Optimization of Multilayer Shields Made of Composite Nanostructured Materials

60 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 1, FEBRUARY 2012

Optimization of Multilayer Shields Madeof Composite Nanostructured Materials

Davide Micheli, Carmelo Apollo, Roberto Pastore, Daniele Barbera, Ramon Bueno Morles, Mario Marchetti,Gabriele Gradoni, Member, IEEE, Valter Mariani Primiani, Member, IEEE, and Franco Moglie, Member, IEEE

Abstract—In this paper, we propose a multilayer nanostructuredcomposite for broadband shielding applications. Layers disposal,electrical parameters, and thicknesses are optimized through awinning particle optimization algorithm to achieve the minimiza-tion of the transmitted waves. The structures are simulated byincluding the forward/backward scattering matrix formalism inthe optimization code. The adopted algorithm is the recently intro-duced winning particle optimization. Manufacturing of the com-posites is grounded on the optimization procedure. Thanks to themacroscopic absorption features of such nanostructured layers,very thin and lightweight composites can be produced. Severalweight percentages of multiwall carbon nanotubes are consideredin composite base material manufacturing, also including 6wt%and 15wt% in order to enhance the electromagnetic shielding per-formance. Prototypes are tested in the microwave region, showingthe reliability of the optimization procedure.

Index Terms—Carbon nanotubes, carbon–carbon, modeling,radar absorbing materials, shielding effectiveness (SE), winningparticle optimization (WPO).

I. INTRODUCTION

ABRANCH of scientific research about composite mate-rials is focused on electromagnetic characterization and

subsequent application of electric conductive polymers. Theuse of such structures is relevant in aerospace/aeronautics [1],for electromagnetic protection from natural phenomena (light-ning) [2], and intentional interference with radar absorbingmaterial [3], in electromagnetic compatibility (EMC) [4], forequipment-level shielding, high-intensity radiated fields protec-tion, anechoic chambers (for the realizations of wedges andpyramidal arrays), and human exposure mitigation.

Recent study of nanotechnology applications in EMC arewidely addressed to interconnects [5]–[8] and to the shielding

Manuscript received April 29, 2011; revised July 30, 2011 and September 1,2011; accepted October 4, 2011. Date of publication November 8, 2011; dateof current version February 17, 2012.

D. Micheli, C. Apollo, R. Pastore, D. Barbera, R. B. Morles, andM. Marchetti are with the Department of Astronautic, Electrical andEnergetic Engineering, “Sapienza” University of Rome, 00138, Rome,Italy (e-mail: [email protected]; [email protected];[email protected]; [email protected]; [email protected]; [email protected]).

G. Gradoni is with the Institute for Research in Electronics and AppliedPhysics, University of Maryland, College Park, MD 20742 USA (e-mail:[email protected]).

V. Mariani Primiani and F. Moglie are with Dipartimento di Ingegneriadell’Informazione, Universita Politecnica delle Marche, 60131 Ancona, Italy(e-mail: [email protected]; [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/TEMC.2011.2171688

effectiveness (SE). In particular, SE covers nanotubes [9], meta-surfaces [10], multilayer materials [11], periodic screens [12],and metallic foams [13].

In this paper, composite reinforced by carbon nanostruc-tured materials are considered, mainly because of their inter-esting electromagnetic characteristics, such as high electricalconductivity and excellent microwave absorption and shield-ing behavior [14]–[16]. Numerical design of wide frequencyband radar absorbing structures is presented and discussed indetail. It is crucial to highlight the need of interdisciplinaryresearch fields to go through nanomaterials besides nanotech-nology, electromagnetic wave propagation theory, evolution-ary computation algorithms, composite materials manufacturingtechniques, non destructive electromagnetic measurement tech-niques and use those to obtain the “electromagnetic absorber”is strongly required. Composite materials considered in this pa-per for shielding structure are based on epoxy matrix reinforcedwith several species of carbon nanomaterials. These latter havebeen chosen taking into account the lowest market prices: theeconomic aspects, normally neglected in small laboratory ap-plications, are on the contrary important in real applicationswhere the amount of carbon nanopowders fillers could be rel-atively high. In such a scenario, a good compromise in termsof cost/performances has been obtained using industrial grademultiwall carbon nanotubes (MWCNTs). Materials used areMWCNTs (type NANOCYLTM NC7000), bought atNANOCYL (diameter around 9.5 nm, length 1.5 μm, purity90%); epoxy-resin is PrimeLM 20LV (density 1.123 g/cm3),Hardner (density 0.936 g/cm3). Carbon nanofibers (CNFs)bought at SigmaAldrich (diameter around 75 nm and length50–100 μm).

