Transmission Control of Electromagnetic Waves by...

Research ArticleTransmission Control of Electromagnetic Wavesby Using Quarter-Wave Plate and Half-Wave Plate All-DielectricMetasurfaces Based on Elliptic Dielectric Resonators

Ali Yahyaoui12 Hatem Rmili13 Karim Achouri4 Muntasir Sheikh3

Abdullah Dobaie3 Adnan Affandi3 and Taoufik Aguili1

1University of Tunis El Manar (UTM) National Engineering School of Tunis (ENIT) Communications Systems Laboratory (SysCom)BP 37 Belvedere 1002 Tunis Tunisia2Electrical and Computer Engineering Department University of Jeddah PO Box 80327 Jeddah 21589 Saudi Arabia3Electrical and Computer Engineering Department King Abdulaziz University PO Box 80204 Jeddah 21589 Saudi Arabia4Department of Electrical Engineering Ecole Polytechnique de Montreal Montreal QC Canada H3T 1J4

Correspondence should be addressed to Ali Yahyaoui aliyahyaouienitutmtn

Received 30 May 2017 Accepted 2 August 2017 Published 10 October 2017

Academic Editor Paolo Burghignoli

Copyright copy 2017 Ali Yahyaoui et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We present the design of all-dielectric Quarter-Wave Plate (QWP) and Half-Wave Plate (HWP) metasurfaces based on ellipticdielectric resonators (EDRs) for the transmission control of electromagnetic waves over the frequency band 20ndash30GHz Firstan extensive numerical analysis was realized by studying the effect of the resonators geometry (thickness and ellipticity) onthe transmission of both 119909- and 119910-polarized waves Then based on the numerical analysis we have realized and characterizedexperimentally both QWP and HWP all-dielectric metasurfaces

1 Introduction

Metamaterials are artificial structures typically engineeredby arranging a set of scattering elements in a regular patternthroughout a volumetric region of space This arrangementallows for desirable bulk electromagnetic responses that aretypically not found naturallyThe extraordinarymetamaterialcontrol of electromagnetic waves is due to the possibilityof engineering effective negative refractive index near-zeroindex cloaking materials and so forth Over the pastseveral years metamaterials have evolved from a theoreticalconcept to a mature and groundbreaking technology withreal-world applications [1ndash5] However three-dimensionalmetamaterials suffer from major issues such as high lossesbulkiness and difficulty of fabrication Most of these disad-vantages may be eliminated by reducing their dimensionalityby arranging electrically small scattering elements intoa two-dimensional pattern at a surface or interface This

two-dimensional version of a metamaterial has beengiven the name metasurface [6 7] For many applicationsmetasurfaces can be used in place of metamaterials with theadvantage of taking up less physical space and having lowerlosses

When the electric andmagnetic resonance frequencies ofthe dielectric resonators are different the phase variation ofthe transmission coefficient is limited to 120587 whereas this valuecan reach 2120587 by superposition of both resonances at the samefrequency [8]

Metasurfaces have a wide range of potential applicationsin electromagnetics including but not limited to control-lable surfaces miniaturized cavity resonators novel wave-guiding structures angular-independent surfaces absorbersbiomedical devices fast switches and fluid-tunable frequen-cy-agile materials Recently several experimental researchworks have been published on the realization of metasurfaceswith such novel functionalities [9]

HindawiInternational Journal of Antennas and PropagationVolume 2017 Article ID 8215291 8 pageshttpsdoiorg10115520178215291

2 International Journal of Antennas and Propagation

The spatial distribution of the subwavelength elementscomposing the metasurface acts on the incident wave interms of amplitude phase and polarization whichmay affectits electromagnetic response and offers the possibility ofobtaining specific functionalities

However the majority of metasurfaces were designedby using metallic elements with Ohmic losses which maylimit their performances especially at optical frequencies Inorder to overcome these limitations all-dielectric metasur-faces have attracted particular interest recently and somesuccessful designswith low-losses high overall efficiency andvarious functionalities [10ndash15] were obtained in microwaveand optical frequencies

Dielectric resonators are the main structure used in all-dielectric metasurfaces because they can excite both electricandmagnetic resonantmodes in addition to the possibility ofreducing the size by using high dielectric constant 120576119903 Severalresonators shapes such as spheres cubes cylindricalellipticaldisks and rods were investigated in order to design all-dielectricmetasurfaces especially at THz and optical frequen-cies [12ndash15]

Therefore in all-dielectric metasurfaces based on dielec-tric resonators the geometrical parameters of the resonatorsand the spacing between them are the main factors affectingthe phase variation as well as the metasurface performances[16ndash18]

Recently we are interested in the design of all-dielectricmetasurfaces based on EDRs operating at microwave fre-quencies The main design parameters of these resonatorsare their ellipticity orientation and thickness In the firststudy [18] we have investigated numerically the effect ofthe resonators ellipticity and orientation on the metasurfacetransmission In this paper we propose a complementarystudy to first determine numerically by using the Ansys-HFSS software the effect of the resonators thickness Thenwe realize and characterize experimentally the optimizedprototypes of the QWP and HWP metasurfaces

