Power Stored and Quality Factors in Frequency Selective Surfaces at THz Frequencies

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011 2205

Power Stored and Quality Factors in FrequencySelective Surfaces at THz Frequencies

Juan José Sanz-Fernández, Student Member, IEEE, Rebecca Cheung, Senior Member, IEEE,George Goussetis, Member, IEEE, and Carolina Mateo-Segura, Student Member, IEEE

Abstract—A study of the external, loaded and unloaded qualityfactors for frequency selective surfaces (FSSs) is presented. Thestudy is focused on THz frequencies between 5 and 30 THz, whereohmic losses arising from the conductors become important. Theinfluence of material properties, such as metal thickness, conduc-tivity dispersion and surface roughness, is investigated. An equiv-alent circuit that models the FSS in the presence of ohmic lossesis introduced and validated by means of full-wave results. Usingboth full-wave methods as well as a circuit model, the reactive en-ergy stored in the vicinity of the FSS at resonance upon plane-waveincidence is presented. By studying a doubly periodic array of alu-minium strips, it is revealed that the reactive power stored at res-onance increases rapidly with increasing periodicity. Moreover, itis demonstrated that arrays with larger periodicity—and thereforeless metallisation per unit area—exhibit stronger thermal absorp-tion. Despite this absorption, arrays with higher periodicities pro-duce higher unloaded quality factors. Finally, experimental resultsof a fabricated prototype operating at 14 THz are presented.

Index Terms—Equivalent circuits, frequency-selective surfaces(FSS), infrared measurements, power stored, Q factors.

I. INTRODUCTION

F REQUENCY selective surfaces (FSS) consisting ofdoubly periodic arrays of conducting elements, or aper-

tures in a conducting sheet, have been studied thoroughly inthe microwave regime [1]. Due to their selectivity in frequency,polarization and angle of incidence, FSS have been employedmainly in radomes, polarizers, filters and absorbers for radar,satellite and antenna systems [2], [3]. Recently, there is anincreased interest in employing FSS for applications at higherfrequencies. Infrared (IR) filters and beam splitters [4]–[8] areemployed in instrumentation for astronomy, astrophysics andearth science research [9]. Spectral control of thermal radiation

Manuscript received August 24, 2009; revised October 04, 2010; acceptedNovember 29, 2010. Date of publication April 19, 2011; date of current versionJune 02, 2011. The work of G. Goussetis was supported by the Royal Academyof Engineering under a five-year research fellowship.

J. J. Sanz-Fernández and R. Cheung are with Scottish MicroelectronicsCentre, Institute for Integrated Systems, The University of Edinburgh, EH93JF, Edinburgh, U.K. (e-mail: [email protected]).

G. Goussetis is with the Institute of Electronics Communications and Infor-mation Technology (ECIT), Queen’s University Belfast, Northern Ireland, BT39DT, U.K. (e-mail: [email protected]).

C. Mateo-Segura is with the Wireless Communications Research Group, De-partment of Electronic and Electrical Engineering, Loughborough University,Leicestershire LE11 3TU, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.2011.2143654

for use in thermophotovoltaic (TPV) energy conversion devicescan be achieved by tailoring appropriately the FSS response inthe near-infrared [10]–[12]. FSS can be designed to enhancethe purity of a laser [13] and to act as reflecting element ininfrared lasers or Fabry-Perot cavities [14], [15]. Unique FSSemission/absorption characteristics can be employed in infraredsources [16]–[19]. Sharp resonances and near-field enhance-ment in FSS have been suggested for Terahertz (THz) sensingsystems in pollutant, biomolecular and chemical sensing andsecurity applications [20]–[26]. Other applications include FSSas light-guiding structures [27] or as mirrors for solar powerapplications [28], [29].

In the microwave regime, metallic elements in FSS can beassumed to be nearly planar perfect conductors (without ohmiclosses), because dielectric losses are the main source of thermalpower dissipation [30]. However, ohmic losses become moresignificant at high frequencies and can no longer be neglected[30], [31]. The study of the FSS response at THz in relation topower dissipation is motivated by the increased ohmic loss ofmetallic conductors [30], [31]. In addition, unique issues arisingat THz and optical frequencies in conducting mediums, such asthe anomalous skin-depth effect, surface roughness and conduc-tivity dispersion, might contribute to add further ohmic lossesand must be considered [32]–[37].

In resonant systems, such as FSS, the quality factor is a goodmeasure of the power dissipation, since it represents the ratio ofthe stored reactive power over the dissipated power. In the FSSliterature the quality factor definition has so far been restricted tothe loaded quality factor, which is estimated through the far-fieldresponse by the inverse of the fractional 3 dB bandwidth [38].However, the intrinsic properties of any resonator are best de-scribed by the unloaded quality factor [39], which to the best ofour knowledge has yet to appear in the FSS literature. In addi-tion a rigorous study of the reactive power stored in the vicinityof FSS is also missing from the literature. Yet an understandingof these features is essential in designing FSSs both as filter el-ements [4]–[8] and as sensors [20]–[26].

In this paper, we present a thorough study of the quality fac-tors of FSS at THz frequencies. A comparison between differentmodels for the bulk metal conductivity is carried out and the ef-fects of the metallization thickness and surface roughness areconsidered. An equivalent circuit (EC) model for a FSS that in-cludes ohmic losses is introduced and validated by means of rig-orous full-wave method of moments (MoM) [2]. A capacitive,doubly periodic array of Aluminum (Al) strips is employed asa working example. The induced currents in the dipoles and thereactive power stored in the vicinity of the FSS at resonance

0018-926X/$26.00 © 2011 IEEE

2206 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011

Fig. 1. (a) Capacitive FSS with elements of arbitrary shape, (b) equivalent cir-cuit of the FSS with perfectly conducting elements, and (c) equivalent circuit ofthe FSS with elements of finite conductivity.

upon plane-wave incidence are extracted using both MoM aswell as an EC model. Details for the fabrication of THz FSSand Fourier transform infrared (FTIR) measurements of a fab-ricated device are presented.

II. RESONANT CHARACTERISTICS OF FSS

In isolation, a resonator can be typically modelled by an RLCcircuit [39] and can be characterized by its resonant frequencyand its reactance slope parameter [42]. The inductance andcapacitance are associated with the power stored in the mag-netic and electric field respectively, while the resistance isassociated with dissipated power in the form of thermal absorp-tion, so that in the absence of thermal dissipation, the equivalentimpedance of the resonator is purely reactive.

