1. Introduction

Microwave absorbers have important applications in many fields, such as radar stealth, energy collection, communication, and sensing. However, conventional microwave absorbers which typically rely on natural absorbing materials have the disadvantages of narrow bandwidth, large size, and unreconfigurable, which make them inadequate in applications nowadays. Hence, it is crucial to explore new methodologies to design improved microwave absorbers. Utilizing metasurfaces stands out as a promising approach in this pursuit.

In recent years, research on metasurfaces has developed rapidly due to their excellent performance. Metasurfaces are composed of periodic subwavelength metal or dielectric structures that can resonate and couple with incident electromagnetic waves, exhibiting various functions such as wavefront shaping [1,2], polarization conversion [3,4], energy concentration [5,6], and radiation control [7]. Based on different features, metasurface devices can be used as superlenses [8,9], beam shapers [10], filters [11], holographic imaging plates [12], absorbers [13–15], etc. Among them, metasurface microwave absorbers have unique superiority compared to conventional microwave absorbers. Metasurface absorbers can achieve the characteristics of broadband absorption, small size, and reconfigurable. Early in 2008, Landy et al. practically produced the first metasurface microwave absorber [16], which achieved an absorption of 88% at 11.5 GHz. The most prominent advantage of this absorber is that its thickness is only 1/35 of the relevant wavelength λ. Afterward, lots of metasurface microwave absorbers designed on different methods have been reported. For example, Yao et al. designed a metasurface microwave absorber based on a folded line structure [17], which can increase the effective electrical length of the resonator, allowing the device to operate at a low frequency of 1.92 GHz. In addition, the appropriate use of lumped elements in metasurface absorbers can obtain better performance and also reduce the unit size [18,19]. Cheng et al. used capacitors and resistors in a metasurface microwave absorber and got an absorption over 90% on a bandwidth of 1.5 GHz, with a thickness of approximately 1/10λ [20]. To design a multi-band absorber, a study proposed putting three different sizes of resonators on a plane and thus achieved a three-band absorber [21]. Also, placing different sizes of resonators in different layers can realize multi-band absorption [22]. Patten's design is important for absorbers, and one of the popular designs is the fractal structure, such as Pythagorean-tree fractals [23], hexagonal nanoring fractal structures [24], and four-fold symmetric fractal cross structures [25]. The unique self-similarity of fractal structures results in high symmetry and multi-scale characteristics, bringing polarization-insensitivity, tunability, and expandable operating frequency for absorbers. For sensing applications, researchers combine metasurface absorbers with microfluidic channels and finally obtain an ethanol chemical sensor [26]. Besides, the design of tunable and multifunctional absorbers has received much concern. Some researchers achieve multifunctionality within the limited space of metamaterial absorbers by utilizing the photoelectric effect [27] or thermal phase transition characteristics [28] of materials, as well as by designing a longitudinal structure such as stacked ferrite elements [29] or vertically arranged elliptic-ring metallic structures [30]. More interestingly, some researchers used unconventional materials in metasurface absorbers, giving absorbers with special properties. For example, metasurface absorbers that use water as resonator material can be simply folded [31], which makes them suitable for applications with curved shape requirements.

With the development of radar detection technologies, broadband microwave absorbers have shown their importance. However, although currently there are many design methods for metasurface absorbers, designing an efficient broadband microwave metasurface absorber is still a challenge. In recent years, many broadband absorbers have been proposed. A typical structure is the pyramid structure proposed by Ding et al. [32]. This multilayer design achieved a broadband absorption range from 7.8 GHz to 14.7 GHz. And Wang et al. numerically presented a scale-invariance logarithmic spiral metasurface absorber [33], with an absorption of over 95% in the frequency range from 6 GHz to 37 GHz. However, their large thickness or complex structures will bring higher fabricated difficulty. Besides, some researchers combined metasurfaces with radar-absorbing materials [34] or classical p-i-n junction based on amorphous silicon [35] to increase the absorption bandwidth, but these absorbers mainly rely on the intrinsic absorption of materials instead of a metamaterial-dominant response, which makes it difficult to promote to other frequencies. Moreover, some researchers add lumped elements [36,37] or other electronic components [38,39] to manufacture absorbers, but the use of these components may make the absorbers less robustness when working in complex and harsh environments. In summary, although the previously mentioned absorbers can achieve broadband absorption, their complex structures, dependence on natural materials, or use of electronic components hinder practical application and widespread use. Therefore, it is necessary to propose a broadband microwave metasurface absorber with a simple structure, natural absorbing materials independence, robustness, and well performance.

