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Abstract
Wide-angle polarization-insensitive triple-band perfect metamaterial absorbers (PMAs) based on single resonators are investigated. Generally speaking, the single resonator can only generate an absorption peak induced by the excitation of a fundamental resonance. Here, the designed absorbers with a single cave-ring resonator appear three perfect peaks for different polarization angles at 6.53 THz, 7.09 THz and 7.64 THz. For the case of the transverse electric (TE) mode, the resonant peaks are controlled by the angle of incidence. Compared with previous studies about angular stability, the absorptivity still exceeds 92% around 6.53THz even when the incident angle for the TE mode is up to 80°. For the case of the transverse magnetic (TM) mode, the absorptance at 7.64 THz is still greater than 92% even up to 70°. Simulated electric field (Ez) and magnetic field (/H/) distributions indicate that perfect absorption arises from the excitation of the multipolar response and surface plasmons. Besides, the complementary structure also displays three absorption peaks. We have demonstrated that simple ultrathin PMA has good absorption stability under an oblique incidence up to 70° at 2.62 THz, and that the resonance frequency at 2.62 THz is almost unchanged for the incident angle ranging from 0° to 70°. These proposed absorbers may be used in many applications, such as THz imaging, sensors, and detectors.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial medium with specially effective permittivity and permeability, and have shown great potential application in electromagnetic cloak [1], negative refraction [2], perfect absorber [3–9]. Among them, metamaterial absorbers (MAs), which was firstly demonstrated by Landy et al., have been widely researched in microwave [3], millimeter [4], terahertz (THz) [5], infrared [10] and optical spectroscopy [11–13]. Typically, MAs are composed of three layers: the top periodic metallic pattern as frequency selective resonator, the middle medium layer as supportive substrate and a continuous metallic bottom plane as the limitation of transmission waves. By carefully designing the patterned structure or increasing the number of the substrate, MAs can exhibit various absorption characteristics including single band [3], dual band [14], triple band [15, 16], multiband [17], polarization independence [18] and incident-angle stability [19].
Among the whole frequency bands, THz gap have recently attracted extensive attention as native absorbing materials are lacking in this area. In 2008, the first THz MA which obtains an absorptivity of 70% is proposed by Tao et al [9]. Since then, much works have been devoted to this kinds of absorber. For example, a single-band THz MA was reported by employing split ring resonators (SRR) [19]. For spectroscopic and imaging application, multiband absorption in the THz region is required. Polarization-sensitive MA based on a dual band electric-field-coupled structure can achieve two absorption peaks [20]. Polarization-independent dual band MA by using two concentric ring resonator was experimentally demonstrated [21]. Three concentric square-rings structure was used to form three absorption bands [22]. It is undeniable that the above resonances are all narrowband. By stacking three metal-insulator layers, broadband absorption in the THz spectrum can be obtained by simulation and measurement [23]. In the above discussion, the high absorption is caused by fundamental resonance. Moreover, multiband and broadband absorption is due to overlapping of the fundamental resonance by changing geometric structure of top metal or the number of the middle layer.
Although the design method based on the fundamental and overlapping fundamental resonances have realized multiband or broadband absorption, it need take longer time to optimize and fabricate the complicated structure, leading to consume manpower and material resources. In fact, high-order resonances in a single structure can contribute to multiband absorption. Dayal et al. presented multiband MA based on the multipolar resonances [24]. Hu et al. proposed four-band THz MA by utilizing the combination of fundamental and electric dipole resonances of a #-shaped resonator [25]. Wang et al. numerically demonstrated quad-band absorption of two split ring resonators which stems from the dipole and quadrupole resonances [26]. Cheng et al. reported six-band perfect absorber by using a cross-cave patch, which originates from multipolar resonances [27]. However, many researchers only concentrate on increasing the absorption peaks but neglect the stability of polarization and incident angles. So far, many MAs based on the multipolar resonances are polarization dependence and their incident-angle tolerance is rarely investigated. To the best of our knowledge, high absorption with a larger range of incident angle for TE mode is difficult to obtain. Therefore, it is desirable to design polarization-insensitive THz MA with larger-angle tolerance by a simple pattern.