2 Metasurface Design

Theproposed all-dielectricmetasurface consists of an infinitetwo-dimensional array of connected EDRs as shown inFigure 1(a) made of dielectric (Rogers RO3210) of relativepermittivity 102 loss tangent 0003 and thickness ℎ

Theminor (along 119909) andmajor radii (along 119910) of the EDRare denoted as 119886 and 119887 respectively whereas its ellipticity is120591 = 119887119886 The size of the unit cell is 119871119909 times 119871119910 times 119871119911 In thisregard 119871119909 = 99mm (119871119909 lt 120582) 119871119910 = 99mm (119871119910 lt 120582)and 119871119911 = 16120582 where 120582 = 10mm is the wavelength associatedwith the upper frequency limit 30GHz and the longitudinaldimension 119871119911 is great compared to the wavelength 120582 (119871119911= 160mm) The resonators are connected along 119909-directionwith thin connection of length 119871119888 = (1198711199092) minus 119887 and width119882119888 = 125mm We have excited the structure with normalincidence (Floquet ports) along 119911-direction

The ellipticity of the resonator was studied by varying theratio 120591 of EDRs while fixing the minor radius at 119886 = 2mm(1205825) without affecting the cell size (120591 is bounded within theranges 1 le 120591 le 247 with a step of 001) Finally the height ℎ

of both the EDRs and the connections is varied from 064 to256mm with a step of 064mm

3 Simulated Results

The simulation of the metasurface was performed by usingthe commercial software Ansys-HFSS In Figure 1(b) wepresent the simulation model where the unit cell boundarycondition was used along 119909- and 119910-directions The model isexcited under normal incidence with Floquet ports along 119911-direction in the frequency range 20ndash30GHz

In order to study the transmission of the designed all-dielectric metasurface we have analyzed its response whenexcited under normal incidence with two orthogonal polar-ization parallel to 119909- and 119910-axes as shown in Figure 1(a)

We define then 119879119909119909 = |119864119909119905||119864119909

119894| and 119879119910119910 = |119864119910119905||119864119910

119894| asthemodule transmission ratio of 119909- and 119910-linear polarizationof the electric field respectively and Δ120601 = 120601119909 minus 120601119910 asthe phase difference between the 119909- and 119910-components ofthe transmitted electromagnetic fields Consequently themoduli 119879119909119909 and 119879119910119910 will vary from 0 to 1 and the phasedifference Δ120601 varies from minus360∘ to +360∘ The QWP andHWP metasurfaces are obtained when the moduli are equal(119879119909119909 = 119879119910119910) and the phase difference is Δ120601 = plusmn90

∘ and plusmn180∘respectively

31 Effect of the Resonator Geometry We have investigatedthe effect of the main design parameters affecting the trans-mission of the all-dielectric metasurface in particular theresonators thickness ℎ size and shape (ellipticity 120591) Theeffect of the resonator size on the metasurface transmissionwas studied mainly by varying the EDR major axis 119887 Resultsfor radius 119886 = 1205825 are illustrated in Figure 2 The effectof the EDR ellipticity on the metasurface transmission wasanalyzed from moduli (119879119909119909 and 119879119910119910) phases (120601119909 and 120601119910)the ratio between moduli (we take log(119879119909119909119879119910119910) for bettervisualization) and the phase shift Δ120601 for four consideredresonator thicknesses ℎ1 = 064mm ℎ2 = 128mm ℎ3 =192mm and ℎ4 = 256mm

In Figure 2 we have studied over the frequency band20ndash30GHz the effect of the resonator ellipticity 120591 andthickness ℎ on themetasurface transmissionWe can remarkeasily that the exciting frequency and the resonators geom-etry (ellipticity and thickness) affect deeply the metasurfacetransmission behavior We can notice also that ellipticity ofthe resonators affects more moduli and phases of 119910-polarizedincident waves (120601119910) than 119909-polarized waves (120601119909) due to theorientation of the resonators along the 119910-axis

However by analysis of colors distribution in Figure 2(a)we can note that the red color which represents high trans-mission moduli (119879119909119909 and 119879119910119910) is more dominant in graphscorresponding to metasurfaces excited with 119910-polarizedwaves This result can be explained by the connection exten-sion along the 119909-axis which reduces slightly the transmissionalong this direction

From Figure 2(b) we can notice the equality betweenmoduli represented with green color

On the other hand we can note that the phases 120601119909 and120601119910 (Figure 2(c)) as well as the phase shift Δ120601 (Figure 2(d))

International Journal of Antennas and Propagation 3

Ey

k

Ex

(a)

Lx

Ly

Lz

Lc

ℎ

Wca

b

(b)

Figure 1 Schema of the proposed all-dielectric metasurface (a) 2D connected EDR array with 119909- and 119910-polarization of the electric field and(b) HFSS-model for the unit cell

variations are increased for higher values of the metasurfacethickness ℎ which means that the phase difference Δ120601 spansa wider range of values for thick metasurfaces

