Cataloged from PDF version of article.In this paper, a novel approach, based on the employment of frequency selective surfaces, to enhance the power transmission through sub-wavelength apertures at the microwave frequencies is presented. A heuristic interpretation of the phenomenon is given, as well as an analytical model, based on the transmission line network representation. Finally, the performance of the proposed structure is validated through a set of full-wave numerical simulations. © 2011 Springer-Verlag

Bilotti, F.

Ozbay, E.

Scorrano, L.

Vegni, L.

Luca Scorrano

Filiberto Bilotti

Ekmel Ozbay

Lucio Vegni

Crossref

Applied Physics A

FSS-based approach for the power transmission enhancement through electrically small apertures

In this paper, a novel approach, based on the employment of frequency selective surfaces, to enhance the power transmission through sub-wavelength apertures at the microwave frequencies is presented. A heuristic interpretation of the phenomenon is given, as well as an analytical model, based on the transmission line network representation. Finally, the performance of the proposed structure is validated through a set of full-wave numerical simulations

Özbay, Ekmel

Bilkent University Institutional Repository

Appl Phys A (2011) 103: 927–931DOI 10.1007/s00339-011-6254-yFSS-based approach for the power transmission enhancementthrough electrically small aperturesLuca Scorrano · Filiberto Bilotti · Ekmel Ozbay ·Lucio VegniReceived: 30 March 2010 / Accepted: 3 December 2010 / Published online: 20 January 2011© Springer-Verlag 2011Abstract In this paper, a novel approach, based on the em-ployment of frequency selective surfaces, to enhance thepower transmission through sub-wavelength apertures at themicrowave frequencies is presented. A heuristic interpreta-tion of the phenomenon is given, as well as an analyticalmodel, based on the transmission line network representa-tion. Finally, the performance of the proposed structure isvalidated through a set of full-wave numerical simulations.1 IntroductionAt the end of the 1990s, Ebbesen’s group successfullydemonstrated the possibility to overcome the diffractionlimit at the visible frequencies by using properly designedperiodic corrugations in metal screens with nanoscale holes[1]. This phenomenon, known as Extraordinary OpticalTransmission (EOT), has been elegantly explained by Olinerand Jackson, in terms of the excitation of leaky surface plas-mons coupling to the aperture [2]. During the last years, thestrong interest in the EOT, as well as the introduction of newartificial materials (i.e. metamaterials—MTMs), led to theidea of scaling this phenomenon down to the microwave fre-quencies.To the authors’ best knowledge, the first setup proposedto accomplish this task has been presented in [3], based onL. Scorrano () · F. Bilotti · L. VegniDepartment of Applied Electronics, University “Roma Tre”,Via della Vasca Navale, 84, 00146 Rome, Italye-mail: lscorrano@uniroma3.itE. OzbayNanotechnology Research Center, Bilkent University, Bilkent,06800 Ankara, Turkeyproperly designed MTM covers with Near-Zero (NZ) consti-tutive parameters and supporting proper leaky modes. How-ever, the actual excitation of such modes, turned out to berather challenging, due to the small imaginary part of thecorresponding propagation constant. Another issue was thethickness of the MTM slab which is electrically large, beingthe index of refraction extremely low. As a consequence,the setup presented in [3] has not been practically imple-mented yet. Therefore, in order to foresee a possible actualimplementation of this setup, we focused our effort in imple-menting the same physical mechanism by using a differentapproach, based on a frequency-selective surface (FSS), andplaced in front of the perforated metallic plate.2 THE proposed setupAccording to the classical theory by Bethe [4], neglectingthe retardation effects due to the thickness of the screen andassuming that the screen is perfectly conducting, the trans-mission through an electrically small hole can be describedin terms of an