When in free space and illuminated by a plane wave, a FSSconsisting of perfect metallic conductors (capacitive screen) canbe represented by the circuit of Fig. 1(b), whererepresents the terminal impedance of the array [1]. The shuntreactance is associated with the reactive energy stored inthe FSS. The load is associated with the power exchangebetween the FSS and free space. In the vicinity of the reso-nance, the real and imaginary parts of the terminal impedanceare approximately constant and linear with frequency, respec-tively [1].

(1)

The reactance slope parameter for a series-type resonator is de-fined as [42]:

(2)

and is approximately constant in the vicinity of the resonance.In the presence of finite conductivity, a further resistance

is introduced to model the power dissipated on themetallic elements. The equivalent circuit of Fig. 1(b) is thenmodified to that of Fig. 1(c). The performance characteristicsof the FSS can be well predicted through this equivalent circuit.The reflection and transmission coefficients as well as theabsorption can be readily obtained as follows:

(3)

(4)

(5)

where . The lossless case is represented by. Resonance occurs when the reactive impedance is zero

, and in the absence of ohmic loss ,the reflection coefficient becomes 1. However, in the presenceof losses , the ratio is respon-sible for decreasing the amplitude of the reflection coefficient,allowing some transmitted wave and giving rise to power dissi-pation. The 3 dB bandwidth of the circuit of Fig. 1(c) is readilyfound to be:

(6)

where is the 3 dB bandwidth for the case of an arraywithout any thermal losses. As shown from (6) the introductionof is expected to broaden the bandwidth of the reflec-tion/transmission curves around the resonant frequency.

An important parameter of a resonant circuit is the qualityfactor [39]. The quality factor (Q) is defined generally as theratio between the average reactive energy stored over the powerloss in a resonator in a period of oscillation:

(7)

The unloaded quality factor refers to the resonator in isola-tion. In the definition of , the power loss is therefore associ-ated solely with the power loss by thermal dissipation.

When the resonator is coupled to its environment, some en-ergy transfer occurs between the resonator and the input/outputports. With reference to the resonator, this is experienced as in-creased power loss additional to any thermal dissipation. Theloaded quality factor is also defined by (7) but now thepower loss also includes the power coupled to the input andoutput port [42]. It can be demonstrated that within certain ap-proximations, the loaded quality factor can be obtained fromthe 3 dB fractional bandwidth [39], [42]:

(8)

The loaded and unloaded quality factors are related throughthe external quality factor which is associated solely withthe apparent loss due to the power transfer to the input/outputas well as the power stored in the resonator by [39]:

(9)

SANZ-FERNÁNDEZ et al.: POWER STORED AND QUALITY FACTORS IN FREQUENCY SELECTIVE SURFACES AT THz FREQUENCIES 2207

III. MATERIAL CONSIDERATION FOR THZ FSS

In the presence of ohmic losses, the resistancemodels the power dissipated on the metallic elements, asshown in Fig. 1(c). In contrast to the terminal impedance ,which is essentially controlled by the FSS geometry, the ohmicresistance also depends on the material properties. Atlow frequencies, the metallic elements are often assumed tobe planar 2D surfaces with a well defined conductivity [2].However, at higher frequencies unique material properties,such as surface roughness, anomalous skin depth effect andconductivity dispersion, can become significant and contributeto alter the effective bulk conductivity of the metals. It is there-fore important to study the influence of these effects on the FSSperformance when working at THz and optical frequencies.In this section material properties are addressed and theireffects are discussed. The study here is limited to free-standingmetallic FSSs [45]. The effect of the dielectric substrate will bediscussed in a separate publication.

A. Effect of Metal Thickness

When a plane electromagnetic wave impinges a conductingmedium the electric field inside the conductor is not zero. Thedepth of penetration at which the electric field decays 1/e of itsinitial value is called skin depth and can be obtained as [44]:

(10a)

According to this formulation, the skin depth for Al (DC con-ductivity at room temperature [33]) rangesfrom 0.8 at 10 GHz to 8 nm at 100 THz. However, this for-mulation for the skin depth is valid only near DC and breaksdown the closer we get to the plasma frequency (15 eV or 3.6PHz). A more accurate expression (derived from Beer’s law) canbe expressed in terms of the extinction coefficient of the metal[34]:

(10b)

where and represent the attenuation and extinction co-efficients, respectively. The consequence of using (10b) is thatthe skin depth of metals at higher frequencies will be larger thanif calculated using (10a) (e.g. at 100 THz the skin depth is 8 nmor 15 nm using (10a) or (10b), respectively).

In any case, as the frequency is increased, the current is moreconfined to the surface of the conductor. When the thicknessis comparable to the skin depth, the propagation inside theconductor must be considered. However, for conductors muchthicker than the skin depth (which is the common situation atTHz frequencies), the propagation inside the conductor can beaccurately modeled by a surface impedance with value equalto the intrinsic impedance inside the conductor. In general, theequivalent surface impedance of a metallic sheet varies withits thickness as well as the frequency. The equivalent surface

Fig. 2. Surface resistance (11) versus frequency of Al films with varying thick-ness. The skin depth at each frequency is also shown for reference. At 100 THztwo values of skin depth are shown, corresponding to (10a) and (10b).

impedance of a metallic sheet as a function of the thickness andfrequency can be approximated by [38], [46]:

(11)

When the skin depth is greater than the thickness , the sur-face impedance can be approximated to the DC limit

. In this case, the surface impedance is inversely propor-tional to thickness of the conducting medium until the skindepth is reached. However, for metal thickness greater thanthe skin depth, the surface impedance is no longer dependenton the thickness, and can be approximated by a resistive model(12)

(12)

Fig. 2 shows the variation of the surface resistance of Al filmsversus frequency for different thicknesses using (11). The skindepth is calculated using (10b) and its value at different frequen-cies is also shown. For comparison, the for 25 nm thick Allayer is also plotted using the skin depth in (10a), confirming theinaccuracy of (10a) as we move towards higher frequencies.

The surface impedance is therefore shown to vary with themetal thickness as expected. At frequencies in which the metalthickness is lower than the skin depth, the surface impedanceincreases with the metal thickness. At frequencies in whichthe metal thickness is higher than the skin depth, the surfaceimpedance is constant and does not depend on the metalthickness. For instance, at 1 THz the surfaceresistance decreases from 1.05 for to 0.32 for

, and then it remains constant at 0.32 for greaterthickness ( , 400 nm, and 1 ).

In order to investigate the influence of the metal thicknessin the FSS response, the reflection coefficient of a strip-basedFSS ( , , , and

) is obtained for variable metal thicknesses in the range, which is well above the skin depth and

below the operation wavelength. Commercial HFSS software


Fig. 3. Reflection parameter of strip-based FSS with variable thickness �.

