## 1. Introduction

In the last 50 years, many research activities have been focused on materials and structures able to reduce the electromagnetic reflection coefficient (RC) in certain frequency ranges. Applications are mostly in military technology, with radar absorbing materials (RAM) and radar absorbing structure (RAS) [1–6], and in electromagnetic compatibility (EMC) for EM shielding and EM interference (EMI) suppression purposes [7–9], as well as for antenna testing in anechoic chambers [10, 11]. Nowadays, the increase of wireless communication systems demands the use of specific technologies or technical solutions to reduce the mutual telecommunication (TLC) systems interference. In fact, in order to reduce the energy impact and the constraints imposed by cost savings, most different wireless systems are often co-located in the same place, that is, sharing the same basic infrastructures. The proximity of such TLC systems can give rise to mutual radio frequency (RF) interferences due to intermodulation products in the shared antenna systems and/or to low efficiency in filtering out the spurious RF components. In this complex context, the availability of a new kind of materials, able to be frequency selective, absorbing, and tunable, is particularly attractive to reduce mutual EMI issues in specific frequency ranges [12]. Another field where configurable EM wave absorbers appear useful is the metrological science and technology. For example, in remote sensing, operations are sometimes necessary to often verify the sensors capability to detect and recognize certain material signatures on the Earth surface [13, 14]. Such type of testing and better sensors and algorithms calibration could be easily tuned in situ by using standard metrological samples, able to reproduce the desired EM target signatures. Further applications of tunable EM wave absorbers are conceivable in the security field. Nowadays, some studies are focused on the detection of explosives using appropriate radar signatures [15, 16]: the possibility to design metrological samples able to reproduce some particular explosive matter radar signatures could represent an interesting aid for the safety upgrade in strategic/critical environment.

This chapter is composed of three main sections. The first describes the nanocomposite materials database obtained from the dielectric characterization, by means of vector network analyzer (VNA) measurements, the mathematical modeling of the layered absorber, and the objective function optimization, used by the PSO algorithm. The second reports the main results of simulations, related to several ideal RC targets addressed; the third provides a discussion of the results based upon a FEM numerical analysis by COMSOL Multiphysics code.

## 2. Materials and methods

### 2.1. Nanocomposite materials

Several microwave reflection profiles, even having complicated shapes, have been devised to design absorbers with fitting EM responses. The proposed strategy to achieve the target behavior is to combine different components from the microwave materials database in a multilayer assembly. Such a soft approach allows to exploit a variety of dielectric properties provided by the available constituents in the materials database, as well as the characteristics of the EM field propagation, through the physical discontinuities occurring at the several layers interfaces. Polymeric composites filled with carbon nanoparticles provide an ideal platform in this framework, thanks to the possibility to explore a wide range of EM transport properties, from the insulating matrix to rather conductive composites, just by tuning the nano-filler concentration within the basic polymer. A materials database of 23 carbon micro-powder- and nano-powder-filled polymeric composites has been set up and exploited. Such materials were obtained using commercial low cost products, in a well-established time-saving manufacturing procedure, in view of possible forthcoming scaling-up developments. In particular, a low-viscosity epoxy resin (Prime™ 20 LV—Gurit) was employed as polymeric matrix, while industrial grade multi-walled carbon nanotubes (MWCNT, NC7000—Nanocyl), carbon nanofibers (CNF—Sigma–Aldrich), graphene nanoplatelets (GNP, C750—XG Science), and polyaniline emeraldine base powder (PANI—Sigma–Aldrich) were added to the matrix as reinforcing materials, in different concentrations (from 0 up to 3 wt.%). The composite samples were shaped by means of an ensemble of hollow cylindrical molds (**Figure 1**) with 3 mm of internal diameter and 7 mm of the external one, as required by the specific technique adopted for the microwave characterization. The latter is based on the transmission line by means of coaxial air-line 50 Ω probe and has been carried out by means of a vector network analyzer (VNA, Agilent PNA-L N5235), via coaxial airline method in the frequency range of 2–18 GHz. The output of the measurements is obtained by means of the samples microwave reflection/transmission parameters and the materials complex electrical permittivity; the other typical dielectric properties of interest (loss tangent, skin depth, intrinsic impedance, etc.) can be then easily retrieved. The magnetic permeability of all the materials has not be taken into account during the analysis, since it is always very close to 1 (as expected for non-magnetic materials), as confirmed by the experiments. In **Figure 1**, the sample holder used to build ring samples of different reinforced materials is shown. Each hole of the sample holder is able to host the poured composite after the mixing and sonication procedures; after the curing process, the sample holder is open and the samples can be easily extracted. In **Figure 2**, the 50 Ω coaxial airline used for the VNA scattering parameters [17–19] measurements and for the subsequent computation of the relative dielectric parameters is shown: the samples are inserted around the central conductor of the coaxial airline.