In this paper, we have numerically demonstrated a high-absorption broadband microwave metasurface absorber based on a multi-scale fractal pattern design. This device is composed of a single-layer metal-dielectric-metal (MIN) structure, eliminating the need for natural absorbing materials and electronic components. We explore the generation of localized surface plasmon resonance (LSPR) and Salisbury-Screen-type mechanisms within the device and methods to control them. By successfully integrating the LSPR and Salisbury-Screen-type mechanism absorption bands, we have achieved a broadband absorber that exceeds 80% absorption in the range of 11.5 GHz to 27.1 GHz, with peak absorption levels reaching close to 100%. Notably, this absorber exhibits a fractional bandwidth (FBW) of 95.3% and a full width at half maximum (FWHM) bandwidth spanning over one optical octave. Furthermore, owing to the structure's fourfold symmetry, the absorber is polarization-insensitive. Additionally, we've explored its insensitivity to incidence angles under TE/TM waves. This study presents a viable method for designing a straightforward yet efficient broadband microwave metasurface absorber.

2. Configuration, equivalent circuit and principle

Our device adopts an MIM structure design, which includes the patterned top layer, the dielectric intermediate layer, and the total reflection bottom layer, as shown in Fig. 1(a). The period of this absorber is P. Figure 1(b) shows the x-z view of the device. We use indium tin oxide (ITO) for the top layer and bottom layer, with thicknesses of h and g (g = 0.3 mm), respectively. ITO has a frequency-independent conductivity σ_ITO, and this conductivity is adjustable [40]. FR406 is used as a dielectric layer with a relative dielectric constant of ε_r= 3.92(1 + 0.0172i) and thickness of d. The top layer consists of the four-order triangular fractal resonator, as shown in Fig. 1(c). The basic pattern of the n^th (n = 1,2,3,4) order is equilateral triangles with a side length of L_n, and then obtains fourfold symmetry through symmetry operations. An equilateral triangle is a simple pattern that convenient for pattern combinations. The 1^st and 2^nd order patterns are put along the x/y axis, with an angle of 45° between the 3^rd and 4^th order patterns. Besides, the distance from the outer angle of n^th order equilateral triangle to the x/y axis is defined as pattern position W_n, as shown in Fig. 1(c). The multi-scale fractal structure can broaden the absorption bandwidth and the fourfold symmetry can provide polarization insensitivity. Figure 1(d) shows the equivalent circuit of the absorber, which is convenient for qualitative analysis. The equivalent resistance, capacitance, and inductance of the n^th order pattern is R_n, C_n, and L_n, thereby the equivalent impedance is ${Z_n} = {R_n} + j({\omega {L_n} - 1/\omega {C_n}} )$. The total equivalent impedance of the dielectric intermediate layer and bottom layer is Z_d, which is influenced by the thickness of the dielectric layer and incident angle. Each Z_n is connected in parallel with Z_d and form an oscillation circuit, the oscillation frequency ${f_n} = 1/(2\pi \sqrt {{L_{nt}}{C_{nt}}} $), where L_nt and C_nt represents the total inductance and capacitance of the n^th oscillation circuit, respectively. The combination of different order patterns is reflected as a parallel relationship in the equivalent circuit. But at the same time, this combination will generate parasitic capacitance C_ij (i,j = 1,2,3,4, i≠j) between different order patterns, which will make the oscillation frequency ${f_n}$ have a shift. The total impedance of the entire equivalent circuit is Z, and according to transmission line theory, the minimum reflectivity can be obtained when Z is equal to the free space impedance Z₀.