Fig. 4. Absorption of the strip-based FSS of Fig. 3 as a function of thickness �.

based on finite element method (FEM) is employed in this study.Surface impedance boundaries were used, where was cal-culated from the classical model (see (13) in the next section),which agrees well with the values of obtained from real op-tical properties at the frequencies simulated. The fields insidethe structure are not solved, but this is a reasonable approxima-tion because the thickness of the conductor is much larger thanthe skin depth at the frequencies simulated.

As shown in Figs. 3, 4, the thickness of the elements has,in fact, an effect in the FSS performance even for thicknesseswell above the skin depth ( for Al at 17 THz). Forthin films with thickness well below the operation wavelength

, three effects can be identified, namely, a drop in theabsorption, a shift towards higher frequencies and an increase ofthe bandwidth. These results are in agreement with similar re-sults previously reported in [38], [40], [41]. As it will be shownin Section IV when studying the induced currents in FSS, thechanges in absorption and bandwidth in FSS are strongly relatedto changes in the amplitude and distribution of the induced cur-rents in the FSS elements.

B. Metal Conductivity

Real conductors exhibit non-zero intrinsic impedance andcan be modeled as “lossy dielectric” [44]. For good conductors

, the surface impedance can be approximated bythe resistive model of (12). However, for increasing frequencythis approximation does not hold and the more general classicalmodel described by (13) must be employed [44]

(13)

where , and represent the complex magnetic permeability,the complex dielectric permittivity, and the complex conduc-tivity of the metal, respectively. For non-magnetic materials thepermeability becomes that in free-space . Assuming themetal behavior related solely to conduction electrons (Drude orfree electron model for metals), we have and . Inaddition, for sufficiently low frequencies the conductivity canbe approximated to the DC conductivity.

As the frequency is increased, the value of the frequency-in-dependent real DC conductivity is no longer applicable and thecomplex frequency-dependent AC conductivity must be em-ployed [31]–[36]

(14)

where represents the Drude relaxation time or damping con-stant. This model is sufficient to describe the skin depth in FIR.At even higher frequencies another effect, known as anomalousskin depth effect [32], [47], [48], occurs. When the skin depthis comparable to the mean free path of electrons, the assump-tion that the electrons velocity, and hence the current density,depends on the electric field at the observation point alone doesnot hold. Therefore, the conduction current is not directly pro-portional to a local electric field, but is a nonlocal function ofthe electric field distribution in the conductor.

In general, the energy dissipated in metals accounted by thefree electron model is solely due to collisions. This mechanismfor the dissipation of energy is present at all frequencies and,therefore, does not produce fast frequency-dependent variationsof the metal properties. However, abrupt changes of the proper-ties of measured real metals versus frequency and significantdisparity between different metals are evident [33], [34]. Thesestrong frequency-dependent variations in the measured proper-ties are due to the onset of new mechanisms for absorption ofenergy, such as interband transitions (e.g., Al exhibits interbandexcitation of valence electrons for incident radiation with wave-length around 0.8 wavelength) [33], [34].

Experimental data from measured bulk or thin-film samplescan be employed to determine accurately the properties of realmetals (complex , , and ), taking into account all previouseffects. The measured properties of metals are commonly ob-tained in the form of the power reflectance and/or the com-plex index of refraction , where and are theindex of refraction and the extinction coefficient, respectively[34]. The surface resistance can then be calculated accuratelyfrom the experimental data according to:

(15)where represents the intrinsic impedance of freespace.

Fig. 5 shows the power reflectance (dash-dot line) in com-parison to the surface resistance (black dotted line) (15), usingexperimental data for Al from [34]. In order to examine dif-ferent conductor models and their accuracy throughout the THzregion, Fig. 5 also presents the surface resistance as obtained


Fig. 5. Power reflectance (dash-dot line and right �-axis) and surface resistancefor Al (left �-axis) using the experimental model (15) in dotted line and classicalmodels (12), (13) in dashed and solid lines, respectively. The inset zooms in thefar-IR band and shows just the � .

from the classical models (dashed and solid lines), described by(12), (13). The graph is subdivided into different THz bands,namely IR, optics and ultraviolet (UV). As shown, most of theinfrared band exhibits near total reflection and low surface re-sistance. However, at near-IR and optical frequencies, the re-flectance drops significantly due to the onset of interband tran-sitions around 0.8 . The classical models do not account forthese effects and, therefore, fail to estimate accurately the sur-face resistance in conductors for higher frequency.

At near-IR and optical frequencies, the surface resistance ismostly underestimated by the classical models (which do notaccount for the drop in reflectivity around 0.8 ). At mid-IRfrequencies, the classical models slightly overestimate the sur-face resistance. On the other hand, at far-IR frequencies, whichis the frequency region of interest in this paper (5 THz–30 THz),the classical model defined in (13) (lossy dielectric) accuratelyestimates the surface resistance and fits well the experimentalmodel, while the approximation of a good conductor (12) (re-sistive model) overestimates the surface resistance of Al by afactor of about 1.41 in this region of frequencies.

C. Surface Roughness

At frequencies where the wavelength is in the order of cen-timeters or millimeters, any metallic film can be considered to beperfectly flat, since small defects (a few, tens or even hundredsof nanometers) in the morphology of the surface do not haveany noticeable effects on the value of the conductivity. How-ever, at higher frequencies surface roughness is responsible forscattering and coupling to surface plasmons, which gives rise toan additional drop in the power reflectance [34]. As noted be-fore, this drop in the reflectance corresponds to an increase inthe surface resistance, which is produced by a decrease in theconductivity. The conductivity of a rough surface can be ap-proximated by the following expression [37]:

(16)

where and denote the conductivity with a rough and aflat surface, respectively, represents the surface roughness, and

is the skin depth.At near-IR, optical, and higher frequencies, the effect is sig-

nificant even for a surface roughness as low as 2 nm. However,at far-IR frequencies, the effect does not have a great impact forlow surface roughness. For instance, the conductivity at 15 THzwith a surface roughness of 5.5 nm decreases just 5% from thatof a flat surface. The same roughness gives rise to a 35% de-crease in the conductivity at 150 THz. Current metal depositionmethods are capable of exhibiting surface roughness in pure Althin films as low as 1.2 nm [49] and 5.5 nm [50]. Further Al al-loys can improve surface roughness even below 1 nm [51].

In addition to the surface roughness, Al thin-films (like othermetals) are susceptible to the formation of a very thin layer ofnative oxide ( for Al), even in high vacuum conditions,that could reduce the power reflectance of the Al thin-film [34],thus increasing the surface resistance. The thickness of the na-tive oxide varies depending of the conditions that the thin-filmhas been exposed to. For instance, evaporated films exposed tonormal atmosphere conditions may exhibit between 2 and 5.5nm thick native oxide, while this thickness can be fairly in-creased in moist environments [34]. However, at infrared theoxide thickness is much lower than the wavelength of opera-tion and its influence is negligible. Moreover, is highlytransparent at wavelengths from 6 to 180 nm, and, there-fore, has little influence at near-IR and optical frequencies, andat the lower ultraviolet frequencies [34].