32 Application QWP and HWP Metasurfaces In orderto design all-dielectric QWP and HWP metasurfaces wehave considered the previous results of the parametric study(Section 31) Both of QWP and HWP metasurfaces requirehigh transmission and particular phase shift (|Δ120601| = 90∘for QWP and |Δ120601| = 180∘ for HWP) In Table 1 we haveregrouped main data deduced from Figure 2 related to thedesign of QWP and HWP devices For each metasurfaceof thickness ℎ (064mm 128mm 192mm and 256mm)we have presented the bandwidths (column 2) associatedwith QWP and HWP metasurfaces where the transmissionsmoduli 119879119909119909 and 119879119910119910 (columns 3 and 4) are considered to begreater than 07 and the phase shift is |Δ120601|=90∘ plusmn 5∘ forQWP(column 5) and |Δ120601| = 180∘ plusmn 5∘ for HWP (column 6) theseresults are obtained for ellipticity ranges given in column 7

From Table 1 we can deduce that the transmission levelof the 119909- and 119910-polarization (119879119909119909 and 119879119910119910) is increased withthe thickness ℎ cases (where moduli gt 09) are obtainedwith the thickness 256mm We can note also that exceptfor the thickness 128mm we can design QWP and HWPmetasurfaces with good performances however only thethickness 256mm allows us to design both QWP and HWPoperating in different frequency ranges

4 Experimental Validation

Two metasurface prototypes each one composed of 7 times 7cells were fabricated with Rogers RO3210 substrates of thick-ness ℎ = 256mm (asymp12058238) relative permittivity 120576119903 = 102and loss tangent tan 120575 = 00027 The total thickness 256mmwas obtained by superposition of 4 identical layers eachone of thickness 064mm The unit cell size is 99mm (asymp120582)The dielectric connections are oriented along 119909-direction asillustrated in Figure 3 The two devices were characterized bymeasuring their 119909- and 119910-polarized transmission coefficientsin an anechoic room over the frequency band 20ndash30GHz

The first fabricated metasurface is a QWP structure(Figure 3(a)) designed to transmit both 119909- and 119910-polarizationwith phase shift difference |Δ120601| asymp 90∘ and equal moduli (119879119909119909= 119879119910119910) The resonators ellipticity 120591 = 119887119886 is equal to 146(asymp12058267) where the minor and major elliptic resonators radiiare 119886 = 2mm (asymp1205825) and 119887 = 292mm (asymp12058234) respectivelyThe measured transmitted power for both of 119909- and 119910-polarization over the band 24ndash30GHz is given in Figure 4

We have regrouped in Table 2 both simulated andmeasured results for the designed QWP and HWP metasur-faces We can notice from these results that we have goodagreement between simulation and measurement in termsof moduli and phase difference of the transmitted powerwith a certain frequency shift attributedmainly to fabricationimperfections and error measurements

We can notice from Figure 4 that at the frequencyof 282GHz both 119909- and 119910-polarized transmission mod-uli are equal (asympminus15 dB which correspond to 70 of thetransmitted power) whereas the phase difference is closeto 90∘ Therefore the designed QWP metasurface acts as apolarization converter at 282GHz and permits convertinglinear to circular polarization

The second metasurface presented in Figure 3(b) is aHWP device designed to transmit both 119909-polarization and119910-polarization with equal moduli and phase shift difference|Δ120601| asymp 180∘ With minor radius 119886 = 2mm (asymp1205825) andmajor radius 119887 = 226mm (asymp12058244) the resonators ellipticity120591 is 113 (asymp12058287) Observing the transmitted power over thefrequency band 21ndash28GHz (see Figure 5) shows that the twotransmission curves corresponding to 119909- and 119910-polarizationoverlap at the frequency 219GHz with a transmission levelclose to minus22 dB (which correspond to 60 of the transmittedpower) and a phase difference of 180∘ Therefore at 219 GHzthe proposed HWP metasurface can change the handednessof circularly polarized wave or rotates a linear polarization by90∘

We can explain the behavior difference between the twotransmitted coefficients (119879119909119909 and 119879119910119910) by the effect of theasymmetric geometry of the elliptic resonators and with thenonnegligible effect of the connections


ℎ1

ℎ2

ℎ3

ℎ4

Ellip

ticity

22

1

f (GHz)3020 28

18

14

262422

22

13020

Ellip

ticity

28

f (GHz)

18

14

262422

22

13020

Ellip

ticity

28

f (GHz)

18

14

262422

22

13020

Ellip

ticity

28

f (GHz)

18

14

262422

Ellip

ticity

22

13020 28

f (GHz)

18

14

262422

Ellip

ticity

22

13020 28

f (GHz)

18

14

262422

Ellip

ticity

28

22

13020

f (GHz)

18

14

262422

Ellip

ticity

28

22

1

f (GHz)3020

18

14

2624220

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1Txx Tyy

(a)

ℎ1 ℎ2

26 28 30242220

22

18

14

128 3026242220

22

18

14

1

3026 28242220

22

18

14

13026 28242220

22

18

14

1

Ellip

ticity

Ellip

ticity

Ellip

ticity

Ellip

ticity

f (GHz)f (GHz)

f (GHz)f (GHz)

ℎ3 ℎ4

ＦＩＡ(TxxTyy)

0

2

4

0

2

4

0

5

minus2

minus4

minus5

0

5

minus5

minus4

minus2

(b)

