AIP Advances 10, 105201 (2020); https://doi.org/10.1063/5.0016373 10, 105201

© 2020 Author(s).

An extremely ultrathin flexible Huygens’stransformerCite as: AIP Advances 10, 105201 (2020); https://doi.org/10.1063/5.0016373Submitted: 04 June 2020 . Accepted: 11 September 2020 . Published Online: 01 October 2020

Alireza Ghaneizadeh , Khalil Mafinezhad , and Mojtaba Joodaki

COLLECTIONS

Paper published as part of the special topic on Chemical Physics, Energy, Fluids and Plasmas, Materials Science

and Mathematical Physics

AIP Advances ARTICLE scitation.org/journal/adv

An extremely ultrathin flexible Huygens’stransformer

Cite as: AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373Submitted: 4 June 2020 • Accepted: 11 September 2020 •Published Online: 1 October 2020

Alireza Ghaneizadeh,1,a) Khalil Mafinezhad,1,b) and Mojtaba Joodaki2,3,c)

AFFILIATIONS1Department of Electrical Engineering, Sadjad University of Technology, 9188148848 Mashhad, Iran2Department of Electrical Engineering, Jacobs University Bremen, 28759 Bremen, Germany3Department of Electrical Engineering, Ferdowsi University of Mashhad, 9177948974 Mashhad, Iran

a)E-mail: a.ghaneeizadeh@gmail.comb)Author to whom correspondence should be addressed: kh_mafi@sadjad.ac.ir and khmafinezhad@gmail.comc)Electronic addresses: m.joodaki@jacobs-university.de and joodaki@um.ac.ir

ABSTRACTThe current study aims to present the physical perception of a meta-surface energy harvester’s (MEH’s) design based on space-time physics ofa traveling wave. Regarding the relation between the wave-velocity and field-impedance, the balance condition in Huygens’s meta-atomsis provided. Accordingly, it was demonstrated that MEH behaves as a transformer at far-field. It was observed that the location of themetallic-via is mimicked by the number of loop coils in the secondary of the transformer in the unit-cell. In addition, the impedancematching between the wave impedance in a lossless medium and MEH’s load was to be tuned by adjusting the size parameters of the unit-cell at a desired resonance frequency. For this purpose, the present study developed a simple design framework to achieve the resonancefrequency at a more optimum pace based on surrogate modeling. The theoretical analyses are validated by the results of full-wave and cir-cuit simulations. Finally, a recently developed flexible MEH was further extended to a multi-polarization structure using more compactcells. The fabricated flexible MEH has 10 × 10 number of deep subwavelength thick cells (≈0.004λ0), while traditional MEH was basicallydesigned only to fit on the planar surface. The new design paves the way for the multi-polarized MEH to wrap around the cylindricalsurface as a 2D-isotropic MEH. The results of the data analyses show that the simulation and experimental results enjoy an acceptableagreement.

© 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0016373., s

I. INTRODUCTION

Internet of things (IoT) has been shown to be quite an interest-ing subject in different communities of researchers, yet its functions,capabilities, and potentials are to be investigated further. Basically,IoT serves as a function of a given object connecting to other objectsthrough wireless connections to others and vice versa. However,what stands out as a vital issue to be discussed is its power sup-ply sources.1–4 Despite the fact that the IoT covers many types ofdata centers, devices, and so on, there are numerous miniaturizedsmart sensors at inaccessible locations allowing for a better qual-ity.1–4 Accordingly, it is reasonable to omit wiring/batteries as theirpower supplements, i.e., the financial and human costs of environ-mental pollution decline, such as costs for replacing the battery

and monitoring.1–5 In order to overcome the aforementioned costs,researchers can use the energy harvesting coming out of the sur-rounding ambience, particularly from the ambient electromagnetic(EM) wave.1–5

Ambient RF-signal energy harvesting is typically conductedemploying rectenna systems consisting of rectifier circuits andantennas.4–6 The fundamental features in the field of antenna the-ory, which are mentioned in the literature, are usually gain, pat-tern, polarization, and impedance matching.7 However, a typicallyrecurrent problem of most antennas is the fact that they employmaximally 50% of the available incident plane-wave power on thephysical aperture that could be delivered to its terminal (e.g., inthe polarization and conjugation matching), and the rest is scat-tered from the receiving antenna and could be attenuated.7–9 This

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-1

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

issue raises the issue of optimizing the efficiency of the antennaaperture.

It is known that impedance matching can be used as the cri-terion for controlling the level of wave propagation between thetwo different EM-media with a maximum power transmission.7,10–13

This can be modeled by changing the field impedance on thetwo media defined as the intensity ratio of the electric to mag-netic field.12,14 Lately, a new impedance transformer has been mod-eled based on bianisotropic Huygens’s meta-surfaces.13 However,this transformer has been restricted to the impedance matchingbetween two dielectric media with different relative permittivities(see Fig. 1 in Ref. 13), which cannot match the lump-ports. Onemight think this limitation could be resolved using matching tech-niques in antennas such as the quarter-wave impedance transformerwith defects in bandwidth/size engineering trade-offs.13 Accord-ingly, in this study, we are to scrutinize this issue to a furtherextent.

Recently, a model of a meta-surface energy harvester (MEH)has been devised, which was inspired by the meta-surface absorber(MA) concept conducted by Ramahi et al.3,15–17 Both MEH and MAcan absorb the incident wave power so as to serve as a solutionto the issues of radar cross section (RCS) and EM interference/EMcompatibility (EMI/EMC).16–18 However, only MEH can match theload/medium impedances converting radiation-power to AC-powerinstead of converting them to heat (or something else).16–18 Never-theless, many architectures of planar MEH are reported in the litera-ture.3,15–17,19–22 This study intends to illustrate the potential physicalmodeling to further the current studies on MEH. Therefore, for thesake of more clarifications, we may reiterate the fundamental EMequations.

Although MEH can have various applications in the implantableand wearable electronics,1,2 to the best of the authors’ knowledge,most researchers are working on the planar MEH (see Table I),

offering a restricted field of view.3 Principally, the angle of radi-ation (θ) from the surrounding space is random, i.e., the randomTransverse Electric (TE-) and Transverse Magnetic (TM-) polarizedplane-wave incidences lead to an unknown value of the surface waveimpedances (Z) based on3

ZTM = Z0 × cos(θ), (1)

ZTE = Z0/ cos(θ). (2)

A different value of θ leads to the lack of ability of the planarMEH to strike a match between their fixed-loads and the surfacewave impedances.3,23 This issue originates from the behavior of acosine function in (1) and (2), i.e., the diversity of MEH loads isneeded.3,23,24 To address this problem, for the first time, we designedand implemented a two-dimensional (2D) isotropic flexible MEHby curving the MEH around a cylinder for a better reception of theambient RF-signals.21 Despite the fact that the thickness of the MEHwas ∼0.004 times of resonance wavelength, the proposed MEH wasproperly matched not only by the communication device (50 Ω) butalso by the free-space wave impedance (Z0 = 120π Ω).21 However,this preliminary work21 was sensitive to polarization, which limitedthe potential applications of energy harvesting.

To the best of the authors’ knowledge, after a complete inves-tigation of the literature, there was almost no other flexible multi-polarize MEH reported in the literature except for the model intro-duced in our previous study,3 presenting cells with four ports leadingto some difficulties in the process of power collection. This workexpands the previous one21 with symmetric super-cells to demon-strate the optimized potential of the proposed MEH considering thepolarization insensitivity characteristics.

In the current study, the researchers aim to present a system-atic approach to design an MEH based on the scientific underpin-nings of meta-surface’s physics to bridge the knowledge gap between

TABLE I. A comparison of our MEH with the published works related to convert radiation to AC power at θ = 0.

References P/λg t (mm) t/λ0 Style of MEH FOM

25 0.47 0.787 0.0152 Planar 6.626 0.71 3 0.1380 Planar 10.627 a 0.50 0.79 0.0146 Planar 12.828 b 0.37 1.524 0.0284 Planar 35.629 c 0.26 4 0.0326 Planar 4617 0.23 4.572 0.0373 Planar d31 0.47 1.542 0.0154 Planar d32 0.21 3 0.0250 Planar d33 0.22 2.54 0.0207 Planar d16 0.38 2.5 0.0205 Planar d3 e 0.49 0.254 0.0049 Flexible 24.821 e 0.43 0.254 0.0045 Flexible 23This work 0.41 0.254 0.0048 Flexible 23.9

aThe dielectric constant of the Rogers Duroid RT5880 substrate is considered to be 2.2.bThe dielectric constant of the Rogers RO4003 substrate is considered to be 3.5.cThe ratio of thickness to resonance wavelength was 0.07, but the t to λ0 ratio calculated was 0.03 regarding the FOM.dNot available.eOur previously published works.

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-2

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

FIG. 1. A simple picture of the 2D-isotropic MEH viewing in the incidence-plane asthe XY-plane.

transmit-array and MEHs. The impedance matching between thewave impedance in a lossless medium and loads of the proposedstructure is achieved, which was inspired by an ideal transformerand the balance condition in Huygens’s meta-atoms. Furthermore,a surrogate physical model of the high impedance surface (HISs)is studied to have a prompt optimization of the MEH. It needs tobe said that a certain advantage of this idea is the reduction in thecomputation time process and the higher level of compactness ofunit-cells. However, a principle objective of this work is to create amulti-polarized flexible MEH for a better reception of the ambientincident plane-wave (see Fig. 1). To meet the requirements of thisobjective, the central axis of the cylinder has to be orthogonal to the

incidence plane. To clarify how the MEH works, a simple picture ofthe 2D-isotropic MEH is shown in Fig. 1, showing the incidence-plane as the XY-plane. In this figure, three parts are highlighted withdashed-dotted lines to represent (i) a sample of random incidentplane waves, (ii) a sample of random linear polarization of incidentplane waves, and (iii) a sample of flexible unit-cell wrapping arounda cylindrical structure. As a result, there may be a transmitter in thevicinity facing cells on our cylindrical structure to transmit wavesapproximately perpendicular to them, as shown in Fig. 1. Moreover,an equivalent circuit model has been proposed to analyze the EMbehavior of MEH using lump components. Its results are validatedwith full-wave simulations. To test the proposed design approach,the MEH was fabricated by low-cost PCB manufacturing technol-ogy. The simulation results proved to be in acceptable agreementwith the experimental ones.