 

Fig. 1. The schematic of the absorber in (a) stereoscopic view, (b) side view, and (c) overview. (d) The equivalent circuit of the absorber.

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This device will achieve broadband absorption by utilizing two absorption mechanisms. One of them is the LSPR absorption. Under the incidence of suitable electromagnetic waves, it will occur oscillating current in the multi-scale fractal resonators due to LSPR, which means an electric resonance. At the same time, the bottom layer in the MIM will induce a parallel reverse oscillating current if the distance between the top layer and the bottom layer is small enough. More importantly, the magnetic fields generated by these two oscillating currents have the same directions in the dielectric layer, which means the formation of magnetic resonance. The combination of electric resonance and magnetic resonance will together result in an absorption band based on LSPR. Another mechanism is the Salisbury-Screen-type absorption based on multi-interference. Similar to the Salisbury-Screen, the MIM structure has two reflecting surfaces and it can lead to an interference-cancelling-based absorption band when matching the phase difference requirement. However, there is a difference to the Salisbury-Screen that the top layer of our device has a multi-scale fractal structure, which will make the reflected light occur an additional phase change and let the absorption frequency shift. However, the absorption frequency also can be controlled by the thickness of the dielectric layer.

3. Results and discussion

3.1 From single-scale to multi-scale

We use the numerical simulation software COMSOL for studying our device with different parameters. The specific values of reflection coefficient S₁₁ and transmission coefficient S₂₁ can be obtained after simulation, then we can get the reflectivity $R(\omega )= {|{{S_{11}}} |^2}$ and transmittance $T(\omega )= {|{{S_{21}}} |^2}$. Due to the thickness of the bottom layer being much larger than the relevant skin depth, the transmission $T(\omega )$ is zero. So, the absorption of this absorber can be written as $A(\omega )= 1 - R(\omega )= 1 - \; {|{{S_{11}}} |^2}$.

Firstly, we study the influences of different parameters on one-order fractal pattern structure under normal incidence with a y-polarization wave (all results in this paper are obtained under this incident wave, unless otherwise stated). Its diagram and equivalent circuit are shown in Fig. 2(a). With other parameters unchanged, we simulate the absorption spectra of different side lengths L, as shown in Fig. 2(b). As L increases, the absorption peak frequency shifts to a lower frequency, which is because a larger size pattern will make the LSPR absorption wavelength longer. The electric and magnetic field distribution at the peak frequency with L = 7 mm shown in Fig. 2(c) reveals that LSPR makes most of the electric field tightly localized at the edge of the pattern structure. Due to the MIM structure design, it occurs opposite dipole oscillations in the top layer and bottom layer, which makes the magnetic field localized in the dielectric layer. Based on the absorption spectra, we can obtain the corresponding relationship between the parameter L and the peak frequency, as plotted in Fig. 2(d). It shows a linear relationship between L and peak frequency. But in fact, the relationship between them should be non-linear. This approximate linear relationship only can be applied in this small range that we study. Figure 2(e) illustrates the absorption spectra of different thicknesses h of the top layer. It can be observed that the peak frequency will redshift gradually as h increases. This movement can be explained through the equivalent circuit, where an increase in h leads to an increase in inductance L_L (the subscript _L represents the side length of the pattern), and thereby the oscillation frequency will be lower. Besides, we can find that the absorption becomes higher as thicknesses h decrease, which is mainly due to the patterns with various thicknesses will have different resistances. However, the influence of resistance on absorption should be analyzed through the normalized impedance. When resonance occurs, the imaginary part of the normalized impedance is zero, and thus it has a reflection coefficient $r = ({R_{in}} - 1)/({R_{in}} + 1)$, where R_in represents the real part of the normalized impedance of the device, which is determined by the resistances of device. This expression indicates that it will obtain higher reflectivity if the difference between R_in and 1 is larger. Figure 2(e) also plots the real part of the normalized impedance (R_in) under various thicknesses. It shows a larger difference between R_in and 1 as thicknesses h increase, which means a lower absorption will be obtained. Furthermore, the conductivity σ_ITO of ITO also influences the resistances of the device and changes the absorption. As shown in Fig. 2(f), the absorption will be higher as the σ_ITO decreases.