equivalent electric dipole moment (orthogonalto the screen) with amplitude pe and an equivalent magneticdipole moment (parallel to the screen) with amplitude pm:pe = − 13π r3E0, pm = − 23π r3H0 (1)being E0 and H0 the electric and magnetic field amplitudeson the hole and r the hole radius. Our idea is to designan FSS-based screen, which has been shown to be a validalternative to replace bulk MTMs [5], whose complex sur-face impedance (ZFSS) [6] is such that the amplitude of theequivalent magnetic dipole moment of the aperture resultsdramatically enhanced when the FSS is placed in front ofthe perforated metallic screen. The sketch of the proposed928 L. Scorrano et al.Fig. 1 Layout of the proposed setup (the disk shape of the FSS unitcell is used as a mere example) and the corresponding equivalent circuitrepresentation. In the TL representation, the FSS is modeled throughits surface impedance and the hole contribution has been neglected,due to its sub-wavelength dimensionssetup is reported in Fig. 1, along with its transmission line(TL) equivalent model.3 Design of the FSS based setupAiming at enhancing the power transmission through thesub-wavelength aperture, the FSS surface impedance ZFSSshould be designed to increase the tangential magnetic fieldamplitude on the screen. The value of the equivalent shuntimpedance of the FSS is derived as follows. Let us considera monochromatic TE(z) plane wave excitation (the TM casecan be easily obtained by duality) in the form:ETE = xˆE0(e−jkz(z+d) + RTEejkz(z+d))e−jkyyHTE = jk0Z0∇ × ETE(2)where k0 = ω√ε0μ0, ky = k0 sin θi , kz =√k20 − k2y . Ex-ploiting the equivalent circuit representation depicted inFig. 1, the tangential magnetic field on the perfectly con-ducting screen can be easily obtained asHTEy∣∣z=0= yˆ 2E0e−jkyyk2zk0Z0× ZFSSkzZFSS cos(kzd) + j (kzZFSS + k0Z0) sin(kzd) (3)Requiring the denominator to vanish on the screen, the fol-lowing design formula is straightforwardly derived:ZTEFSS = −(k0/kz)Z0 sin(kzd)[j cos(kzd) + sin(kzd)] (4)The real part of (4) is always negative, in contrast with thesupposed passivity of the FSS. This means that, in general,the denominator cannot vanish exactly. However, under theassumption that the spacing between the FSS and the screenis electrically small (kzd  1), a first order Taylor expansionof (4) givesZTEFSS = −d(j + kzd)k0Z0  −jk0Z0d (5)In the same way, for an incident TM(z) plane wave the fol-lowing design formula is obtained:ZTMFSS = −(kz/k0)Z0 sin(kzd)[j cos(kzd) + sin(kzd)] (6)Applying, again, a first order Taylor expansion, expression(6) becomesZTMFSS  −jZ0(k2z /k0)d (7)Using either (5) or (7), it is possible to design, for a givenfrequency and distance d between the FSS and the screen,the needed reactive impedance value leading to an increasedamplitude of the tangential magnetic field on the apertureplane. A clear example is reported in Fig. 2(a), where theplot of the enhancement of the tangential magnetic field am-plitude on the screen, normalized to the case without theFSS, is shown.In a real-life application employing a passive FSS, thenegative, yet small, value of the real part of ZFSS has to beneglected, affecting thus the enhancement performance ofthe setup (Fig. 2(b)). However, even if the real part of thesurface impedance is completely neglected (which is the ac-tual case), the amplitude of the tangential magnetic field ishighly enhanced anyway (around 10 dB with respect to thecase of the screen alone without the FSS). A simple actualimplementation can be based on the patterned squared loopmetallic surface represented in Fig. 3(a), designed to exhibitthe required reactive value of ZFSS at f0 = 15 GHz.This is an extremely simplified setup, designed to ver-ify the reliability of the proposed approach. The angularbandwidth of this configuration is, in fact, mainly lim-ited by the FSS unit-cell shape, being the distance d elec-trically small. Further improvements are expected usingmore complex designs of the base element shape and atriangular lattice with circular shaped element of smallersize [6]. The structure shown in Fig. 3(a) has been