Figure 2 Continued


Ellip

ticity

f (GHz)

y

22

18

14

13026 28242220

Ellip

ticity

1

22

18

14

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

x

22

18

14

1

f (GHz)3026 28242220

minus50

0

50

minus100

minus50

0

minus100

0

100

minus100

0

100

minus100

0

100

minus100

0

100

minus100

0

100

minus50

0

50

ℎ1

ℎ2

ℎ3

ℎ4

(c)

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

ℎ1

22

18

14

1

Ellip

ticity

El

liptic

ity

0

100

200

0

200

0

50

100

150

0

minus200

200

minus100

minus200

minus50

f (GHz) f (GHz)

ℎ4ℎ3

Ellip

ticity

El

liptic

ity

ℎ2

Δ = x minus y

f (GHz)f (GHz)

(d)

Figure 2 Variation over the frequency band 20ndash30GHz of the 119909- and 119910-polarized transmission coefficients with the resonator ellipticity 120591and thickness ℎ (a) moduli (b) ratio between moduli (c) phases (d) phases difference


(a) (b)

Ey

Ex

Figure 3 Prototypes of the realized all-dielectric QWP (a) and HWP (b) metasurfaces

Txx

Tyy

25 26 28 29 302724Frequency (GHz)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

(a)

Δ asymp 90∘

f asymp 282 GHz

25 26 28 29 302724Frequency (GHz)

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

(b)

Figure 4 Experimental characterization of QWP metasurface (a) measured normalized transmitted powers 119879119909119909 (red) and 119879119910119910 (blue) (b)phase difference between 119909- and 119910-polarization

2523 26 2822 272421Frequency (GHZ)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

Txx

Tyy

(a)

Δ asymp 180∘

f asymp 219 GHz

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

2523 26 2822 272421Frequency (GHz)

(b)

Figure 5 Experimental characterization of HWP metasurface (a) measured normalized transmitted powers 119879119909119909 (red) and 119879119910119910 (blue) (b)phase difference between 119909- and 119910-polarization


Table 1 Main data (deduced from Figure 2) related to all-dielectric QWP and HWP metasurfaces

ℎ (mm) Bandwidth (GHz) 119879119909119909 119879119910119910QWP1003816100381610038161003816Δ1206011003816100381610038161003816

HWP1003816100381610038161003816Δ1206011003816100381610038161003816

Ellipticity (120591)

064 2760ndash2773 070ndash074 070ndash074 85ndash87 mdash 137ndash141

128 2538ndash2903 070ndash074 070ndash074 85ndash89 mdash 129ndash2392918ndash2923 072ndash077 072ndash084 mdash 177ndash183 182ndash191

192 mdash mdash mdash mdash mdash mdash


Table 2 Simulated and experimental results for the designed QWP and HWP metasurface

Simulation Measurement119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency

QWP minus06 dB 93∘ 264GHz minus15 dB 90∘ 282 GHzHWP minus09 dB 180∘ 233 GHz minus22 dB 181∘ 219GHz

The operation bandwidths deduced from measured val-ues extend from 259GHz to 2868 for the QWPmetasurfacefrom 2178GHz to 2215GHz and from 23GHz to 2312 GHzfor the HWP metasurface Due to losses in the structure wehave considered limits for the 119909- and 119910-transmissions coef-ficients modulus and phases less restrictive than simulatedones We estimate that the obtained transmission levels arestill acceptable for operation of the structure as QWPHWPin the mentioned bands above

Note that the transmission coefficients presented inFigures 4 and 5 have been normalized with respect to theexciting horn antenna reference transmission coefficients inthe presented band

5 Conclusion

In this paper we have investigated numerically and experi-mentally the design of all-dielectric QWP and HWP meta-surface operating in the microwave band 20ndash30GHz Firstwe have studied the effect of the resonators thickness andellipticity on the transmission Then we have realized thestructures and measured their transmissions for both 119909-and 119910-polarized incident waves Good agreement is obtainedbetween simulation and measurement It is found that therealizedQWPandHWPmetasurfaces operate at the frequen-cies 282GHz and 219GHz respectively with transmissionrates of 70 and 60 of the incident power respectively

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This project was funded by the Deanship of ScientificResearch (DSR) King Abdulaziz University under Grantno 25-135-35-HiCi The authors therefore acknowledge

technical and financial support of KAU The authors wouldlike to thank Professor Rabah Aldhaheri from ECE Depart-ment Faculty of Engineering at KAU for his help duringsimulations

References

[1] F Capolino Theory and Phenomena of Metamaterials CRCPress 2009

[2] J B Pendry ldquoNegative refraction makes a perfect lensrdquo PhysicalReview Letters vol 85 no 18 pp 3966ndash3969 2000

[3] J B Pendry D Schurig and D R Smith ldquoControlling electro-magnetic fieldsrdquo American Association for the Advancement ofScience Science vol 312 no 5781 pp 1780ndash1782 2006

[4] U Leonhardt ldquoOptical conformal mappingrdquo American Associ-ation for the Advancement of Science Science vol 312 no 5781pp 1777ndash1780 2006

