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Abstract
Traditional broadband metamaterial absorbers are typically based on the combining effects of several fundamental mode responses resulted from different dimensions of metallic elements. We report here that simple single-sized cross-shaped resonator (placed on an insulator dielectric slab and an opaque metallic mirror) having the modes of fundamental response and surface lattice resonance can be used to achieve the broadband absorption performance. A continuous bandwidth of 1.97 THz with absorptivity bigger than 50% is realized at central frequency of 2.72 THz. The device relative absorption bandwidth (RAB) can be up to 72.43%, which is superior to traditional broadband absorption devices with multiple different-sized resonators (i.e., the complex structure designs). The device RAB can be further broadened by varying the frequencies of the fundamental mode response or surface lattice resonance using different geometrical parameters. In addition, the device performance can be tuned from broadband absorption to dual-band absorption with the decrease of the dielectric slat thickness.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Perfect light metamaterial absorbers (abbreviated as PLMAs) have received more and more attention in recent years for its excellent ability in aspects of near 100% absorption, ultra-thin dielectric slab thickness, and controllable resonance performance [1–3]. Despite these merits, the practicality and flexibility of the PLMAs are restricted by the present situations of narrow resonance bandwidth, narrow acceptance angle and even polarization sensitive. Many types of structure designs have been given to overcome these limitations encountered [4–10]. For example, polarization insensitive PLMAs were realized by employing some four-fold (or eight-fold) symmetric patterns [4–6]. Some of these high degree of symmetry patterns also show the ability to solve the issue of the narrow accepted angle [6–8]. In other words, the shortcomings of polarization sensitive and narrow acceptance angle can be simultaneously addressed using the highly symmetrical resonators.
However, it is quite difficult to extend the resonance bandwidth of PLMAs (or to obtain broadband absorption response) by only optimizing the structure designs because of the common feature of the single-band fundamental mode resonance absorption of the metallic resonator. The most direct and simplest way to obtain the broadband PLMAs is to integrate several different but similar narrow-band (or single-band) fundamental mode resonance frequencies, where each of frequency point corresponds to one metallic resonator [3], [11], [12]. With this simple design idea, the rest is how to arrange these different sizes of metallic resonators to achieve the broadband absorption. A large number of literature surveys found that there are two commonly used structure arrangement methods [13–32]. The first one is to periodically arrange several resonators with different-sized in the horizontal direction [13–22], while the second is to arrange these resonators in the direction of the vertical [23–32]. Based on these two construction strategies, during the past several years, we have witnessed the rapid and vigorous development of the broadband PLMAs.
Although the two methods can achieve the broadband absorption, they have to face some issues. Firstly, the horizontal arrangement way has the shortcomings of large unit dimension and strong interaction between elements. Secondly, the vertically stacked arrangement method possesses the disadvantages of complex structure design and time-consuming construction processes. Thirdly and importantly, the resonance mechanisms of these broadband PLMAs are fairly single, which are usually attributed to the superposition of several fundamental mode resonances [13–32]. Therefore, it is an urgent need to solve (or overcome) these issues in the design of the broadband PLMAs. In fact, researchers have tried some ways to simplify the structure design and to introduce the novel physical mechanism to design the PLMAs [33–39]. For example, some references are not merely analyzed the fundamental mode resonance and extended the frequency range to investigate the high-order responses [35–39]. However, it is difficult to obtain the broadband absorption response because the frequencies of the fundamental mode and the high-order resonances of the single-sized metallic resonator are far apart and cannot provide the forming condition of the broadband PLMAs.
In this paper, simple single-sized cross-shaped resonator, deposited on an opaque metallic board spaced by an insulator dielectric slab, with two different but narrowing separated resonance frequencies is suggested to realize the broadband absorption at terahertz frequency. In sharp contrast to previous broadband PLMAs, three major advantages (or differences) canbe provided by the cross-shaped resonator. Firstly, the basic cell of the broadband device has only one metallic pattern, which will significantly simplify the design complex of the unit structure, and thus it is helpful to the experimental manufacture of the device. Secondly, a continuous spectral range of 1.97 THz at central frequency of 2.72 THz with the absorption greater than 50% can be gained, where its relative absorption bandwidth (RAB) can be as high as 72.43%, which is higher than previous broadband PLMAs. Particularly, its RAB can be further broadened by varying the frequencies of the two closely separated resonance modes. Thirdly and importantly, basic mechanism of the broadband device is caused by the combining effect of the fundamental mode response and surface lattice resonance of the single-sized metallic resonator, which is totally different from previous ones that merely employ the fundamental mode responses in many resonators with different sizes. With the excellent performance in the aspects of simple unit structure, wide resonance bandwidth (or RAB), as well as the novel operating mechanism, the presented design concept can be used as an alternative to current broadband absorption methods.
2. Structure model and design
A sandwich structure model [its side view is illustrated in Fig. 1(a)
] formed by an Au pattern resonator, insulator dielectric slab and an opaque Au plane is required to achieve the intended absorption response, which can be investigated using the finite difference time domain algorithm. The Au pattern is actually a cross-shaped resonator, see its top view in Fig. 1(b), which has the length and width of l = 40 μm and w = 6 μm, respectively. In fact, some references devoted to the investigation of the resonance performance of the cross-shaped resonator have been demonstrated [40–42]. However, these efforts merely involved the fundamental resonance response of the cross-shaped structure, which are different from the focus of the work. The basic cell of the structure design has the repeat dimension of a = 80 μm. The Au layers used here have the conductivity of 4.09 × 107 S/m, the thickness of the dielectric slab is t = 15 μm. A plane wave with the frequency range of (0.5 ~4.0 THz) polarized along the x-axis is applied as the incident source, which is irradiated perpendicularly the sandwich structure along the z-axis. To eliminate the scattering of the incident light, perfectly matched layers are applied in the propagation direction of the light, i.e., the z-axis. Meanwhile, in both directions of the x- and y-axis, the periodic boundary conditions are used to simulate the layout of the infinite expansion.3. Results and discussion
The absorption response of the suggested cross-shaped resonator is given in Fig. 2(a)
Fig. 2 (a) Absorption spectra of the suggested device; (b), (c) and (d) are respectively the dependence of the absorption spectra of the suggested device on the parameter changes of period a, cross length l, and cross width w.