IV. QUALITY FACTORS IN FSS

In the following we proceed to estimate the quality factorsfor the capacitive FSS under consideration at IR. We employa working example of an FSS based on dipoles of length

, width , and thickness (so thataccording to Fig. 3 no thickness effects are present). The unitcell length along the y-axis is fixed at (Fig. 6). AtIR, the main source of thermal absorption comes from the ohmiclosses on the conductors [30], [31]. We therefore concentrate ourstudies assuming only ohmic losses. We commence our investi-gation by studying the FSS in the absence of ohmic losses. Forthis case we extract the equivalent circuit parameters and the re-active power stored in the array. Subsequently, we demonstratethat the terminal resistance and reactance of the equiva-lent circuit do not vary significantly with the addition of realisticlosses. Using these results, we proceed to account for the effectof losses on the Q-factor. The study is undertaken initially forperiodicity along the x-axis varying in the region –

.

A. Power Stored in FSS (No Ohmic Losses)

The far-field reflection coefficient of a normally incidentplane wave as obtained by a full-wave MoM code [2], [43]is shown in Fig. 7 for three different values of periodicity

. For this study, zero ohmic losses are assumed so that thedissipated power is zero. The far-field reflection can alsobe predicted by the EC model of Fig. 1(a) using (3) and themethod described in [1], and is superimposed for comparisonwith MoM results in Fig. 7. Good agreement between the


Fig. 6. Capacitive FSS based on parallel strip of length �, width � and thick-ness �. The strips are periodically arranged at a distance � and � from eachother. � , � and � represent the surface current density induced in thedipoles, the dissipated power and power stored (either in the electric or mag-netic field), respectively.

Fig. 7. Reflection coefficient of the lossless FSS depicted in Fig. 2 with dimen-sions (in ��) � � �, � � �, � � �� and varying � as calculated by MoMand EC.

MoM and EC results is observed, with the exception of thegrating lobes which manifest as dips in the full-wave results.When grating lobes occur, part of the energy is directed inother angles, leading to an apparent power loss at the directionof incidence [1]. Multi-modal behavior occurs when a gratinglobe is present and therefore the RLC circuit fails.

Assuming the surface-current density on the dipolewithin the unit cell, the average current along the dipole isobtained as:

(17)

The average currents excited on the elements as calculatedby the full-wave method (17) are shown in Fig. 8. Likewise,the average currents obtained from the EC are superimposed inFig. 8. The values of the terminal resistance and reactanceslope parameter can be rigorously obtained using the methoddescribed in [1] and are plotted in Fig. 9 as a function of theperiodicity .

As observed in Figs. 7, 8, the resonant frequency of the arraydrops with increasing periodicity and tends to approach the

Fig. 8. Average current induced in the dipoles in the lossless FSS of Fig. 7 ascalculated by MoM and EC for dipoles separated by a distance � . The insetshows the peak value of the average current induced in the dipoles versus theperiodicity.

Fig. 9. Terminal resistance (left �-axis) and reactance slope parameter (right�-axis) for the FSS of Fig. 7 and different values of periodicity � .

resonance of the dipole elements. This is due to the fact thatmore closely packed dipoles interact more strongly. Hence, theresonance of the dipole elements in the array deviates more fromthe resonance of the free-standing element for small spacings.In addition, sparser arrays experience a lower load leadingto sharper resonant features (stronger currents at resonance andhigher loaded quality factors).

Since the reflection coefficient from the FSS at resonance inthe lossless case is exactly equal to 1, the power transferedfrom the FSS to free-space per unit cell is equal to the powerincident on each unit cell. The power transfered can be obtainedthrough a surface integral of the Poynting vector of the incomingplane-wave along the unit cell:

(18)where the plane of integration is normal to the direction of theincoming wave. For a normally incident plane wave in free space


with 1 V/m -polarized electric field, the power incident on theFSS unit cell is:

(19)The power radiated to free space can also be calculated by theEC as the power consumed on the terminal resistance atresonance:

(20)

The average reactive power stored in the near field of the FSScan be estimated from the EC as the reactive power stored at theterminal at resonance:

(21)

where is the amplitude of the average current excited on thedipole at resonance, as shown in Fig. 8. The power stored canalso be calculated from full-wave data and the following volumeintegral:

(22)

where represents the reactive field in the vicinity of thearray at resonance. Assuming operation below the grating-loberegime, can be obtained by the MoM formulation as the totalcontribution of all but the propagating Floquet space harmonics(FSHs). The volume, , is defined in the transverse plane bythe unit cell dimensions and along the normal of the array itis truncated at the distance from the array surface where thecontribution from the FSH with the smallest attenuation ratedrops below 1% from its maximum value. In addition, in orderto ensure convergence in the near-field estimation, FSHs whichcontribute up to 5% of the FSH with the smallest attenuationrate have been considered [54].

The average reactive energy stored at resonance in a periodof oscillation as well as the power radiated to free space perunit cell are plotted in Fig. 10. Both MoM and EC results areshown. The average current and terminal impedance depicted inFig. 8 and Fig. 9, respectively, were utilized in applying (20) and(21). The agreement observed validates the circuit model. Thepower radiated by the unit cell at resonance increases linearlywith the FSS periodicity in accordance with the unit cell area.The average energy stored increases with the periodicity of theFSS more rapidly than the power radiated, reflecting the sharperresonance characteristics observed in Figs. 7 and 8. Identicalstudies have been performed for variable length and width ofthe dipoles. For these studies the periodicity is fixed at 8

, while the length varies from 5 to 10 , and the widthranges from 0.5 to 3 . It was found that the reactivepower stored increases in shorter and narrower strips, due tostronger induced currents (figures not shown).

Fig. 10. Power radiated from the FSS of Fig. 7 to free space at resonance (19),(20) and power stored at the FSS of Fig. 7 at resonance (21), (22) for varyingperiodicities � .