As far as optimization algorithms, winning particle opti-mization (WPO) recently introduced has been adopted [17],[18]. WPO has been applied in order to design and optimizemultilayer materials able to effective absorbing/shielding mi-crowaves. Microwave absorption concepts are quite often ex-ploited in radar absorbing materials [19]–[21], while microwaveshielding concepts are more often adopted in electromagneticinterference (EMI) applications [22], [23].

This paper is organized as follows. In Section II, the physi-cal and electromagnetic properties of the material used are de-scribed. In Section III, the electromagnetic models of absorbingand shielding structures are described. In Section IV, the adoptedexperimental setup is accurately described also showing the testfixture. In Section V, results are presented showing compar-isons of absorption and shielding properties between simulatedand manufactured composite materials. The shielding capabil-ity of high concentration MWCNTs (up to 15wt%) composite

0018-9375/$26.00 © 2011 IEEE

MICHELI et al.: OPTIMIZATION OF MULTILAYER SHIELDS MADE OF COMPOSITE NANOSTRUCTURED MATERIALS 61

TABLE ICODING OF MATERIALS IN THE DATA BASE

TABLE IIRELATIVE DIELECTRIC CONSTANT OF MATERIALS (REAL

AND IMAGINARY PART)

materials are also analyzed and compared to that of carbon–carbon (C–C). In Appendix, the WPO algorithm is describedtogether with its objective functions.

II. MATERIAL CODING AND PROPERTIES

The considered composite materials consist in epoxy-resin loaded with carbon nanopowders. Conductive fillers(MWCNTs and CNFs) have been uniformly dispersed in epoxy-resin at different weight percentages (0.5%wt, 1%wt, 2%wt,2.5%wt, and 3 %wt) (see Table I), and the resulting compositeshave been characterized using waveguide measurements apply-ing canonical algorithm to retrieve electric permittivity [18],[19]. In [18], the electrical permittivity of composite materialsis reported as function of the frequency. Table II reports thosevalues for some frequencies. Each composite material has beenused to build a single layer of the multilayer structure. Mor-phology and scanning electron microscope (SEM) pictures ofmaterials in Table I are reported in [18]. A critical point is toobtain the nanoparticles dispersion in epoxy-resin with a homo-geneous and isotropic distribution. This is also due to the Vander Walls [24] forces that tend to aggregate the nanoparticles toeach other. In materials preparation, the dispersion of the carbonnanomaterials within the polymer matrix has been achieved bysonication at room temperature. The sonication has been carriedout at 20 kHz for about 15 min by means of Sonics Ultranson-icator (VCX750 model), setting 20% amplitude with respect tothe full-scale oscillation magnitude of ultrasonic processor.

Fig. 1. SEM image of carbon nanotube 15wt% composite material samplefracture. Large scale view. It is easily visible nanoparticles presence, duethe huge quantity of agglomeration zones. Those can be spotted on all the15 wt% specimens cross section, thanks to a good dispersion although the highMWCNTs percentage.

Fig. 2. SEM image of carbon nanotube 15wt% composite material samplefracture. Detailed view. This SEM image focus on an agglomeration zone,already from this magnification is well visible a fibrous structure, mainly on thebrighter zones where the contrast is better. Also here it is clear that we obtaineda good and homogeneous dispersion.


Fig. 3. SEM image of carbon nanotube 15wt% composite material samplefracture. More detailed view. This is an high magnification of the Fig. 2, al-ways on the fracture line. Here is well visible the MWCNTs high presenceinto the composite, and mainly its fibrous structure. This type of structurepresents MWCNTs beams, due the high MWCNTs percentage dispersed in theepoxy-resin.