 

Fig. 2. (a) Schematic diagram of single-scale pattern and its equivalent circuit. (b) Absorption spectra of different side lengths L (with d = 1.2 mm, h = 1.1 mm, σ_ITO= 5e4 S/m, P = 31 mm, and W = 7 mm). (c) The electric and magnetic fields distribution with L = 7 mm. (d) The peak frequency as the function of L. (e) Absorption spectra of different h (with L = 7 mm, d = 1.2 mm, P = 31 mm, σ_ITO= 5e4 S/m, and W = 10 mm). (f) Absorption spectra of different σ_ITO (with L = 7 mm, d = 1.2 mm, h = 1.2 mm, P = 31 mm, and W = 10 mm).

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After obtaining the absorption response of different parameters under a one-order fractal resonator, we combine different sizes of resonators to form a complete absorber, and then adjust the parameters based on the results obtained above to achieve broadband LSPR absorption. But generally, the planar multi-scale resonator structure will be limited by the balance between absorption and bandwidth, which means that only several sizes of resonators can be combined while ensuring high absorption. Figure 3(a) illustrates the absorption spectra of different order patterns. It can be observed that after combining, the absorption peak frequencies corresponding to the previous order will have shifted, indicating that the resonators with different sizes do not completely operate independently. There is energy coupling between them, which also has been implied by the parasitic capacitance C_ij mentioned in section two. But overall, with different appropriate sizes of resonators combined, the LSPR absorption bandwidth becomes broader. Observing the absorption spectrum of a four-order fractal pattern, the LSPR absorption band ranges from 11.8 GHz to 18 GHz, with an absorption over 80%. And its average absorption is 94.5%. The electric and magnetic field distribution at peak frequencies a-d in the LSPR absorption band is plotted in Fig. 3(b), showing that it is not simply each size of the pattern corresponding to one absorption peak. Especially at 13.8 GHz, there are three sizes of patterns that have strong resonance simultaneously, which also indicates that different sizes of patterns will interact with each other.

 

Fig. 3. (a) Absorption spectra of different order superimposed patterns (with L₁= 3.95 mm, L₂= 5.52 mm, L₃= 5.75 mm, L₄= 7.01 mm, d = 1.2 mm, h = 1.1 mm, P = 31 mm, σ_ITO= 1e4 S/m, W₁= 15 mm, W₂= 9.5 mm, W₃= 9.5 mm, W₄= 14 mm). (b) The Electric and magnetic fields at peak frequency a-f (as marked in (a)). (c)The calculated absorption spectra of different d based on the Salisbury-Screen-type mechanism. (c) The simulated absorption spectra of different d.

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Notably, there is another absorption band in the spectrum of four-order fractal pattern, which ranges from 23.4 GHz to 30 GHz. As shown in Fig. 3(b), the electric and magnetic field distributions at the frequency of 24.4 GHz and 26.8 GHz illustrate diffraction pattern type distributions. With further analyzation, it indicates that this absorption band may be related to the “λ/4 interference”. According to the thickness of the dielectric layer d = 1.2 mm and its refractive index n ≈ 1.98, we can get the “λ/4 interference” frequency of 31.6 GHz (interference wavelength λ= n*d*4 = 9.504 mm), which is located near that absorption band. Although there is a difference between the “λ/4 interference” frequency and that absorption band, it is probably due to the phase adjustment capability of the metasurface top layer, which makes the “λ/4 interference” frequency a shift. In fact, a previous work has reported that utilize the phase adjustment capability of the metasurface and “λ/4 interference” to realize broadband absorption Salisbury Screen [41], which may be similar to this phenomenon. Therefore, we also assume that this absorption band is generated by a mechanism that similar to the Salisbury Screen. According to the mechanism of the Salisbury Screen, the absorption band is strongly related to the thickness d of the dielectric intermediate layer. It can be predicted that increasing the thickness d will make the absorption band move to a lower frequency. To prove our assumption, we firstly remove the bottom layer and obtain the reflection coefficient and transmission coefficient when incident from free space and dielectric layer, respectively. Then through theoretical calculations based on multi-interference theory, the absorption spectra with various of d can be obtained, as shown in Fig. 3(c). In addition, we also simulate the spectra of different d for the complete absorber, as shown in Fig. 3(d). Comparing Fig. 3(c) and (d), there are many differences in details. This is mainly because the spectra of Fig. 3(c) are calculated based on interference theory and do not consider the electromagnetic resonance in the MIM structure. However, on the whole, both the calculated and simulated spectra show a redshift as the thickness d increases and the positions of absorption bands are similar. It indicates that the assumed Salisbury-Screen-type mechanism does indeed exist and it leads to a multi-interference absorption band.

