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Abstract
1-D cavity modes in 1-D resonators, such as strips, have been used to design multiband metamaterial perfect absorbers. As for 2-D resonators, such as squares and crosses, most studies still focus on exciting the 1-D cavity modes. In this paper, a symmetry-breaking idea is proposed for 2-D cavity mode excitation. An asymmetric sword-shaped notched square resonator is proposed to excite a new 2-D (1, 1) cavity mode, in addition to the 1-D (1, 0) and (3, 0) cavity modes. Thus, a triple-band MPA was successfully produced with average absorptivity of 98.8% in the infrared range. The 2-D cavity mode provides better performance as a biosensor than the 1-D cavity modes do. To obtain more absorption bands, a six-band metamaterial perfect absorber with average absorptivity of 97.2% was successfully produced by combining two sword-shaped notched square resonators with different sizes. A nine-band metamaterial perfect absorber was successfully produced with average absorptivity of 94.5% by combining three sword-shaped notched square resonators with different sizes.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since the first GHz metamaterial-based absorber was presented by Landy et al. [1], metamaterial perfect absorbers (MPAs) have attracted great attention due to their potential applications as microbolometers [2,3], infrared detectors [4–8], thermal imagers [9], biosensors [10,11], thermal emitters [12,13], and color filters [14,15]. The most common configuration of MPAs is the triple-layered metal-dielectric-metal structure. The top layer of periodic resonators is separated from the bottom metallic film layer by a dielectric layer. Incident electromagnetic waves can excite the localized surface plasmonic resonance (LSPR) at some particular frequency by inducing the collective oscillation of conduction electrons in the periodic resonators on the top layer. Based on the fundamental plasmonic resonance mode, many single-band MPAs were presented over a broad frequency range, including the GHz [16,17], THz [18], infrared [19,20], and visible ranges [21]. Obviously, MPAs with only single band may have limited applications, like selective detection of multiband radiation signals. Therefore, it is necessary to design multiband high-performance metamaterial absorbers [22–24].
A direct strategy for obtaining multiband absorption involves combining resonators with different sizes to form super resonators due to the dependence of the absorption frequency on the geometry of the top periodic resonators. For example, dual-band MPAs can be produced by combining two different sized split ring resonators [25], square ring resonators [26], or disk resonators [27]. Triple-band [28–31] and four-band [32–35] MPAs can also be produced with the same strategy. However, it is not easy to obtain multiple absorption bands while maintaining high absorptivity with super resonators, since the perfect absorption conditions are sensitive to the geometry of adjacent structures [36] and can be broken easily. It can be very difficult to optimize the geometry of super resonators when the number of basic resonators is greater than four.
Another strategy is to excite higher-order plasmonic resonances in addition to the fundamental resonance. The traditional cavity resonance model [37,38] was recently used to qualitatively study the resonances in MPAs based on the metal-dielectric-metal structure. For 1-D strip resonators, dual-band resonances in MPAs [39,40] can be generated by exciting the fundamental 1-D (1, 0) cavity resonance and a higher-order (3, 0) cavity resonance simultaneously by designing an appropriate structure. The (1, 0) and (3, 0) cavity modes indicate that the electric fields exhibit first and third order resonances in one direction and no resonances in the other direction. In 2-D resonators like squares [41–44] and crosses [37,45], most research still focuses on exciting higher-order 1-D cavity resonances, and few researchers studied the excitation of higher-order 2-D cavity modes. Chang Long et al. [46] recently reported a significant absorptivity enhancement of the 2-D (2, 1) cavity resonance in the GHz range by vertically stacking square resonators, which will increase the thickness of the absorber. Research on exciting other higher-order 2-D cavity resonances in the infrared range is still in progress.
In this paper, a symmetry-breaking idea is introduced into the design of a metamaterial perfect absorber in order to excite higher-order 2-D cavity modes. A triple-band MPA based on sword-shaped notched square resonators in the infrared range exhibited an average absorptivity above 90%, which can be used to excite a new 2-D (1, 1) cavity mode in addition to two 1-D cavity modes. The electric field distribution was analyzed to determine the underlying physical mechanism. The dependence of the absorption bands on the side length of the square resonators and the performance of our proposed absorber as a biosensor were also investigated. We then investigate the spectral absorptivity of our proposed absorber by replacing Al with other metals like Au and W. To obtain more absorption bands, we designed two other MPAs by combining sword-shaped notched square resonators with different sizes.
