IET Optoelectronics

Research Article

Polarisation insensitive tunable metamaterialperfect absorber for solar cells applications

ISSN 1751-8768Received on 9th January 2016Revised 5th April 2016Accepted on 16th April 2016doi: 10.1049/iet-opt.2016.0003www.ietdl.org

Patrick Rufangura1, Cumali Sabah2 1Sustainable Environment and Energy Systems, Middle East Technical University, Northern Cyprus Campus, Kalkanli, Guzelyurt, 99738, TRNC/Mersin 10, Turkey2Department of Electrical and Electronics Engineering, Middle East Technical University, Northern Cyprus Campus, Kalkanli, Guzelyurt, 99738,TRNC/Mersin 10, Turkey

E-mail: sabah@metu.edu.tr

Abstract: Developing a perfect absorber based on metamaterials (MTMs) is a promising technique towards improving theefficiency of solar photovoltaic cells. In this study, a novel MTM-based perfect absorber (MPA) is proposed for solar cellapplications, which exhibits an excellent single-band with high absorption rate of 99.7% in visible frequency regime (resonancefrequency of 614.4 THz) with an outstanding absorption bandwidth of 15.5%. The proposed design presents a high symmetryflexibility which makes it easy to fabricate. Besides, the simulation results for the defined different incident angles and differentpolarisation (transverse electric and transverse magnetic) confirm the quality of the proposed design by showing how insensitiveit is to both the defined incident angles (normal and oblique incident) and different polarisation angles of electromagnetic wave.The parametric study on dielectric spacer shows the tunability characteristic of an intended MPA structure. The proposed MPAdesign is a good candidate for fabrication of high-efficiency solar cell operating in a visible frequency range.

1 IntroductionAn engineered man-made material known as ‘metamaterial(MTM)’ has brought a great deal of contribution to electromagnetic(EM) research field. This artificial material exhibits extraordinaryproperties which cannot be found in nature. To name a few, theseproperties are negative electric permittivity (ɛ(ω)), negativemagnetic permeability(μ(ω)), negative index of refraction (n),reverse Doppler effects, backward wave propagation and so forth[1–6]. Among these exotic EM properties what motivated theresearch is the ability of MTMs to display negative ɛ and μ the realpart and imaginary part of which can be controlled separately inorder to manipulate the propagation path of EM wave. Theexistence of materials which display negative EM properties wasimpossible in real sense for several years till a first work on theexistence of such strange material was presented in a seminal paperby Veselago in 1967 [7]. In his paper, Veselago theoreticallyexplained the possibility to create a material with simultaneousnegative ɛ and μ. However, his work was neglected for threedecades till 2000 when Smith and co-workers [4] experimentallyverified the existence of negative refractive index. From that timetill present, many scholars have turned their research interests tothe field of MTM where thousands of research papers on MTMsand their various applications are published yearly. The advent ofMTMs was characterised by potential applications in invisiblecloak and creation of superlens/perfect lenses which wasdiscovered by Pendry and his research group [8–10] with time,many other interesting applications started developing; thanks toEM properties (negative electric permittivity, negative magneticpermeability and negative index of refraction) of MTMs. Some ofthese applications are MTM-based sensor filters [11–13], wirelesssensors [14–16], antenna [17, 18] and MTM-based perfectabsorbers (MPAs) [19–22]. Developing perfect absorber based onMTM (MPAs) is one of the biggest achievement in the past twodecades since MTMs discovery, this is due to many applicationsthat arose after the realisation of the first MTM absorber. Wideangle ultra-thin MTM-based absorber can be used for developmentof higher efficiency thermal photovoltaics [23] and photovoltaics[24], where for application in photovoltaics the high-efficiencysolar cells can be gained from strong field resonance inside theabsorbing MTM [25].

Normally, the absorption A(ω) rate of material depends on twobasic parameters: reflection rate R(ω) = |S11|2 and transmission rateT(ω) = |S12|2. �(�) = 1− �(�) + �(�) (1)

where |S11|2 and |S12|2 are scattering parameters describingreflected and transmitted electric fields from computer simulationof a MTM unit cell, respectively. Generally, a MTM unit cellcomprises of periodic arrangement of smaller components (meta-atoms) which produces high loss. Electrically, a MTM unit cell canbe represented by electric circuit elements, capacitance andinductance, which play an important role in obtaining EMresonance.