II. GEOMETRICAL AND STRUCTURALCHARACTERISTICS OF THE MEH

Having taken a look into the background of the study, theresearchers will discuss the proposed multi-polarized MEH intro-duced previously.21 It should be emphasized that, in this study, thepolarization of the incident wave is considered to be linear. Besides,the polarization sensitivity and insensitivity characteristics of MEHare usually referred to as single-polarized MEH and multi-polarizedMEH, respectively.

Figure 2 exhibits the dimensions and geometry of the MEH.The design process of the proposed unit-cell in Fig. 2(a) wasdescribed as it was in our previous work in detail.21 Addition-ally, a figure-of-merit (FOM) is introduced in (3) for a comparisonbetween our planar style of MEH and the other state-of-art workapproaches in the literature, as shown in Table I,

FOM = HPBW × η × cos(θ)t × P ×√εr

× λ02. (3)

As seen in the literature, one key reason why an FOM approachis adopted is the fact that the result value of such quantities hasbeen closely competing, and although the maximum efficiency (η)

FIG. 2. (a) 3D drawing of our previous unit-cell (from Ref. 21) with dimensions of P = 6.506 mm, D = 6.356 mm, B = 0.45 mm, G = 0.15 mm, S = 0.2 mm, L = 2.475 mm, R= 2.7 mm, t = 0.254 mm, A = 2.4 mm, and N = 0.95 mm. In addition, the proposed multi-polarized super-cell (b) top surface and (c) ground printed over a Rogers RO3010PCB as the dielectric substrate with a dielectric constant of εr = 11.2 and the loss tangent of tan(δ) = 0.0022. [Notice that (a) is in different scales, R in (a) is the location ofthe loaded-via from the center of the unit-cell, and the red areas of each antipad in (c) are two parallel loads of 100 Ω.]

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-3

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

at an angle of incidence to MEH is the most important quantityfor MEH, there are other valuable parameters including the radia-tion angles (θ), half-power bandwidth ratio (HPBW), thickness (t),and size of the unit-cell (P). Since higher values of η, HPBW, andθ serve as more desirable values to compete in the literature, theyare in a direct relation with FOM. However, the lower value of Pand t causes MEH to have a higher level of compactness and thin-ner thickness. For this reason, they are in the denominator of FOM.Comparing with the state-of-art works, t and P were normalizedaccording to λ0 (free-space wavelength) and λg (guided wavelength)at the middle frequency of HPBW, respectively. The design approachfor multi-polarized characteristics based on surrogate modeling hasled to a decrease in the size of the unit-cell from 43% in Ref. 21 to41% of their corresponding operation guided wavelength, as shownin Table I.

III. CONCEPT, THEORY, AND MODELINGA basic prerequisite to MEH engineering is its parameteriza-

tion. In other words, it needs to be said that there are several effectivesurface features, one of which can be considered as the physical jus-tification of its EM behavior, e.g., admittances (and/or impedances),polarizabilities, or susceptibilities.23,24,34 According to the unique-ness theorem,10 these obvious physical features are equivalent andcan be transformed34 into one another, characterizing the MEH. Inthis paper, the researchers have employed an impedance languagefor the parameterization of the proposed structures.

Basically, arbitrary wave transformations can be determined byman-made composite EM sheets, called the meta-surfaces.24,30,34–45

Commonly, the passive meta-surfaces can respond to the inci-dent EM waves based on the dipole moments including theinduced electric and/or magnetic dipole moments and their inter-actions.24,34–46 These induced dipole moments can be engineeredto generate the corresponding surface currents resulting in thedesired radiation.39,42 Most of the meta-surfaces are periodic struc-tures whose periodicity length is much lower than the operationalwavelength, resulting in suppression of the unwanted higher-orderpropagating-wave modes in the far zone.23 Practically, the engi-neered responses can be mostly achieved by an extreme manipula-tion of the shape, geometry, and arrangement of the sub-wavelengthpolarizable particles.34–39 The mentioned resonance particles areknown as the surface meta-atoms.34,38,40 Their distributions aremacroscopically considered as a continuous distribution across themeta-surface locally seen by the EM incident wave.34 These parti-cles are embedded on the infinitesimal thin thickness of the hostmedium.24 Although non-zero physical thickness is required toreach the induced fictitious magnetic current sheets, the meta-surface thickness can be approximately considered as zero in viewof the incident wave.38 Therefore, the meta-surface as an inter-face can be modeled by using its equivalent surface boundaryconditions.38,41

To satisfy the continuity of EM fields at the interface (i.e., a vari-ation in space of μ and ε11), the fields applied on the discontinuityare to induce the required electric and/or magnetic current densi-ties on the surface.39–42 Quite simply, these fictitious surface currentsare dictated on MEH by the well-known Schelkunoff equivalenceprinciple leading to the conservation the tangential fields across theEM boundary.10,39 The magnetic (Ms) [electric (Js)] surface current

densities on a wave discontinuity equate with the tangential part ofthe electric (E) [magnetic (H)] field distributions on either side ofthe discontinuity, as shown in Fig. 3,23,24,34,39–42

Js = n × (H2 − H1) = n × ΔH, (4)

Ms = −n × (E2 − E1) = −n × ΔE. (5)

In Fig. 3, E1,2 and H1,2 are different distributions of the vectorquantity of total EM fields on each side of the boundary, includingthe incident, reflected, and transmitted fields. In addition, the unitnormal vector and the unit tangent vectors are denoted by n, t1,and t2, respectively. t1 and t2 are in the plane of the meta-surfaceindicated by the dashed line.23,24,41,42

Therefore, every limitation of the meta-surfaces is originatedfrom the ability of their boundary conditions for supporting theinduced surface current densities. It means that if these ficti-tious currents can be physically realized, the engineering of theirmutual-coupling, magnitudes, and phases will provide us with theopportunity to access a more extreme manipulation of the EMwave-fronts.23,24,34–48 Actually, a similar pattern of behavior can beobserved between Huygens’s meta-atom responses and the incidentwaves, which can radiate the EM fields in a more desirable manner.For example, a planar transmitted Huygens’s array, as an ideal trans-former, has been proposed and analyzed in detail with the lattice-network model and full-wave simulations by Eleftheriades’s group.13

One of the capabilities of their planar structure is the impedancematching between media,13,49 as shown in Fig. 1 of Ref. 13. Nev-ertheless, the MEH3,15–17,19–22,25–33 acts as an energy and impedancetransformer between a medium and a load. The proposed multi-polarized MEH has flexible characteristics for receiving the ambientincident plane-waves, as depicted in Fig. 4(b). It should be men-tioned that the MEH can actually be used for converting propagationwaves to guided waves, e.g., in a coax cable, microstrip, or coplanarwaveguide, which is different from that of the planar transmittedarray shown in Fig. 4(a).13,49

A. Balance conditions in Huygens’s meta-atomsAs already mentioned, in fact, the periodicity length of meta-

atoms is significantly lower than the wavelength of an incident wave.Although the mutual coupling tensors between the dipole momentsshould be considered for a rigorous analysis of complex meta-atoms,which can be modeled by simple electric and magnetic dipoles aswell.22,46 These simplified models may be helpful for a better concep-tual understanding of EM behavior of the meta-atoms as it is shownin the following.

FIG. 3. The simplest model of the EM responses of Huygens’s meta-surface as aninterface between two different media based on the equivalence principle.24,41,42

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-4

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

FIG. 4. (a) An impedance transformerbetween two dielectric media from Ref.13 and (b) the simplest picture of the pro-posed flexible multi-polarized MEH formatching between different media andloads. [Notice that in (b) the incidentplane-wave is considered the TE- andTM-polarized wave.]

From an electrostatic stance, a positive point charge (Q) in thefree-space has the isotropic flux of electric line (φ) in a distance (R)equal to the electric field intensity as φ = Q/4πε0R2.50,51 Once thepolarity of the charge is repetitively changed over time (e.g., a simpleoscillating of the charge in the sinusoidal harmonic motion), clearlythe physical concept of this flux changes. Nevertheless, in this sim-plified model, an observer at a distance (R) in the far-field regionidentifies EM propagation, produced by time-harmonic varying ofcharge polarities (i.e., an accelerated charge), with a delay equal toR/v.50,51 Lately, Schantz represented the local wave-velocity of plane-waves in the free-space (v) as a ratio that is equal to energy flux[Poynting vector (P)] divided by the EM energy density (UM + UE)as14

ν = PUM + UE

= E × H12(μ0∣H∣2 + ε0∣E∣2)

, (6)

where ε0 and μ0 are permittivity and permeability of the free-space,respectively. The difference between the corresponding retardedtimes related to the equivalent magnetic and electric charge oscil-lations may not be identified by the observer who sees the EMpropagation of the balanced Huygens’s meta-atoms. Looking at thecase from the energy space-time point of view,14 the oscillation ofthe incident fields can lead to a slight local motion of the equiv-alent charges in upward/downward, resulting in the polarizationcurrents.22,39 The space-time behavior of the traveling wave energyflow in the near-field of meta-atoms leads to resonate both equiva-lent charges in meta-atoms.3 Conceptually, an incident plane waveobserves Huygens’s meta-atoms from the far-field region similar toa harmonic source at the same frequency, which creates an electro-magnetic field, canceling the incident plane-wave.24,34,42 This non-reflective behavior of Huygens’s meta-atoms is because of the vary-ing rate of the equivalent charge polarities in meta-atoms that aresynchronized by the speed and intensity of changing of the incidentEM fields,14 though the wave number in the meta-atoms is not thesame as that of the free-space medium.11 In other words, the EMresponses of meta-atoms have been balanced by the incident fieldsat the same resonance frequency with different wave numbers. Thus,the ability to tune this retarded time difference in EM responses ofthe meta-atom is discussed as follows.