[5] A Silva F Monticone G Castaldi V Galdi A Alu and NEngheta ldquoPerforming mathematical operations with metama-terialsrdquo American Association for the Advancement of ScienceScience vol 343 no 6167 pp 160ndash163 2014

[6] C L Holloway E F Kuester J A Gordon J OrsquoHara JBooth and D R Smith ldquoAn overview of the theory andapplications of metasurfaces The two-dimensional equivalentsof metamaterialsrdquo IEEE Antennas and Propagation Magazinevol 54 no 2 pp 10ndash35 2012

[7] C L Holloway M A Mohamed E F Kuester and A Dien-stfrey ldquoReflection and transmission properties of a metafilmWith an application to a controllable surface composed ofresonant particlesrdquo IEEE Transactions on Electromagnetic Com-patibility vol 47 no 4 pp 853ndash865 2005

[8] J Cheng D Ansari-Oghol-Beig and H Mosallaei ldquoWavemanipulation with designer dielectric metasurfacesrdquo OpticsLetters vol 39 no 21 pp 6285ndash6288 2014

[9] H-T Chen A J Taylor and N Yu ldquoA review of metasurfacesphysics and applicationsrdquo Reports on Progress in Physics vol 79no 7 Article ID 076401 2016

[10] K Achouri G Lavigne M A Salem and C Caloz ldquoMetasur-face spatial processor for electromagnetic remote controlrdquo IEEETransactions on Antennas and Propagation vol 64 no 5 pp1759ndash1767 2016


[11] A Arbabi Y Horie M Bagheri and A Faraon ldquoDielectricmetasurfaces for complete control of phase and polarizationwith subwavelength spatial resolution and high transmissionrdquoNature Nanotechnology vol 10 no 11 pp 937ndash943 2015

[12] I Staude A E Miroshnichenko M Decker et al ldquoTailoringdirectional scattering throughmagnetic and electric resonancesin subwavelength silicon nanodisksrdquoACSNano vol 7 no 9 pp7824ndash7832 2013

[13] M A Salem and C Caloz ldquoManipulating light at distance by ametasurface using momentum transformationrdquo Optics Expressvol 22 no 12 pp 14530ndash14543 2014

[14] K Achouri M A Salem and C Caloz ldquoGeneral metasurfacesynthesis based on susceptibility tensorsrdquo Institute of Electricaland Electronics Engineers Transactions on Antennas and Propa-gation vol 63 no 7 pp 2977ndash2991 2015

[15] K Achouri A Yahyaoui S Gupta H Rmili and C CalozldquoDielectric ResonatorMetasurface forDispersion EngineeringrdquoIEEE Transactions on Antennas and Propagation vol 65 no 2pp 673ndash680 2017

[16] A Yahyaoui H Rmili L Laadhar and T Aguili ldquoNumericalanalysis of a metasurface based on elliptic dielectric resonatorsfor transmission control of electromagnetic wavesrdquo in Proceed-ings of the 16th Mediterranean Microwave Symposium MMS2016 Abu Dhabi UAE November 2016

[17] A Yahyaoui H Rmili M Sheikh A Dobaie L Laadhar and TAguili ldquoHalf-wave and quarter-wave plates metasurfaces withelliptic dielectric resonators for microwave applicationsrdquo inProceedings of the 16th Mediterranean Microwave SymposiumMMS 2016 Abu Dhabi UAE November 2016

[18] A Yahyaoui H Rmili M Sheikh A Dobaie L Laadhar and TAguili ldquoDesign of All-Dielectric Half-wave and Quarter-wavePlates Microwave Metasurfaces Based on Elliptic DielectricResonatorsrdquo ACES Journal vol 32 no 3 pp 229ndash236 March2017

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The spatial distribution of the subwavelength elementscomposing the metasurface acts on the incident wave interms of amplitude phase and polarization whichmay affectits electromagnetic response and offers the possibility ofobtaining specific functionalities

However the majority of metasurfaces were designedby using metallic elements with Ohmic losses which maylimit their performances especially at optical frequencies Inorder to overcome these limitations all-dielectric metasur-faces have attracted particular interest recently and somesuccessful designswith low-losses high overall efficiency andvarious functionalities [10ndash15] were obtained in microwaveand optical frequencies

Dielectric resonators are the main structure used in all-dielectric metasurfaces because they can excite both electricandmagnetic resonantmodes in addition to the possibility ofreducing the size by using high dielectric constant 120576119903 Severalresonators shapes such as spheres cubes cylindricalellipticaldisks and rods were investigated in order to design all-dielectricmetasurfaces especially at THz and optical frequen-cies [12ndash15]

Therefore in all-dielectric metasurfaces based on dielec-tric resonators the geometrical parameters of the resonatorsand the spacing between them are the main factors affectingthe phase variation as well as the metasurface performances[16ndash18]

Recently we are interested in the design of all-dielectricmetasurfaces based on EDRs operating at microwave fre-quencies The main design parameters of these resonatorsare their ellipticity orientation and thickness In the firststudy [18] we have investigated numerically the effect ofthe resonators ellipticity and orientation on the metasurfacetransmission In this paper we propose a complementarystudy to first determine numerically by using the Ansys-HFSS software the effect of the resonators thickness Thenwe realize and characterize experimentally the optimizedprototypes of the QWP and HWP metasurfaces