In this letter, we design and demonstrate a polarization- and angle- insensitive THz MA using a simple cave-ring and complementary resonators. The designed MA owns three perfect absorption peaks with the absorptivities of ~100%. Because of the rotational symmetric structure, polarization independence is obtained. More importantly, the high absorption around 6.53THz maintains stable in a wide range of angle of TE incidence from 0° to 80°. In addition, the absorptivity of the complementary-resonator MA still exceeds 83% at 2.62 THz for both TE and TM mode even up to 70°. Simulation results of complementary resonator manifest that wide angular absorption at the specific resonance peak originates from the excitation of dipole and gap surface plasmon resonances.
2. Design and simulation of the cave-ring resonator
MA is designed, which consists of cave-ring pattern and a continuous metallic film separated by dielectric spacer in Fig. 1. The top and bottom metal is made of gold with the electric conductivity of σ = 4.56 × 107 S/m. The geometry of its unit cell is displayed in Fig. 1(a), and the optimized parameters are g = 0.2 μm, R = 7 μm, r = 0.52 μm and P = 20 μm. In Fig. 1(b), the middle layer with 3.4 μm thickness is constructed by gallium arsenide (GaAs) substrate of ε = 12.9 + 0.0774i at room temperature [28, 29]. GaAs is not sensitive to heat due to these important properties of high electron mobility, low noise, saturated electron velocity and wide bandgap. In addition, it would be well suited to be a part of MA because of its direct bandgap [30]. Finally, the PMA with arraying 3 × 3 unit cells is shown in Fig. 1(c). The optimized process of final parameters is performed by CST Microwave Studio software. Periodic boundary conditions are set in x and y directions. When a plane EM wave with electric field (E) and magnetic field (H) works into the unit cell of MA along Z direction, the scattering parameter (S-parameter) can be produced. Reflection (R) and transmission (T) can be expressed by and , respectively. Absorptance (A) is derived by. There is no transmission (T = 0) due to its bottom metal thicker than the penetration depth. The minimized reflection (R) can be given when the relative impedance is by adjusting the geometric structure of unit cell.
Fig. 1 Schematic of the proposed PMA with dimensions and three-dimensional (3D) coordinates: (a) front view of the unit cell, (b) cross section of unit cell, (c) 2D array.
3. Simulation results and discussion
The characteristics of the MA are discussed in detail by numerical simulation. The absorption spectra under normal incidence and different polarization angles (φ) is shown in Fig. 2. The whole absorptance is greater than 56% in the frequency range from 6.4 THz to 7.82 THz. In Fig. 2(a), three different perfect absorption peaks are observed at 6.53THz (fa), 7.09THz (fb) and 7.64THz (fc) with the absorptivities of 99.65%, 99.95% and 99.96%. Interestingly, the resonance peak fb coincidentally locates in the middle point between fa and fc. Due to highly rotational symmetry of the designed structure, we only calculate its absorption performance under the polarization angles from 0° to 45°, as shown in Fig. 2(b). Obviously, the absorptivities and resonant frequencies keep unchanged under different polarization angles at normal incidence. Therefore, the single patterned structure can exhibit good absorption stability for different polarization angles in practical application.
Fig. 2 Absorption spectrum of THz MA with cave-ring resonator: (a) at normal incidence, (b) under different polarization angles of normal incidence.