�0 = 1�� (2)

With ω0, L and C representing the resonance frequency, inductanceand capacitance, respectively. Therefore through ohmic loss anddielectric loss which are generated by magnetic resonances frominduced antiparallel currents, inductance and capacitance store upenergy at resonant frequency or ‘resonant absorption.’ on the otherhand, the characteristics of L and C depend on the values of ɛ andμ. As a result, the ability to control EM parameters of MTMs (ɛand μ) is the key to this success (creation of perfect absorbers)where by changing the real and imaginary parts of both electricpermittivity and magnetic permeability the impedance of a MTMunit cell can be matched with the one for free space.

�(�) = �� (3)

�0(�) = �0�0 (4)

With Z0(ω) and Z(ω) representing impedance of free space and thestructure, respectively, while μ0 and ɛ0 are the magneticpermeability and electric permittivity of free space,

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correspondingly. Once this condition (impedance match) isfulfilled, the reflectance of a MTM structure declines up to thenegligible coefficient (nearly zero reflection rate). From (1), oncethe reflection rate is minimised, the only parameters to preventperfect absorption is the transmittance (transmission of radiationthrough the ground plane to the space). In order to remove suchlosses in MTM absorber designs, a process known as ‘couplesystem’ [26] is commonly used, where a metallic layer placed onthe bottom of a MTM absorber unit cell with a thickness muchgreater than its skin depth at the working frequencies. This processwas used by Landy et al. [19] in 2008 to design the first MPA.Their MPA structure consisted of three layers (two metallic layersand a dielectric spacer). The top layer (electric ring resonator‘ERR’) together with the ground metallic plane produced electricresonance well through the strong coupling of incident electricfield at resonance frequency. Magnetic resonance was generated byantiparallel current induced from ERR. In this first MPA structure,a narrow absorption rate of 99% was attained at 11.65 GHz.Following the work of Landy and his research group, single, dualand multiple-band MTMs which present different applications indifferent frequency range (from RF to optical frequencies range)were proposed [27–36]. However, the challenges still exist inmajority of these designs working in a narrow-band frequencyresponse and they are polarisation sensitive. Another challenge stillpersisting is the slow development of MPAs in high-frequencyregime such as visible frequency. One of the challenges impedingthe development of MPAs structure in visible frequencies is that aMPA structure needs to be of a much smaller size than thewavelength of interest; therefore MTMs in visible frequency rangemust be of certain size of tens of nanometres which makes itdifficult to fabricate. Nevertheless, solar radiations are higher inthis region in comparison with other frequency ranges which mustmake the visible range of solar spectrum more attractive to theresearchers than other frequency ranges. Even though some workshave so far been done, such as [37–39], lots of effort need to beadded in the development of perfect MTM absorbers with responsein a visible frequency regime. Against this backdrop, the paperproposes a novel single-band tunable polarisation and incidentangle insensitive perfect MTM absorber in order to harness solarenergy resources in a visible frequency range. One of theadvantages of the proposed design is how it offers a highsymmetric flexibility which causes it to give a resonant absorptionof near a unit in visible spectrum of EM wave while offering a verygood absorption bandwidth of more than 15% with respect to theresonant (central) frequency. In addition, the present design is

simple for fabrication. It is believed that the realisation of a highersolar radiation absorber structure will lead to improvement in thecurrent efficiency of solar cell while playing a great role in thisprocess.