**Figure 3** shows the loss tangent and the intrinsic wave impedance of the nanocomposite materials present in the database, averaged in the frequency band 2–18 GHz. It can be seen that the CNT- and CNF-filled composites show higher EM losses and lower wave impedances, thus anticipating the employment of such materials in layers where a significant EM absorption capability is required; on the other hand, the behavior of PANI/GNP-filled materials is similar to that of the naked resin, thus suggesting the use of such materials in impedance matching layers. The behavior of the electric permittivity of CNT-based nanocomposites is reported in **Figures 4** and **5** (real and imaginary parts, respectively). In the plots, a remarkable variation of permittivity can be observed upon variation of the CNT weight concentration, according to the change of resistive losses due to the conductive filler inclusion: such trend is more evident at lower frequencies, due to skin-depth effects. In **Table 1**, the database of materials is listed by the code number, thereafter used. In **Table 1**, the dielectric complex permittivity averaged over the microwave range investigated is also reported to allow the readers a quick idea about the materials properties. A detailed description of the materials manufacturing procedure, as well as the full database microwave characterization plotting and analysis, is available in a previously published work [20].

### 2.2. Mathematical model and objective function optimization

The multilayered EM absorber design is based on the mathematical modeling of an EM wave propagating through a sequence of slabs made of different materials. Since the goal is to reproduce a given microwave reflection profile, it is worth to remind that the reflection coefficient (*RC*) at an air-matter interface can be evaluated by the relationship:

which relates the free-space impedance (*Z*_{0} ≈ 377 Ω) to the input impedance (*Z*_{i}) seen at the impinged surface for a given *i*th value of frequency. Such quantity depends on the dielectric properties of the material; for a multilayer structure, it is affected by multiple reflections occurring at the material interfaces and can be obtained by iterating Eq. (1) layer by layer through the formalism:

where each layer (*u*) is denoted by its proper thickness (*t*_{u}) and by the EM intrinsic wave impedance (*η*_{iu}) of the constituent material at the *i*th value of frequency (*f*). The intrinsic wave impedance and the wave number (*k*_{iu}) are linked to the relative electric permittivity and magnetic permeability of the material constituting the *u*th layer (*ε*_{ru} and *μ*_{ru}, respectively) and to the vacuum electric permittivity and magnetic permeability (*ε*_{0} and *μ*_{0}, respectively).

The adopted particle swarm optimization (PSO) algorithm evolves iteratively by minimizing the following objective function (*OF*):

where *T*_{RC} is the target RC, and *S*_{RC} is the simulated RC of a given multilayer—that is, a “particle” filling the space of solutions—obtained by combining Eqs. (1) and (2). Input of the design/optimization code is the target RC profile to fit and the electric permittivity of the materials in the database (the magnetic permeability is here neglected since the measurements of the dielectric parameters have shown that *µ*_{r} is unitary for all the materials under test). The output is the composition of the multilayered structure, that is, number of layers, layering sequence, and material/thickness of each layer. The PSO ranges within the space of solutions in order to minimize the *OF* defined in Eq.(4): the constraints are mainly imposed by the freedom degrees in exploring the database of available materials, in order to select the most appropriate for each layer, as well as the related thickness, limiting to a maximum of ten-layer structures. Further details on the EM wave/multilayer interaction modeling with a full description of the developed PSO algorithm can be found in some recent publications [21–23].

## 3. Results

The results of CEMA solutions for several RC targets are listed in **Tables 2**–**5**, where the target parameter, the materials of each layer coded with a number referred to **Table 1**, the thickness of each layer and the total thickness of the multilayer are reported. All the solutions are represented as ten-layer sequences: of course, a zero thick layer means that the PSO algorithm optimized the final layered material without the necessity of using that particular layer. In some cases, the indication of the PSO parameter *α* is also provided [21–23], whose meaning is here briefly recalled: by this parameter, the OF optimization is weighted with respect to the multilayer total thickness (e.g., *α* = 1 means that only OF will be taken into account by PSO, without taking care of the thickness minimization). In the next **Figures 6**–**15**, the plot of the RC simulations is reported, comparing to the corresponding targets (red dashed lines). Almost all the simulations are based on RC target imitation by providing a PEC at the end of the layered material, except two. In particular, CEMA 02 has been designed providing free-space environment on both sides, that is, without the presence of PEC as the back-end of the structure. For CEMA 24, two different design scenarios have been taken into account: the first one represents the usual RC target imitation with a PEC-backed multilayer, while the second one explores the possibility to consider the TC as target parameter to be assigned to the PSO algorithm, thus requiring free space at both sides (here the other PSO parameter *γ* is introduced, to point out the weight in RC/TC addressing: *γ* = 0 indicates the RC optimization with no regard to TC, vice versa for *γ* = 1, intermediate values represent an optimization process that takes into account for TC and RC imitation simultaneously—cfr. CEMA02 plot). In this special case, the expected EM losses phenomena within the material increase with the frequency, thus progressively lowering down the TC values: such unwanted collateral effect is unavoidable since the higher the frequency the greater the skin-depth effect, which in turns increases the EM wave losses within thick materials.