2 Metasurface Design

Theproposed all-dielectricmetasurface consists of an infinitetwo-dimensional array of connected EDRs as shown inFigure 1(a) made of dielectric (Rogers RO3210) of relativepermittivity 102 loss tangent 0003 and thickness ℎ

Theminor (along 119909) andmajor radii (along 119910) of the EDRare denoted as 119886 and 119887 respectively whereas its ellipticity is120591 = 119887119886 The size of the unit cell is 119871119909 times 119871119910 times 119871119911 In thisregard 119871119909 = 99mm (119871119909 lt 120582) 119871119910 = 99mm (119871119910 lt 120582)and 119871119911 = 16120582 where 120582 = 10mm is the wavelength associatedwith the upper frequency limit 30GHz and the longitudinaldimension 119871119911 is great compared to the wavelength 120582 (119871119911= 160mm) The resonators are connected along 119909-directionwith thin connection of length 119871119888 = (1198711199092) minus 119887 and width119882119888 = 125mm We have excited the structure with normalincidence (Floquet ports) along 119911-direction

The ellipticity of the resonator was studied by varying theratio 120591 of EDRs while fixing the minor radius at 119886 = 2mm(1205825) without affecting the cell size (120591 is bounded within theranges 1 le 120591 le 247 with a step of 001) Finally the height ℎ

of both the EDRs and the connections is varied from 064 to256mm with a step of 064mm

3 Simulated Results

The simulation of the metasurface was performed by usingthe commercial software Ansys-HFSS In Figure 1(b) wepresent the simulation model where the unit cell boundarycondition was used along 119909- and 119910-directions The model isexcited under normal incidence with Floquet ports along 119911-direction in the frequency range 20ndash30GHz

In order to study the transmission of the designed all-dielectric metasurface we have analyzed its response whenexcited under normal incidence with two orthogonal polar-ization parallel to 119909- and 119910-axes as shown in Figure 1(a)

We define then 119879119909119909 = |119864119909119905||119864119909

119894| and 119879119910119910 = |119864119910119905||119864119910

119894| asthemodule transmission ratio of 119909- and 119910-linear polarizationof the electric field respectively and Δ120601 = 120601119909 minus 120601119910 asthe phase difference between the 119909- and 119910-components ofthe transmitted electromagnetic fields Consequently themoduli 119879119909119909 and 119879119910119910 will vary from 0 to 1 and the phasedifference Δ120601 varies from minus360∘ to +360∘ The QWP andHWP metasurfaces are obtained when the moduli are equal(119879119909119909 = 119879119910119910) and the phase difference is Δ120601 = plusmn90

∘ and plusmn180∘respectively

31 Effect of the Resonator Geometry We have investigatedthe effect of the main design parameters affecting the trans-mission of the all-dielectric metasurface in particular theresonators thickness ℎ size and shape (ellipticity 120591) Theeffect of the resonator size on the metasurface transmissionwas studied mainly by varying the EDR major axis 119887 Resultsfor radius 119886 = 1205825 are illustrated in Figure 2 The effectof the EDR ellipticity on the metasurface transmission wasanalyzed from moduli (119879119909119909 and 119879119910119910) phases (120601119909 and 120601119910)the ratio between moduli (we take log(119879119909119909119879119910119910) for bettervisualization) and the phase shift Δ120601 for four consideredresonator thicknesses ℎ1 = 064mm ℎ2 = 128mm ℎ3 =192mm and ℎ4 = 256mm

In Figure 2 we have studied over the frequency band20ndash30GHz the effect of the resonator ellipticity 120591 andthickness ℎ on themetasurface transmissionWe can remarkeasily that the exciting frequency and the resonators geom-etry (ellipticity and thickness) affect deeply the metasurfacetransmission behavior We can notice also that ellipticity ofthe resonators affects more moduli and phases of 119910-polarizedincident waves (120601119910) than 119909-polarized waves (120601119909) due to theorientation of the resonators along the 119910-axis

However by analysis of colors distribution in Figure 2(a)we can note that the red color which represents high trans-mission moduli (119879119909119909 and 119879119910119910) is more dominant in graphscorresponding to metasurfaces excited with 119910-polarizedwaves This result can be explained by the connection exten-sion along the 119909-axis which reduces slightly the transmissionalong this direction

From Figure 2(b) we can notice the equality betweenmoduli represented with green color

On the other hand we can note that the phases 120601119909 and120601119910 (Figure 2(c)) as well as the phase shift Δ120601 (Figure 2(d))


Ey

k

Ex

(a)

Lx

Ly

Lz

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ℎ

Wca

b

(b)













ℎ1

ℎ2

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ℎ4

Ellip

ticity

22

1

f (GHz)3020 28

18

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262422

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28

f (GHz)

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262422

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13020

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262422

Ellip

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13020 28

f (GHz)

18

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262422

Ellip

ticity

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13020 28

f (GHz)

18

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262422

Ellip

ticity

28

22

13020

f (GHz)