In order to enhance the electromagnetic shielding perfor-mance also 6wt% and 15wt% MWCNTs composite base mate-rials have been manufactured and tested. These two last com-posite materials have not been coded in Table I in fact, due tothe high percentage weight content has not been possible tocompute the corresponding electric permittivity using standardwaveguide method. By the literature is known that strength ofcomposite materials decreases with the increase of the weightpercentage of MWCNTs in the resin. In particular, the strengthdecreases to 50% at 1wt% of MWCNTs [25]. In our scenario,the composite materials we prepared have not been conceivedas structural mechanical materials but simply as shielding ma-terials. In Figs. 1–3, large scale and detailed SEM images ofcarbon nanotube 15wt% composite material sample fracture areshown, and homogeneous dispersion of nanomaterials can beobserved.

III. MODELING AND OPTIMIZATION

We assume an oblique plane wave impinging onto the multi-layer composite. Both the reflection and the propagation throughthe layers stack can be traced by the forward/backward scatter-ing matrix theory. We have previously shown how such formal-ism can be integrated with a genetic algorithm to obtain fastand reliable design tools for absorbing structures [26]. Here,we focus on the computer-aided design of microwave shieldingstructure (MSS), involving the same electromagnetic simulation

Fig. 4. General multilayer scheme of MSS.

strategy. The WPO algorithm is applied to cope with the com-plex problem of multilayer shield design with several degreesof freedom, namely the number, the material type, the ordering,and the thickness of layers.

Proposed structures are made of carbon nanostructured com-posite materials. Such degree of freedom makes it hard to findthe optimal MSS without the adoption of the evolutionary com-putation and/or iterative search process. Here, the MSS designand optimization is based on objective function minimizationprocedure which seeks the best tradeoff between structure thick-ness (to be minimized) and absorbed electromagnetic power(to be maximized). The maximum shielding goal is basicallyachieved minimizing the transmission between interfaces: thisturns into maximizing both the reflection at each interface andthe absorption inside each layer [26]. In particular, absorptionmechanisms in nanotubes are related to the fraction of the trans-mitted power being localized inside each nanostructured layer.Fig. 4 shows a general situation where a multilayer structure isexcited by a oblique plane wave: each layer is labeled by theindex x. SE is defined as

SE = 20 log|Ex+1 ||E0 |

. (1)

The computation of the transmitted field E0 is a canonical elec-tromagnetic problem. Its solution is well known for both trans-verse electric (TE) and transverse magnetic (TM) modes [27],[28], in terms of transmission (TC) and reflection (RC) coeffi-cients through the wave impedance η of each layer. Each layeris made of one composite material, and TE/TM characteristicwave impedances are computed knowing dielectric propertiesof composite materials and incidence angles of electromagneticwaves acting on each single layer

ηTMx =

√μ0

ε0

√μrx

εrx

cos(ϑx) (2)

ηTEx =

√μ0

ε0

√μrx

εrx

1cos(ϑx)

(3)

where for the Snell’s law

ϑx = arcsin[√

εrx + 1

εrx

sin(ϑx+1)]

. (4)

As far as geometric properties of multilayer structures areconcerned, the thickness of each layer can be defined by WPO


Fig. 5. Directional SE measurement scheme. (a) Front view. (b) Top viewwhere absorbent pyramidal wall is shown.

in the range 0–10 mm, while the number of layers is upper-bounded to maximum ten layers. The effective number of layersis established by the WPO optimization procedure which isable to remove one or more useless layers from the multilayerstructure. The order of layer materials is not “a priori” fixed;the WPO algorithm accesses the materials, coded in Table I, anddecides the most appropriate material for each layer. A detaileddescription of the WPO algorithm is reported in the Appendix.