It is worth mentioning that the conventional method todesign a passive Huygens’s meta-surface is to adjust a set of twodipole moments with perpendicular polarization directions sinceonly the transverse components of EM fields can carry the EMpower in the Poynting vector.50,52 Apart from this, these dipolemoments should be placed within the induced meta-atom to strike a

balance in their responses.52 Likewise, the intensity of resonancesof both induced dipole moments (the electric and magnetic res-onances of the induce meta-atoms) should have a spectral over-lap.52 Therefore, these dipole moments can produce orthogo-nal equivalent magnetic and electric current densities across themeta-surface.41

The EM field structures, which are in space and surround themeta-atoms, vary at different distances from meta-atoms.3,14 Thereis approximately π/2 radian phase-angle difference between theorthogonal magnetic and electric fields surrounding the meta-atomin the near-field (see Fig. 3 in Ref. 3). The electric dipole momentstores the reactive energy of its surrounding within the meta-atoms,while the magnetic dipole moment emits energy simultaneously,and then, this process continues in a reverse manner.3,14,53 Thesetransient behaviors are repeated, while the passive meta-atoms areilluminated by the incident plane-wave.3 For a better understandingof the discussion, the magnetic and electric fields and surface currentdistributions of the MEH unit-cell are simulated, while unit-cells areilluminated by different relative phases of a normal incident wave, asshown in Fig. 5.

From an electrodynamics viewpoint, the equivalent chargeinstigations in meta-atoms, as mentioned above, show a similarbehavior to the moment of applying the Lorentz force (FL) inEq. (7) on a single positive charged particle (Q) if it moves with aninstantaneous velocity of v, e.g., current in a small Hertzian dipoleantenna,10,50,53

FL = QE + Qν × B. (7)

As shown in Fig. 5, the polarization of electric field occurs in thesame direction as the current distribution on the bridge on theCQSRR (complementary quad split ring resonator) patch, whilethe intensity of the current is synchronized by the phase of themagnetic fields based on Faraday’s law. Theoretically, the mag-netic force is applied to the equivalent electric charged particlein meta-atoms with a difference of 90 from the motion direc-tion of the charge (oscillation) based on the right-hand principle.Essentially, it should be noted that the mutual couplings betweenmagnetic and electric dipole moments are ignored for the sakeof simplicity. Thus, the magnetic force is not attributed to thepower transferred from EM fields to the electric charge. However,the magnetic fields contribute to transferring EM power to theequivalent magnetic charges with the same magnetization basedon the duality principle in EM theory.10,50 The aforementionedmotions of equivalent charges within the ideal Huygens’s meta-atoms demonstrate that the energy of the incident EM fields has

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-5

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

FIG. 5. [(a)–(c)] Magnetic field, [(d)–(f)]electric field distributions in the unit-cell,and [(g)–(i)] surface current distributionon the top surface of the unit-cell whensingle-polarized MEH is illuminated bya normal incident plane wave for differ-ent relative phases of 0, 45, and 90,respectively, at the frequency of 6.4 GHz.The size of the unit-cell is the same asFig. 2 except R and L that are 1.6265 mm= P/4 and 1.4015 mm, respectively.

been transferred to meta-atoms at the same rate of their momentumdensity.

Figuratively speaking, this external energy may transform intoa kinetic one with the equivalent charges based on Newtonianmechanics, resulting in the polarization and conduction currentsthat will create self-fields.35 Therefore, the behavior of these twoexciting electric and magnetic dipole moments in Huygens’s meta-atoms is similar to a structure that can be modeled with an equiv-alent mechanical system.50,51 For example, this mechanical systemcan include a perpendicular set of two planar springs inside aninfinitesimally thin chamber that is shown in Fig. 5. These twosprings are designed for a balanced state of the pressure distributionsin a minimum time-period (i.e., in time-phase quadrature). Thismeans that in a quarter-period, the downward pressure is applied toone of the springs, also the upward-pressure is applied to the otherone simultaneously and vice versa (as the consumption/storage pro-cesses14,53). These movements continue periodically. Besides, themechanical behavior of these two springs may experience mutual-coupling similar to the EM behavior of bianisotropic meta-atoms.45

The researchers pointed out a pair of springs because if the balanc-ing conditions are not met, the equivalent resonance for maximallystoring the reactive power and consuming the real power may nothappen. In other words, this balanced state is similar to a car withtwo cylinders whose pistons move up and down (Harmonic) in theopposite direction of each other. Above and beyond, a horizontal

shaft connected to the pistons has synchronized its rotations withthe motions of the pistons. However, an unbalance state such asthe rotations of the timing belt (camshaft) and the shaft are outof adjustment and the engine may experience a loss or be locked.Needless to say, the radiation is ignored in these classical mechanicmodels.51

B. Impedance transformer between medium and loadA common boundary condition is the impedance boundary

condition (IBC) as a transition condition (TC)36 that can be appliedto thin structures such as 2D material, FSS, and so on.36,54 IBCcan analyze the magnetic or electric field discontinuities,36 know-ing the fact that IBC cannot deal with the modeling of Huygens’smeta-surfaces as a complex discontinuity.36 Concerning the equiv-alence principle, it is known that equal to electric conductivity inohms’ law,24 the electric and magnetic immittances have been intro-duced.24,39,42 Besides, the ratio of the averaged tangential compo-nents of the desired fields (Eav and Hav) in the bottom (n = 0−) andtop (n = 0+) of the discontinuity is in relation with the surface mag-netic admittance (Yms) and electric impedance (Zes) tensors.23,24,54,55

To specify the wave-matter interaction in the homogenized state ofthe meta-surface, the IBC is to be generalized with its magnetic dualintroducing Yms.23,24 This generalization is known as the general

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-6

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

sheet transition conditions (GSTCs)23,24,34,55 as

Eav = 0.5[ Et ∣n=0+ + Et ∣n=0−], (8)

Hav = 0.5[ Ht ∣n=0+ + Ht ∣n=0−], (9)

Eav = Zes[ n × ΔH∣n=0±] = Zes ⋅ Js, (10)

Hav = Yms ⋅ [− n × ΔE∣n=0±] = Yms ⋅ Ms, (11)

where t is the transverse component of the fields (e.g., in the XY-plane34) and n is a normal component vector to the meta-surfaceplane, as shown in Fig. 3. As can be seen in Eqs. (10) and (11),one interesting point of GSTCs is that meta-atoms can be physicallycharacterized by their electric and magnetic immittances, not thefictitious currents in the equivalence principle.24 These immittancesare the transfer functions between the desired and excited fields.24,42

The current densities can be tuned by Zes and Yms applied to thedesired fields. In other words, the designer can tune the parame-ters across an interface to obtain their corresponding currents uponillumination. Unlike such leakage current that produces unwantedradiation and EMC problems, these induced currents are the sourceof the desired radiation.23,24,42 Therefore, Zes and Yms act as two keyfactors for actually realizing the induced currents that are not shownby the equivalence principle in Fig. 3.24 It should be mentioned thata designer can only manipulate the impedance and admittance usingEqs. (10) and (11) and cannot handle the mutual-coupling betweenthem.23,24 In fact, each one of Ms and Js on the meta-surface canbe induced by both fields together simultaneously.23,24 This meansthat their magnetic and electric responses can be coupled by addingan extra degree of freedom to GSTCs as magneto-electric couplingtensors (K).23,24 The well-known bianisotropy properties of Huy-gens’s meta-surface are raised by introducing these new parametersfor modulating the boundary conditions.24,45 For example, this bian-isotropic behavior leads to the conditions in which the MAs are gen-erally divided into two basic bianisotropic groups: non-reciprocal(e.g., moving and Tellegen types) and reciprocal (e.g., chiral andomega types) studied in detail in Refs. 38, 45, 56, and 57. Gener-ally, these immittances are tensors due to account of all polarizationof the desirable fields.24 For simplicity, the bianisotropic GSTC rela-tions with choosing the polarization of the fields can be characterizedby the scalar quantities of Zes, Yms, and Kem as follows:24

Eav = Zes ⋅ Js − Kem ⋅ [n × Ms], (12)

Hav = Yms ⋅ Ms − Kem ⋅ [n × Js]. (13)

Finally, we completed our theoretical analysis of the meta-atomswith the design philosophy of MEH differing from designing theclassical Salisbury absorber.21 For example, these absorbers are basedon a longitudinal distance of the resistive sheet from a metallicground plane equal to one quarter-wavelength.21 The thickness ofour MEH is near to 0.004 times of the free-space wavelength ofthe operation. According to the Poynting theorem, the resonanceof MEH in the path of the incident wave is engaged with the realparts of permittivity (ε) and permeability (μ) of the MEH.3,48 Thatis why the stored power exchanges between reactive magnetic and

electric fields at each cycle of time-harmonic fields in the near-fieldof MEH.3,53,58,59 Although these parts are essential for creating theresonance of MEH, they can be ignored to calculate the real partof average power.3,50,51 However, the imaginary parts of ε and μ actas power consumption at the resonance frequency of MEH, whoseEM response can be imitated by a real resistance (see Ref. 3). Notethat in the direction of the motion of the EM wave in the free space,the wave can carry an equal amount of electric and magnetic ener-gies.14,59 This is because these traveling waves are in a balanced stateat the free-space medium14,59 before exchanging their energy withthe meta-atom’s energy. Actually, this balancing can be maintained,and the real part of average power of the incoming wave is mostlyconsumed at the loads in an ideal MEH with no reflections. This isexplained in detail as follows.