18

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262422

Ellip

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28

22

1

f (GHz)3020

18

14

2624220

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1Txx Tyy

(a)

ℎ1 ℎ2

26 28 30242220

22

18

14

128 3026242220

22

18

14

1

3026 28242220

22

18

14

13026 28242220

22

18

14

1

Ellip

ticity

Ellip

ticity

Ellip

ticity

Ellip

ticity

f (GHz)f (GHz)

f (GHz)f (GHz)

ℎ3 ℎ4

ＦＩＡ(TxxTyy)

0

2

4

0

2

4

0

5

minus2

minus4

minus5

0

5

minus5

minus4

minus2

(b)

Figure 2 Continued


Ellip

ticity

f (GHz)

y

22

18

14

13026 28242220

Ellip

ticity

1

22

18

14

f (GHz)3026 28242220

Ellip

ticity

22

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1

f (GHz)3026 28242220

Ellip

ticity

22

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1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

x

22

18

14

1

f (GHz)3026 28242220

minus50

0

50

minus100

minus50

0

minus100

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100

minus100

0

100

minus100

0

100

minus100

0

100

minus100

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100

minus50

0

50

ℎ1

ℎ2

ℎ3

ℎ4

(c)

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

22

18

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1

302826242220

ℎ1

22

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14

1

Ellip

ticity

El

liptic

ity

0

100

200

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200

0

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100

150

0

minus200

200

minus100

minus200

minus50

f (GHz) f (GHz)

ℎ4ℎ3

Ellip

ticity

El

liptic

ity

ℎ2

Δ = x minus y

f (GHz)f (GHz)

(d)



(a) (b)

Ey

Ex


Txx

Tyy

25 26 28 29 302724Frequency (GHz)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

(a)

Δ asymp 90∘

f asymp 282 GHz

25 26 28 29 302724Frequency (GHz)

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

(b)


2523 26 2822 272421Frequency (GHZ)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

Txx

Tyy

(a)

Δ asymp 180∘

f asymp 219 GHz

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

2523 26 2822 272421Frequency (GHz)

(b)





HWP1003816100381610038161003816Δ1206011003816100381610038161003816








1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency




5 Conclusion




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ey

k

Ex

(a)

Lx

Ly

Lz

Lc

ℎ

Wca

b

(b)













ℎ1

ℎ2

ℎ3

ℎ4

Ellip

ticity

22

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f (GHz)3020 28

18

14

262422

22

13020

Ellip

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18

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262422

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13020

Ellip

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f (GHz)

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262422

22

13020

Ellip

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28

f (GHz)

18

14

262422

Ellip

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22

13020 28

f (GHz)

18

14

262422

Ellip

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22

13020 28

f (GHz)

18

14

262422

Ellip

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28

22

13020

f (GHz)

18

14

262422

Ellip

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28

22

1

f (GHz)3020

18

14

2624220

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

05

1

0

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1Txx Tyy

(a)

ℎ1 ℎ2

26 28 30242220

22

18

14

128 3026242220

22

18

14

1

3026 28242220

22

18

14

13026 28242220

22

18

14

1

Ellip

ticity

Ellip

ticity

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Ellip

ticity

f (GHz)f (GHz)

f (GHz)f (GHz)

ℎ3 ℎ4

ＦＩＡ(TxxTyy)

0

2

4

0

2

4

0

5

minus2

minus4

minus5

0

5

minus5

minus4

minus2

(b)

Figure 2 Continued


Ellip

ticity

f (GHz)

y

22

18

14

13026 28242220

Ellip

ticity

1

22

18

14

f (GHz)3026 28242220

Ellip

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22

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f (GHz)3026 28242220

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f (GHz)3026 28242220

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f (GHz)3026 28242220

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f (GHz)3026 28242220

Ellip

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f (GHz)3026 28242220

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ticity

x

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1

f (GHz)3026 28242220

minus50

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50

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minus100

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ℎ2

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ℎ4

(c)

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

ℎ1

22

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1

Ellip

ticity

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liptic

ity

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200

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150

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200

minus100

minus200

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f (GHz) f (GHz)

ℎ4ℎ3

Ellip

ticity

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liptic

ity

ℎ2

Δ = x minus y

f (GHz)f (GHz)

(d)



(a) (b)

Ey

Ex


Txx

Tyy

25 26 28 29 302724Frequency (GHz)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

(a)

Δ asymp 90∘

f asymp 282 GHz

25 26 28 29 302724Frequency (GHz)

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

(b)


2523 26 2822 272421Frequency (GHZ)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

Txx

Tyy

(a)

Δ asymp 180∘

f asymp 219 GHz

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

2523 26 2822 272421Frequency (GHz)

(b)





HWP1003816100381610038161003816Δ1206011003816100381610038161003816








1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency




5 Conclusion




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ℎ1

ℎ2

ℎ3

ℎ4

Ellip

ticity

22

1

f (GHz)3020 28

18

14

262422

22

13020

Ellip

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28

f (GHz)

18

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262422

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13020

Ellip

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f (GHz)

18

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262422

22

13020

Ellip

ticity

28

f (GHz)

18

14

262422

Ellip

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13020 28

f (GHz)