IV. EXPERIMENTAL SETUP DESCRIPTION

Fig. 5 schematizes the adopted setup. The use of horn an-tennas for SE measurements is not totally new. An example ofnear-field test setup can be found in [29]. The setup we proposeoperates in far-field conditions, and it works for arbitrary an-gles of incidence. Its principle is to measure the attenuation ofa microwave reference signal when it passes through a certainmaterial, in free-space propagation conditions and with a pre-cise incidence angle. The measured attenuation represents theshielding capability of material under test. In Fig. 6, a detailedschema of our in-house ad-hoc designed test fixture is shown.The sample holder is an aluminum mold where the sample iscast. When the holder is closed by its lid, the liquid compositematerial is injected to make shielding material and multilayerstructure. After the curing phase, the lid is removed and theholder is connected to the horn antenna to perform SE mea-surements. The sample is never removed from the holder; anew holder is used for a new sample to be tested. This sample

Fig. 6. Sample holder system used in manufacturing shielding materials andto host horn antenna during shielding measurement.

manufacturing procedure and the use of metallic holder avoidleakages around the edges of the sample. The blocking antennasystem allows a good electrical contact between the antenna andthe sample holder. More precisely, the sample holder aperturedimensions are equal to the internal dimensions of the antennamouth. The small thickness of the antenna wall (about 1.5 mm)allows a good antenna fixing. Thanks to this small indentation inthe holder, the antenna can be easily mounted without coveringits mouth. We verified that the antenna reflection coefficient wasnot appreciably influenced by the sample holder presence.

The measurement of shielding capability of a certain structureor material is computed by means of scattering parameter Sij ,available on the vector network analyzer (VNA) connected to thetransmitting and receiving antennas. In particular, the receivinghorn antenna is equipped with a sample holder able to hostthe structure/material to be tested. The measurement of SEM

is evaluated as the difference in decibels, or the ratio in linear,between the received signal when the sample holder is empty andthe received signal when it is filled with materials. Sensitivityof measurement system is computed closing the sample holderaperture with the metallic lid and performing the same ratio ofscattering parameters. This last SE test represents an index ofthe maximum SER measurable by our system.

SEM (dB) = 10 log

( ∣∣SO21

∣∣2∣∣SM21

∣∣2)

(5)

SER (dB) = 10 log

(∣∣SO21

∣∣2∣∣SS21

∣∣2)

(6)

where S21 is the scattering parameter measured by VNA, the su-perscripts M means “Material,” R means “Reference,” S means“Short,” and O means “Open.” Measurements involve mainlythe absolute amplitude of scattering parameter:


Fig. 7. Sample holder system for SE measurements. The two pictures showthe Q-par Angus LTD antenna (type QSH16S10), mounted on the manufacturedsample holder support. Horn antenna frequency range is 8.2–12.4 GHz, the gainis 10 dBi.

1) SM21 is measured when shielding materials are located

within sample holder;2) SO

21 is measured when no shielding materials are locatedwithin sample holder;

3) SS21 is measured when metallic enclosure is located within

sample holder.In order to avoid as much as possible that spurious re-

flected signal could affect the SE measurement, the receivingantenna and sample holder have been inserted in a wall made ofECCOSORB microwave absorbing materials effective in thefrequency band above 5 GHz. In such a manner, all the po-tentially unwanted reflected signals around the aperture of re-ceiving antenna should be lowered down. To grant good S/Nconditions, the output power of VNA has been set to +3 dBm.The antennas are Q-par Angus horn antennas in the 8.2–12.4GHz frequency range. In shielding measurements, it is requiredthat all microwave measured signals are the only ones passingthrough materials to be tested; this condition is needed to per-form accurate measurements of shielding properties of a certainmaterial/structure. The sample holder we built is able to ac-complish this requirement. In Fig. 7, a practical realization ofantenna supports for shielding measurement is shown.

V. RESULTS

Scheme of tested materials and structures is shown in Fig. 8.Measurements of materials and multilayer structures are furtherdiscussed. Materials considered are the following:

1) single layer: 6.5 mm of CNFs 3wt%;2) single layer: 6.5 mm of MWCNTs 6 wt%;3) single layer: 6.5 mm of MWCNTs 15 wt%;4) two layers: 5 mm composed by 4 mm epoxy-resin and

1 mm MWCNTs 3wt%;5) four layers: 10 mm composed by 3 mm epoxy-resin, 1

mm MWCNTs 1wt%, 1 mm MWCNTs 2wt%, 5 mmMWCNTs 3wt%.

