Freestanding transparent terahertz half-wave plate using subwavelength cut-wire pairs

0.77 MB·

by  Yosuke Nakata

Freestanding transparent terahertz
half-wave plate using subwavelength
cut-wire pairs
YosukeNakata,1,∗YudaiTaira,2ToshihiroNakanishi,3andFumiaki
Miyamaru1,2
7 1CenterforEnergyandEnvironmentalScience,ShinshuUniversity,4-17-1Wakasato,Nagano
1 380-8553,Japan
0 2DepartmentofPhysics,FacultyofScience,ShinshuUniversity,3-1-1Asahi,Matsumoto,
2 Nagano390-8621,Japan
3DepartmentofElectronicScienceandEngineering,KyotoUniversity,Kyoto615-8510,Japan
n
∗[email protected]
a
J

9
2 Abstract: We designed a cut-wire-pair metasurface that works as a
transparentterahertzhalf-waveplate,bymatchingtheelectricandmagnetic

] resonances of the structure. Due to the impedance matching nature of
s
c the resonances, a large transmission phase shift between the orthogonal
i polarizationswasachieved,whilepermittingahightransmission.Theelec-
t
p tric and magnetic responses of the proposed structure were confirmed by
o
evaluating the electric admittance and magnetic impedance. The structure
.
s wasfabricatedonaflexiblefilmanditshelicity-conversionfunctioninthe
c
terahertzfrequencyrangewasexperimentallydemonstrated.Thethickness
i
s of the device is less than 1/10 of the working vacuum wavelength, and a
y
h high amplitude helicity conversion rate over 80% was achieved. Finally,
p using simulations, we demonstrate the feasibility of the gradually rotating
[ cut-wire-pairarrayinterahertzwave-frontcontrol.

1 © 2017 Optical Society of America. One print or electronic copy may be made
v
forpersonaluseonly.Systematicreproductionanddistribution,duplicationofany
6
materialinthispaperforafeeorforcommercialpurposes,ormodificationsofthe
4
contentofthispaperareprohibited.
3
8 OCIScodes:(160.3918)Metamaterials;(130.5440)Polarization-selectivedevices;(300.6495)
0 Spectroscopy,terahertz.
.
1
0
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1. Introduction
Duringthelasttwodecades,therehasbeenrapidprogressinterahertzspectroscopytechniques
andtheyhavebeenappliedinseveralfields[1].Especially,therecentprogressinthedevelop-
ment of high-power terahertz sources has accelerated the growth of terahertz nonlinear spec-
troscopy [2], and imaging technologies [3]. In spite of these remarkable developments, com-
merciallyavailabledevicestocontrolterahertzwavesarestilllacking.Theprogressofterahertz
polarization-dependentspectroscopyandimagingapplicationsdemandterahertzwaveplates.
Although achromatic terahertz waveplates have been developed [4, 5], the size of conven-
tional terahertz devices is typically much larger than the terahertz wavelength. To make the
terahertz system compact, it is highly desirable to develop ultrathin waveplates. Artificially
designedmaterials,ormetamaterials,havebeendevelopedtoovercomethisproblem[6].Two-
dimensionalmetamaterialscalledmetasurfaces,whichhavethicknessesmuchlessthanwork-
ing wavelengths, and their ability to control electromagnetic waves have been studied inten-
Fig.1.(a)Symmetricelectricmode.(b)Anti-symmetricmagneticmodeofthecurrenton
ametalliccut-wirepair.
sively [7]. So far, the application of terahertz metasurfaces in quarter wave plates have been
investigated[8,9,10,11].