2 Design, simulation and discussion of resultsThe proposed perfect MTM absorber unit cell consists of threebasic layers (ground metallic plane, dielectric spacer and patches(two metallic layers with a sandwiched dielectric material) on thetop of a dielectric spacer as shown in Fig. 1. The ground layer ismade of a metallic material made of gold lossy with a much higherthickness than its surface roughness in the frequency of interest andits electric conductivity σ  = 4.561 × 10 7 Sm−1 in GHz and/or THzfrequencies. The selection of gold is based on some of its goodproperties such as its ability to resist to the excessive heat and ithas high reflectance in the presence of high-frequency radiations.This makes it a good candidate in designing MPA for visiblefrequency radiations; however, depending on the intendedapplications for any proposed MPA structure, other metals such asaluminium, copper and silver [40–42] can be used in the place ofgold, while the absorption characteristics of the MPA remainsunchanged. This is because the absorption behaviour of a MTMstructure has no huge dependency on the material compositioninstead it is governed by the unit-cell geometrical parametersarrangement such as its shape, orientation and size. Another fact isthat in high-frequency (visible) range, several metals behave likelossy materials. Note that, the optical properties of the metal for thestudied region (visible frequencies) is defined as frequency-dependent complex parameters and the required parameters aretaken from [40–42] in which it is described as a Drude materials(Drude–Lorentz model).

On top of the ground metallic plane there is a dielectric spacermade of gallium arsenide lossy with electric permittivity ɛ  = 12.9and tangent delta of 0.006. The top most layer is made of periodicarrangement of two patches (metals) made of gold holding betweenthem gallium arsenide. The geometric parameters of a proposedMPA are: a = 550 nm, z = 80 nm, t = 100 nm, b = 342.9 nm, c = 240 nm, d = 100.9 nm and k (thickness of the top patches) =5 nm.

The simulation is performed by using a full-wave EM simulatorwhich uses finite integrate technique with high-frequency solver[43–46]. The intended structure is to work in visible frequenciesranging from 450 to 750 THz. The radiations are polarised in a waythat both electric field (E) and magnetic field (H) are in phase withthe plane of incident, whereas a wave vector (k) is perpendicular tothe geometric plane of the MPA unit cell. Here, the periodicboundary conditions are selected, whereas open free space isselected as the simulation environment.

Since the coupled model system is used in this study (groundmetallic with thickness much greater than the skin depth of gold ina visible frequency), then the transmission losses are eliminated.As a result, the term T(ω) in (1) is no longer in use and the onlyparameter involving in simulation results is reflection coefficientR(ω). In Fig. 2, the simulation results for both reflection andabsorption rates are reported. As it can be seen from Fig. 2, nearlya unit (0.997) absorption rate is gained at 614.4 THz whichcorresponds to a very minimum reflection coefficient (0.054) atthis frequency.

The source of this perfect absorption is the strong coupling ofincident electric and magnetic fields with the top patches(combination of both metallic and dielectric layers) and a dielectricspacer and the ground metallic plane which cause electric andmagnetic resonance and lead to the perfect absorption at theresonant frequency. As one can observe, the single-band MTMabsorber in this paper has an outstanding bandwidth of 15.5% withrespect to the resonance frequency (central frequency) whichoriginates from high surface plasmon resonance resulted from thecoupling of the two top metallic layers (top patches) and thedielectric layer between them.

The dependence of the bandwidth of the proposed design on thematerial used for ground plane was verified by performing itssimulation under different types of metal (gold, copper, silver andaluminium). The choice of metal for the fabrication of the MPA

Fig. 1  Proposed MPA unit cell(a) Perspective view and, (b) Top view (Patches)

Fig. 2  Simulated absorption and reflection rates at resonance frequency of614.4 THz

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carries major importance because it determines how well one cancouple to the surface plasmons and whether the excitation is strongenough to achieve the perfect absorption. In Fig. 3, the simulationresults for different metals are depicted. In Fig. 3, the peakabsorption remains high irrespective of the type of metal used. Butthe bandwidth is different for every used metal, with the highestbandwidth observed for gold and aluminium (nearly 15%). Inaddition, the magnitude of the main resonance is not affected bythe change of the metallisation, while the shape of the frequencyresponse of the absorption is changed [47]. One can see theadditional weak resonances in the absorption spectrum. The best

performance is observed for gold and aluminium as mentioned.The main resonance for different metals is not affected because itarises from the coupling of the incident wave to surface plasmons.In addition, the effective impedance is perfectly matched tovacuum at the main resonance which explains the occurrence of theperfect absorption. As a result, a MPA with suitable geometricaldesign parameters allow us to obtain perfect absorption with astrong main resonance (almost independent from the type of themetal) [47].