2. Structure and simulation method
The structure of our proposed metamaterial perfect absorber is a typical metal-dielectric-metal configuration, as shown in Fig. 1. Symmetry breaking is introduced into the design of the top layer of periodic resonators to excite higher-order 2-D cavity modes. We break the symmetry of square resonators by introducing a sword-shaped notch. Arrays of sword-shaped notched square aluminum (Al) resonators are separated from the bottom aluminum film by a dielectric layer. Silicon was chosen as the dielectric layer after comparing the spectral response of other materials like ZnS, SiN, and SiO2. The thickness of the top, middle, and bottom layers are T1, T2, and T3, respectively. The side length of the square is D, the notch width is W, and the notch lengths are L1 and L2. Electromagnetic waves are vertically incident on the nanostructure and the electric fields point along the x-direction. The periods of the nanostructure along the x and y directions are Px and Py, respectively. Absorption in our proposed structure was determined using finite difference time domain (FDTD) calculations. Only one unit cell was considered in the simulation due to the periodicity of the structure. Periodic boundary conditions are applied in the x and y direction, and the PML boundary condition was applied in the z-direction. In the simulation, the permittivity of aluminum was taken from experimental data [47], and the permittivity of silicon is 11.6.
Fig. 1 Schematic of our proposed metamaterial perfect absorber. We break the symmetry of the square resonators by including a sword-shaped notch. Arrays of sword-shaped notched square aluminum (Al) resonators are separated from the bottom aluminum film by a silicon layer.
3. Results and discussion
The optimized dimensions in the simulation are as follows: Px = Py = 1100, D = 1000, W = 400, L1 = 600, L2 = 100, T1 = 300, T2 = 160, and T3 = 200 (units: nm). We first calculated the spectral absorptivity of the absorber based on square resonators (SR), and the results are shown in Fig. 2 with a dashed line. There are two absorption bands in the infrared range at f1 = 27.6 THz and f3 = 87 THz with absorptivity of 85.7% and 99.9%, respectively. The traditional cavity resonance model [33,34] was used to qualitatively predict MPA resonances based on the metal-dielectric-metal structure. The resonance frequency fmn for 2-D rectangular cavity resonators can be calculated with the following equation:
where c is the speed of light, n is the refractive index of the middle dielectric layer, D is the length of the square resonators, and m and n are integers for the mode number along with the x and y directions, respectively. According to Eq. (1), the resonance frequency of the (3, 0) cavity mode should be nearly a factor 3 larger than that of the (1, 0) cavity mode. For square resonators, f1 = 27.6 THz corresponds to the fundamental 1-D (1, 0) cavity mode while f3 = 87 THz is nearly a factor 3 larger than f1 with the only 5% deviation. However, the frequency of the (1, 0) cavity mode calculated with Eq. (1) has about 36% deviation from the result calculated with the FDTD simulation, because the electric fields are uneven and primarily accumulate at the sides and corners of the resonators.Fig. 2 Spectral absorptivity of our proposed metamaterial perfect absorber with a top layer of square resonators (dash line) and sword-shaped notched square resonators (solid line).
Only 1-D cavity resonances were observed in square resonators, similar to that reported in the literature [37–40]. Symmetry breaking was introduced into the design of the top layer of periodic resonators to excite higher-order 2-D cavity modes. The spectral absorptivity for these modes in the sword-shaped notched square resonators are shown in Fig. 2 (labelled SSNSR in the figure). There are three absorption bands in the infrared range at f1 = 22.6 THz, f2 = 57.6 THz, and f3 = 83.7 THz with absorptivities of 98.5%, 99.8%, and 98.1%, respectively. Compared to the symmetry square resonators, the asymmetric sword-shaped notched square resonators have a new absorption band whose frequency is between the (1, 0) cavity mode and the (3, 0) cavity mode. The average absorptivity of the three absorption bands reaches up to 98.8%.
To further investigate the physical mechanism of the three absorption bands in the sword-shaped notched square resonators, Fig. 3 shows the distribution of the z-component of electric fields (Ez) in the xy plane. The Ez distribution at f1 = 22.6 THz is shown in Fig. 3(a). Only a first order resonance is present along the x-direction and no resonance is present along the y-direction. Thus, the absorption band at f1 = 22.6 THz corresponds to the excitation of the 1-D (1, 0) cavity mode, which is also called the fundamental mode. The Ez distribution of the absorption band at f2 = 57.6 THz is shown in Fig. 3(b). Here, a first order resonance is excited along the x and y directions. Thus, the absorption band at f2 = 57.6 THz corresponds to excitation of the 2-D (1, 1) cavity mode, which is a higher-order mode. We successfully excited a new 2-D cavity mode by breaking the symmetry of square resonators with sword-shaped notches. The Ez distribution at f3 = 83.7 THz is shown in Fig. 3(c). A third order resonance is present along the x-direction and no resonance is present along the y direction. Thus, the absorption band at f3 = 83.7 THz corresponds to excitation of the 1-D (3, 0) cavity mode, which is a higher-order mode. Our proposed sword-shaped notched square resonators can be used to excite two 1-D cavity modes or a 2-D (1, 1) cavity mode.