Fig. 9 reports SE results for the worst case situation of nor-mal incidence and for the situation of an incidence angle of45◦. Comparison between simulated and measured SE of man-ufactured materials shows good agreement, confirming the re-liability of the SE simulation code. It can be noted how thenon-normal incidence slightly increases the SE. Fig. 10 re-ports other SE for other cases together with a comparisonwith shielding capability of C–C [30], [31]. In such materi-als, it is possible to observe a high SE which becomes com-

Fig. 8. Analyzed MSS.

parable to that of C–C, reaching sensitivity limits of the mea-surement system. In these cases, only measurements are re-ported because the high material conductivity make impossibleto recover correct permittivity values from the adopted wave-guide method. It is worth noticing that the SE performanceof C–C is mainly based on a high reflection coefficient, whilein the case of the optimized multilayer, the loss mechanismalso contributes to the shielding action allowing a reflectionreduction. As an example, Fig. 11 shows the reflection coeffi-cient corresponding to the case “(f)” of Fig. 8. Reflection is lowand remains below −20 dB beyond 9 GHz. On the other hand,we can note that the C–C practically behaves as a short circuit.


Fig. 9. SE for MSS: (g) epoxy-resin and MWCNT 1,2,3%, the wave inci-dence is 45◦; (f) epoxy-resin and MWCNT 1,2,3%, the wave incidence is 0◦;(e) epoxy-resin and MWCNT 3%, the wave incidence is 0◦; (a) CNF 3%,the wave incidence is 0◦. A comparison between simulated (dashed line) andmeasured (continuous line) curves is reported.

Fig. 10. SE for MSS and C–C materials: (s) the sensitivity of measurementsystem is measured by closing the horn antenna aperture with the metallicenclosure; (d) carbon–carbon, wave incidence 0◦; (c) MWCNT 15%, waveincidence 0◦; (b) MWCNT 6%, wave incidence 0◦.

Fig. 11. Reflection and transmission coefficients for the following cases:(d) RC, reflection coefficient of carbon-carbon, wave incidence 0◦; (f) RC, reflec-tion coefficient of epoxy-resin and MWCNT 1,2,3%, the wave incidence is 0◦;(f) TC, transmission coefficient of epoxy-resin and MWCNT 1,2,3%, the waveincidence is 0◦.

This behavior can be appealing in those applications where highshielding and low reflections are needed.

VI. CONCLUSION

With the aid of optimization, we demonstrated the possibilityof achieving very interesting microwave absorbing and shieldingstructures through the usage of carbon nanomaterials as filler inepoxy-resin. The comparison between measured and simulatedparameters confirms the validity of developed theoretical elec-tromagnetic model. It is shown that composite materials builtwith MWCNTs 15wt% exhibit shielding properties comparableto that of C–C materials. Such high shielding properties putC–C and MWCNTs 15wt% composite materials as interestingcandidates in most EMI shielding applications.

APPENDIX

WPO DESCRIPTION

WPO is a simple algorithm where at each time epoch ofevolution, the particle, which best fit the objective function, isdeputed to pilot the trajectory of the remaining particles withinthe multidimensional space of solutions, i.e., variables to beoptimized.

In Fig. 12, WPO flow chart is shown. At the beginning ofthe iterations, particles are randomly distributed within the n-dimensional search space. At each iteration time, the objectivefunction of each particle is computed. Then, particles are com-pared to each other using value of their objective function andthe best fitting particle is marked with its proper index. Eachparticle position is completely defined by its coordinates andtheir number represents the dimension of the space where allparticles jump searching for the optimal solution. Trajectory ofeach particle, except that of the best fitting particle, is defined inthe following way: if mth-coordinate of a certain particle Pk islesser then the corresponding mth-coordinate of the current bestparticle P q , then the new mth-coordinate will result from thesum of current particle and best particle mth-coordinates; whileif mth-coordinate of a certain particle Pk is greater than thecorresponding mth-coordinate of the current best particle P q ,then the new mth-coordinate will result from the difference be-tween the current particle mth-coordinates and the best particlemth-coordinates. Here, q is the index of the best particle foundin each iteration and the condition which needs to be grant isq �= k, i.e., all kth particles can be displaced except the best qthparticle. Equation (7) describes the mentioned approach. Parti-cle position at the (i + 1)th iteration as a function of particleposition in the previous ith iteration is