High absorption mainly depend on ohmic and dielectric losses in the system. To analyze each contribution of metallic and dielectric layers in this MA, absorption responses for their different physical properties are depicted in Fig. 3. We firstly investigate the influence of various metals (Ge, Al, Au, Ag, Cu, and PEC) of two metallic layers on absorption performance in Fig. 3(a). Above metals correspond to different electric conductivities. When the conductivity (2.17 S/m) in metallic layers is very low, the absorptance is lower than 10%. The decrease of its absorptivity arises from the impedance mismatching to free space. When the value of electric conductivity increases to the order of magnitude of 107, the small changes under the same order of magnitude have no obvious effect on the absorption performance. There occur a precipitous reduction and blueshift of three resonance peaks (fa, fb, and fc) with increasing the electric conductivity from 6.3 × 107 S/m to infinity (PEC) [31]. In Fig. 3(b), the absorption performance in the case of lossy and lossfree dielectric is also explored. The location and intensities of three absorption peaks almost maintain fixed. Therefore, simulated results indicate that ohmic losses determined by metal contribute to perfect absorption of three resonance peaks.
Fig. 3 Absorption spectrum under (a) different electric conductivities of two metallic layers, (b) different loss tangents of the middle substrate.
In addition to the impact of ohmic and dielectric losses on MA, the absorption performance are determined by geometric parameters of the proposed structure. Here, the influence of three main parameters (r, R, and h) on perfect absorption is studied at normal incidence, as displayed in Fig. 4. In simulation, the other parameters of MA are fixed when one is varied. In Fig. 4(a), two high resonance peaks (fb and fc) are deeply affected by the variation of inner radius (r) while the lowest absorption peak (fa) is relatively stable. The resonance peak fb appears a blueshift and gradually disappears as inner radius (r) increases from 1.0 μm to 3.0 μm. The resonance frequency fc also experiences blue-shift and its high absorptance still remain unchanged. Consequently, the value of inner radius (r) determines the number of absorption peak. The designed MA changes from triple band to dual ones when inner radius (r) increases towards 3.0 μm. In Fig. 4(b), MA can always excite three resonance peaks when outer radius (R) increases from 6.6μm to 7.4μm. Moreover, overall resonance peaks move to lower frequencies with increasing outer radius (R). Based on LC circuit model, the decrease of three absorption frequencies is due to the increase of the effective capacitance (C). In Fig. 4(c), three absorption frequencies exhibit overall redshift as well as the corresponding absorptivities increase at first and then decrease when changing the dielectric thickness (h) from 3.0μm to 3.8μm. Thus, there exist an optimal thickness of the middle spacer in the designed MA.
Fig. 4 Absorption spectra with different geometry parameters: (a) inner radius r, (b) outer radius R, and (c) thickness h of dielectric spacer.
So, the frequencies and intensities of the absorption peaks are strongly dependent on geometrical sizes. This offers us a chance to change the resonance peaks and frequencies of MA by adjusting these parameters.
Three perfect absorption peaks have been obtained in the paper. Now, their physical mechanism need be understood. The distributions of electric field (Ez) and magnetic field (/H/) are plotted in Fig. 5 and 6. Due to the overlapping of plasmon resonance, it is difficult to distinguish electric-field patterns. The distributions of z component of electric field (Ez) at 6.53 THz and 7.09 THz are shown in Fig. 5(a) and (b). Electric fields (Ez) of resonance peaks fa and fb are mainly confined at the outer edges and sharp angle of each circular sector. Based on the number of nodes along E(x) direction, the electric-field patterns at the different parts correspond to different resonance modes. In Fig. 5(a), the outer edges and sharp parts of cave-ring pattern simultaneously excite hexapole mode. The middle dielectric substrate of MA also generate gap surface plasmons at 6.53 THz. In Fig. 5(b), the outer position of cave-ring pattern excites dipole resonance while the sharp parts generate hexapole mode [32]. At 7.09 THz, surface plasmons is excited on the middle dielectric substrate along E(x) direction. In Fig. 5(c), the electric fields (Ez) at the resonance fc are regularly distributed at the gap edges of cave-ring resonator. So, tetradecapole mode is excited in the outer parts while the sharp positions weakly generate dipole resonance [32]. It is carefully observed that surface plasmons on the dielectric surface between the neighboring elements are generated at 7.64 THz. In summary, higher-order modes are excited [33]. Moreover, higher-order modes at the top surface of metal are anti-phase with that at metal/dielectric interface.