A half-wave plate has the ability to convert helicity, e.g. from right-circular polarization
(RCP)toleft-circularpolarization(LCP).However,inprinciple,ahighlytransparenthalf-wave
platewithanamplitudeconversionefficiencyfromLCPtoRCP(RCPtoLCP)over50%can-
notberealizedusingasingle-layermetasurface[12].Therefore,multilayerdesignsarerequired
toachievethisfunctionality.Recently,Wuetal.discoveredthattwolayersofdouble-cutsplit
ring resonators work as a highly transparent subwavelength half-wave plate, and experimen-
tallyrealizedtheminthemicrowavefrequencyrange[13];however,theguidingprincipleused
to design the structure is unclear. Another approach to realize a highly transparent half-wave
plateistheuseofamultilayerdipolearray.Y.Heetal.proposedtheuseofthree-layerdipole
structurestoimplementaninfraredhalf-waveplate,basedonthemicrowavephase-shifterthe-
ory[8].However,inordertomakethefabricationprocesssimpler.itisdesirablehavealower
numberofdipolelayers.
Inthispaper,weshowthatametasurfacecomposedofcut-wirepairs,interactingwitheach
other, can act as a highly transparent half-wave plate in the terahertz frequency range. The-
oretically, the metasurface is designed by matching the electric and magnetic resonances of
cut-wire pairs. In spite of the extremely simple design of the metasurface, it exhibited broad-
band impedance matching during simulations. We fabricated the structure on a flexible film,
anddemonstrateditshelicity-conversioncapabilityintheterahertzfrequencyrange.Theappli-
cationofametasurfaceinterahertzwave-frontcontrolisalsodiscussed.
2. Design
From a macroscopic point of view, an isotropic metasurface can be characterized by a zero-
thickness surface with an effective electric sheet admittance Y and and magnetic sheet
e
impedance Z . We assume that this surface is located at z=0. The macroscopic parameters
m
relate the effective surface electric current density K and the magnetic current density K ,
m
flowing on z=0, with the coarse grained electric field E and magnetic field H at z=0, as
K=Y E ,K =Z H ,where“av”indicatesthatthefieldsontheupside(z=+0)anddown-
e av m m av
side(z=−0)areaveraged.Foranormallyincidentplanewave,thecomplexelectricamplitude
transmission and reflection coefficients are denoted ast and r, respectively. The effective pa-
rametersY andZ canbegivenbythefollowingequations[14]:
e m
Y 1−r−t Z 1+r−t
e =2 , m =2 . (1)
Y 1+r+t Z 1−r+t
0 0
(cid:112)
Here,Z = µ /ε (=1/Y )istheimpedanceoffreespace.Definingy =Y /(2Y )andz =
0 0 0 0 e e 0 m
Z /(2Z ), we also have t =(1−y z )/[(1+y )(1+z )],r =(z −y )/[(1+y )(1+z )].
m 0 e m e m m e e m
From these equations, the impedance matching z =y leads to zero reflection, although the
m e
phase oft could be an arbitrary value. For example,t =(1−jb)/(1+jb) induces the phase
ϕ =−2arctanbfory =z = jb,b∈R.
e m
Now,weconsiderametasurfacecomposedofmetalliccut-wirepairs[15,16,17,18,19,20].
Apairofparallelcutwirescoupledwitheachotherhastworesonantmodes:anelectricmode
formedbythesymmetricallyflowingcurrents[Fig.1(a)],andamagneticmodeformedbythe
antisymmetrically flowing currents [Fig. 1(b)]. The electric mode can be induced by an os-
cillatingelectric fieldparallel tothe current.On theotherhand, atime-varying magneticflux
penetrating the cut-wire pair will excite the magnetic mode composed of rotating currents in
thecut-wirepair.Thus,theelectricandmagneticmodesaffectY andZ ,respectively.Match-
e m
ingtheresonantfrequenciesofthesemodescouldinducealargephaseshift,whilepermitting
a high transmission. Based on this idea, the structure was designed using the finite element
methodwithCOMSOL.Forthis,weconsideredthecut-wirepairstobearrangedintheformof
hexagonallattices.Notethefollowingdesignstrategyisapplicabletootherlatticesymmetries
includingsquarelattices.TheunitcellofthestructureisdepictedinFigs.2(a)and2(b).Peri-
odicboundaryconditionswereutilizedforthesimulation.Themetalliccutwireswereplaced
on both sides of the substrate, which was made of cyclic olefin copolymers (COC) having a
thicknesst=40µmandrefractiveindexn˜=1.53−0.001j[21].