Pkm (i + 1) = δRm Pk

m (i) + gP qm (i) (7)

where g = +1 if Pkm (i) < P q

m (i); g = −1 if Pkm (i) > P q

m (i); kis the particle index; q is the best fitting particle index (q �= k);n is the space dimension; the index m ranges in [1, n]; Rm is arandom number in [0, 1]; δ is a convergence parameter; and i isthe current iteration. Rm is used to randomly define the amountof displacement of each single coordinate. Such randomizationdevelops the searching phase by conferring some causality tothe amplitude of jumps. Convergence parameter δ helps the finalconvergence of the WPO algorithm as follows. At the beginningof the iterations, the WPO must be capable to explore the largestspace of solutions as possible. On the other hand, close to the


Fig. 12. WPO flow chart.

end of the iterations, high amplitude of jumps could representa drawback since a position representing the optimal solutioncould forbidden. In order to improve the WPO convergence,a mechanism providing a progressive reduction of “maximumjumps amplitude” has been introduced and it is identified bythe δ parameter. Calling N the total number of iterations andsupposing ith the current iteration, then the value of δ is givenby

δ = σ

(1 − i

N + 1

)P

(8)

where σ = J(Rm − 0.5) with J the “jump amplitude.” In (8),the meaning of σ and P parameters is in fast or slow convergenceof the WPO algorithm. In particular, the higher the σ, the greaterthe initial jumps amplitude and the greater the distances whereparticles will start to explore the search space. As far as P isconcerned the higher its value, the faster the convergence toa suboptimal solution. The parameter σ is made using J andRm . This last is a random number between [−1/2,+1/2]. Therandom part of σ develops the search capability of the algorithm.

At the end of each WPO iteration, check of boundary conditionsfor the new set of particles coordinates is made in order to avoidto overcome the constraints.

The multilayer absorbing structures considered in the de-sign procedure can have up to ten layers so dimension oflayer space is 10 i.e., m = 10, 9, . . . , 1. Since the optimiza-tion are for both “layer thickness” and “layer material type,”WPO algorithms need to be structured in order to take intoaccount for both quantities. In the WPO algorithm, we haveT k (i) =

[Tk

10(i), Tk9 (i), . . . , T k

1 (i)]

as array of thicknesses,where Tk

m (i) is the “thickness” of the mth layer and Pk (i) =[Pk

10(i), Pk9 (i), . . . , P k

1 (i)] as array of material type, wherePk

m (i) is the “type of material” associated to the mth layer.The equations related to layer thicknesses and layer material foreach single particle are simply updated according to

T km (i + 1) = δRm 1 T k

m (i) + gT T qm (i) (9)

Pkm (i + 1) = round

[δRm 2 Pk

m (i) + gM Pqm (i)

](10)

where Rm 1 and Rm 2 are random number in the closed range[0 − 1], T k

m (i) is the current kth particle, mth layer thicknessat the ith iteration, while Pk

m (i) is the current kth particle, mthlayer material at the ith iteration. Rounded values in materialequation are required since the index of material of each layermust be an integer number ranging from 1 to materials numberavailable in the data base of materials, here set to 9. Other WPOparameters and variables are

gT =

{1 if T k

m (i) < T qm (i)

−1 if T km (i) > T q

m (i)(11)

gM =

{1 if Pk

m (i) < Pqm (i)

−1 if Pkm (i) > Pq

m (i)(12)

where q is the index of best particles (T ) and (P); k is the indexof particles with k �= q; n is the dimension number; m is thecurrent dimension ranging between [1, n]. In the presented im-plementation, the values of P and σ of convergence parametershave been set to 1, the number of WPO particles has been fixedto 200, and number of iterations to N = 800.