In Ref. 60, a near-perfect power harvester has been pro-posed and measured at 3 GHz by Almoneef and Ramahi. Also, theimpedance of their MEH is calculated in a specific level of thicknessas Z = (1.01 − j0.003) ×√μ0/ε0 = η0(1.01 − j0.003) that is approxi-mately equal to the free-space impedance.60 Therefore, it is conve-nient to show the energy-velocity/field-impedance by the dimen-sionless vectors/quantity.14,59 Correspondingly, the energy velocity(v) and impedance of EM fields (E/H) are normalized by the speedof light (c) and impedance of the medium (Zs), respectively, as14

γ = νc= P

c(UM + UE) =E × H

c( 12 ε0∣E∣2 + 1

2μ0∣H∣2)

= 2(Ee ×Hh)√ε0/μ0∣E∣2 +

√μ0/ ε0∣H∣2

= 2E/H(e × h)(1/Zs)(E/H)2 + Zs

= 2z(1 + z2)(e × h), (14)

where z = (E/H)/(Zs), e = E/ ∣E∣, and h = H/ ∣H∣.It should be noted that the medium in (14) is considered as

the free-space medium with an impedance of Zs =√μ0/ε0.14 There-

fore, the energy velocity in the equation of (6) can be related tothe normalized impedance in (14). This formula clearly implies thatif z = 1, the magnitude of γ equals to one.14 This means that theenergy velocity is synchronized with the speed of light, and theEM energy can be transmitted to the medium without any reflec-tions.14 In this condition, the electric and magnetic energies are ina balanced state.14,59 However, any changes in the resonance fre-quency of our structure can cause an imbalance in the energy onthe interface between the top surface of MEH and the medium(i.e., z ≠ 1). This imbalance condition decreases the energy veloc-ity, and the wave is distorted by interfering with the reflections.14

Fortunately, international organizations (e.g., FCC and IEEE) havebeen permitted to some communication services to operate within(semi)urban regions in a range of frequency spectra limited to lessthan 10 GHz (e.g., WiFi, LTE, and GSM).2,3,5 Thus, the researcherschoose the crowded frequency of 5.77 GHz that is employed in WiFithat would be available in all of the smart buildings soon. Anotheradvantage of these crowded frequency bands is that they are free ofcharge.

The second problem that causes to disrupt the balance betweenelectric and magnetic energies from the MEH surface point of viewindividually [see (1) and (2)] is the field impedances of TE- and

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-7

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

TM-polarized incidence waves at different θs.3 For example, if θincreases from 0 to 90, the impedance of TM-polarized incidentfields to MEH decreases from 120π Ω to 0 Ω based on Eq. (1).61

Equivalently, this increasing of θ means that the tangential compo-nent of the electric field on the MEH surface goes to zero. Since theload of an ideal MEH is fixed, the top surface of our structure canbe matched without the reflection in an impedance of field (e.g., 60πΩ in Ref. 3). This impedance of the field can be obtained by onedirection of the incident wave to MEH. For this reason, if the MEHis skillfully designed to have maximum absorption (up to 100%60),MEH can maximally match with a surface field impedance that isin the corresponding direction of the incident wave. To obviate thisdifficulty, we propose a flexible cylindrical MEH whose cells con-sider the incident wave as an approximately normal incident, asdescribed in Fig. 1.3 The third common problem in MEH is polar-ization matching between the incident wave and dipole moments inmeta-atoms. To resolve this issue, the researchers intend to use asuper-cell that is robust to polarization of the orientation of wave-polarization, as demonstrated in the next session. As a result, MEHacts as an impedance transformer at far-field between a medium anda load, which can open up a new avenue for extreme applications,e.g., Metanna (meta-surface antenna62).

Recently, the challenging design of the impedance trans-former at a higher frequency has been studied in Ref. 13, e.g.,size/bandwidth limitations of the quarter-wavelength transformer.13

A new technique for impedance matching of MEH has been pro-posed in Ref. 3, which is inspired by the “T-match antenna” tech-nique. The manner in which the time-changing magnetic flux leadsto an induced electromotive force has been demonstrated in Ref.3. However, in this technique, the researchers needed at least twovias for impedance matching. There is a theoretically simple deriva-tion of this issue based on the Maxwell equations. Our unit-cellproperties with a single via located out of its center are depen-dent on the polarization of the incident wave.21,63 These singlevias are the basis components in the proposed designing approachof energy-/impedance-transformer between the medium andload.

Regarding the principle of conservation of energy, each idealHuygens’s meta-atom should equivalently function as Huygens’ssource with the same classic definition.10 This means that each cellshould have its own induced magnetic flux to excite magnetic dipolemoments in the cell, while the cell is illuminated by a linear polar-ization normal incident wave at the resonance frequency of the cell.If the aforementioned vias are located in the center of unit-cell, thecells become symmetric. This symmetric property in the proposedcell causes the magnetic flux within the cell to pass with an equalamount from both side regions of via [see Fig. 6(a)]. Clearly, it meansthat the center via cannot sense the spatial varying of the magneticfields. Thus, it is impossible to create a curl of the magnetic fieldaround the via between the top and bottom surface based on theAmpere–Maxwell law as50

∇× H = J +∂D∂t

. (15)

To trap the maximum power in the unit-cell, the loaded vias movecloser to the edge of the unit-cells until the impedance matching hasbeen achieved, which means the curl of the magnetic field transfersto the currents [see Eq. (15) and Fig. 6(b)].

FIG. 6. Magnetic field distribution in the unit-cell when MEH is illuminated by anormal incident plane wave. (a) L and R are equal to zero and (b) L = 1.4015 mmand R = P/4 = 1.6265 mm.

To come to a better understanding of these phenomena in theproposed unit-cell, it is convenient to consider an ideal transformermodel (turns ratio ≠ 1),13 which can be used to match the two realimpedance values. Note that the square turns ratio of the coils inthe primary and secondary of the transformer is equal to the ratiobetween input/output (I/O) resistances, as shown in Fig. 7.13,50,64

This is because the time-changing magnetic flux is passing throughboth the primary and secondary parts of the transformer with thesame value.50,64 It should be emphasized that unlike an ideal trans-former model whose input power is equal to output power (i.e., itsefficiency is considered to be 100%), the leakage/loss of the substrateand copper leads to a failure to reach 100% efficiency of our structureas an effective transformer.

Regarding the free-space impedance at the normal incidentplane-wave to the MEH as a constant input impedance in the I side(R1 = Zs = 120π Ω, i.e., εr1 = μr1 = 1), the idea is that if the via issituated closer to the unit-cell edges, a stronger magnetic field willbe constructed at one side of the via, and particularly, this causes anon-zero curl of the magnetic field [see Fig. 6(b)]. The location offsetof the via [i.e., a distance (R) from the center of the unit-cell] con-trols the amount of magnetic flux passing from each side. This canbe mimicked by the number of coil turns (N2) carrying the same cur-rent in the secondary part of the transformer in Fig. 7.13,64 Basically,a larger number of coil turns in the secondary of the transformerincreases the induced electromotive force (EMF) as more magneticflux passes through the windings (see Fig. 7).50,51,64 This is caused bya higher level of real impedances (R2), which is demanded in the Oside to satisfy the principle of conservation of energy. Indeed, thesetwo components (R and N2) are related directly. As already men-tioned, R is the location of the loaded via from the center of theunit-cell, as shown in Fig. 2. N1 and N2 are the number of turns ofcoil in the primary and secondary part of the transformer, as shownin Fig. 7.50,64 R1 is the load of primary of the transformer and is alsothe impedance of a medium (Zs) where the wave is propagating. R2is the load of secondary of the transformer and is also the load ofthe MEH.

In order to come to a validation of our idea, different R, L,and loads (R1 and R2) are tested using the full-wave simulation ofthe normal incidence wave to the single-polarized MEH, as shownin Figs. 8 and 9. In these figures, efficiency is used as a metric for

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-8

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

FIG. 7. A simple model of the trans-former with the leakage and main fluxpaths.50,64

delivering available power (i.e., a plane-wave incident power on thearea of the unit-cell) to the load. In other words, the arrangement ofour structure can transform the EMF from one level to another levelaccording to the principle of conservation of energy (see Subsections

8–10 in Ref. 50). In fact, the transformation of the EMF can be mod-ified by tuning the location of the via and its load. For example, theresults of different via locations (R) in Figs. 8(a) and 8(b) demon-strate that when MEH is loaded with a higher resistance (R2 = 50

FIG. 8. Full-wave simulation results ofthe efficiency (a) and (b) with R varia-tions (i.e., the other cell characteristicsare mentioned in Fig. 2), and (c) and (d)with R and L variations (i.e., the other cellcharacteristics are mentioned in Fig. 2),when the single-polarized MEH is illu-minated by the normal incident wave.[Notice that the cell’s load is 50 Ω in (a)and (d) and is 10 Ω in (b) and (c).]

