The Minkowski loops as shown in Fig. 1 were chosen as the unit cell of fractal FSSs, named X1(Fig. 1(a)) and X2 (Fig. 1(b)). The aluminum were printed on one side of 0.05-(mm)-thickness polyethylene substrate (relative dielectric constant ε_r=2.25), with dimensions as follows: (a) L₁=8 mm, G₁=3 mm, D₁= D₂=2 mm; (b) L₂=18 mm, G₂= 6 mm, D₃=0.5 mm, D₄= D₅= D₆=2 mm. Particularly, both the X1 and X2 loops had the same periodic dimension P=20 mm, and the same line width W=0.2 mm. In theory, the real fractal FSS is generated after infinite times of iterations; however, the fractal FSS with finite iterative times can meet the practical demands. The constructing procedure for single-layer fractal FSS (X2) originated from the previous one (X1). The step of constructing X2 in the process was to copy four self-similar loops to the four corners of X1, respectively. Each iteration involved transformations of scaling and translating the previous iteration. The resulting points of the geometry could be expressed as follows^{[ 10]}:

Previous points:

Transformational formula:

Resulting points:

Fig. 1

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	Fig. 1 Schematic diagrams of proposed fractal FSS

Where p _i+1, the resulting set of points for the i+1 iteration was composed of the union of the previous iteration points p _i and the transformed points, T₁through T₄.

The laser etching technique was proposed to fabricate the real fractal periodic FSS samples (X1 and X2) due to its advantages of high precision. Meanwhile, the flaky metal magnetic powders were chosen as absorbents and the hydrogenation acrylonitrile-butadiene rubbles (HNBR) as aggloment. After the procedures of blending, roll mixing and vulcanizing, two traditional MAM samples named MA and JPN were prepared with the thicknesses of 1.2 mm and 0.5 mm, respectively. Both the FSS and the MAM samples have the same dimensions of 400 mm×400 mm.

As shown in Fig. 2, after the periodic FSS layers X1 and X2 being pasted: (1) on the surface; (2) in the middle; (3) at the bottom of the two MAM layers MA and JPN, respectively, MMA samples with different kinds of arrangements were fabricated. The prepared plates were properly used in certain arrangements illustrated in Table 1. In order to find out the effect of FSSs on the absorbing properties of microwave absorbers in L and S frequency bands, the reflectivity of samples were measured using an 8722ES network analyzer within the swept frequency range.

Fig. 2

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	Fig. 2 Structure of MMA samples with FSSs located at different positions

Table 1

Table 1

Table 1 Arrangements of the MMA samples Samples Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Thickness/mm S1 Metal MA — — — 1.2 S2 Metal JPN — — — 0.5 S3 Metal MA JPN — — 1.7 S4 Metal JPN MA — — 1.7 S5 Metal JPN MA X1 — 1.75 S6 Metal JPN MA X2 — 1.75 S7 Metal JPN MA X1 X2 1.8 S8 Metal JPN X1 X2 MA 1.8 S9 Metal X1 JPN X2 MA 1.8 S10 Metal JPN X1 MA X2 1.8 S11 Metal X1 JPN MA X2 1.8

Table 1 Arrangements of the MMA samples

The measured relative permittivity ε and permeability μ of the flaky metal magnetic powders were presented in Fig. 3. Based on these materials, the fabricated MAM layers of MA and JPN could exhibit different absorbing properties, with reflectivity results as shown in Fig. 4. The single MAM layer S₁has an absorbing peak value of -29.17 dB at 3.87 GHz, however, the reflectivity value at 1 GHz is only -1.36 dB. For the case of sample S₂, though the reflectivity value is -3.29 dB at 1 GHz, the peak value is only -3.79 dB at 1.26 GHz. Clearly, neither S₁nor S₂ is good enough for the demands at low frequency bands. When S₁ and S₂ were combined to produce the double-layer-composite sample S₃, much of the incident microwave within about 2-4 GHz was reflected. Therefore, S₃ behaved bad performances at low frequencies, in spite of the increase for the peak value and reflectivity value at 1 GHz. After switching the places of S₁ and S₂, the reflectivity of the sample S₄ is nearly all under -3 dB within about 1.1-4 GHz and it presents much better absorbing performances. The absorbing peak value for S₄ is -8.98 dB around 1.84 GHz. However, the reflectivity value of S₄ is only -0.68 dB at 1 GHz, and it is possible to introduce FSSs into this original multilayer composite for developing its absorbing properties at low frequencies.