B. Power Dissipated (Ohmic Losses)

Taking into consideration the high-frequency effects dis-cussed in Section III, we proceed now to calculate the ohmicresistance and the power dissipated in a lossy FSS.We first validate the assumption that the terminal impedance( and ) of the FSS does not vary significantly oncerealistic ohmic losses are assumed. The experimental model(15) is employed for the surface resistance of Al throughoutthis section. The thickness of the metallic elements is set to bewell above the skin depth at these frequencies ( ,

) and well below the operation wavelength. The surface roughness is neglected at these fre-

quencies, as discussed previously. Fig. 11 shows the full-wavesimulations of Fig. 7, where now ohmic losses are present.Fig. 11 also shows the reflection characteristics obtained fromthe circuit of Fig. 1(c). The same values of and as thoseshown in Fig. 9 have been employed. In order to match theabsorption levels, the ohmic resistance varies as shownin Fig. 12. The good agreement between the full-wave andcircuit results validates the assumption stated at the beginningof this paragraph. This implies that the external quality factor

does not significantly change in the presence of realisticlosses (see also the discussion in Section IV-C).

The absorption coefficient can be obtained from (5) andis plotted in Fig. 13 using both the full-wave results as wellas the EC model. Good agreement between the two methodsis observed until the fictitious absorption corresponding tothe grating lobes is observed in the full-wave results towardshigher frequencies (e.g. at 21 THz for ). Thedissipated power at resonance for increasing array periodicityis summarized in Fig. 14. Interestingly, the power dissipationis increased for increasing periodicity, in opposite trend tothe ohmic resistance. This is due to the fact that the terminalresistance decreases more rapidly with periodicity than theohmic resistance and hence the ratio(also plotted in Fig. 12) increases with periodicity.

The same study has been performed for variable length andwidth of the dipoles. The periodicity is fixed at 8 , whilethe length varies from 5 to 10 , and the width ranges from0.5 to 3 . It was found that the dissipated power increasesin shorter and narrower strips due to stronger induced currents


Fig. 11. Reflection coefficient of the FSS of Fig. 7 where the metallic elementsare fabricated using aluminum calculated by MoM and the EC for different pe-riodicities � .

Fig. 12. Ohmic resistance � (left �-axis) and ratio � � � ��(right �-axis) corresponding to the FSSs of Fig. 11 versus the array periodicity� .

Fig. 13. Absorption coefficient of the FSS of Fig. 11 as calculated by MoMand EC for different periodicities � .

Fig. 14. Power dissipated at resonance for the FSS of Fig. 11 for varying peri-odicity � .

Fig. 15. External quality factor in the lossless FSS of Fig. 7 calculated by thedefinition, EC, and the inverse of the 3 dB fractional bandwidth for differentperiodicities � .

(lower terminal resistance) and despite exhibiting lower ohmicresistance, following the same reasoning as above (figures notshown for brevity).

C. External, Loaded and Unloaded Quality Factors

The external quality factor can be obtained by the defini-tion (7), where the power radiated from the FSS to free space isassumed in the denominator (as power loss). It can also be de-rived from the EC according to [42]:

(23)

In the absence of power dissipation, is infinite, and ac-cording to (9) . Therefore, the external quality factorin the lossless case can be obtained from the loaded qualityfactor. The external can be obtained from the far-field re-flection response, since the loaded quality factor can be ap-proximated by the inverse of the 3 dB fractional bandwidth (8).Fig. 15 shows the external quality factor as calculated bythe definition (7), by the EC (23) and by the inverse fractionalbandwidth (8). Good agreement is observed between the threemethods. As shown, the external quality factor increaseswith increasing periodicity. This suggests a weaker coupling ofthe incident plane-wave to the resonating array. The externalquality factor has also been found to increase for shorter andnarrower strips (figures not shown).

Since for realistic values of ohmic losses the external qualityfactor is to a good approximation equal to that obtained forthe lossless case, this value can be employed in (9) to extractthe unloaded quality factor . The loaded quality factorcan be estimated as the 3 dB fractional bandwidth of the reflec-tion curves shown in Fig. 11 for lossy FSSs. As expected from(9), the loaded quality factor in the presence of losses is alwayslower than the external quality factor, as shown in Fig. 16. Theextracted is plotted in Fig. 17. As shown, increases lin-early with increasing periodicity despite the increased absorp-tion shown in Fig. 14. This is because higher reactive powerlevels are stored in the array as increases (see Fig. 10). In ad-dition, we can see that the unloaded quality factor is nearly anorder of magnitude higher than the loaded quality factor. This isbecause represents the intrinsic or near-field quality factor


Fig. 16. Loaded quality factor for the FSS of Fig. 7 (lossless) and Fig. 11 (lossy)for varying periodicity � .

Fig. 17. Unloaded quality factor for the FSS of Fig. 11 for varying periodicities� .

of the FSS as a resonator in isolation, without interacting withthe in/output ports.

V. EXPERIMENTAL RESULTS

In this last section, we validate our developed theory by fab-ricating and testing an FSS structure exhibiting response in theTHz region.

A. Fabrication Process

For the fabrication of a FSS with micro-scale features, 100mm diameter double-sided polished sacrificial silicon (Si)wafers are employed as rigid substrate for mechanical strengthduring and after processing. Since Si substrates exhibit exces-sive losses at mid/far-IR, a thin layer of Polyimide (PI), hasbeen chosen as supportive layer for the FSS array. The PI ischaracterised by a permittivity of , exhibits acceptabletransparency at these frequencies and can be readily spun on thewafer. Prior to the deposition of a PI layer of thickness 1.7 ,a silicon dioxide interlayer between the Si wafer andthe PI membrane has been thermally grown (1 ) to act as astop layer during the future deep Si etching step and to protectthe subsequent PI layer from being damaged. RF sputtering hasthen been used to deposit a 200 nm aluminium (Al) thin film,which was subsequently patterned photolithographically andetched using reactive ion etching (RIE).

Fig. 18. Fabricated device consisting of Si substrate (500 ��), free-standingPI membrane (1.7 ��), and 4 mm� 4 mm FSS array of Al strips (� � � ��,� � � ��, � � � ��, and � � �� , � � �� ).

In order to obtain the final device consisting of the metallicFSS array on a free-standing PI membrane, the Si substrate wasetched away. Deep reactive ion etching (DRIE) has been em-ployed in inductive coupled plasma (ICP) equipment in orderto overcome the disadvantages of wet Si etching such as potas-sium hydroxide (KOH) [52]. These include damaging the thinmembrane when removing the protective mask/layer, and in-compatibility with IC fabrication processes (e.g. Al bond padsare rapidly attacked and damaged) which would cause problemsin fabricating other configurations such as electronically tunableFSSs. Finally, the oxide interlayer is etched by a solution of am-monium fluoride and acetic acid which does not damage eitherthe Al elements of the FSS or the PI membrane. A detailed de-scription of the fabrication process can be found in [53].