Fig. 5 Distribution of z component of electric fields (Ez) at (a) 6.53 THz, (b) 7.09 THz, and (c) 7.64 THz. Left figures represent the top surface of cave-ring resonator and right figures represent the interface between the top cave-ring metal and the middle substrate.
Fig. 6 The x-z cross-section view for the distribution of magnetic field (/H/) at y = 0 (Black line represent the position of cave-ring resonator).
Figure 6(a), (b) and (c) display the magnetic field (/H/) distributions at 6.53 THz, 7.09 THz and 7.64 THz, respectively. At 6.53 THz and 7.64 THz, the magnetic field is not only gathered in the central regions of the dielectric spacer but also focused in the dielectric area between the neighboring unit cells in Fig. 6(a) and (c). It indicates that magnetic response can be generated in the dielectric regions [34]. At 7.09 THz, the magnetic field is only confined in the area beneath the cave-ring resonator in Fig. 6(b). The high magnetic resonance is excited in the central area [34]. Thus, both higher-order modes and magnetic response contribute to perfect absorption of three resonance peaks.
In many cases, THz MAs are required to maintain high absorptance under oblique incidence. Thus, we investigate the absorption behavior of the cave-ring MA when the incident angle (θ) for both TE and TM mode increases from 0° to 80°.
In Fig. 7(a),, the number of the resonant peaks obviously changes from three bands to a single one as the incident angle in TE mode increases. Below 20°, the absorptivities of three resonance peaks are always greater than 90%. It is clear that the first resonance peak fa moves to higher frequency and the second resonance frequency fb shifts to lower one as θ increases. So, the absorption peaks fa and fb combine to form a single peak with over 92% absorptance at 6.73 THz when up to 80° incidence. The third absorption peak fc occurs blue-shift and its absorptivity gradually decreases to lower than 3.5% up to 80°. The reason is that the y component of magnetic field quickly drops with increasing the value of θ, leading to weaken antiparallel currents. Finally, the single absorption can reach over 92% and the off-resonance absorption is lower than 3.5% even at the incident angle of 80°. The dynamic property of wide-angle absorption has never been reported in previous literatures. In brief, the number of resonance peaks for TE polarization is controlled by the incident angle. It is believed that the aforementioned advantages would be used into some potential applications in terahertz based devices.
Fig. 7 Absorption performance of triple-band MA at different incident angles: (a) TE mode, (b) TM mode. The insets illustrate the polarization direction.
For TM mode in Fig. 7(b), the resonance peak fa experiences blue-shifted while the resonance frequencies fb and fc nearly remain fixed as incident angle increases. The reason of blueshift is: the multipolar resonances between each cave-ring resonator is in phase at normal incidence. However, the higher-order resonance is out of phase with the adjacent resonator under oblique incidence, leading to blueshift of resonance peaks fa. Below 20°, the average absorptivity of three peaks can achieve 95.8%. For the resonant frequency fa, the absorptivity firstly decreases and then increases to 84.8% up to 80°. For the resonant frequency fb, the absorptance still exceed 92.6% below 30°. The absorptivity still maintain over 90% at the resonant frequency of fc even when the incident angle reaches 70°. Moreover, the broad absorption band of 0.33 THz can be observed in the frequency range from 7.39 THz to 7.72 THz at 70°.