First,theeigenfrequenciesoftheelectricandmagneticmodeswerematched.Theeigenfre-
quenciesofthemetasurfacewerecalculatedbyusingtheeigensolverfunctioninCOMSOL.In
order to reduce the simulation complexity for the eigenfrequency analysis, metallic cut wires
wereassumedtobezero-thickperfectelectricconductor(PEC),andonlythez≥0domainwas
considered.Forthemagneticmodes,thePECboundaryconditionwasimposedonz=0.For
theelectricmodes,theperfectlymagneticconductorboundaryconditionwasimposedonz=0.
The perfectly matched layers were attached to the upper boundary of the air domain, so that
therewouldbeaproperabsorptionoftheleakageradiationinthezdirection.Afteroptimiza-
tion,weobtaineda=585µm,l=215µm,andw=169µm.Thecalculatedeigenfrequencies
ofthestructureareshowninTable1.Itcanbeseenthatboththeelectricandmagneticmodes
ofthecurrent(cid:107)yexistaround0.51THz.Thesemodesmayleadtotheimpedancematchingof
thestructure,andcouldinducealargephaseshiftwhilemaintainingahightransmission.
Next, we calculated the transmission property of the metasurface. A plane wave normally
enters the metasurface from z>0 to z<0. The metallic cut wire was treated as a transition
boundary equivalent to a 0.5µm-thick silver film having a conductivity of 46S/µm [22]. For
comparison,wealsocalculatedtransmissionspectraofalosslessmetasurfacecomposedofPEC
cut-wire pairs with a lossless substrate having a refractive index n˜=1.53. For a β-polarized
incident electric field E e exp(jkz) in z>0, the α-polarized component of the transmitting
0 β
electric field in z<0 is represented by E e t exp(jkz), using amplitude transmission co-
0 α αβ
efficients t , a constant E , the wavevector k (>0) in air, and two orthonormal vectors e
αβ 0 α
(α=1,2)perpendiculartothez-axis.Thecalculatedamplitudeandphasetransmissionspectra
of the optimized metasurface for x and y polarized plane waves are shown in Figs. 2(c) and
2(d). At 0.506THz, the functions of the half-wave plate can be observed to be |t |≈0.99,
xx
|t |≈0.85,andarg(t )−arg(t )≈3.2forthesilvermetasurface.Surprisingly,ahightrans-
yy xx yy
mission amplitude |t | over 0.8 is observed in the broadband region. This indicates that the
yy
oscillator strength and line width of the electric and magnetic resonant modes are approxi-
Table1. Calculatedeigenfrequenciesforcut-wirepairson40µm-thickcycloolefincopoly-
mersubstratewitha=585µm,l=215µm,andw=169µm.
electricmode magneticmode
current(cid:107)x 0.473THz 0.422THz
current(cid:107)y 0.514THz 0.510THz
matelybalanced.Incomparisonwiththelosslessmetasurface,|t |ofthesilvermetasurfaceat
yy
theworkingfrequencyisdegradedbythemetalandsubstrateloss.Cryogenictemperaturescan
beapathtowardsdecreasingunavoidablelosseffect[23].
Theelectricandmagneticresponsesofthesilvermetasurfaceforeachpolarization,|Y |and
e
|Z |,calculatedbyEq.(1),areshowninFigs.2(e)and2(f).Foranx-polarizedwave,itcanbe
m
seenthatthefrequenciesof|Y |and|Z |peaksaredifferent,andtheyarefar-off-resonantfrom
e m
theoperationfrequency0.506THz.Alternatively,foray-polarizedwave,thepeakfrequencies
arealmostsame,andimpedancematchingisapproximatelyachievedinthebroadbandregion.
Therefore, we can realize not only a half-wave plate, but also an efficient phase plate with
differentphaseshiftsfordifferentworkingfrequencies.