The PSO algorithm shows an intriguingly effective mimic capability in almost all the cases, even for the most demanding (actually ”not physical”) targets conceived. Of course, the reliability degree is strictly linked to the target shape, that is, to the peaks number and depth as well as to the sharpness of the RC variations to be hunted. T_{RC} 00 and T_{RC} 02 present a simple filter-shaped profile: the corresponding solutions are able to broadly follow the target trend, even if the sharp (ideal) square-like behavior, with deep peaks up to 20 dB, does not allow a satisfactory imitation around the edges. In particular, CEMA 02 almost loses track of the target at the frequency range boundaries, probably due to the TC weighting in this free-space backed situation. Other regular square-like target profiles (multi-filter behavior) with RC oscillations of about 15 dB confirm both potentialities and issues of the method. In particular, the very difficult task of T_{RC} 23 imitation is actually impossible to tackle, even if the quasi-total reproduction of all the oscillating peaks by CEMA 23 represents a surprising result in this case. T_{RC} 16 is much easier to be imitated due to the greater peaks width, even if some inaccuracies are discovered for both the CEMA 16 solutions at lowest frequencies. The results obtained by CEMA 24 can be seen as intermediate case of the latter two. An excellent mimic effectiveness is provided by CEMAs 15, 17, and 20, which are able to closely follow the corresponding targets: in such cases, the algorithm is “aided” by the lower peaks depth and mainly by smoother RC variations in frequency. The difference in pursuing triangle-shaped *versus* square-shaped RC oscillations is well established by the two CEMA 13 solutions, which alternatively match and miss the exotic “stair-profile” of T_{RC} 13. For the T_{RC} 13, 15, 16, 17, and 20, two CEMA solutions have been proposed by slight variation of *α*. It can be noticed that at lower *α* (0.96) the algorithm finds solutions with thinner total thickness: that is reflected by the simulations, which shows a little bit more inaccuracy (black dashed lines) around the sharpest RC variations. Concerning the transmission targets (*γ* ≠ 0), difficulty to conceive appreciable solutions in such framework due to the abovementioned intrinsic skin-depth effects, evident in both the situations investigated, needs to be pointed out. In T_{RC} 02, the parameter *γ* is set to 0.5 (i.e., the optimization of RC and TC is equally weighted) and a constant low transmission rate is defined: besides the loss effects, the simultaneous research of a layering to follow the RC target leads to an intermediate solution, not suitable for the required transmission (otherwise a quasi-full absorbing structure would have been identified). As for the T_{TC} 24 (*γ* = 1), a challenging square-shaped transmission profile is defined (by analogy with T_{RC} 24, *γ* = 0). The quite fast target oscillations are only remotely hinted by the CEMA 24 solution, whose average TC substantially decreases at higher frequency; nevertheless, it is worth noticing that the corresponding reflection presents a peaks series roughly reversed, in respect to the transmission target.