The frequency point A is actually the fundamental mode response of the cross-shaped resonator, while the surface lattice resonance is the physical origin of the frequency point B. To verify their operating mechanisms preliminarily, the dependence of the broadband absorption on the parameter changes (including the period a, cross length l and width w) of the suggested device is given. As presented in Fig. 2(b), we observed that the frequency point B is extremely sensitive to the change of the period a, while the frequency point A is insensitive to the period a change, indicating the mode A should be the localized resonance response of the cross-shaped resonator while the mode B should be due to the surface lattice resonance of the device [43–52]. In fact, the size changes of the cross-shaped resonator can provide further evidence to support the resonance mechanism. For the change of the resonator length l, see Fig. 2(c), it is found that the frequency point A can be strongly affected by the length l, whereas the shift (or change) of the frequency point B is nearly neglected. Results also show that the change in resonator width w in Fig. 2(d) has no effect on the frequency point B, while slightly affects the frequency point A.
From the above discussion about the parameter variations, we can get the following conclusions: (a) The frequency point A is mainly dictated by the sizes of the cross-shaped resonator itself, while (b) the frequency point B is intensely affected only by the period a, has nothing to do with the changes in cross length l and width w. It is generally known that the localized resonance response is typically determined by the parameters of the resonator (insensitive to the period a), while the resonance frequency of the surface lattice resonance only depends on the period a and is independent of the resonator dimensions. Therefore, the physicalmechanisms of the frequency points A and B can be respectively identified as localized resonance response of the cross-shaped resonator and surface lattice resonance of the device. Further evidence can be given by analyzing the field distributions of the two frequency points in below Fig. 3
Fig. 3 (a), (b), and (c) are respectively the |E|, real Ez, and |Hy| field distributions of the frequency point A of the suggested device; (d), (e), and (f) are respectively the |E|, real Ez, and |Hy| field distributions of the frequency point B of the suggested device.
The field distributions of the frequency points A and B (in Fig. 3) are provided to explore further the basic principle of the broadband absorption. The electric field (|E|) of the frequency point A in Fig. 3(a) is primarily enhanced in both sides of the cross-shaped resonator. Meanwhile we found that the distribution positions of the real Ez in Fig. 3(b) for the frequency point A are very similar to that of the |E| field. These |E| and real Ez field distributions prove that the mode A is caused by the localized resonance response of the cross-shaped resonator. We further observed that its magnetic field (|Hy|) in Fig. 3(c) with one strong domain is mostly concentrated on the insulator dielectric sheet below the cross-shaped resonator, indicating the frequency point A is due to 1st-order localized resonance (i.e., the fundamental mode response) of the cross-shaped resonator. For the frequency point B, the field [|E| of Fig. 3(d) and real Ez of Fig. 3(e)] distributions of the mode are not only gathered in the edges of the cross-shaped resonator (i.e., the metallic region) but also in the non-metallic region between the units. That is to say, the |E| (or real Ez) field of the frequency point B has the non-localized distribution characteristic that can be enhanced in almost the whole unit cell, including the metallic section of the cross-shaped resonator and the non-metallic section. These field distributions can offer further evidence to support surface lattice resonance as the basic principle of the frequency point B [43–52]. Therefore, the operating mechanism of the broadband absorption with simple single-sized metallic resonator is ascribed to the combined effects of fundamental mode response and the surface lattice resonance, which is completely different from previous broadband PLMAs having complex structure designs that merely use their fundamental mode responses.
Different from the parameter changes in Fig. 2 that only affect the mode A (or mode B) of the broadband absorption, we found that the insulator dielectric slab thickness t plays an important role in simultaneous adjusting the resonance performance of the frequency points A and B. As shown in Fig. 4
Fig. 4 Left section of the figure provides the dependence of the absorption spectra of the suggested device on the change of the dielectric slab thickness t; (a) and (b) are respectively the |E| and real Ez field distributions of the frequency point C of the designed device in thickness t = 5 μm; (c), and (d) show respectively the |E| and real Ez field distributions of the frequency point D of the designed device in thickness t = 5 μm.
4. Conclusion
In summary, a simple single-sized cross-shaped resonator with two resonance modes of fundamental mode response and surface lattice resonance to realize a wide absorption bandwidth at terahertz frequency is given and discussed in this paper. The FWHM of the device can span a wide range of 1.97 THz ranging from 1.73 THz to 3.70 THz with the central frequency of 2.72 THz, and its RAB can reach 72.43%, which is superior to the traditional broadband absorption devices with complex structure designs typically based on the combined effects of several fundamental mode responses. Results further reveal that the device RAB can be adjusted by varying some certain geometric parameters, such as the length of the cross-shaped resonator and the device repeat period.
Funding
National Natural Science Foundation of China (Grant No. 11647143); Natural Science Foundation of Jiangsu Province (Grant No. BK20160189); Fundamental Research Funds for the Central Universities (Grant No. JUSRP51721B).
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