WPO tries to minimize a global objective function (GOF)which, in turn, are built using elementary objective functions(EOFs). The EOF for TM and TE modes are named as ρTM ,ρTE for reflection coefficient, ΓTM , ΓTE for the transmissioncoefficient, and T for thickness. The formal definition of theEOF for TM and TE modes are shown in (13)–(15). We canobserve that for each particle (k) of WPO, the correspondingEOF is evaluated over the entire frequency band and over theentire incidence angle range

ρTM/TE(P ) =fu∑

f =fl

ϑu∑ϑ=ϑl

ρTM/TE (P, f, ϑ) (13)

where P is the current particle of WPO particles family, f is thefrequency step, fl and fu are the start and stop frequency band,ϑ is the current step angle, and ϑl and ϑu represent the angular


range bounds.

ΓTM/TE(P ) =fu∑

f =fl

ϑu∑ϑ=ϑl

ΓTM/TE (P, f, ϑ) . (14)

The definition of the EOF for thickness is

T =10∑

i=1

Ti(P ) (15)

where Ti is the thickness of the ith layer. Two different weightingfactors are introduced: one is called α, (0 ≤ α ≤ 1), weightingT w.r.t. ρ and Γ, and the other one is called γ, (0 ≤ γ ≤ 1),weighting ρ w.r.t. Γ. Such weighting factors are chosen by theuser and their meaning have to be intended as the capabilityof the tool to design the multilayer structure making privilegeto the electromagnetic performances w.r.t. the thickness whenα tends to 1, or making privilege in lowering the transmissioncoefficient (MSS, mainly in shielding applications) rather thanlowering the reflection coefficient (radar absorbing materialsmainly in absorbing applications) when γ tends to 0. Final GOFis a linear combination of the described EOFs

GOF(P ) = α [γO1(P ) + (1 − γ)O2(P ) + (1 − α)O3(P )](16)

where

O1(P ) =ρTM(P )

A+

ρTE(P )A

(17)

O2(P ) =ΓTM(P )

A+

ΓTE(P )A

(18)

O3(P ) =T (P )

C(19)

A and C are normalization factors: A is the product betweenthe frequency step number and the angle step number, whereasC is the product between the maximum layer number and themaximum layer thickness.

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Davide Micheli was born in Ancona, Italy, in 1967.He received the University degree in electronics engi-neering from the University of Ancona (now Univer-sita Politecnica delle Marche), Ancona, Italy, in 2001,and the University degree in astronautic engineeringand Ph.D. degree in aerospace engineering from the“Sapienza” University of Rome, Rome, Italy, in 2007and 2011, respectively.

He is currently with the Telecom Italia Labo-ratory, as a Researcher with Mobile Telecommuni-cations and Neural Networks and collaborates with

“Sapienza” University of Rome, where his research activities are related toelectromagnetic fields and composite materials interaction. His current researchinterests include electric conductive polymers and radar-absorbing structuresmodeling.

Carmelo Apollo was born in Catanzaro, Italy, onApril 20, 1974. He received the Dottore Ingegneredegree in electronics engineering from the Univer-sity of l’Aquila, l’Aquila, Italy, in 2007, and theM.Sc. degree in composites and nanotechnology foraerospace from the School of Aerospace Engineer-ing, “Sapienza” University of Rome, Rome, Italy, in2008.

He has been a Researcher Assistant with the“Sapienza” University of Rome since 2009. His re-search interests include electromagnetic fields and

composite and nanomaterial interaction.

Roberto Pastore was born in Napoli, Italy, on May25, 1977. He received the University degree inphysics from Napoli Federico II University, Napoli,Italy, in 2004. He is currently working toward thePh.D. degree at the School of Aerospace Engineer-ing, “Sapienza” University of Rome, Rome, Italy.

His experience concerns material science andnanotechnology and production of carbon nanotubes(CNTs). His current research interests include CNTs,nanostructured physical modeling, and coil guns.

Daniele Barbera was born in Rome, Italy, in 1986.He received the B.S. degree in science of materialfrom the University “Tor Vergata” Rome, Rome, in2010.

He is currently with the “Sapienza” University ofRome, Rome, where he is involved in low- and high-percentage carbon nanotubes inclusion in epoxy resinmatrix for space application, studying electrical be-havior. He also works on space structures and materialdesign; actually, he is developing a space sails con-cept. His research interests include material science,

nanotechnology, CVD process, and space structures.

