† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant No. 51302312), the Fund for Discipline Construction of Beijing University of Chemical Technology (Grant No. XK1702), and the Fundamental Research Funds for the Central Universities, China (Grant No. Jd1601).
Despite widespread use for extending absorption bandwidth, the coexistence and coupling mechanism of multiple resonance is not well understood. We propose two models to describe the multi-resonant behavior of a broadband metamaterial absorber with geometrical-array substrate (GAS). The multi-resonance coupling of GAS is well described by logarithmic law. The interaction between metasurface and GAS can further broaden the absorption bandwidth by generating a new resonance which coexists with original resonances in substrate. The proposed models can thoroughly describe this multiple-resonance behavior, highlighting guidelines for designing broadband absorbers.
Dielectric and magnetic materials of electromagnetic response capability have drawn significant attention in the aerospace industry due to the great applications in stealth technology[1–5] and energy usage.[6–9] In the GHz frequency range, traditional homogeneous absorbers[10–12] mainly rely on the establishment of resonance absorption, which is easy to achieve high absorption at sub-wavelength thickness. However, the absorption is efficient only in a narrow frequency band due to the thickness dependent resonance. With the progresses made in multiband or broadband communication technology, broadband absorption is highly desired. Many wideband absorbers with special structures are reported, including porous,[13] multilayer,[14] and pyramidal structures.[15] Unfortunately, these wideband absorbers were achieved at the sacrifice of the thickness. At a given thickness, metamaterial absorbers enable offering absorption peaks in either a lower or a higher frequency range to extend the absorption band. For instance, Wang et al.[16] fabricated a metamaterial absorber with a thickness of 1.60 mm and an over 90% absorption from 8.85 GHz to 14.17 GHz. Sui et al.[17] proposed a topology design of a broadband frequency selective surface absorber whose thickness is 3.60 mm for an effective frequency band from 6.68 GHz to 26.08 GHz. He et al.[18] realized a tunable polarization-independent wideband absorber owning a thickness of 4.15 mm for both C and X bands. Consequently, the design of metamaterial absorbers is considered to be a possible strategy for obtaining broadband absorbing materials.[19–26] Nevertheless, the design of metamaterial absorbers mainly focuses on periodically patterned resonators with the spacers usually constructed by a uniform dielectric sheet or air,[27–31] resulting in a thick multilayer structure corresponding to multiple resonance, which is necessary for achieving the broadband absorbers.[32,33] It is critical to increase resonance numbers for extending the absorption band at a limited thickness.[34–37] In fact, the geometrical design of traditional absorption material is also able to extend the absorption band at a limited thickness.[38,39] Therefore, a combination of single-layer metasurface with geometrical-array substrate (GAS) would efficiently increase the absorption band within a small thickness.
To understand the coexistence and coupling mechanism of multiple resonances in a broadband metamaterial absorber with the geometrical-array substrate, in this work, we propose the logarithmic law and equivalent circuit model to explain the multi-resonance coupling and coexistence in the broadband metamaterial absorber with the geometrical-array substrate. The consistence between the theoretical and simulated results suggests good comprehension of the strategy for designing broadband microwave absorption metamaterials.
The simulations are all carried out in the microwave simulation software CST studio suite 2014. As shown in Fig.
The absorption band (< −10 dB) of the GAS covers 7.76 GHz–30 GHz, which is much wider than those of the 3-mm and 6-mm plates (Fig.
Extending the absorption band by multiple λ/4 resonances in a patterned microwave absorber is confirmed experimentally.[38,39] The GAS can be equivalent to a composite material comprised of parts A and B (Fig.
In order to clarify the influence of structure scattering, the typical Floquet port and unit cell boundary are used to calculate the reflectivity without diffraction beam. With structure size and material parameters fixed, the calculated reflectivities with (including absorption) and without diffraction beam (including absorption and scattering) are compared in Fig.
To enhance the absorption of the GAS at low frequency, a square copper ring is assembled on the top of each geometrical array. The thickness of the metasurface is as thin as 0.1 mm. The side length l and width d of each of copper ring are set to be l = 8 mm and d = 0.5 mm, respectively. The minimum frequency of reflection loss ⩽ −10 dB for the GAS is 7.76 GHz (Fig.
The α peak is dominated by side length l and width d. As shown in Fig.
Figures
According to the Taylor formula, equation (12) can be simplified into the following form
Figure
In this work, a broadband metamaterial absorber with geometrical substrate is proposed. The GAS broadens the absorption band by coupling multiple λ/4 resonances, and the area ratio dependence of resonance frequency for GAS is well described by logarithmic law. The interaction between metasurface and GAS generates a new resonance coexisting with original resonances in the substrate, resulting in the further increase of absorption bandwidth. According to the equivalent resonance circuit, we develop a quantitative model that completely describes the dependence of this resonance on the surface metallic cell size. This work, therefore, is helpful for understanding and utilizing multiple resonances in broadband absorption metamaterials.
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