Fig. 3 Distribution of the z-component of the electric field (Ez) in the xy plane at (a) f1 = 22.6 THz, (b) f2 = 57.6 THz, and (c) f3 = 83.7 THz.
According to the traditional cavity model, the resonant frequencies of cavity modes should be inversely proportional to the cavity length. Therefore, we investigated the dependence of the peak frequencies of the absorption bands on the side length of the square. Figures 4(a) and 4(b) show that the absorption peak frequencies of (1, 0), (1, 1), and (3, 0) cavity modes exhibit an apparent linear increase as the side length of square decreases from 1020 to 960 nm. We also investigated whether our proposed absorber could be used as a biosensor. Figures 4(c)-4(f) show the spectral absorptivity and absorption peaks as functions of the environmental refractive index. When the environmental refractive index increases from 1.0 to 1.6, the three absorption bands exhibit high absorptivity, but the peak absorption peak frequencies decrease. The performance of a biosensor can usually be evaluated from the figure of merit (FOM), which is defined as the ratio of the refractive index sensitivity S and the full-width-half-maximum (FWHM) for the corresponding absorption peaks:
The refractive index sensitivity S is defined as the ratio of the absorption peak frequency change ∆f to the change in refractive index ∆n:The calculated FOM values for the (1, 0), (1, 1), and (3, 0) cavity modes are 1.7 RIU−1, 2.8 RIU−1, and 2.5 RIU−1, respectively. It is obvious that the sensing performance with higher-order modes is better than that for the fundamental modes, and the 2-D (1, 1) cavity mode is a good candidate for use as a biosensor. The sensing performance of our designed absorber is superior to that published in the literature [48].Fig. 4 (a) Spectral absorptivity and (b) absorption peaks as functions of the side length of a square D. (c) Spectral absorptivity and absorption peaks of (d) the (1, 0) cavity mode, (e) (1, 1) cavity mode, and (f) (3, 0) cavity mode as functions of the environmental refractive index. Spectral absorptivity as a function of the incident angle for (g) TM-polarized and (h) TE-polarized waves.
We also investigated the spectral absorptivity of our designed absorber as functions of the incident angles for TM-polarized waves and TE-polarized waves, as shown in Fig. 4(g) and 4(h). For vertical incident TM-polarized waves, there are three absorption bands at f1, f2, and f3 which correspond to the 1-D (1, 0), 2-D (1, 1), and 1-D (3, 0) cavity modes, respectively. When the incident angles increase from 0 to 40°, the peak frequency and absorptivity of the 1-D (1, 0) and 2-D (1, 1) modes remain nearly constant. The peak frequency of the 1-D (3, 0) mode increases as the absorptivity decreases. There is a new absorption band due to the inclined incidence, which is the 1-D (2, 0) mode [39,40,42]. There are only two absorption bands f1 and f3 for vertically incident TE-polarized waves, which correspond to the 1-D (1, 0) and 1-D (3, 0) modes, respectively. However, there is no 2-D (1, 1) mode. When the incident angle increases from 0 to 40°, the peak frequency of the 1-D (1, 0) and 1-D (3, 0) modes both increase. The absorptivity of the 1-D (1, 0) mode changes slightly, and the absorptivity of the 1-D (3, 0) modes decreases.
All the above results are based on the use of aluminum and silicon as the dielectric material. Aluminum is cheap and suitable for industrial applications, but aluminum also has a low melting point and is easily oxidized. In contrast, gold has very good electrical and thermal conductivity and is chemically stable. Tungsten has a very high melting point, which is suitable for applications in high temperature environments. We investigated the spectral absorptivity of our proposed absorber by replacing Al with Au and W, as shown in Fig. 5. The permittivity of Au and W were taken from experimental data [47]. Compared to symmetric square resonators, one can see that the asymmetric sword-shaped notched square resonators made of Si and Au or W can also be used to excite a 2-D (1, 1) cavity mode in addition to two 1-D cavity modes. This shows that other materials can be used to fabricate the sword-shaped notched square resonators.