This fabrication process allows fabricating several FSSdesigns simultaneously (within the same wafer) and thereforeit is also suitable for multilayered configurations (by stackingthe different FSS fabricated in the same wafer). In contrast,layer-by-layer fabrication approaches would require repetitionof deposition, lithography, and etching steps. Fig. 18 showsa photograph of the fabricated device as well as optical mi-croscope pictures of the patterned elements. The fabricatedFSS prototype consists of a 4 mm 4 mm array of Al stripssupported on a large, thin and free-standing PI membrane.

B. FTIR Characterization

Spectroscopic measurements of the transmission of the fabri-cated device were carried out in the IR range between 7.5 THz(250 ) and 30 THz (1000 ) by a PerkinElmer Spec-trum 100 FT-IR spectrometer. In order to ensure that all the en-ergy is transmitted from the IR source through the FSS arrayarea to the detector, a 4 mm 4 mm metallic aperture is em-ployed to fit the size of the IR beam to that of the FSS array.Fig. 19 shows the measured transmission, normalized to the PItransmission, in comparison with the simulated response.

The measured transmission is centred at 14 THz, in goodagreement with the simulated response. The amplitude of themeasured transmission in the reflection band is higher than thatfrom the simulations. This is because the IR source of the FTIRis unpolarized. Therefore, only the vertical component is re-flected by the FSS, resulting in energy transmitted in the hor-izontal component to the IR detector which did not occur in the


Fig. 19. Measured and simulated transmission for the FSS of Fig. 18.

simulated response, where the incident wave was assumed ver-tically polarized. The loaded quality factor in the measured re-sponse is found to be , which is in good agreementwith the value extracted from the simulation .

VI. CONCLUSIONS

The quality factors in FSSs based on finitely conductingmetallic strips have been investigated by rigorous full-waveanalysis based on the method of moments and equivalentcircuits. The influence of material properties arising at THzfrequencies has been discussed. A comparison between dif-ferent models for the bulk metal conductivity has been carriedout and it was revealed that the classical model is not validbeyond far-IR, where measured data must be employed toaccount for conductivity dispersion. Surface roughness hasbeen found to dramatically drop the conductivity for increasingfrequency. While a surface roughness of 5.5 nm produces a5% drop in the conductivity at 15 THz, the same roughnessgives rise to a 35% decrease in the conductivity at 150 THz.Parametric studies for varying periodicity, length and widthof the strips have been carried out in order to investigate theinfluence of the geometry on the electrical parameters of theFSS array (the terminal impedance, reactance slope parameterand ohmic resistance), induced currents, resonance properties(resonant frequency and bandwidth), absorption, and qualityfactors. FSSs with increased periodicity have been found togive rise to higher thermal absorption and higher unloaded .In contrast, FSS consisting of larger or wider strips exhibitlower unloaded , despite exhibiting lower thermal absorption.An FSS prototype has been fabricated and characterized bymeans of FTIR, validating the accuracy of the simulations.

REFERENCES

[1] B. A. Munk, Frequency Selective Surfaces: Theory and Design. NewYork: Wiley, 2000.

[2] J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and De-sign. Taunton, Somerset: Research Studies Press/Wiley, 1997.

[3] T. Cwik, R. Mittra, K. C. Lang, and T. K. Wu, “Frequency selectivescreens,” IEEE Trans. Antennas Propag. Soc. Newsl., vol. 29, pp. 5–10,1987.

[4] R. Ulrich, “Far infrared properties of metallic mesh and its comple-mentary structure,” Infrared Phys., vol. 7, pp. 37–55, 1976.

[5] K. D. Möller, J. B. Warren, J. B. Heaney, and C. Kotecki, “Cross-shaped bandpass filters for the near- and mid-infrared wavelength re-gions,” Appl. Opt., vol. 35, no. 31, pp. 6210–6215, Nov. 1996.

[6] C. M. Rhoads, E. K. Damon, and B. A. Munk, “Mid-infrared filtersusing conducting elements,” Appl. Opt., vol. 21, no. 15, pp. 2814–2816,Aug. 1982.

[7] C. Winnewisser, F. Lewen, J. Weinzierl, and H. Helm, “Transmissionfeatures of frequency-selective components in the far infrared deter-mined by terahertz time-domain spectroscopy,” Appl. Opt., vol. 38, no.18, pp. 3961–3967, Jun. 1999.

[8] S. T. Chase and R. D. Joseph, “Resonant array bandpass filters for thefar infrared,” Appl. Opt., vol. 22, no. 11, pp. 1775–1779, Jun. 1983.

[9] K. P. Stewart, J. Fischer, J. W. Baldwin, A. D. Milller, and K. D.Möller, “Microstructure optics design and fabrication at NRL andNJIT,” presented at the NASA Science Technology Conf. (NSTC2007),Jun. 2007.

[10] T. K. Wu, “Infrared filters for high-efficiency thermovoltaic devices,”Microw. Opt. Technol. Lett., vol. 15, no. 1, pp. 9–12, 1997.

[11] G. Kiziltas, J. L. Volakis, and N. Kikuchi, “Design of a frequency selec-tive structure with inhomogeneous substrate as a thermophotovoltaicfilter,” IEEE Trans. Antennas Propag., vol. 53, no. 7, pp. 2282–2289,2005.

[12] R. T. Kristensen, J. F. Beausang, and D. M. DePoy, “Frequency selec-tive surfaces as near-infrared electromagnetic filters for thermophoto-voltaic spectral control,” J. Appl. Phys., vol. 95, no. 9, pp. 4845–4850,2004.

[13] E. J. Danielewicz and P. D. Coleman, “Hybrid metal mesh dielectricmirrors for optically pumped far infrared lasers,” Appl. Opt., vol. 15,pp. 761–767, 1976.

[14] R. Ulrich, T. J. Bridges, and M. A. Pollack, “Variable metal mesh cou-pler for infrared lasers,” Appl. Opt., vol. 9, pp. 2511–2516, 1970.

[15] R. Sauleau, P. Coquet, J. P. Daniel, T. Matsui, and N. Hirose, “Study ofFabry-Perot cavities with metal mesh mirrors using equivalent circuitmodels. Comparison with experimental results in the 60 GHz band,”In. J. Infrared Millimiter Waves, vol. 9, no. 12, 1998.

[16] I. Pusçasu, W. L. Schaich, and G. Boreman, “Resonant enhancementof emission and absorption using frequency selective surfaces in theinfrared,” Infrared Phys. Technol., vol. 43, pp. 101–107, 2002.

[17] S. O. C. Giraud and D. G. Hasko, “Mesoscale thermal infrared sources,”Microelec. Eng., vol. 41/42, pp. 579–582, 1998.

[18] J. LeGall, M. Olivier, and J. J. Greffet, “Experimental and theoreticalstudy of reflection and coherent thermal emission by a SiC grating sup-porting a surface-phonon polariton,” Phys. Rev. B, vol. 55, no. 15, pp.10 105–10 114, 1997.