simu-lated through CST Studio Suite [7] inside a parallel-platewaveguide, bounded by two perfect magnetic boundarieson the right/left sides in order to excite the TEM(z) fun-damental mode. In the inset of Fig. 3(b), the variation ofthe magnetic field amplitude at the design frequency alongthe propagation direction passing through the hole, is re-ported. The expected strong magnetic field resonance is vis-ible between the FSS and the metallic screen, where the holeis placed. The power transmission enhancement is close to20 dB (Fig. 3(b)).FSS-based approach for the power transmission enhancement through electrically small apertures 929Fig. 2 (a) Amplitude in [dB] of the tangential magnetic field on themetallic screen (normalized to the case of absence of the FSS) as afunction of the complex values of the shunt impedance of the FSS fora design frequency f0 = 15 GHz and d = 0.25 mm. The enhancementpeak of Hy is obtained for ZFSS = −2.98 − j33.39 . (b) Tolerancesto a mismatch of the real part moving from the exact design value,100% Re{ZFSS}, to its complete neglection, 0% Re{ZFSS}, calculatedby the equivalent TL model of Fig. 1Fig. 3 (a) FSS-based layout. The squared-unit-cell FSS sheet hastransverse dimensions 17 mm × 17 mm. The thickness of the cop-per metallization is t = 0.07 mm. The distance FSS-screen is d =0.25 mm. The center–center distance between two inner elementsfor both x and y directions is p = 4 mm. The radius of the hole isr = 0.4 mm. The inner gap g = 0.4 mm. The element side l = 2.9 mm.(b) Power transmission enhancement for the structure depicted in (a)normalized to the case of absence of the FSS structure at the design fre-quency. (b, up inset) Amplitude of the tangential magnetic field alongthe normal axis to the hole at 15 GHz in the case of a TEM(z) imping-ing wave. The hole plane is placed at z = 0 mm. The magnetic fieldamplitude in z = 0 mm without the FSS cover is 5 mA/mFinally, due to the intrinsic symmetry of any setup in-volving the transmission through an aperture placed on anopaque screen, it is also expected that, pairing two iden-tical structures on both sides of the screen would result,by reciprocity [3], in a significant further increase of thepower transmission. By placing an identical FSS as the onein Fig. 3(a) at the exit face of the screen (Fig. 4(a)), we havefound the results reported in Fig. 4(b).The second resonant sheet introduces a split in the en-hancement peak, due to the coupling between the two equiv-alent resonating circuits, placed at the entrance and exit sidesof the hole. As the coupling is rather weak, being the ra-dius of the hole electrically small, the frequency shift resultsslightly pronounced.As a final countercheck, we also verified that the trans-mission enhancement is not caused by an array of periodi-cally spaced holes, due to the introduction of perfect electricand magnetic boundaries in the simulation, but only by thecontribution of a single aperture (see Fig. 4(c)). This is animportant test, because enhanced transmission can be easily930 L. Scorrano et al.Fig. 4 (a) Geometrical sketch of the symmetrical structure consist-ing of two identical FSS sheets placed at both sides of the perforatedmetallic screen. (b) Comparison between the power transmission en-hancement of the structure depicted in Fig. 3(a) and the one of (a).(c) Power transmission enhancement for the structure depicted in (a)and for other similar structures with the same base element, periodic-ity, hole dimensions, and different transverse extensions of the metallicscreen that are nine times (b) and twenty-five times (c) bigger than thereference case (a) of Fig. 3(b), respectivelyFig. 5 TL circuit representation of a setup based on a pair of FSSsplaced on the left side of the screen. Each FSS sheet is modeled throughits surface impedance and the contribution of the hole is again ne-glected, due to its sub-wavelength dimensionsobtained also from an array of holes, by a proper choice oftheir periodicity [8].Finally, we show the effect of using multiple FSS sheets,placed on one side of the screen only. We consider, for in-stance, the case of two FSS sheets, placed at a distance d1and d1 +d2 from the metallic plate where the hole is placed.The equivalent TL model for this structure is depicted inFig. 