Fig. 5 Spectral absorptivity of our proposed absorber based on sword-shaped notched square resonators when Al is replaced with (a) Au and (b) W.
A triple-band MPA with average absorptivity of 98.8% was successfully produced using asymmetric sword-shaped notched square resonators, which can be used to excite a 2-D (1, 1) cavity mode in addition to two 1-D cavity modes. Due to the dependence of the absorption frequency on geometry, we design another multiband metamaterial perfect absorber by combining two different sized sword-shaped notched square resonators A and B as shown in Fig. 6(a). Electromagnetic waves are vertically incident on the nanostructure and the electric fields point along the x-direction. The optimized dimensions in the simulation are Px = 1200, Py = 2400, DA = 1000, WA = 400, L1A = 500, L2A = 100, DB = 800, WB = 200, L1B = 400, L2B = 100, T1 = 300, T2 = 160, and T3 = 200 (units: nm). The spectral absorptivity is shown in Fig. 6(b). There are six absorption bands in the infrared range at f1 = 27.4 THz, f2 = 37.4 THz, f3 = 58.6 THz, f4 = 67.8 THz, f5 = 90.7 THz, and f6 = 105.2 THz with absorptivities of 98.2%, 93.6%, 95%, 96.7%, 99.8%, and 99.9%, respectively. Thus, a six-band metamaterial perfect absorber was successfully simulated with average absorptivity of 97.2%.
Fig. 6 (a) Schematic and (b) spectral absorptivity of our designed six-band metamaterial perfect absorber based on super resonators consisting of two sword-shaped notched square resonators A and B with different sizes.
A six-band MPA was produced by combining two sword-shaped notched square resonators A and B with different sizes. Figure 7 shows the distribution of the z-component of electric field (Ez) along the xy plane for six different modes to determine the underlying absorption mechanism. For the absorption band at f1 = 27.4 THz shown in Fig. 7(a), the electric fields primarily accumulate around resonator A; a first order resonance is present along the x direction and there is no resonance along the y direction. Thus, the absorption peak at f1 = 27.4 THz is due to excitation of the 1-D (1, 0) cavity mode in resonator A. The electric field primarily accumulates around resonator B for the absorption band at f2 = 37.4 THz, as shown in Fig. 7(b). A first order resonance is present along the x direction and there is no resonance along the y direction. The absorption peak at f2 = 37.4 THz is due to excitation of the 1-D (1, 0) cavity mode in resonator B. Regarding the absorption band at f3 = 58.6 THz is shown in Fig. 7(c), the electric field primarily accumulates around resonator A; first order resonances are present along the x and y directions. The absorption peak at f3 = 58.6 THz is due to excitation of the 2-D (1, 1) cavity mode in resonator A. For the absorption band at f4 = 67.8 THz shown in Fig. 7(d), the electric fields primarily accumulate around resonator B; first order resonances are present along the x and y directions. Thus the absorption peak at f4 = 67.8 THz is due to excitation of the 2-D (1, 1) cavity mode in resonator B. Regarding the absorption band at f5 = 90.7 THz shown in Fig. 7(e), the electric field primarily accumulates around resonator A; a third order resonance is present along the x direction and there is no resonance along the y direction. Thus the absorption peak at f5 = 90.7 THz is due to excitation of the 1-D (3, 0) cavity mode in resonator A. The absorption band at f6 = 105.2 THz is shown in Fig. 7(f), and the electric field primarily accumulates around resonator B; a third order resonance is present along the x direction and there is no resonance along the y direction. Thus the absorption peak at f6 = 105.2 THz is due to excitation of the 1-D (3, 0) cavity mode in resonator B.
Fig. 7 Distribution of the z-component of the electric field (Ez) in the xy plane at (a) f1 = 27.4 THz, (b) f2 = 37.4 THz, (c) f3 = 58.6 THz, (d) f4 = 67.8 THz, (e) f5 = 90.7 THz, and (f) f6 = 105.2 THz.