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-9

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

FIG. 9. Full-wave simulation results ofthe efficiency when the single-polarizedMEH is illuminated by the normal inci-dent wave in different media by its rela-tive permittivity (εr) and permeability (μr).(a) εr = 9 and μr = 1, (b) εr = 36 and μr

= 1, (c) the distilled water that is char-acterized in ANSYS-HFSS, (d) εr = 1, μr

= 9, and t = 10 mil, (e) εr = 1, μr = 9, andt = 20 mil, and (f) εr = 1, μr = 9, and t= 30mil. [Notice that the cell characteris-tics of all results are from Fig. 2(a) exceptR = 2 mm, and the thickness of thesubstrate (t) of (d)–(f) is as mentioned.]

Ω) and R = 2 mm in Fig. 8(a), its efficiency is approximately equalto the case where the MEH is loaded with a lower resistance (R2 =10 Ω) and R = 1 mm in Fig. 8(b). This equality of Figs. 8(a) and 8(b)confirms that the transformation of EMF is done, i.e., similar to whatoccurs in an ideal transformer.50

It is worth mentioning that these variations, including Rand the impedance of the loads, did not have a strong effecton the resonance frequency. The physical reason for this effectis demonstrated in Ref. 3. However, for further clarification onhow slots on the CQSRR patch may have an effect on the reso-nance frequency, Figs. 8(c) and 8(d) illustrate the full-wave simul-taneous simulations of different L and R. The physical reasonbehind this effect is actually the rise in the L, which leads to anincrease in the length of the current path on the CQSRR patchfor delivering the load, resulting in a decrease in the resonancefrequency.

Figure 9 shows that the energy transformer is a fit candidatefor impedance matching in far-field, e.g., the environments of otherplanets (or refinery-laboratory) rather than the free space with animpedance of 120π Ω. In fact, the transformer’s core saturation is atypical problem of the transformer in practice. This problem causesthe efficiency of the transformer not to reach 100%. To obviate thisproblem, some methods may be employed such as the reduction ofturns of coil in the primary of the transformer (N1) [or (EMF)1]and increasing the size of transformer’ core.50,64 The substrate of ourstructure is a commercial non-magnetic substrate (Rogers RO3010)whose thickness (t = 0.254 μm = 10 mil) is extremely ultrathinin comparison with the operation wavelength. Clearly, a maxi-mum magnetic flux can be handled through this substrate thickness.Although the decrease in R1 [i.e., the impedance of the medium (Zs)]can be effectively handled within this thickness, the increase in R1 (orZs) results in the overload of our structure, which might lead to its

saturation. Therefore, EMF transformation cannot optimally occurin this thickness of the structure. To alleviate this overloading, thethickness of the MEH is increased to an appropriate level, as shownin Figs. 9(e) and 9(f). The different shift of the resonance frequencyof the proposed structure in Fig. 9 is because the medium surround-ing this structure (Zs =

√μ1/ ε1 =

√μr1μ0/ εr1ε0) is varying, as shown

in Fig. 9. It should be emphasized that μ1 and ε1 are considered asthe scalar quantity of permeability and permittivity of the medium,respectively, which may be extended to the complex tensors in thefuture research.

As a matter of fact, the desired resonance frequency of thistransformer can be acquired individually only with adjusting thesize parameters of the proposed unit-cell. To make the design ofthe desired resonance frequency of this structure faster, a surrogatemodeling approach is conducted and introduced in the next ses-sion. Consequently, MEH can be considered as an essential blockof wireless power supply in different media as well as an impedancetransformer between the medium and load.

As discussed in Ref. 24, these impedances may be complexvalues. Thus, it is needed to take the loss and gain mechanismsof the structure or rational Kramers–Kronig relations between theimaginary and real parts of μ and ε into consideration.24,43 In themicrowave regime, the modulation of the meta-atom impedancesrequired for tuning the resonate state of the meta-atoms can bedetermined by typical full-wave simulations and can be fabricatedeasily by PCB manufacturing technology. Practically, the geomet-rical metallic/dielectric scattering patterns are designed, which canbe mapped one-to-one to the electric and/or magnetic responses.13

Many types of these patterns could be found in the FSS literature tooptimize and implement the required electric and magnetic dipolemoments as well,23,38,65 for example, the metallic cut- and loop-wire,printed meandered line, metallic via, canonical omega meta-atom,

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-10

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

traces, split-ring resonator (SRR), ELC, and their complementaryinstances.

C. Lump circuit modelingFor a more clear demonstration of how this structure can act

as a matching network, which, in fact, is the principle objective ofthis paper, a simplified equivalent RLC circuit of the single-polarizedunit-cell is designed, as shown in Fig. 10. Indeed, the frequencyresponse of the resonant MEH structure may be modeled by theRLC resonance circuit in restricting the frequency band.3 The resultsof full-wave simulations with ANSYS-HFSS are proved to be rig-orous though the delay to achieve these results can be a long and

FIG. 10. Locations of the lump elements on (a) top, (b) bottom, and (c) side views ofthe unit-cell used in the circuit model, and (d) a schematic drawing of the proposedsimple equivalent circuit model of the single-polarized unit-cell illuminated (e) byTE60 and (f) and (g) by a normal incident plane-wave with x-polarization, asshown in (a). (e)–(g) A comparison between the results of the ADS and HFSS. Thesize of the unit-cell is the same as in Fig. 2 except R and L that are 1.6265 mm= P/4 and 1.4015 mm, respectively.

time-taking task since the time-consuming finite-element methodis employed in this simulator.41 Therefore, so as to speed up theprocess of the physical behavior of our MEH, an equivalent circuitmodel of the MEH is presented to run an analysis of the mechanismof energy harvesting.

The thin bridge on the CQSRR patch acts as an appropriatechannel to guide most of the surface currents through the load on theground occupying a very small area. The bridge and slots cause thelength of the current path to rise on the CQSRR patch. The etchingof the small areas on the ground acting as the defect ground surfaces(DGSs) can be simply modeled by a capacitor. This capacitor canbe manipulated by a designer to fine-tune the desired resonance fre-quency. The lump resistor of 50 Ω is placed on the ground betweenthe metallic via-pad and the ground for each unit-cell. The thicknessof our MEH and the distance between the edges of the neighboringcells cause an increase in the capacitance between the layers and alsothe neighboring patch.66,67 In fact, the thickness and relative permit-tivity of the substrate have a large effect on the phase of the reflectioncoefficient.61,66–68

In this equivalent circuit model, the reflection and transmis-sion coefficients for a normal incidence and for a TE-polarizedincident wave with an angle of 60 according to relation (2) havebeen studied. The optimized lump elements are obtained by the cir-cuit simulator of the Advanced Design System (ADS) software asL1 = 1.71 nH, C1 = 0.16 pF, L2 = 5.28 nH, C2 = 0.46 pF, L3 = 0.56nH, C3 = 0.56 pF, L4 = 11.12 nH, C4 = 7 pF, L5 = 2.59 nH,C5 = 0.98 pF, L6 = 1.88 nH, L7 = 2.52 nH, L8 = 24.25 nH, R1= 52.9 kΩ, R2 = 6.38 kΩ, R3 = 6.4 kΩ, and R4 = 3.19 kΩ. Indeed,the impedance of free-space (Z) is only changed by (2) in the equiv-alent circuit model. Figures 10(e)–10(g) show a comparison betweenthe results of the scattering (S-) parameters extracted from the full-wave simulator of ANSYS-HFSS and the circuit simulator of theADS software. The results demonstrate an acceptable level of agree-ment among them as the maximum power is harvested and deliv-ered to the load with minimum reflection toward the source ofradiation.

It should be noted that port 1 is considered for the free-spaceimpedance in a normal incident plane-wave (120π Ω) in Figs. 10(f)and 10(g) and in TE-60 of radiation angle (240π Ω) in Fig. 10(e)based on (2). Also, port 2 is specified as a load with a characteristicimpedance of 50 Ω (RL). Needless to say, the change in the char-acteristic impedance of port 1 (e.g., a different medium in Fig. 9.)causes a variance in the required impedance of port 2 for maxi-mum impedance matching.3 In the design of this circuit model, theresearchers are inspired by the previous works illustrated in Fig. 8of Ref. 3. In the microwave regime, the ohmic losses of the metallicCQSRR patch, via, and ground are ignored, but to include insulationlosses in the calculation, a parallel resistor was inserted with eachlossless capacitor,3,61 as shown in Fig. 10.

D. Surrogate modeling of MEH based on HISBased on the subject of high impedance surfaces (HISs),44,69,70

which is a common research topic in the field of microwaveantenna,61,66,71 in this section, the surrogate physical model of theMEH structure is elaborated.

