHz,wherethesecondmodestartspropagating.
cableandadapterforthesakeofsimplicity.However,thisledtominorreductioninreflection,
evenwhenameasurementsamplewasreplacedwithaconductingplate,whichwassupposed
tobelossless.Therefore,thisminorabsorptancefoundwiththeconductingplateA wastaken
0
into account together with the reflection from the material under test S to correct effective
11
absorptanceA:
1−S2 −A
A= 11 0. (1)
1−A
0
Herethedenominatoristore-normalizethereducedabsorptanceto1.0inordertoassumethat
therewasnoabsorptionwhentheconductingplatewasdeployed.
Anotherpointtonotehereisthatthewaveguideusedhadanoperatingfrequencyrangewhere
onlytheTE modeissupported.Aswellknown,cutofffrequencies f canbecalculatedfrom
10 c
c mp 2 np 2
f = 0 + , (2)
c 2p r a b
(cid:16) (cid:17) (cid:16) (cid:17)
wherec isthespeedoflightinvacuum(i.e.c =299,792,458m/s),andaandbarerespectively
0 0
the heightandwidthofthe waveguide(herea=34mm andb= 72mm).m andnrepresent
integers,butnomorethanoneparametercanbezero.Therefore,itisfoundwiththisequation
that the secondmode starts propagatingin the waveguideat approximately4.16GHz, which
means that below 4.16 GHz only TE mode is allowed to propagateunless the frequencyis
10
lowerthanthecutofffrequencyofTE mode(i.e.∼2.08GHz).
10
5. Measurementresults
Measurementresultsofacapacitor-basedmetasurfaceandinductor-basedmetasurfaceareplot-
tedinFig.6,wherethegrayareasrepresentthefrequencyrangewheretheoreticallythesecond
modecanpropagate(ascalculatedfromeq.(2)).Firstofall,thesemeasurementsrequiredlarger
inputpowers,asthecrosssectionofthewaveguidewaslargerthanthatofthesimulations(i.e.
morepowerwasneededtoturnondiodesandtoobtainwaveform-selectivebehaviors).Under
Fig.6.(Coloronline)Measurementresultsof(left)capacitor-basedmetasurfaceand(right)
inductor-based metasurface. The absorptances for CWs are shown in (a) and (b), while
thosefor50-nsshortpulsesarein(c)and(d).
this circumstance, as demonstrated in Fig. 3, the capacitor- and inductor-based metasurfaces
moreeffectivelyabsorbedshortpulsesandCWsignals,respectively,buttheabsorptancepeaks
werebeyond4.16GHz.Thesehighfrequencyshiftscanbeaccountedfortheperiodicitychange
aswellasforthediscontinuitybetweenconductingpatchesandwaveguides,bothofwhichde-
creasedtheeffectivetotalcapacitancesofthemetasurfacesandthusincreasedtheresonant(or
operating)frequenciesofthesestructures.
To clarify that these peaks are due to the absorbing mechanism of the waveform-selective
metasurfaces,twoof0.2pFcapacitorswereadditionallydeployedacrosseachgapinorderto
increasethetotalcapacitanceandshifttheentirefeaturetoalowerfrequencyrangewhereonly
theTE modepropagates(seeFig.5(d)).TheseresultsareplottedinFigs.7(a)to(d),which
10
clearly show that the capacitor- and inductor-basedmetasurfaces respectively absorbed short
pulses and CWs even below 4.16 GHz. The differencesbetween the absorptancesfor pulsed
signalsandthoseforCWscanmoreeasilybecomparedwitheachotherinFigs.7(e)and(f).