A triple-band MPA with average absorptivity of 98.8% was successfully produced by breaking the symmetry of the square resonators with sword-shaped notches, which can excite two 1-D cavity modes and one 2-D cavity mode. Then a six-band MPA was successfully produced based on super resonators consisting of two sword-shaped notched square resonators A and B with different sizes, in which there are four 1-D cavity modes and two 2-D cavity modes. To achieve more absorption bands, we designed an absorber by combining sword-shaped notched square resonators C, D, and E with different sizes, as shown in Fig. 8(a). The optimized dimensions of the structures in the simulation are Px = 1100, Py = 3300, DC = 1000, WC = 400, L1C = 500, L2C = 100, DD = 700, WD = 100, L1D = 300, L2D = 100, DE = 800, WE = 200, L1E = 500, L2E = 100, T1 = 300, T2 = 200, and T3 = 200 (units: nm). The spectral absorptivity is shown in Fig. 8(b). There are nine absorption bands in the infrared range at f1 = 25.3 THz, f2 = 34.4 THz, f3 = 45.9 THz, f4 = 62.3 THz, f5 = 68.4 THz, f6 = 77.1 THz, f7 = 85.3 THz, f8 = 91.9 THz and f9 = 105.4 THz with absorptivity 96%, 93.8%, 99.5%, 91.4%, 99.5%, 92.2%, 99.9%, 84.2%, and 93.6%, respectively. Thus, a nine-band metamaterial perfect absorber was successfully produced with average absorptivity of 94.5%.
Fig. 8 (a) Schematic and (b) spectral absorptivity of our designed nine-band metamaterial perfect absorber based on super-resonators consisting of three different sized sword-shaped notched square resonators C, D, and E.
To determine the underlying physical mechanism of the nine absorption bands, Fig. 9 shows the distribution of z-component of the electric field (Ez) in the xy plane. Figures 9(a)-9(c) show that the electric field primarily accumulates around resonators C, E, and D for the absorption bands at f1 = 25.3 THz, f2 = 34.4 THz, and f3 = 45.9 THz, respectively. A first order resonance is present along the x direction and there is no resonance along the y direction in all resonators. So, the absorption peaks at f1 = 25.3 THz, f2 = 34.4 THz, and f3 = 45.9 THz are due to the excitation of the 1-D (1, 0) cavity mode in resonators C, E, and D, respectively. Figures 9(d)-9(f) show that the electric field primarily accumulates around resonators C, E, and D for the absorption bands at f4 = 62.3 THz, f5 = 68.4 THz, and f6 = 77.1 THz, respectively. A first order resonance is present along the x direction and there is no resonance along the y direction in all resonators. Thus, the absorption peaks at f4 = 62.3 THz, f5 = 68.4 THz, and f6 = 77.1 THz are due to excitation of the 2-D (1, 1) cavity mode in resonators C, E, and D, respectively. Figures 9(g)-9(i) show that the electric field primarily accumulates around resonators C, E, and D for the absorption bands at f7 = 85.3 THz, f8 = 91.9 THz, and f9 = 105.4 THz, respectively. A third order resonance is present along the x direction and there is no resonance along the y direction in all resonators. Thus, the absorption peaks at f7 = 85.3 THz, f8 = 91.9 THz, and f9 = 105.4 THz are due to excitation of the 1-D (3, 0) cavity mode in resonators C, E, and D, respectively.
Fig. 9 Distribution of the z-component of the electric field (Ez) in the xy plane at (a) f1 = 25.3 THz, (b) f2 = 34.4 THz, (c) f3 = 45.9 THz, (d) f4 = 62.3 THz, (e) f5 = 68.4 THz, (f) f6 = 77.1 THz, (g) f7 = 85.3 THz, (h) f8 = 91.9 THz, and (i) f9 = 105.4 THz.
4. Conclusions
In summary, an asymmetric sword-shaped notched square resonator introduces symmetry breaking into the design of metamaterial perfect absorbers. It can be used to excite a new 2-D (1, 1) cavity mode in addition to the 1-D (1, 0) and (3, 0) cavity modes compared to the symmetric square resonators. A triple-band MPA made of Al and Si was produced with average absorptivity of 98.8% in the infrared range by including the sword-shaped notched square resonators. The frequencies of the three absorption bands are inversely proportional to the side length of the resonators. The 2-D cavity mode provides better performance than the 1-D cavity modes when the structure is used as a biosensor. The MPA based on sword-shaped notched square resonators shows good adaptability to other metals like Au and W. A six-band metamaterial perfect absorber was successfully produced with average absorptivity of 97.2% by combining two sword-shaped notched square resonators with different sizes, which can be used to excite two 2-D cavity modes and four 1-D cavity modes. A nine-band metamaterial perfect absorber was successfully produced with average absorptivity of 94.5% by combining three sword-shaped notched square resonators with different sizes, which can be used to excite three 2-D cavity modes and six 1-D cavity modes. An MPA consisting of sword-shaped notched square resonators with different sizes could exhibit many more absorption bands.
Funding
National Natural Science Foundation of China (51576054).
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