5.Assuming a TE(z) polarized electromagnetic field prop-agating through the structure (the TM case can be obtainedagain by duality) and both d1 and d2 electrically small, byimposing the denominator of the magnetic field amplitudeto vanish at z = 0, a solution for ZFSS1 is found asZTEFSS1 = −jk0Z0ZTEFSS2(d1 + d2)(j + 2kzd2)ZTEFSS2(2kzd1 − j) + Z0k0d1,{kzd1  1kzd2  1 (8)If the following two additional conditions are introduced:Re{ZTEFSS2} = 0, d1 = d2 (9)without any loss in generality, the imaginary and real partsof ZFSS1 can be, then, evaluated as a function of the imagi-nary part of ZFSS2 (see Fig. 6). The final result is that, if thedistances of the FSS sheets from the metallic plate are elec-trically small, it is possible to obtain two simple solutions,one purely capacitive, the other purely inductive:ZTEFSS2 = −12jk0dZ0, ZTEFSS1 = 2jk0dZ0 (10)This configuration exhibits, in principle, better angular per-formance and tolerance to a mismatch of the real part of thesurface impedance compared to the one in which a singlecapacitive FSS is used (kz does not appear in the solution,after a first order expansion of the exact solutions, and bothRe{ZFSS2} and Re{ZFSS1} vanish identically). These simpleconsiderations open the doors to more complicated layouts,which can even improve the performance of the setups wehave previously proposed in Figs. 3(a) and 4(a). However,the design and the numerical characterization of such struc-tures is out of the scope of this paper and will be the subjectof a future publication.4 ConclusionsIn this paper, an FSSs-based approach for enhancing thepower transmission through a sub-wavelength aperture hasbeen presented. A design formula for the FSS surface im-pedance has been derived for both TE and TM polarizationsof the impinging field, using a TL circuit equivalent model.FSS-based approach for the power transmission enhancement through electrically small apertures 931Fig. 6 Real and imaginaryparts of ZTEFSS1t as a function ofhe imaginary part of ZTEFSS2under the assumptions (8). Thedistances ared1 = d2 = 0.25 mm and thedesign frequency is 15 GHzThe given analytical models have been validated throughproper full-wave simulations performed through CST StudioSuite. Finally, the possibility of using a proper combinationof both inductive and capacitive FSSs, placed at one side ofthe screen, has been investigated, leading to the result that,if the overall thickness of the structure is electrically small,the tolerances to the incidence angle of the impinging radia-tion and to the real part of the surface impedance can be, inprinciple, significantly improved.References1. D.E. Grupp, H.J. Lezec, T. Thio, T.W. Ebbsen, Beyond the Bethelimit: tunable enhanced light transmission through a single sub-wavelength aperture. Adv. Mat. 11(10), 860–862 (1999)2. A.A. Oliner, D.R. Jackson, Leaky surface-plasmon theory for dra-matically enhanced transmission through a sub-wavelength aper-ture, Part I: Basic features, 2003. IEEE Int. Symp. Antennas Propag.2, 1091–1094 (2003)3. A. Alù, F. Bilotti, N. Engheta, L. Vegni, Metamaterial covers overa small aperture. IEEE Trans. Antennas Propag. 54(6), 1632–1643(2006)4. H.A. Bethe, Theory of diffraction by small holes. Phys. Rev. 66,163–182 (1944)5. M. Caiazzo, S. Maci, N. Engheta, A metamaterial surface for com-pact cavity resonators. IEEE Antennas Wirel. Propag. Lett. 3(1),261–264 (2004)6. B. Munk, Frequency Selective Surfaces: Theory and Design (Wiley,New York, 2000)7. CST Studio Suite, CST computer simulation technology (2009).http://www.cst.com8. F.J. García de Abajo, R. Gómez-Medina, J.J. Sáenz, Full transmis-sion through perfect-conductor subwavelength hole arrays. Phys.Rev. E 72(1), 016608 (2005)

FSS-based approach for the power transmission enhancement through electrically small apertures

Abstract

Similar works

Full text

Available Versions

Crossref

Bilkent University Institutional Repository