First, for most of the commercial MEH devices, polarization-insensitivity is a significant feature. To meet this target, the

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-11

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

researchers employed a symmetric super-cell technique.72 Asalready mentioned, since full-wave simulations and optimizations ofthis super-cell to obtain the desired frequency is a time-consumingprocess, it is proposed that surrogate modeling be used. Knowingthat it does not account for other unknown effects of MEH,54 theresonance frequency of MEH is promptly achieved by discardingthe impacts of inconsequential physical parameters.54 It should bestressed that EM responses of the MEH in Fig. 2(a) were investi-gated in our previous work.21 Therefore, this type of physical sur-rogate modeling is a universal method if the performance of thedesigned MEH is validated by a full-wave and measurement resultsbefore employing surrogate modeling.73 This model relies on theHIS design approach, which has been widely surveyed in recentyears.38,44,69–71

Ideally, the magnitude of the reflection coefficient of HISs at theresonance frequency has to be +1 (0 dB), like that of a PEC.38,44,69,70

In contrast to PEC, the normal incident plane wave to HIS causesan increase up to twice (suppression) in the tangential electric field(surface-wave) on its surface, while the tangential magnetic fielddecreases to zero on its surface.14,38,44,69,70 In a typical HIS, the phaseof reflection waves decreases from + π/2 to – π/2 radians. Thisboundary is typically known as an in-phase reflection.44 Due to thisrange, two waves including the incident- and reflected-wave have

been constructively interfered on the HIS′ surface respected to theelectric field.38,44,69,70

In fact, as one may know, HISs are called the artificial magneticconducting (AMC) or magnetic wall due to their in-phase reflec-tion.38,44 Likewise, their resonance frequency is where the phasecrosses a zero-point, Fig. 11. A conductive sheet of the backsideof HIS is the reason that the transmission coefficient becomeszero from both sides. Therefore, when close to a resonance fre-quency of HIS, the reflection coefficient from each side is asym-metric reciprocal sheets known as PMC-PEC sheets.38 Attributableto the existence of magneto-electric couplings, i.e., omega-typeresponse of electric and magnetic fields,38 this response of HISs isbianisotropic.38,45,56,57

In the microwave regime, the loss of substrate and air-medium(or the supposed part of ε and even μ), skin effect of the copper,and resistance load itself do not show a strong effect on the reso-nance frequency discussed above.73 To take back to first principles,the process is simplified so as to decrease the processing time of theanalysis,73 and the researchers omitted these parameters in the com-putation process. Therefore, there is no need for metallic via or anydefects on the ground for locating the loads. It should be mentionedthat the size of the via and DGSs are relatively small comparing tothe unit-cell and the operation wavelengths. Moreover, the error of

FIG. 11. (a) A schematic drawing ofthe surrogate modeling with three lay-ers included PEC-ground and PEC-CQSRRs and a lossless substrate with-out the vias, DGSs, and loads. The full-wave simulation results of the reflectionphase under a normal incident plane-wave to (b) the surrogate model with justdifferent characteristic sizes of R and Lfrom Fig. 2 and B = 0.45 mm, (c) the sur-rogate model with all characteristics inFig. 2 except R = 1.9 mm, L = R − (B/2),and the different length of the bridge onthe CQSRR as B, and (d) the fine model(as multi-polarized MEH) with all charac-teristics in Fig. 2 except R = 1.9 mm, L= R − (B/2), and the different length ofthe bridges on the CQSRR as B, andits load is 50 Ω for comparison with thesurrogate model in (c).

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-12

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

these simplifications conduces to a small decrease in the resonancefrequency due to the increase in the length of the current path anda gradual increase in the level of the ground plane. The error ofsurrogate modeling can be solved by mapping this frequency drop(e.g., 6.3 GHz–6.4 GHz) to design the final multi-polarized structure.Besides, this metal sheet on the ground acts as a shielding surfacefrom the other side. Full-wave simulation results of Fig. 11 demon-strate these physical concepts of our simplifications over the finalstructure.

It is worth mentioning that with this simplification, the finalmulti-polarized super-cells can be simulated with just a single sur-rogate unit-cell. This simple model can be easily analyzed and opti-mized to acquire the desired resonance frequency with the appropri-ate geometry of the unit-cell. To start the optimization process, weneed an initial approximation of P in Fig. 2, which can be obtainedfrom our previous related work using the following formula: P= λm/2 (λm is the wavelength in the used substrate).3 Then, the sur-rogate model is full-wave simulated and optimized to achieve theoptimized value of P with a dimension of 6.506 mm. P is the squaredimension of the unit-cell periodicity. Note that G, S, N, and A inthis modeling are fixed at 150 μm, 200 μm, 0.95 mm, and 2.4 mm,respectively, as a result of the experimental difficulty, but L, B, R, andP are optimized to find the fine dimension. Finally, the researchersused the same dimension as a surrogate model of the energy har-vester for the final structure (fine model) that is illustrated in Fig. 2;with this point in mind, mapping the resonance frequency of the

surrogate unit-cell is required to come to the final multi-polarizedsuper-cell. More details of the surrogate modeling and well-knownspace-mapping can be found in Refs. 73–75. After optimizing thesurrogate model, the final multi-polarized MEH, whose super-cellis shown in Fig. 2, is full-wave simulated under a normal incidentwave with different polarization angles. The results show that theproposed MEH is insensitive to the polarization [see Fig. 12(a)]. Fig-ure 12(b) is simulated for showing the effects of L and R on the reso-nance frequency and harvesting efficiency of multi-polarized MEH.It should be borne in mind that the final dimension of L, R, and Pcauses the DGS area of the cell to be coupled with the ground of theneighboring cell, as shown in Fig. 2(c), leading to the employmentof two parallel loads of 100 Ω in each DGS. Final dimensions areR = 2.7 mm, L = 2.475 mm, B = 0.45 mm, and P = 6.506 mm≈ 0.12λ0 (λ0 is the free-space wavelength of 5.77 GHz). The simula-tion efficiency (η) at the resonance frequency (5.77 GHz) is 86.43%when the multi-polarized MEH is illuminated by a normal incidentplane wave. In addition, the incident angle stability of the final struc-ture is full-wave simulated under the TM- and TE-polarized wavewith different oblique angles, as shown in Figs. 12(c) and 12(d).

IV. EXPERIMENTAL VERIFICATIONIn order to verify the adopted design approaches, the pro-

posed MEH is fabricated with a finite MEH array with 10 × 10

FIG. 12. The full-wave simulation resultsof the efficiency vs frequency. (a) Whenthe multi-polarized MEH is illuminatedby different polarization angles in a nor-mal incident plane wave, (b) when themulti-polarized MEH is illuminated by thenormal incident wave, but just R andL are different from the characteristicssize mentioned in Fig. 2, and (c) and (d)are for illuminating of the multi-polarizedMEH with all characteristic sizes men-tioned in Fig. 2 by different oblique inci-dent angles TM and TE, respectively.[Notice that the resonance frequency of(b) can be compared with the resonancefrequency of the surrogate model resultsin Fig. 11(b).]

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-13

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

(65.06× 65.06 mm2) resonator unit-cells through the process of PCBmanufacturing, covered by a number of 5 × 5 super-cells, as shownin Fig. 13. The finite array is patterned over a Rogers RO3010 sub-strate with the schematic drawing characteristics of Fig. 2. To havean analogous EM coupling environment with full-wave simulations,the terminals of each-cell are loaded. Indeed, each cell has its ownload welded in DGS between the ground and the via-pad. Theseloads consist of 99 SMD resistors of 49.9 Ω and one 50-Ω SMAconnector connected to one cell of the central super-cell. As a con-ventional method,25–29 the central super-cell is chosen for measuringits delivered power because this super-cell is close to the full-wavesimulation model in terms of infinite cells. It is necessary to mentionthat a large number of cells in the array cause the cells with the largestdistance from the center of array to have a minimum influence onthe central cell energy absorption.26 The fabricated MEH array islocated at a far-field region of a horn antenna by a distance of 5.2 mfor the plane wave illumination. The horn antenna is connected tothe Hewlett Packard 83732B signal generator employed to providea power level of 17 dBm. Then, the delivered AC power on thecentral super-cell is measured using the spectrum analyzer of NS-132. The measurement setup is calibrated regarding the connectors,cable, and antenna losses. As the proposed MEH is a symmetricalstructure, the total power delivered to the central super-cell is mea-sured and accumulated by rotating the MEH array around the SMAin four phases of movement of 90 around the SMA connector.3,26,72

For having a fair comparison between the measurement results ofthe finite array and the full-wave simulation results, it is neededto extract an effective aperture of the central super-cell because thenon-uniform mutual couplings are between the fabricated cells.3 Wehave obtained an effective aperture (Af ) of 2.8 times of the surfacearea (footprint) of the super-cell from our measurement. The energyharvesting efficiency at the central super-cell (η) was calculated bythe Friis equation as follows:3

Pin = Pt ×Gt

4πd2 × Af , (16)

η = Pm

Pin, (17)

where Gt , Pt , Pm, and d are the gain and radiated power ofthe horn antenna, the delivered power to central supercell’sloads, and the distance between the horn antenna and MEH,respectively.

FIG. 13. A 3D view of the fabricated flexible MEH in (a) and (c) the curvedstyle and (b) the flat style of the MEH array by a number of 5 × 5super-cells.

As mentioned in Ref. 3, so as to validate the 2D-isotropic char-acteristic of the proposed MEH in an experimental manner, a curvedMEH (cylindrical shape) is considered with a radius of 48 mm asa small slice of the cylinder, as shown in Fig. 13. The stability ofthe structure over the maximum and minimum polarization changeis validated. Besides, we aimed to conduct this test by rotating thecurved-MEH around the SMA connector under a normal incidentwave. These minimum and maximum angles of polarization are 0