Fig.2. (a)Topviewofthesimulationmodel.(b)Sideviewofthemodel.(c)Amplitude
and(d)phasetransmissionspectraofsilvercut-wirepairsonaCOCsubstratewitha=
585µm,l=215µm,w=169µm,andt=40µmforxandypolarizednormallyincident
waves(losslesscasesarealsoshownforcomparison).Macroscopicelectricadmittanceand
magneticimpedanceofthesilvercut-wirepairsonaCOCsubstratefor(e)x-polarizedand
(f)y-polarizedwaves.
3. Experimentaldemonstrationofterahertzhelicityconversion
The experimental demonstration of the function of the terahertz half-wave plate is described
below.Thesamplewaspreparedasfollows:(i)A10nmtitaniumadhesionlayerfollowedby
a1.4µmaluminumlayerweredepositedonbothsidesofthe40µmCOC(ZEONOR®,Zeon
Corp.) by electron-beam evaporation at room temperature, (ii) cut-wire-pair structures were
formed on both sides of the substrate using a femtosecond laser ablation process. Note that
wedepositeda1.4µm-thickaluminumlayertoavoidtheskineffectasmuchaspossible,but
athicknesssufficientlylargerthantheskindepth≈150nmofaluminumat0.5THzcouldbe
enough.ThefabricatedsampleisshowninFigs.3(a)–(c).InFigs.3(b)and3(c),itcanbeseen
that the boundary of the unit cell is whiter than the other parts. This is because the boundary
is shaved twice by the scanning laser beam. From the microphotographs of the sample, the
measureddimensionsarel=217µmandw=174µm,withadeviationof1µm.
Next,usingaterahertztime-domainspectroscopysystem,wedemonstratedthehelicitycon-
versionfunctionofthehalf-waveplate,whichisapplicabletothewave-frontcontroldiscussed
inSec.4.Here,theco-andcross-polarizedamplitudetransmissionst andt (t andt )for
xx yx yy xy
normallyincidentx(y)polarizedwavesweremeasuredusingastandardcrossellipsometrypo-
larizationprobingsetup[24],andthevaluesof|t |and|t |werecalculated,whereRandL
LR RR
represent RCP and LCP (rotating direction as seen from the detector side), respectively. The
plotsoftheexperimentallyobtained|t |and|t |areshowninFig.3(d).Inthisfigure,itcan
LR RR
be observed that |t | peaks over 0.8, which is beyond the limit of conversion efficiency of
LR
asingle-layermetasurface[12],at0.50THz.Forcomparison,thenumericallycalculated|t |
LR
and|t |forcut-wirepairsof1.4µm-thickaluminumhavingaconductivity22S/µm[22]with
RR
a=585µm, l =217µm, w=174µm, andt =40µm, are shown in Fig. 3(e), where the thin
titaniumlayerwasignoredinthesimulation.Simulatedmaximumconversionefficiencyis0.9,
whichisdegradedbythelosseffectdiscussedinSec.2.Theexperimentallyobtainedspectra
Fig.3. (a)Photographofasample.Microphotographsfrom(b)topand(c)bottomviews
ofthesample.(d)Measuredtransmissionspectraforthesamplefromthebottomsideto
thetopside.(e)Simulatedtransmissionspectrafor1.4µm-thickaluminumcut-wirepairs
ona40µm-thickCOCsubstratewitha=585µm,l=217µm,andw=174µm.
Fig.4. (a)Thetopviewofsimulationmodel.(b)Eyat0.504THzonX–zplane.
agreeswellwiththesimulatedspectra,althoughtheexperimentallyobtainedpeakvalueofhe-
licityconversionisnotashighasthesimulatedone.Thiscanbeattributedtofabricationerror
including over shaving of the substrate. There is still room for device optimization; however,
thebasicfunctionofthehalf-waveplatewasdemonstrated,andthethicknessofthedeviceis
lessthan1/10oftheworkingvacuumwavelength.