[19] B. Monacelli, J. B. Pryor, B. A. Munk, D. Kotter, and G. D. Boreman,“Infrared frequency selective surface based on circuit-analog squareloop design,” IEEE Trans. Antennas Propag., vol. 53, no. 2, p. 745,2005.

[20] C. Debus and P. H. Bolivar, “Frequency selective surfaces for high-sen-sitivity terahertz sensors,” Appl. Phys. Lett., vol. 91, p. 184102, 2007.

[21] N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau,and H. Giessen, “Plasmonic analogue of electromagnetically inducedtransparency at the drude damping limit,” Nature Mater., vol. 8, pp.758–762, 2009.

[22] N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher,C. Sonnichsen, and H. Giessen, “Planar metamaterial analogue of elec-tromagnetically induced transparency for plasmonic sensing,” NanoLett., vol. 10, pp. 1103–1107, 2010.

[23] J. Meléndez, A. J. de Castro, F. López, and J. Meneses, “Spectrallyselective gas cell for electro-optical infrared compact multigas sensor,”Sens. Actuators A, vol. 46–47, pp. 417–421, 1995.

[24] C. Debus, F. Voltolina, and P. H. Bolivar, “Towards cost-efficient THzbiochip technology,” in Proc. IEEE Antennas and Propagation SocietyInt. Symp., 2007, pp. 3380–3383.

[25] I. Al-Naib, C. Jansen, and M. Koch, “Improved terahertz sensors basedon frequency selective surfaces for thin-film sensing,” in Proc. 33rd Int.Conf. on Infrared, Millimeter and Terahertz Waves, 2008, pp. 1–2.

[26] D. W. Peters, G. R. Hadley, A. A. Cruz-Cabrera, L. I. Basilio, J. R.Wendt, S. A. Kemme, T. R. Carter, and S. Samora, “Infrared frequencyselective surfaces for sensor applications,” in Proc. SPIE, 2009, vol.7298, p. 72983L.

[27] G. Schider, J. R. Krenn, A. Hohenau, H. Ditlbacher, A. Leitner, F. R.Aussenegg, W. L. Schaich, I. Pusçasu, B. Monacelli, and G. Boreman,“Plasmon dispersion relation of Au and Ag nanowires,” Phys. Rev. B,vol. 68, no. 15, p. 155 427, 2003.

[28] J. C. C. Fan, F. J. Bachner, and R. A. Murphy, “Thin-film conductinggrids as transparent heat mirrors,” Appl. Phys. Lett., vol. 28, pp.440–442, 1976.


[29] C. M. Horwitz, “A new solar selective surface,” Opt. Common., vol.11, pp. 210–212, 1974.

[30] J. E. Raynolds, B. A. Munk, J. B. Pryor, and R. J. Marhefka, “Ohmicloss in frequency-selective surfaces,” J. Appl. Phys., vol. 93, no. 9, pp.5346–5358, 2003.

[31] J. B. Pryor, “On Ohmic Losses in Frequency Selective Surfaces atNear-Infrared Wavelengths,” Ph.D. dissertation, Ohio State Univ.,Columbus, 2003.

[32] F. Wooten, Optical Properties of Solids. New York and London: Aca-demic Press, 1972, pp. 94–99.

[33] N. W. Ashcroft and N. D. Mermin, Solid State Physics. New York:Holt-Saunders International Editions, 1976, pp. 1–28.

[34] E. D. Palik, Handbook of Optical Constants of Solids. London: Aca-demic Press, 1985, pp. 369–406.

[35] E. Topsakal and J. L. Volakis, “On the properties of materials for de-signing filters at optical frequencies,” in Proc. IEEE AP-S Int. Symp.and URSI National Radio Science Meeting, 2003, vol. 4, pp. 635–638.

[36] J. Weiner and F. D. Nunes, “High-frequency response of subwave-length-structured metals in the petahertz domain,” Opt. Express, vol.16, no. 26, pp. 21256–21270, 2008.

[37] A. Byers, “Accounting for high frequency transmission line loss effectsin HFSS,” in Proc. Ansoft User Workshop, Los Angeles, CA, 2003 [On-line]. Available: http://www.ansoft.com

[38] M. E. McDonald, A. Alexanian, R. A. York, Z. Popovic, and E. N.Grossman, “Spectral transmittance of lossy printed resonant-grid tera-hertz bandpass filter,” IEEE Trans. Microw. Theory Tech., vol. 48, no.4, pp. 712–717, 2000.

[39] D. M. Pozar, Microwave Engineering. New York: Wiley, 1998, pp.300–306.

[40] M. Lambea, M. A. González, J. A. Encinar, and J. Zapata, “Analysis offrequency selective surfaces with arbitrarily shaped apertures by finiteelement method and generalized scattering matrix,” in Proc. Antennasand Propagation Society Int. Symp., 1995, vol. 3, pp. 1644–1647.

[41] N. Farahat and R. Mittra, “Analysis of frequency selective surfacesusing the finite difference time domain (FTDT) method,” in Proc. An-tennas and Propagation Society Int. Symp., 2002, vol. 2, pp. 568–571.

[42] G. Matthai, E. M. T. Jones, and L. Young, Microwave Filters,Impedance-Matching Networks, and Coupling Structures. Boston,MA: Artech House, 1980.

[43] G. Goussetis, A. P. Feresidis, and J. C. Vardaxoglou, “Tailoring theAMC and EBG characteristics of periodic metallic arrays printed ongrounded dielectric substrate,” IEEE Trans. Antennas Propag., vol. 54,no. 1, pp. 82–89, 2006.

[44] J. D. Krauss, Electromagnetics. New York: McGraw-Hill, 1984, pp.378–451.

[45] R. Dickie, R. Cahill, V. Fusco, H. Gamble, M. Henry, M. Oldfield, P.Huggard, P. Howard, N. Grant, Y. Munro, and P. de Maagt, “Submil-limetre wave frequency selective surfaces with polarisation indepen-dent spectral responses,” IEEE Trans. Antennas Propag., vol. 57, no.7, pp. 1985–1994, 2009.

[46] R. E. Matick, Transmission Lines for Digital and Communication Net-works. New York: McGraw-Hill, 1969, pp. 125–128.

[47] R. G. Chambers, “Anomalous skin effect in metals,” Lett.s Nature, vol.165, pp. 239–240, 1950.

[48] P. W. Gilberd, “The anomalous skin effect and the optical propertiesof metals,” J. Phys. F: Met. Phys., vol. 12, no. 8, 1982.