3.2 Broadband absorption based on dual-mechanism

The coexistence of LSPR and multi-interference absorption bands is useful and can be used as a dual-band absorber based on the results mentioned above. But there is a disadvantage that their bandwidths are both narrow. Our original intention is to obtain a large bandwidth absorber, and therefore, we propose to integrate these two absorption bands into a single absorption band with a large bandwidth. We can utilize the regulation that the position of the multi-interference absorption band can be controlled by thickness d and the position of the LSPR absorption band can be controlled by the pattern size L to realize our proposal.

Through optimizing, we obtain a broadband absorption spectrum, with L₁= 3.7 mm, L₂= 5 mm, L₃= 4.6 mm, L₄= 6.9 mm, and d = 1.6 mm, as shown in Fig. 4(a). This spectrum illustrates that an absorption of over 80% is achieved in the range of 11.5 GHz to 27.1 GHz (including the Ku and K bands), with an average absorption of about 90%. In addition, it obtains the highest absorption of nearly 100% at 12.9 GHz (A), 21.4 GHz (B), and 22.4 GHz (C). The total thickness of the absorber is 2.95 mm, which is about 0.113λ_L (λ_L is the wavelength that corresponds to the lowest frequency 11.5 GHz with an absorption higher than 80%), indicating that our device has a sufficiently thin thickness. An important characteristic of a good absorber is the bandwidth fraction (FBW), which is defined as the ratio of FWHM bandwidth $\Delta f$ to the center frequency ${f_c}$. For this absorber, half of the maximum absorption is 0.5, thus FWHM band ranges from 11.1 GHz to 31.3 GHz, with $\Delta f$=20 GHz and ${f_c}$=21.2 GHz. Therefore, the FBW is calculated to be 95.3%. Moreover, the octave number of FWHM bandwidth is $\textrm{lo}{\textrm{g}_2}({f_{max}}/{f_{min}})$=1.49, which means it exceeds one optical octave. Besides, the normalized impedance of this absorber can be calculated by the transmission and reflection coefficients:

 

Fig. 4. (a) Broadband absorption spectra with L₁= 3.7 mm, L₂= 5.0 mm, L₃= 4.6 mm, L₄= 6.9 mm, d = 1.6 mm, h = 1.05 mm, P = 30 mm, σ_ITO= 1e4 S/m, W₁= 12.5 mm, W₂= 8.5 mm, W₃= 7 mm, W₄= 13.3 mm. (b) The normalized impedance of the broadband absorber. The intersections of the dashed lines represent the real part of the normalized impedance is 1 or the imaginary part is 0. (c) The magnetic field distributions at the frequency of 18 GHz, 20 GHz, and 22 GHz.