and 90. The experimental results of the efficiency in Fig. 14(e) showthat the efficiency of the curved MEH remains nearly unchangedwhen the curved MEH is illuminated by a normal incident planewave. Figure 14(f) shows a part of our measurement setup. In addi-tion, the experimental results of the efficiency at different incidentangles for TE- and TM-polarized wave for the flat style of the MEHare shown in Figs. 14(a) and 14(b), respectively. It should be notedthat the discrepancy between the resonance frequency of the full-wave simulation and experimental results of this type of finite arrayis investigated in our previous works.3,21 An example that can bementioned in this case is truncating an infinite array to a finite fab-ricated array or increasing the length of the current path on theground, which is due to the fact that almost all the current shouldbe passed from SMD resistors. In addition, an important factor forthe frequency shift has been recently investigated in detail in Refs.23 and 24, which signifies the error in the relative permittivity (εr)of the substrate used in the simulation. For this reason, we addednew simulation results in Figs. 14(c) and 14(d) with εr = 12.5 for thesubstrate of Rogers RO3010 based on Ref. 23 to be able to comparethem with the experimental results in Figs. 14(a) and 14(b). It shouldbe noted that other simulation results in this paper are for εr = 11.2.The resonance frequency of simulation results for a normal incidentplane wave to the MEH with εr = 12.5 is 5.47 GHz, which has anacceptable agreement with the experimental results of the resonancefrequency near to 5.23 GHz (see Fig. 14). Figure 12 (b) demonstratesthe important effect of the slots and the location of the DGSs andvias on predicting the resonance frequency and bandwidths of theMEH. Figure 9(a) in Ref. 3 demonstrates the effects of the thicknessof the substrate on the resonance frequency of this type of MEH.Therefore, the fabrication imperfections12,76 may account for shift-ing the resonance frequency such as over-etching in the area of theslots in the unit-cells and the decreasing/increasing of the thicknessof the substrate during the fabrication process. Also, a number ofpractical losses60 during the welding of the SMA connector and theSMD resistors led to a misalignment in the periods of unit-cells,which also account for this shift in the resonance frequency. Fur-thermore, the via terminals of each fabricated cell are loaded by oneSMD 49.9 Ω (with a package type of 0603) that has a typical toleranceerror. However, as some parts of DGS area of each cell for locat-ing loads are outside of the same cell, in simulation results, we haveemployed two parallel loads of 100 Ω [red areas in Fig. 2(c)]. Thismismatch between the ports in simulations and the available SMDresistors in the fabricated array is a possible source of the decreaseobserved in the bandwidth level in the experimental results studiedin Ref. 28. There are also a number of experimental limitations of thePCB manufacturing for locating the metallic via in the bridge on theCQSRR patch, known as the typical fabrication tolerances. For thisreason, these specific bridges are wider than B in Fig. 2, which arehighlighted in one super-cell in Fig. 13(b), being another explanationfor the mentioned discrepancy.

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-14

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

FIG. 14. The measured efficiency whenthe finite array of MEH is illuminatedby TE- and TM-polarized plane wavesin different incident angles respectivelyin (a) and (b). The full-wave simulationresults of the efficiency when the struc-ture illuminated by TE- and TM-polarizedplane waves in different incident anglesrespectively in (c) and (d). (e) Themeasured efficiency of the curved MEHunder a normal incident wave with twomaximum different orientation of polar-ization angles. (f) A part of the measure-ment setup. The measured efficiency ofthe flat style MEH under a normal inci-dent plane wave (i.e., TE0, TM0, orTEM) is shown in (a), (b), and (e) by thedotted line for a comparison with otherresults. [Notice that (c) and (d) are forall characteristics in Fig. 2 except the tol-erance error of the substrate permittivityin Rogers RO3010 considered εr = 12.5based on Ref. 23.]

V. CONCLUSIONTo summarize, in this study, the researchers aimed at extend-

ing a previously developed single-polarized structure to the onewith multi-polarized characteristics using more compacted cells.A deep analysis of the MEH is rendered based on the relation-ship between the wave velocity and field impedance. We have pro-posed a new impedance- and energy-transformer for impedancematching between a medium and a load inspired by an ideal trans-former. Regarding the concept of space-time nature of travelingwave energy, the balance conditions of Huygens’s meta-atoms arealso investigated. In addition, a simple equivalent circuit model ofthe cell is proposed, and its results are validated by full-wave simu-lations obtained from ANSYS-HFSS. In this design, we employeda surrogate model for reducing the time processing length of thefull-wave simulations. Our final structure is fabricated and measurednot only through a flat style for comparison with the state-of-the-art

related works but also through the curved style as a small slice of thecylinder proved it to be effective. The results enjoy an appropriatelevel of agreement with the simulations as well as other theoreti-cal studies. The proposed idea for impedance matching between amedium and a load, based on an ideal impedance transformer, mightbe generalized to an arbitrary complex impedance of a medium;12

however, the complex loads of MEH should be carefully designed.The flexible MEH can be employed in the other conformal appli-cations such as implantable and wearable electronics, conformalbiomedicine sensors, and Huygens’s radiators.

ACKNOWLEDGMENTSThe authors would like to thank the Sadjad Research Center

(SRC) at the Sadjad University of Technology and the EMI/EMCand Microwave Technology Research Laboratory at the Ferdowsi

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-15

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

University of Mashhad for providing the laboratory equipmentrequired for the simulation and measurement results in this paper.The authors would like to thank Dr. Navid Nasrollahi for editing theacademic English language of this paper. The authors would like tothank Dr. Mehdi Forouzanfar for his help in measurements of thisresearch.

DATA AVAILABILITY

The data that support the findings of this study are availablewithin the article.

REFERENCES1M. Shirvanimoghaddam, K. Shirvanimoghaddam, M. M. Abolhasani, M. Farhangi,V. Zahiri Barsari, H. Liu, M. Dohler, and M. Naebe, “Towards a green and self-powered internet of things using piezoelectric energy harvesting,” IEEE Access 7,94533 (2019).2S. M. R. Islam, D. Kwak, M. H. Kabir, M. Hossain, and K. Kwak, “The internet ofthings for health care: A comprehensive survey,” IEEE Access 3, 678 (2015).3A. Ghaneizadeh, M. Joodaki, J. Börcsök, A. Golmakani, and K. Mafinezhad,“Analysis, design, and implementation of a new extremely ultrathin 2-D-isotropicflexible energy harvester using symmetric patch FSS,” IEEE Trans. MicrowaveTheory Tech. 68(6), 2108–2115 (2020).4X. Zhang, H. Liu, and L. Li, “Tri-band miniaturized wide-angle and polarization-insensitive metasurface for ambient energy harvesting,” Appl. Phys. Lett. 111,071902 (2017).5M. Cansiz, D. Altinel, and G. K. Kurt, “Efficiency in RF energy harvestingsystems: A comprehensive review,” Energy 174, 292 (2019).6B. Ghaderi, V. Nayyeri, M. Soleimani, and O. M. Ramahi, “Pixelated metasur-face for dual-band and multi-polarization electromagnetic energy harvesting,” Sci.Rep. 8, 13227 (2018).7C. A. Balanis, Antenna Theory: Analysis and Design, 3th ed. (Wiley, Hoboken,NJ, USA, 2016).8D. H. Kwon and D. M. Pozar, “Optimal characteristics of an arbitrary receiveantenna,” IEEE Trans. Antennas Propag. 57(12), 3720 (2009).9D. Pozar, “Scattered and absorbed powers in receiving antennas,” IEEE AntennasPropag. Mag. 46, 144–145 (2004).10C. A. Balanis, Advanced Engineering Electromagnetic, 2th ed. (Wiley NJ, USA,2012).11V. Pacheco-Peña and N. Engheta, “Antireflection temporal coatings,” Optica7(4), 323 (2020).12Z. Zhou, Y. Li, E. Nahvi, H. Li, Y. He, I. Liberal, and N. Engheta, “Generalimpedance matching via doped epsilon-near-zero media,” Phys. Rev. Appl. 13,034005 (2020).13A. H. Dorrah, M. Chen, and G. V. Eleftheriades, “Bianisotropic Huygens’ meta-surface for wideband impedance matching between two dielectric media,” IEEETrans. Antennas Propag. 66(9), 4729 (2018).14H. G. Schantz, “Energy velocity and reactive fields,” Philos. Trans. R. Soc. A 376,20170453 (2018).15O. M. Ramahi, T. S. Almoneef, M. Alshareef, and M. S. Boybay, “Metamate-rial particles for electromagnetic energy harvesting,” Appl. Phys. Lett. 101, 173903(2012).16S. Shang, S. Yang, J. Liu, M. Shan, and H. Cao, “Metamaterial electromag-netic energy harvester with high selective harvesting for left- and right-handedcircularly polarized waves,” J. Appl. Phys. 120, 045106 (2016).17P. Xu, S.-Y. Wang, and W. Geyi, “Design of an effective energy receiving adapterfor microwave wireless power transmission application,” AIP Adv. 6, 105010(2016).18V. K. Chakradhary, H. B. Baskey, R. Roshan, A. Pathik, and M. J. Akhtar,“Design of frequency selective surface-based hybrid nanocomposite absorberfor stealth applications,” IEEE Trans. Microwave Theory. Tech. 66(11), 4737(2018).