[49] S. Noge, H. Ueno, K. Hohkawa, and S. Yoshikawa, “Low resistancethin Al film by simple sputtering deposition,” in Proc. IEEE Ultra-sonics Symp., 1995, vol. 1, pp. 379–382.

[50] H. Nagata, A. Yamaguchi, and A. Kawai, “Characterization of thin-filminterference effect due to surface roughness,” Jpn. J. Appl. Phys., vol.34, pp. 3754–3758, 1995.

[51] L. W. Barron, J. Neidrich, and S. K. Kurinec, “Optical, electrical,and structural properties of sputtered aluminum alloy thin films withcopper, titanium and chromiun additions,” Thin Film Solids, vol. 515,no. 7–8, pp. 3363–3372, 2007.

[52] M. J. Madou, Fundamentals of Microfabrication. Boca Raton, FL:CRC Press LLC, 2000.

[53] J. Sanz-Fernández, G. Goussetis, and R. Cheung, “Perturbed frequencyselective surfaces fabricated on large thin polyimer membranes formultiband infrared applications,” J. Vaccum Sci. Technol. B, vol. 27,no. 6, pp. 3169–3174, 2009.

[54] C. Mateo-Segura, G. Goussetis, and A. P. Feresidis, “Resonant effectsand near field enhancement in perturbed arrays of metal dipoles,” IEEETrans. Antennas Propag., vol. 58, no. 8, pp. 2523–2530, Aug. 2010.

Juan José Sanz-Fernández (S’08) was born inMurcia, Spain, in 1984. He received the Telecom-munications Engineer degree from the TechnicalUniversity of Cartagena (UPCT), Cartagena, Spain,in 2007. He is currently working towards the Ph.D.degree at the University of Edinburgh (UoE), Edin-burgh, U.K.

In 2006, he joined the Department of Communi-cations and Information Technology, UPCT, as a Re-search Student, where he was involved in the anal-ysis and design of leaky-waves antennas. In 2007, he

joined the Institute for Integrated Systems, UoE, where he currently developshis research activities that include modelling and design of frequency selectivesurfaces and EBG structures, MEMS and micro/nanofabrication techniques, mi-crowave and infrared measurements, and numerical techniques for electromag-netics.

Mr. Sanz-Fernández was awarded the Wolfson Microelectronics scholarshipin 2007.

Rebecca Cheung (M’96–SM’02) obtained a sec-ondary and tertiary education in Scotland andreceived the M.Sc. degree (first class honours) inelectronics and electrical engineering and the Ph.D.degree from the University of Glasgow, Glasgow,Scotland, in 1990.

During her Ph.D. study she was a VisitingResearcher with the Semiconductor TechnologyGroup, IBM Thomas J. Watson Research Centre,Yorktown Heights, NY, where high density plasmaetching techniques were developed for GaAs. The

process-induced material damage was characterised using x-ray photoelec-tron spectroscopy and quantum transport techniques. Before joining theUniversity of Edinburgh in 2000, she had been a Visiting Scientist with theMesoscopic Physics Group, Department of Applied Physics, Delft Instituteof Microelectronics and Submicron Technology, The Netherlands; the Semi-conductor Technology Group at the Laboratory for Electromagnetic Fieldsand Microwave Electronics, ETHZ, Switzerland and the NanoelectronicsResearch Center at Glasgow University; working on various topics related tosemiconductor technology, process-induced materials damage, mesoscopicphysics in SiGe heterostructures and microwave circuits in InP for gigabitelectronics. Additionally, she had been a founding member of the “Nanostruc-ture Engineering Science and Technology” (NEST) Group at the Universityof Canterbury in New Zealand in 1998. She has an international reputationfor her contribution in the development and application of micro- and nano-fabrication. Her major research interests to date span: micro- nano- fabricationtechnology; process-related defects; microwave electronics; low dimensionalstructures; micro-electromechanical systems and meta-materials/devices. Shehas published over 130 scientific articles with more than 80 peer-reviewedjournal papers, including eight invited review papers and one book.

Prof. Cheung was awarded a Scholarship from the Croucher Foundation forher Ph.D. studies. She serves in various conference committees, is a Fellowof the IET and is an Honorary Professor with the School of Engineering andPhysical Sciences at Heriot-Watt University.

George Goussetis (S’99–M’02) graduated fromthe Electrical and Computer Engineering School,National Technical University of Athens, Greece,in 1998, and received the Ph.D. degree from theUniversity of Westminster, London, U.K., in 2002,he also received the B.Sc. degree in physics (firstclass) from University College London (UCL), U.K.

In 1998, he joined the Space Engineering, Rome,Italy, as RF Engineer and in 1999 the WirelessCommunications Research Group, University ofWestminster, U.K., as a Research Assistant. Between

2002 and 2006, he was a Senior Research Fellow at Loughborough University,U.K. From 2006 and 2009, he was a Lecturer (Assistant Professor) withthe School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh, U.K. He joined the Institute of Electronics Communications andInformation Technology, Queen’s University Belfast, U.K, in September 2009as a Reader (Associate Professor). In 2010, he was visiting Professor in UPCT,Spain. He has authored or coauthored over 100 peer-reviewed papers three


book chapters and two patents. His research interests include the modelling anddesign of microwave filters, frequency-selective surfaces and periodic struc-tures, leaky wave antennas, microwave heating as well numerical techniquesfor electromagnetics.

Dr. Goussetis received the Onassis foundation scholarship in 2001. InOctober 2006 he was awarded a five-year research fellowship by the RoyalAcademy of Engineering, U.K.

Carolina Mateo-Segura (S’08) was born in Va-lencia, Spain, in 1981. She received the M.Sc.degree in telecommunications engineering from thePolytechnic University of Valencia, Valencia, Spain,in 2006. She is currently working toward the Ph.D.degree jointly between the University of Edinburghand Heriot-Watt University, Edinburgh, U.K.

During the first half of 2006, she joined theSecurity and Defense Department of Indra Systems,Madrid, Spain, as a Junior Engineer. Currently, sheis a Research Associate in the Wireless Communica-

tions Research Group, Department of Electronic and Electrical Engineering,Loughborough University, Leicestershire, U.K. Her research interests includethe analysis and design of frequency selective surfaces, artificial periodicelectromagnetic structures with applications on high-gain array antennas andmedical imaging systems. Her research has been funded primarily by the JointResearch Institute for Integrated Systems, EPSRC, MRC and BBSRC.

Ms. Mateo-Segura was awarded a prize studentship from the Edinburgh Re-search Partnership and the Joint Research Institute for Integrated Systems to jointhe RF and Microwave group at Heriot-Watt University, Edinburgh, Scotland,U.K.

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Power Stored and Quality Factors in Frequency Selective Surfaces at THz Frequencies

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