4. Towardsterahertzwave-frontcontrol
In this section, we discuss the applicability of the cut-wire pairs to wave-front control. If the
structuresthatconverthelicityarerotated,theconvertedwaveattainsthePancharatnam–Berry
phase. Therefore, it is possible to control the wave front by gradually rotating the structures
[12].ThePancharatnam–Berryphaseinducedforreflectedcircular-polarizedwavesisutilized
for the highly efficient control of wave fronts in the near-infrared region [25, 26]. Recently,
activecontroloftheworkingfrequencyforreflectedcircular-polarizedmicrowaveswastheo-
reticallyproposed[27].Thewave-frontcontrolfortransmittingcircular-polarizedwavesusing
three-layermetallic dipoles[28] anddielectric resonators[29] hasbeen studiedwith thehelp
ofsimulations.
Toinvestigatethepossibilityofcontrollingaterahertzwavefront,wealsoperformedasim-
ulation using COMSOL for implementing a beam deflector. For this, 12 unit cells [shown in
Fig. 1(a)] were connected and each meta-atom was rotated, as shown in Fig. 4(a). The basic
setupforthesimulationwasthesameasthatinSec.2.Theangleofrotationofeachunitcell
wasincreasedbyϕ fromthepreviousadjacentunitcell,withϕ =15◦.Theperiodicboundary
conditionswereappliedtothesideofthesimulationdomain.Fromz>0,anRCPwaveenters
the0.5µm-thicksilvercut-wirearrayonthesurfaces(z=−t/2, t/2)ofaCOCsubstratewith
arefractiveindexn˜=1.53−0.001j.Perfectlymatchedlayerswereattachedtotheupperand
bottom boundaries of the air domain for the proper absorption of diffracted waves. The cal-
culated E at 0.504THz on the X–z plane is shown in Fig. 4(b). In Fig. 4(b), we can see the
y
beamisdeflectedbyθ ontheX–zplane,althoughtheequiphaselinesofthetransmittedwave
X
are not perfectly straight lines. The observed θ ≈5◦ shows good agreement with the theo-
X
reticallycalculatedvalueθ(theo)≈4.9◦.Thetransmittingpowerevaluatedbytheintegrationof
X
the Poynting vector is 73%. In order to experimentally demonstrate this functionality in the
terahertzfrequencyrange,accuratefabricationandterahertzimagingtoevaluatethesampleare
required.
5. Conclusion
In this study, we designed an ultrathin terahertz half-wave plate by matching the electric and
magneticresonancesofcutwirescoupledwitheachother.Theelectricandmagneticresponses
wereanalyzedbyevaluatingtheeffectiveelectricadmittanceandmagneticimpedance.These
resultsindicatedthattheelectricandmagneticresonancesleadtoalargephaseshiftwhilemain-
taininghighbroadbandtransmission.Thedesignedsamplewasfabricatedusingafemtosecond
laser ablation process. Next, we experimentally demonstrated its capability for the polariza-
tionconversionofacircularlypolarizedwave,withafrequencyofapproximately0.5THz.The
thicknessofthedeviceislessthan1/10oftheworkingwavelength,andtheobservedampli-
tude helicity conversion efficiency is over 80%, which is beyond the theoretical limit of 50%
thatcanbeachievedbyasingle-layermetasurface.Furtheroptimizationofthedesignandfab-
rication process could lead to higher conversion efficiency. Although the working bandwidth
ofthemetasurfaceislimitedtothenarrowband,itsultrathinsizecanbeutilizedforapplica-
tions involving continuous terahertz waves, which are often used in terahertz communication
technology.Finally,wediscussedthepossibleapplicationofthemetasurfacetohighlyefficient
wave-frontcontrol.Abeamdeflectorcanberealizedbygraduallyrotatingthemeta-atoms.The
experimentalrealizationofsuchwave-frontcontrolcouldbestudiedinfutureworks.
Acknowledgments
The authors thank Yoshiro Urade for the useful discussions. The electron-beam evaporation
wasperformedwiththehelpofKyotoUniversityNanoTechnologyHub,aspartofthe“Nan-
otechnologyPlatformProject”sponsoredbyMEXTinJapan.