AsseeninFig.7(e),thecapacitor-basedmetasurfaceincreasedtheabsorbingperformanceby
upto80%,althoughthiscontrastisslightlyreducedfortheinductor-basedmetasurface.This
is assumedto beduetoa superimposeddirectcurrentcharacteristicwhichreducestheactual
inductance value of an inductor chip, when current flows into it too much. In Fig. 8 (a) the
absorbingperformancesof bothwaveform-selectivemetasurfacesare plottedasa functionof
pulse width at 3.75 GHz. In these measurementsthe input power was fixed at 10 dBm. It is
seeninthisgraphthattheabsorptanceofthecapacitor-basedmetasurfacegraduallydecreased
asthepulsewidthincreased,althoughthatoftheinductor-basedmetasurfaceincreased.Com-
pared to the capacitor-based metasurface, the absorptance curve of the inductor-based meta-
surfacesaturatedatashorterpulsewidthvalue,althoughbothstructureshadalmostthesame
time constants (i.e. RC=10m s for the capacitor-based metasurface and L/R≈18m s for the
Fig.7.(Coloronline)Measurementresultsof(left)capacitor-basedmetasurfaceand(right)
inductor-basedmetasurfacewithadditionalcapacitors(extra0.4pFpergap).Theabsorp-
tancesforCWsareshownin(a)and(b),whilethosefor50-nsshortpulsesarein(c)and
(d).ThecomparisonsbetweenthepulseabsorptanceandCWabsorptanceareshownin(e)
and(f),respectively,forthecapacitor-andinductor-basedmetasurfaces.Thesestructures
exhibitedpulsewidthdependencesasplottedin(g)and(h),respectively,wheretheinput
powerwasfixedat10dBm.
Fig.8.(Coloronline)Pulsewidthdependencesoffourtypesofwaveform-selectivemeta-
surfaceswith10dBmsignals.Thecapacitor-andinductor-basedmetasurfacesmeasured
in Fig. 7 varied absorbing performances at 3.75 GHz as seen in (a). The absorptance of
the parallel-type metasurface at 3.75 GHz is plotted in (b), while that of the series-type
metasurfaceat3.60GHzisin(c).
inductor-basedmetasurface).This also supportsthat the influenceof the superimposeddirect
currentcharacteristicmentionedabovewasinvolvedwithreducingtheactualtimeconstantof
theinductor-basedmetasurfaceandshiftingtheentirecurvetotheleftside.Moreentirepictures
ofbothwaveform-selectivemetasurfacesareseeninFigs.7(g)and(h),wheretheabsortances
for 10-dBm pulses are plotted as a function of frequencywith variouspulse widths. In these
figuresbasicallyincreasingthepulsewidthledtodecreasing/increasingtheabsorbingperfor-
mance ofcapacitor-based/inductor-basedmetasurfacearound3.9GHz. Althoughlargerinput
powers were used for these measurementsthan those for the simulations, fairer comparisons
to the measurements are seen in the appendix of this paper, where these metasurfaces were
simulated with a TE waveguideinstead of periodicboundaries.These simulation results also
support that the measured metasurfaces require larger input powers to achieve the waveform
selectivity,comparedtothoseusedforFigs.3and4(seetheappendixfordetail).
Thecapacitor-andinductor-basedcircuitconfigurationswerethencombinedineitherparal-
lelorseriestoexperimentallydemonstratetemporalenhancementandreductionofabsorptance
asseeninsimulations(i.e.Fig.4(b)).Inthiscase,circuitparametersweremodifiedasdescribed
inTable1.Thesemeasurementswerecarriedoutat3.75GHzfortheparallel-typemetasurface
and3.60GHzfortheseries-typemetasurfacewith10dBmpulses.Asaresult,theparallel-and
series-type metasurfaces varied the absorbing performances by approximately 60 and 50 %,
respectively.Intheseresultsthevariationsintheabsorptancesarerelativelylimitedcompared
to those ofthe capacitor-andinductor-basedmetasurfaces,althoughthisis simplydueto the
limitedrangeofthepulsewidth.However,still theseresultssupportthatallofthefourtypes
ofthewaveform-selectivemetasurfacesareexperimentallyfeasibleandvarytheabsorbingper-
formancesinaccordancewithpulsewidthsofnormalwavesevenatthesamefrequency.
6. Conclusion
We havedemonstratedbothnumericallyandexperimentallyfourtypesofwaveform-selective
metasurfaceswithnormalwavesatthesamefrequency.Thecapacitor-basedmetasurfacesre-
ducedtheabsorbingperformanceswhenthepulsewidthoftheincomingwaveincreased,while
theinductor-basedmetasurfacesenhancedtheabsorbingperformances.Thenbothcircuitcon-
figurationswerecombinedineitherparallelorseries.Asaresult,theparallel-typemetasurfaces
showedtemporarilyreducedabsorbingperformancesforsomepulsesbetweenshortandlong