In order to understand the absorption performance of theproposed MPA structure, a study of electric and surface currentdistribution is performed for resonance frequency of 614.4 THz. InFig. 4, electric field and surface current distributions are depicted.

In Fig. 4a, the strong electric field is distributed at the surfaceof a dielectric spacer and also is stronger at the surface of thedielectric inserted between the top patches. The strong E-fields also

form a symmetric shape (electric multi-poles) around the metallicpatches at the top. The same mechanism is observed for the bottomview of a sandwiched dielectric spacer, as it is labelled in Fig. 4b.This is a strong evidence of electric resonance (absorptionresonance) which results from the strong coupling of the toppatches and their sandwiched dielectric slab and the strongcoupling of the top layer – intermediate dielectric spacer andground metallic plate. The observed electric multipoles (electricpolarisation) produce surface charges which generate inducedmagnetic field and this magnetic field is responsible for bothmagnetic resonance and resonant absorption at the peak frequency.

Fig. 3  Simulated absorption results of the proposed MPA structure byusing different metals (gold, copper, silver and aluminium)

Fig. 4  Electric field and surface current distributions(a) Front of view of electric field distribution, (b) Back view of electric field distribution and, (c) Surface current distributions of the proposed MPA design at the resonancefrequency of 614.4 THz

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In Fig. 4c, surface current is reported. Moreover, high parallel andantiparallel surface currents are concentrating around the patchsurface.

The presence of high parallel surface current proves theexistence of electric response (parallel surface currents areaccountable for electric resonance), while the presence of highanti-parallel (control magnetic resonance) confirms the magneticresponse. Therefore, the generated electric and magnetic resonantcoupled with external EM fields and at the resonance frequencylocal fields are produced and cause perfect absorption of allincident EM radiations (this happens when the impedance matchesconditions discussed in relations (3) and (4) is accomplished). Inthat moment, EM radiations are trapped within absorber parts ofMTM structure and the reflection coefficient declines to a veryminimum value (near zero), while absorption rate reaches to itsmaximum (nearly 100% absorption).

One of the fascinating parts of MTM structures is their EMproperties which strongly rely on their unit-cell geometry. One wayof getting a strong resonance of the proposed structure is tooptimise the dimensions of a dielectric substrate. In doing that theeffective inductance (L) and capacitance (C) of the proposed designcan be adjusted [48–50]. Due to this fact, in order to investigate theabsorption characteristics of the proposed MPA structure, itsgeometrical parameters are examined to get their effect onabsorption rates of its unit cell. First, the structure is simulated for

different thicknesses of an intermediate dielectric spacer, where itsthickness ‘t’ is changed from 90 to 130 nm with step width of 10 nm. The simulated absorption result under different dielectric'sthicknesses is labelled in Fig. 5. As reported in Fig. 5, a shifttowards the left (lower frequencies) of peak frequency is noticed,but, in all cases the absorption rate remains high (perfect). Thephysical reason behind the shift of resonance is that, for largerthickness of a dielectric space, the capacitance and inductance areincreased. Thus, according to (2), the resonance frequency shifts tothe left (lower frequency), while for the thicker dielectric space,capacitance and inductance decrease and then the resonancefrequency shifts to the right (higher frequency).

These results show that the dielectric spacer has a crucial role inabsorption resonance of a MPA unit cell through the couplingmechanism discussed in the previous paragraphs, and it is an addedvalue for a MPA design in the present study.

Secondly, the simulation is carried out by changing top patch'speriodicity ‘b’ to different length and different patch thicknesses‘k’. It can be seen from Fig. 6a, that by changing ‘b’ from 314.4 to348.6 nm with width of 5.7 nm, the absorption characteristic of theproposed MPA does not change much; however, enhancement ofthe resonant absorption bandwidth is noticed for shorter values ofb. Besides, the simulation the results for different value of patchthicknesses are reported in Fig. 6b, and it is clearly seen that thesmaller the path thickness is, the more the absorption resonance isenhanced. It is evident that the best absorption rate is obtained forthe smallest k = 5 nm.