Fig. 3

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	Fig. 3 Relative electromagnetic parameters ε, μ of (a) MA and (b) JPN

Fig. 4

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	Fig. 4 Reflectivity of MAMs: MA and JPN

Figure 5 demonstrates the effects of FSSs on the reflectivity of MMAs at low frequencies. For the cases of proposing single FSS layer, the peak value of sample S₅ is -9.81 dB, which is much stronger than that of sample S₆(-8.6 dB). This may be caused by the fact that the schematic diagram of X2 is much more complicated than that of X1 and this means that the aluminum-metal overlay area for X2 is much wider than that for X1. Therefore, when X2 is placed on the surface, much more incident microwave could be reflected compared with the case of X1, leading to weaker absorbing performances. However, the samples S₅ and S₆almost have the same reflectivity values at 1 GHz: -2.64 and -2.93 dB, respectively, neither of which could satisfy our demands of application. Based on this, the sample S₇with X1 and X2 both introduced into the original multilayer composite S₄ was investigated. Though the peak value of S₇ dropped to -8.29 dB, its reflectivity curve indicated that the reflectivity value at 1 GHz is -4.28 dB, decreased by a large amount compared with those of samples S₁-S₆, which is mainly due to the stronger electromagnetic resonance of the introduced X1 and X2 layers^{[ 10, 11]}. As a consequence, proposing double FSS layers provides the possibilities of enhancing the absorption properties for MMAs.

Fig. 5

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	Fig. 5 Reflectivity of MMAs with and without FSS layers

Figure 6 exhibits the reflectivity of the samples S₈-S₁₁containing double FSSs embedded at different positions at low frequencies. The double FSS layers could be arranged on the surface, in the middle and at the bottom of the two MAM layers, respectively, as shown in Fig. 2. The different arrangements have been illustrated in Table 1. Definitely, after introducing the double FSS layers, the reflectivities of S₈-S₁₁ are under -3 dB within the full frequency band of 1-4 GHz which mainly originated from composite effects of the MAM and the introduced double FSS layers. It means that the multi-bands resonance properties of the introduced double FSS layers could enhance the absorbing properties of the composite MAM. Based on the results of S₇ in Fig. 6, the connected double FSS layers X1 and X2 of S₈ are removed from the top to the bottom and the peak values is decreased to -7.48 dB and the reflectivity value at 1 GHz is increased to -3.12 dB, which indicates the trends of bad performances on the absorbing properties at low frequencies by proposing connected double FSS layers. The introduced FSS layers X1 and X2 were arranged separated from each other by spacing traditional microwave absorbers in MMAs, producing the samples of S₉-S₁₁. Though both S₉and S₁₀ have almost the same peak value, the reflectivity value at 1 GHz of S₁₀ is -4.44 dB, larger than that of S₉of -3.33 dB, which is mainly due to the stronger electromagnetic coupling resonance effect of the introduced X1 and X2 layers^{[ 11]}. Then the reflectivity value of S₁₁ indicate that arranging the FSS layers X2 and X1 on the surface and at the surface places, respectively, the reflectivity value at 1 GHz could be still kept under -3 dB and moreover the peak value is enhanced to -9.35 dB. Therefore, owing to the strong electromagnetic coupling resonance effect of the FSS, introducing double FSS layers in a proper arrangement is able to provide a practicable way to strengthen the absorbing properties effectively within low frequency bands.

Fig. 6

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	Fig. 6 Reflectivity of MMAs containing double FSSs embedded at different positions

In summary, we designed ultra-thin composite absorbers consisting of different arrangements of MAM rubber plates and FSS in low frequency. The single and double Minkowski metal loop FSS layers were designed and pasted with the MAM rubber plates in different arrangements to produce MMA samples. The reflectivity results measured with NRL-arch testing systems presented that the introducing fractal FSS layers could improve the absorbing properties of MMAs effectively at low frequencies. Moreover, proposing two FSS layers could exhibit better absorption performances compared with the case of single FSS layer. At the thickness of only 1.8 mm, the MMA sample with X1 and X2 placed at the bottom and on the surface, respectively, is able to gain the peak value of -9.35 dB and the reflectivity value at 1 GHz of -3.49 dB. Thus, the FSS layers could supply a potential new way to satisfy the urgent demands of developing absorbing properties at low frequency bands.