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To minimize reflectivity, it is necessary to make the equivalent impedance Z of the device equal to the free space impedance Z₀, which means the normalized impedance should be Z/Z₀= 1 + 0i. The intersections of the dashed lines in Fig. 4(b) are the positions where the real part of the normalized impedance is 1 or the imaginary part is 0. Due to these perfect impedance matching, it gets an absorption that is close to 1 at the corresponding frequencies A, B, and C. We also present the magnetic field distributions at different frequencies, as shown in Fig. 4(c). It can help us to distinguish between LSPR and multi-interference absorption bands in the spectrum. The magnetic field at 18 GHz is mainly distributed below the pattern structure, which is the characteristic of LSPR. The magnetic field at 22 GHz exhibits a diffraction-like distribution, which means the multi-interference absorption. Whereas, the magnetic field at 20 GHz has both characteristics of LSPR and multi-interference, indicating that it is the position where the two absorption bands integrate. The results demonstrated above prove that the integration of two absorption bands generated by different mechanisms is feasible, and it can realize broadband absorption ultimately.

In addition to bandwidth, another characteristic of a good absorber is the sensitivity to polarization angle and incident angle. Figure 5(a) shows the absorption spectra at different polarization angles under normal incidence. The absorption is observed to remain consistent across various polarization angles, which is attributed to the fourfold symmetry of the top layer. However, although this device is not sensitive to polarization angles, its electric field distribution is completely different under different polarization angles. Figure 5(b) plots the electric field at 12.8 GHz under different polarization angles, showing that the electric fields tend to distribute in the direction of corresponding polarization angles. Figures 5(c) and (d) illustrate the absorption under different incident angles for TE and TM waves, respectively. For TE waves, when the incidence angle changes from 0° to 60°, most of the frequencies can maintain an absorption of 80% of that at normal incidence. However, the absorption in some frequencies will decrease faster as increasing incidence angle. As for TM waves, the sensitivity to incident angles is generally higher than that of TE waves, which may be due to the z-component of the electric field of TM waves not participating well in resonance. At an incident angle of 40° for TM waves, most of the frequencies still have an absorption exceeding 60%. It is worth pointing out that whether it is TE waves or TM waves, the absorptions at 20 GHz both decrease more significantly as the incident angle increases. This is because the LSPR and multi-interference absorption bands are integrated at 20 GHz, and the LSPR and multi-interference absorption bands have different reactions as the incident angle changes, which makes them separate gradually. Overall, this broadband microwave absorber is polarization-insensitive and it can maintain good performance at a large incidence angle.

 

Fig. 5. (a) Broadband absorption spectra of different polarization angles. (b) The Electric fields at 12.8 GHz under different polarization angles. (c) Absorption at different incidence angles (0°–60°) for TE waves. (d) Absorption at different incidence angles (0°–60°) for TM waves.

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4. Conclusion

In summary, we propose a broadband, high absorption, polarization-insensitive metasurface microwave absorber, and numerically obtain an absorption bandwidth fraction of 95.3%. This absorber consists of a single-layer MIN structure, with a total thickness of 0.113λ_L. The top layer of the absorber has a four-order fractal pattern structure, which can form a wide LSPR absorption band by adjusting the sizes of fractal patterns. On the other hand, due to the thickness of the dielectric layer approach to “λ/4” and the phase control capability of the top metasurface layer, it produces a Salisbury-Screen-type mechanism and results in a multi-interference absorption band. Broadband absorption is realized by integrating the LSPR and multi-interference absorption bands through parameter adjustment. We achieve an absorption exceeding 80% over a bandwidth of 15.6 GHz (11.5 GHz-27.1 GHz) and a FWHM bandwidth of over one optical octave. In addition, since the fourfold symmetry of the structure, this device is polarization-insensitive. The investigation of the impact of incident angles shows that the sensitivity to incident angle for TE waves is lower than that of TM waves, but they both can maintain good absorption within the incident angle of 0° to 40°. The absorption bandwidth and absorptivity of this device are not good enough compared with many other reports, but more importantly, these results are obtained by two absorption mechanisms under a simple structure. A simple structure makes the absorber more reliable and robust under harsh environments, which is beneficial to practical application. Moreover, it does not rely on natural absorption materials and electronic components, which makes it conducive to its fabrication and widespread use.