The direction of solar radiations changes at every times of dayin the sky and also some of them hit the unit cell in a un-polarisedform. Thus, in order to optimise absorption coefficient of a MTMunit cell for all incident EM radiations at the operating frequency,the MTM structure must be independent of both incident anglesand polarisation angles for EM (transverse electric (TE) andtransverse magnetic (TM)) radiations. Therefore, the absorptioncapability of MPA unit cell in the present study is inspected forboth TE and TM polarisation and for the defined different incidentangles of EM radiations. In Figs. 7a and b, simulated absorptionresults for a proposed MPA structure at different polarisation (TEand TM wave) are shown. The polarisation angle can be defined asthe angle variation on the x–y plane (see Fig. 1) for TE and TMwave cases. 90° polarisation angle refers to the E-field componentof the polarisation wave rotating on the x–y plane.

By changing the polarisation angles of a polarised EM wavefrom 0° to 90° with a step width of 15°, it is realised that theabsorption rate remains constant over a wide range of angles forboth TE and TM polarised waves. In addition to that, evidenceFig. 7b shows that in TM polarised wave the absorption bandwidthbecomes much wider than in the case of TE. In Fig. 7c due to thehigh symmetry of the MPA structure in this paper, its absorptionrate remains unchanged for over wide range of angles of incidenceEM radiations, whereby changing the defined incident angle of EMradiations from 0° to 90° (see the figure inset, the rotation in thegreen vector), the absorption results remain high and constant in allcases. Therefore the proposed MPA structure is a very goodcandidate for fabricating outstanding solar cells without issues ofpolarised waves and an advantage of absorption being independentof azimuthal angle or the position and direction of solar radiations.

3 ConclusionsIn this paper, a single-band MTM perfect absorber has beenproposed, simulated and characterised for its absorption capabilityby using coupling model system (impedance matching condition).Firstly, an outstanding single band of 99.7% absorption with anoutstanding bandwidth of 15.5% with respect to the centralfrequency has been obtained. Secondly, the parametric studies haveconfirmed the high flexibility character of a proposed MPA, andtunability for a dielectric thickness has been observed. Thirdly, inorder to understand the absorption mechanism of the proposedMPAs, the electric field and surface current distributions wereanalysed. Moreover, the proposed structure was tested for itsabsorption characteristic under different ground metallic materials.At last, the high symmetry and flexibility of the proposed structure

Fig. 5  Absorption characteristics of the proposed MPA unit cell fordifferent dielectric thicknesses ‘t’ of dielectric spacer

Fig. 6  Simulated absorption characteristics of the proposed MPA structurewith different patch geometric parameters(a) Different values of patch periodicity ‘b’, (b) Different patch thickness ‘k’

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has been examined by testing its absorption characteristic underdifferent incident angles and polarisation angles, and for both casesthe proposed MPA unit cell proved to be insensitive to incidenceEM radiations for a wide range of incident angles and alsoinsensitive to polarisation angles for TE and TM radiations. Theproposed design is an outstanding candidate towards high-qualitysolar cell in a visible frequency regime.

4 AcknowledgmentsP.R. acknowledges the support of the government of Rwanda forgraduate studies through Rwanda Education Board, sponsorshipnumber 911/12.00/SR/2013. The work reported here was carriedout at Middle East Technical University – Northern CyprusCampus (METU–NCC). It is supported by METU-NCC under thegrant number of BAP-FEN-15-D-3.

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Fig. 7  Simulated absorption results for the proposed MPA structure atdifferent polarization(a) Simulated absorption characteristics of the proposed MPA for different TEpolarisation angles (ϕ), (b) Simulated absorption rate for different TM polarizationangles (ϕ), (c) Simulated absorption characteristics of the proposed MPA unit cell fordifferent incident angles (normal and oblique incident) (γ) of EM wave

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