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14

262422

Ellip

ticity

22

13020 28

f (GHz)

18

14

262422

Ellip

ticity

28

22

13020

f (GHz)

18

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262422

Ellip

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28

22

1

f (GHz)3020

18

14

2624220

05

1

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1

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05

1

0

05

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0

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1Txx Tyy

(a)

ℎ1 ℎ2

26 28 30242220

22

18

14

128 3026242220

22

18

14

1

3026 28242220

22

18

14

13026 28242220

22

18

14

1

Ellip

ticity

Ellip

ticity

Ellip

ticity

Ellip

ticity

f (GHz)f (GHz)

f (GHz)f (GHz)

ℎ3 ℎ4

ＦＩＡ(TxxTyy)

0

2

4

0

2

4

0

5

minus2

minus4

minus5

0

5

minus5

minus4

minus2

(b)

Figure 2 Continued


Ellip

ticity

f (GHz)

y

22

18

14

13026 28242220

Ellip

ticity

1

22

18

14

f (GHz)3026 28242220

Ellip

ticity

22

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1

f (GHz)3026 28242220

Ellip

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f (GHz)3026 28242220

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f (GHz)3026 28242220

Ellip

ticity

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f (GHz)3026 28242220

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ticity

22

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14

1

f (GHz)3026 28242220

Ellip

ticity

x

22

18

14

1

f (GHz)3026 28242220

minus50

0

50

minus100

minus50

0

minus100

0

100

minus100

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100

minus100

0

100

minus100

0

100

minus100

0

100

minus50

0

50

ℎ1

ℎ2

ℎ3

ℎ4

(c)

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

22

18

14

1

302826242220

ℎ1

22

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14

1

Ellip

ticity

El

liptic

ity

0

100

200

0

200

0

50

100

150

0

minus200

200

minus100

minus200

minus50

f (GHz) f (GHz)

ℎ4ℎ3

Ellip

ticity

El

liptic

ity

ℎ2

Δ = x minus y

f (GHz)f (GHz)

(d)



(a) (b)

Ey

Ex


Txx

Tyy

25 26 28 29 302724Frequency (GHz)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

(a)

Δ asymp 90∘

f asymp 282 GHz

25 26 28 29 302724Frequency (GHz)

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

(b)


2523 26 2822 272421Frequency (GHZ)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

Txx

Tyy

(a)

Δ asymp 180∘

f asymp 219 GHz

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

2523 26 2822 272421Frequency (GHz)

(b)





HWP1003816100381610038161003816Δ1206011003816100381610038161003816








1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency




5 Conclusion




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ellip

ticity

f (GHz)

y

22

18

14

13026 28242220

Ellip

ticity

1

22

18

14

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

ticity

22

18

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f (GHz)3026 28242220

Ellip

ticity

22

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f (GHz)3026 28242220

Ellip

ticity

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1

f (GHz)3026 28242220

Ellip

ticity

22

18

14

1

f (GHz)3026 28242220

Ellip

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x

22

18

14

1

f (GHz)3026 28242220

minus50

0

50

minus100

minus50

0

minus100

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100

minus100

0

100

minus100

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100

minus100

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minus100

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100

minus50

0

50

ℎ1

ℎ2

ℎ3

ℎ4

(c)

302826242220

22

18

14

1

302826242220

22

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14

1

302826242220

22

18

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302826242220

ℎ1

22

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14

1

Ellip

ticity

El

liptic

ity

0

100

200

0

200

0

50

100

150

0

minus200

200

minus100

minus200

minus50

f (GHz) f (GHz)

ℎ4ℎ3

Ellip

ticity

El

liptic

ity

ℎ2

Δ = x minus y

f (GHz)f (GHz)

(d)



(a) (b)

Ey

Ex


Txx

Tyy

25 26 28 29 302724Frequency (GHz)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

(a)

Δ asymp 90∘

f asymp 282 GHz

25 26 28 29 302724Frequency (GHz)

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

(b)


2523 26 2822 272421Frequency (GHZ)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

Txx

Tyy

(a)

Δ asymp 180∘

f asymp 219 GHz

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

2523 26 2822 272421Frequency (GHz)

(b)





HWP1003816100381610038161003816Δ1206011003816100381610038161003816








1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency




5 Conclusion




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

Ey

Ex


Txx

Tyy

25 26 28 29 302724Frequency (GHz)

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

(a)

Δ asymp 90∘

f asymp 282 GHz

25 26 28 29 302724Frequency (GHz)

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

(b)


2523 26 2822 272421Frequency (GHZ)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

TxxT

yy

(dB)

Txx

Tyy

(a)

Δ asymp 180∘

f asymp 219 GHz

0

50

100

150

200

Phas

e diff

eren

ce (∘

)

2523 26 2822 272421Frequency (GHz)

(b)





HWP1003816100381610038161003816Δ1206011003816100381610038161003816








1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency




5 Conclusion




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












HWP1003816100381610038161003816Δ1206011003816100381610038161003816








1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency 119879119909119909 = 119879119910119910

1003816100381610038161003816Δ1206011003816100381610038161003816 Frequency




5 Conclusion




Acknowledgments



References




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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