4. Simulation of complementary resonator
Another absorber by using a simple method is explored, as displayed in Fig. 8(a). The MA consists of complementary resonator and same substrate backed by a gold film. Figure 8(b) shows that the single complementary structure can also excite three absorption peaks at 2.62 THz, 7.40 THz, and 8.1 THz with the absorptivities of 99%, 99.8% and 78%, respectively. Obviously, there are two perfect absorption peaks. Especially, the thickness and periodic size of the MA at 2.62 THz are λ/34 and λ/6 (λ is the resonance wavelength), respectively. The corresponding quality factor Q is 9. The complementary-resonator MA is polarization-insensitive owing to the rotational symmetry. Based on the above advantages, we only analyze the absorption stability of 2.62 THz under oblique incidence. In fact, another perfect peak is not given in the paper due to absorption instability under wide angles of incidence.
Fig. 8 (a) Schematic of the proposed MA with complementary resonator, (b) absorption spectra for different polarization angles
The dependence of the absorption response on incident angles for both TE and TM mode is discussed in Fig. 9. For the case of TE mode in Fig. 9(a), the complementary resonator can still maintain high absorptance even up to 70° incidence. Importantly, the resonant frequency at 2.62 THz is nearly unchanged as the incident angles (θ) increase. The reason is that the complementary resonator still excites dipole resonances and gap surface plasmons under different angles of incidence though the intensities of dipole resonances in the adjacent elements are different at 30°, 50°, and 70°, as shown in the insets of Fig. 9(a). In addition, the dipole resonance is in phase with gap surface plasmons. For the case of TM mode in Fig. 9(b), similarly, the absorptance remains very high even when up to 70°. The difference is that the resonant frequency slightly shifts to higher one at 70°. It is observed from the electric field (Ez) in the insets of Fig. 9(b) that the intensities of gap surface plasmons in the neighboring cells is not consistent over a wide incident angles ranging from 0° to 70°. At 70°, the gap surface plasmons of the left cell is much stronger than that in right, resulting in slight shift of the resonance peak. Therefore, the designed structure shows absorption stability with a wide angles of incidence at 2.62 THz although wide-angle absorption in TE mode is generally difficult to reach.
Fig. 9 Absorption response under different incident angles: (a) TE mode, (b) TM mode. The insets exhibits z component of electric field (Ez) at the MA/air interface; the left and right elements of insets represent two adjacent unit cells of MA under different angles of incidence.
To highlight some advantages of the complementary-resonator MA, It is compared with the similar THz MA over the large angle of incidence in Table 1 [33, 35–41]. In the previous literatures, the thicker substrate was used into MA, and many MAs were sensitive to polarization. Although Ref [38]. shows good absorptance under TM mode at 70°, the shift of the resonant frequency was obviously generated. Our designed MA exhibits many advantages: Firstly, its thickness is only 0.029λ (ultrathin). Secondly, three absorption bands are all insensitive to polarization. Thirdly, its absorptivity under TE mode is greater than the case of other THz MAs and the resonance frequency nearly keeps unchanged even up to 70° incidence.
Table 1. Compared performance of the complementary-resonator MA with similar THz MAs
5. Conclusions
To conclude, we have designed and described triple-band THz MA supported by the single cave-ring and complementary resonators. Simulated results reveal that a single patterned resonator can obtain three perfect absorption peaks under various polarization angles. The good absorption mainly comes from the contribution of two metallic layers in MA. Next, we investigate the dependence of the absorption performance of MA on some geometric sizes and incident angles. The absorption peaks are controlled by the incident angles and 92% absorptivity still maintain well even at 80° of TE incidence. Besides, it is found that three resonance peaks mainly originate from the multipolar resonances. Here, the complementary resonator is also explored, exhibiting triple absorption bands. At 2.62 THz, the absorber realizes a larger angle tolerance compared with the previous reports. Therefore, it reminds us that a simple approach can get another MA with good performance.
Funding
National Key R&D Program of China (Grant No. 2018YFB0106301); Scientific Projects of State Grid Corporation of China (Grant No. 0231132705); National Natural Science Foundation of China (NSFC) (Grant No. 11575066); Graduates' Innovation Fund (Grant No.5003131025), Huazhong University of Science and Technology
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