19L. Li, X. Zhang, C. Song, and Y. Huang, “Progress, challenges, and perspectiveon metasurfaces for ambient radio frequency energy harvesting,” Appl. Phys. Lett.116, 060501 (2020).20A. A. G. Amer, S. Z. Sapuan, N. Nasimuddin, A. Alphones, and N. B. Zinal, “Acomprehensive review of metasurface structures suitable for RF energy harvest-ing,” IEEE Access 8, 76433 (2020).21A. Ghaneizadeh, K. Mafinezhad, and M. Joodaki, “Design and fabrication of a2D-isotropic flexible ultra-thin metasurface for ambient electromagnetic energyharvesting,” AIP Adv. 9, 025304 (2019).22A. Ghaneizadeh, M. Joodaki, J. Börcsök, and K. Mafinezhad, “A new extremelyultrathin metasurface energy harvester and its simple modelling based on resonanthalf-wave dipole antenna,” in Proceedings EEE MTT-S International MicrowaveWorkshop Series on Advanced Materials and Processes (IMWS-AMP), Bochum,Germany, July 16–18 (IEEE, 2019), pp. 64–66.23M. Chen and G. V. Eleftheriades, “Omega-bianisotropic wire-loop Huygens’metasurface for reflectionless wide-angle refraction,” IEEE Trans. AntennasPropag. 68(3), 1477 (2020).24M. Chen, E. Abdo-Sánchez, A. Epstein, and G. V. Eleftheriades, “Theory,design, and experimental verification of a reflectionless bianisotropic Huygens’metasurface for wide-angle refraction,” Phys. Rev. B 97, 125433 (2018).25F. Yu, X. Yang, H. Zhong, C. Chu, and S. Gao, “Polarization-insensitive wide-angle-reception metasurface with simplified structure for harvesting electromag-netic energy,” Appl. Phys. Lett. 113, 123903 (2018).26H.-T. Zhong, X.-X. Yang, X.-T. Song, Z.-Y. Guo, and F. Yu, “Wideband meta-material array with polarization-independent and wide incident angle for harvest-ing ambient electromagnetic energy and wireless power transfer,” Appl. Phys. Lett.111, 213902 (2017).27B. Alavikia, T. S. Almoneef, and O. M. Ramahi, “Complementary split ringresonator arrays for electromagnetic energy harvesting,” Appl. Phys. Lett. 107,033902 (2015).28B. Alavikia, T. S. Almoneef, and O. M. Ramahi, “Wideband resonator arrays forelectromagnetic energy harvesting and wireless power transfer,” Appl. Phys. Lett.107, 243902 (2015).29X. Duan, X. Chen, Y. Zhou, L. Zhou, and S. Hao, “Wideband metamaterialelectromagnetic energy harvester with high capture efficiency and wide incidentangle,” IEEE Antennas Wireless Propag. Lett. 17(9), 1617 (2018).30A. Ghaneizadeh, K. Mafinezhad, and M. Joodaki, “A new compact dual-band perfect absorption ultrathin planar metasurface energy harvester in X- andV-bands with a wide incident angle,” AIP Adv. 10(8), 085007 (2020).31M. E. Badawe, T. S. Almoneef, and O. M. Ramahi, “A metasurface for conver-sion of electromagnetic radiation to DC,” AIP Adv. 7, 035112 (2017).32X. Zhang, H. Liu, and L. Li, “Electromagnetic power harvester using wide-angleand polarization-insensitive metasurfaces,” Appl. Sci. 8, 497 (2018).33B. Ghaderi, V. Nayyeri, M. Soleimani, and O. M. Ramahi, “Multi-polarizationelectromagnetic energy harvesting with high efficiency,” IET Microwave AntennasPropag. 12(15), 2271 (2018).34A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalenceprinciple: Design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).35S. A. Tretyakov, “Metasurfaces for general transformations of electromagneticfields,” Philos. Trans. R. Soc. A 373, 20140362 (2015).36Y. Vahabzadeh, N. Chamanara, K. Achouri, and C. Caloz, “Computationalanalysis of metasurfaces,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 37(2018).37K. Achouri and C. Caloz, “Design, concepts, and applications of electromagneticmetasurfaces,” Nanophotonics 7(6), 1095 (2018).38S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Smiovski,“Metasurfaces: From microwave to visible,” Phys. Rep. 634, 1–72 (2016).39C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave frontswith reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).40A. Epstein and G. V. Eleftheriades, “Arbitrary power-conserving field trans-formations with passive lossless omega-type bianisotropic metasurfaces,” IEEETrans. Antennas Propag. 64(9), 3880 (2016).41J. P. S. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization consid-erations for scalar Huygens metasurfaces and characterization for 2-D refraction,”IEEE Trans. Microwave Theory. Tech. 63(3), 913 (2015).

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-16

© Author(s) 2020

AIP Advances ARTICLE scitation.org/journal/adv

42M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagneticfields using orthogonal electric and magnetic currents for wavefront manipula-tion,” Opt. Express 21, 12, 14409 (2013).43C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D.R. Smith, “An overview of the theory and applications of metasurfaces: The two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2),10 (2012).44A. Li, S. Singh, and D. Sievenpiper, “Metasurfaces and their applications,”Nanophotonics 7(6), 989 (2018).45V. S. Asadchy, A. Díaz-Rubio, and S. A. Tretyakov, “Bianisotropic metasurfaces:Physics and applications,” Nanophotonics 7(6), 1069 (2018).46X.-X. Liu, Y. Zhao, and A. Alu, “Polarizability tensor retrieval for subwavelengthparticles of arbitrary shape,” IEEE Trans. Antennas Propag. 64(6), 2301 (2016).47C. Guan, Z. Wang, X. Ding, K. Zhang, B. Ratni, S. N. Burokur, M. Jin,and Q. Wu, “Coding Huygens’ metasurface for enhanced quality holographicimaging,” Opt. Express 27(5), 7108–7119 (2019).48R. Zhao, Z. Zhu, G. Dong, T. Lv, Y. Li, C. Guan, J. Shi, and H. Zhang, “High-efficiency Huygens’ metasurface for terahertz wave manipulation,” Opt. Lett.44(14), 3482–3485 (2019).49G. Lavigne and C. Caloz, Manipulation of Fresnel Coefficients Using CrossAnisotropic Metasurface Coating (United States National Committee of URSINational Radio Science Meeting (USNC-URSI NRSM), Boulder, CO, USA, 2019),pp. 1–2.50J. D. Kraus and K. R. Carver, Electromagnetics, 2th ed. (McGraw-Hill, Inc., USA,1973).51J. A. Stratton, Electromagnetic Theory (McGraw-Hill, Inc., New York, USA,1941).52Z. Wang, J. Liu, X. Ding, W. Zhao, K. Zhang, H. Li, B. Ratni, S. N. Burokur,and Q. Wu, “Three-dimensional microwave holography based on broadbandHuygens’ metasurface,” Phys. Rev. Appl. 13, 014033 (2020).53H. G. Schantz, “Electromagnetic energy around Hertzian dipoles,” in IEEEAntennas and Propagation Society International Symposium, Digest. Held in Con-junction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010)(IEEE, Orlando, FL, 1999), Vol. 2, pp. 1320–1323.54S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House,2003).55E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Aver-aged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans.Antennas Propag. 51(10), 2641 (2003).56Y. Ra’di, V. S. Asadchy, and S. A. Tretyakov, “Total absorption of electromag-netic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61(9), 4606(2013).57Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for elec-tromagnetic waves: Theory, design, and realizations,” Phys. Rev. Appl. 3, 037001(2015).58S. M. Mikki and Y. Antar, New Foundations for Applied Electromagnetic: TheSpatial Structure of Fields (Artech House, Norwood, MA, USA, 2016).

59H. G. Schantz, The Art and Science of Ultrawideband Antennas, 2nd ed. (ArtechHouse, 2015).60T. S. Almoneef and O. M. Ramahi, “Metamaterial electromagneticenergy harvester with near unity efficiency,” Appl. Phys. Lett. 106, 153902(2015).61F. Costa, S. Genovesi, A. Monorchio, and G. Manara, “A circuit-based modelfor the interpretation of perfect metamaterial absorbers,” IEEE Trans. AntennasPropag. 61(3), 1201 (2013).62M. El Badawe, T. S. Almoneef, and O. M. Ramahi, “A true metasurface antenna,”Sci. Rep. 6, 19268 (2016).63F. Yang and Y. Rahmat-Samii, Electromagnetic Band Gap Structures in AntennaEngineering (Cambridge University Press, 2010).64A. R. daniels, Introduction to Electrical Machines (Higher and Further EducationDivision, 1985).65B. A. Munk, Frequency Selective Surfaces: Theory and Design (John Wiley &Sons, New York, 2005).66O. Luukkonen, F. Costa, C. R. Simovski, A. Monorchio, and S. A. Tretyakov, “Athin electromagnetic absorber for wide incidence angles and both polarizations,”IEEE Trans. Antennas Propag. 57(10), 3119 (2009).67F. Costa, A. Monorchio, and G. Manara, “An equivalent-circuit modeling ofhigh impedance surfaces employing arbitrarily shaped FSS,” in InternationalConference on Electromagnetics in Advanced Applications (IEEE, Torino, 2009),pp. 852–855.68S. Y. Jun, B. Sanz Izquierdo, and E. A. Parker, “Liquid sensor/detector using anEBG structure,” IEEE Trans. Antennas Propag. 67(5), 3366 (2019).69D. F. Sievenpiper, “High-impedance electromagnetic surfaces,” Ph.D. disserta-tion (Department of Electrical Engineering, University of California, Los Angeles,CA, USA, 1999).70D. Sievenpiper, L. Lijun Zhang, R. F. J. Broas, N. G. Alexopolous, andE. Yablonovitch, “High-impedance electromagnetic surfaces with a forbiddenfrequency band,” IEEE Trans. Microwave. Theory. Tech. 47(11), 2059 (1999).71S. A. Tretyakov and S. I. Maslovski, “Thin absorbing structure for all incidenceangles based on the use of a high-impedance surface,” Microwave Opt. Tech. Lett.38(3), 175 (2003).72S. Shang, S. Yang, M. Shan, J. Liu, and H. Cao, “High performance metamaterialdevice with enhanced electromagnetic energy harvesting efficiency,” AIP Adv. 7,105204 (2017).73S. Koziel and S. Ogurtsov, Antenna Design by Simulation-Driven Optimization(Springer, New York, NY, USA, 2014).74S. Koziel and A. Bekasiewicz, Multi-Objective Design of Antenna Using SurrogateModels (World Scientific Publishing Europe, Ltd., London, UK, 2017).75S. Koziel, X. S. Yang, and Q. J. Zhang, Simulation-driven Design Optimizationand Modeling for Microwave Engineering (Imperial College Press, London, UK,2013).76M. Kim and G. V. Eleftheriades, “Design and experimental demonstrationof impedance-matched circular-polarization-selective surfaces with spin-selectivemodulations,” Phys. Rev. Appl. 13, 014009 (2020).

AIP Advances 10, 105201 (2020); doi: 10.1063/5.0016373 10, 105201-17

© Author(s) 2020