A promising level of confidence is suggested from the reported results in each phase of the work, from the database materials preliminary characterization to the mathematical modeling of the EM field/matter interaction, up to the PSO algorithm design optimization. The capability of the layering approach lies in the frequency selective interaction between the different materials and the EM field. Such concept is well explained by a finite element method (FEM) simulation where CEMA13 (*α* = 0.96) has been deeply analyzed by studying the multilayer structure inserted in a 50 Ω coaxial airline of the same type used to measure the dielectric properties of the database materials. The FEM analysis shows how the EM field propagates through the several layers at two different frequencies, 2.5 and 14 GHz, where the reflection coefficient, respectively, results maximum and minimum. Commercial code COMSOL Multiphysics has been used for the FEM analysis [20, 24]. In **Figure 16**, the mesh of the multilayer within the coaxial waveguide is depicted: the blue part on the left is the empty section of the airline, while the other is the part filled with ten layers of nanocomposite materials. The airline is simulated using a perfect electric conductor for inner, outer, and back surfaces. The Port1 is placed at the beginning of the coaxial airline on the left side of the figure. The maximum element size of the mesh is 1/10 of the minimum EM wavelength (*λ *= 3 × 10^{8}/*f*_{max} ~ 1.6 cm), while the minimum element size of the mesh is in the order of 10^{−7} m: these dimensions enable an optimal growth of the mesh and guarantee the needed accuracy in the EM analysis. In the coaxial airline, Port 1 is used to compute the scattering parameter S_{11}, related to the reflection coefficient. In the numerical simulation, the power set at the port is 3 dBm (2 mW) as in the real measurement. All the parameters adopted to run the FEM simulation are chosen in such a way to reproduce the experimental conditions of the microwave characterization. In particular, the real and imaginary part of the complex electrical permittivity measured over the 2–18 GHz frequency band to create the database of nanocomposite materials have been adopted: such values are interpolated by COMSOL code in order to get out a functional relationship between dielectric properties and frequency. The EM interfaces of the code cover the modeling of EM fields and waves in the frequency domain, formulating and solving the differential form of Maxwell’s equations together with the initial and boundary conditions.

In **Figures 17** and **18**, the electric field (V/m) is reported at 2.5 and 14 GHz respectively. In **Figures 19** and **20**, the current density (A/m^{2}) arrow lines and magnetic field (A/m) circular lines for the ten layers of CEMA13 are shown (arrow lines are used to show the region where the highest EM losses occur along the structure). In **Figures 21** and **22**, the power loss density (W/m^{3}) at 2.5 and 14 GHz, respectively, is shown. At 14 GHz, the multilayer design provides the impedance matching with free space, thus resulting in a higher level of EM absorption, as compared to the values of the electric field at 2.5 GHz. Alongside, the significant current density at 14 GHz is well visible in the first and second layers, whereas at 2.5 GHz the impedance mismatch causes a great reflection of the EM field at the first layer, thus determining a lower power loss within the deep bulk. In fact, the power loss density at 2.5 GHz is quite lower compared to the value obtained at 14 GHz, where geometrically power losses are mainly confined within the 5 first layers. In other words, at 2.5 GHz, the EM field propagates through all the layers due to the impedance mismatch end. Due to the higher value of the reflection coefficient, the majority of the power is reflected back at the first air-multilayer interface. At 14 GHz, the multilayer is impedance matched, the reflection coefficient is quite lower and the absorbed power dramatically increases. In **Figure 23**, a comparison between the RC Target, RC simulated with mathematical model and RC simulated by FEM analysis is shown. The discrepancies with FEM simulation are due to the mesh and the approximation of the EM field solution, which is more difficult at high frequencies.

## 4. Conclusions

In this chapter, an attempt to identify a novel approach to design and optimize EM reference materials for metrological applications was introduced. The results highlight the intriguing potentialities of the proposed strategy, since even hard microwave reflection target profiles are successfully addressed by the numerical design optimization technique developed. It is clear that several upgrades can be introduced in order to better refine the process. The above mentioned examples highlight some root of inaccuracy, especially when quite sharp edges occur along the target profile. Of course, the harder it is to follow a given profile, the more complex the optimized structure will become out in terms of layers number and thinness. Although the intriguing capability of the PSO algorithm to find solutions fitting such challenging targets, it has to be outlined that the corresponding CEMA solutions are composed by at least four layers (almost always six or more), with total thickness over 4 cm, in the most of the situations. Furthermore, quite often the layers that fulfill the crucial EM absorbing role have thickness well below 1mm, thus pointing out that an eventual production process could represent a big task in this framework. Beyond possible PSO algorithm enhancements (convergence parameters, particles population, iterations), the effectiveness of the proposed strategy in terms of mimic capability would be significantly improved by enriching the materials database. The possibility to draw on a “quasi-continuous” spectrum of dielectric properties should allow the PSO algorithm to find solutions for reproducing any RC profile even more faithfully. On the other hand, by proper constraints in terms of layers number and thickness, the increased availability of materials should make the algorithm able to identify multilayered combinations easy to be practically achieved. In this respect, the employment of composites reinforced with nanoparticles sounds as the right way forward. With respect to the conventional materials, in fact, the family of nano-filled composites allows the unique opportunity to finely adjust the EM absorption property just by tuning the weight percentage of the nanofiller within the matrix. At this purpose, the lower the incremental step in weight percentage, the greater the possibility of fine tuning: thus, the greater the database population, the better the possibility to select appropriate materials for mimic purposes. The research development will thus be addressed to enrich the database population, in order to obtain even more precise and feasible solutions for the widest variety of electromagnetic requirements.