Ramon Bueno Morles was born in Maracaibo,Venezuela, on November, 30, 1979. He received theUniversity degree in physics from Universidad delZulia, Maracaibo, Venezuela, in 2007. He is cur-rently working toward the Ph.D. degree at the Schoolof Aerospace Engineering, “Sapienza” University ofRome, Rome, Italy.

His experience concerns material science and nan-otechnology and production of carbon nanotubes. Hiscurrent research interests include carbon nanostruc-tures production and morphological characterization.

Mario Marchetti was born in San Marcello, Italy,on May 30, 1943. He received the University degreein aeronautical engineering from Milan Polytechnic,Milan, Italy, in 1972.

He then joined the School of Aerospace Engineer-ing, “Sapienza” University of Rome, Rome, Italy,where he is currently a Full Professor of the Engi-neering Faculty, in charge of the “Space Structures”course, the Director of the Department of Astronautic,Electric and Energetic Engineering, and is responsi-ble for the SASLab laboratories.

Gabriele Gradoni (M’11) was born in Ancona,Italy, in 1982. He received the M.S. degree in com-munication engineering in 2006, and the Ph.D. de-gree in electromagnetics and bioengineering in 2009,both from the Universita Politecnica delle Marche,Ancona, Italy.

From May to October 2008, he was a Visiting Re-searcher at the Time, Quantum & ElectromagneticsTeam of the National Physical Laboratory, London,U.K., where he pursued different projects on randomfield theory and experiments. Since June 2010, he

has been an Associate Researcher at the Institute for Research in Electronicsand Applied Physics, University of Maryland, College Park. He is involved inthe area of statistical and computational electrodynamics. His current researchinterests include statistical physics, quantum and semi-classical wave chaosof coupled cavities, scattering in large spatiotemporally electromagnetic sys-tems, time-reversal, nonergodic stochastic processes, reverberation chambers,electromagnetic theory of complex environments, random and stratified media,nanomaterials, plasmonic metamaterials, and theoretical optics.

Dr. Gradoni is a recipient of the URSI Commission B Young Scientist Award2010.


Valter Mariani Primiani (M’93) was born in Rome,Italy, in 1961. He received the degree of “DottoreIngegnere” in electronics engineering from the Uni-versity of Ancona (now Universita Politecnica delleMarche) Ancona, Italy, in 1990.

He is currently an Associate Professor of elec-tromagnetic compatibility (EMC) with the Univer-sita Politecnica delle Marche, Ancona, Italy. He ismember of the Department of Information Engineer-ing, Universita Politecnica delle Marche, where heis responsible for the EMC Laboratory. His research

interests include the prediction of digital printed circuit board radiation, theradiation from apertures, the electrostatic discharge coupling effects modeling,and the analysis of emission and immunity test methods. More recently, he hasextended his research activity in the field of the application of reverberationchambers for compliance testing and for metrology applications.

Prof. Mariani Primiani is a member of the IEEE EMC Society, IEEE Instru-mentation and Measurement Society, and the Italian Electromagnetics Society.

Franco Moglie (M’91) was born in Ancona, Italy,in 1961. He received the “Dottore Ingegnere” de-gree in electronics engineering from the University ofAncona (now Universita Politecnica delle Marche),Ancona, Italy, in 1986, and the Ph.D. degree in elec-tronics engineering and electromagnetics from theUniversity of Bari, Bari, Italy, in 1992.

Since 1986, he has been a Tenured Researcher withthe Dipartimento di Elettronica ed Automatica, Uni-versita Politecnica delle Marche, where, since 2011,he has been with the Department of Information Engi-

neering. His current research interests include electromagnetic (EM) numericaltechniques and power applications of EM field. His research interests includethe field of the application of reverberation chambers for compliance testing andfor metrology applications.

Dr. Moglie is a member of the IEEE Electromagnetic Compatibility Societyand the Italian Electromagnetics Society.

Optimization of Multilayer Shields Made of Composite Nanostructured Materials

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