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A tunable polarization insensitive ultra-broadband absorber based on the plasma metamaterial
Optics Communications 453 (2019) 124435
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
A tunable polarization insensitive ultra-broadband absorber based on the plasma metamaterial Xin-Ru Kong a , Hai-Feng Zhang a,b,c ,∗, Ri-Na Dao a , Guo-Biao Liu a a
College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China State Key Laboratory of Millimeter Waves of Southeast University, Nanjing, 210096, China c Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA b
ARTICLE
INFO
Keywords: Plasma metamaterial Polarization insensitive absorber Ultra-broadband Tunability
ABSTRACT In this article, we proposed a tunable polarization insensitive ultra-broadband absorber (TPIUA) in THz band make use of the plasma metamaterial, which is the solid state plasma. Because the foments of solid state plasma can be controlled by the external voltage, such an absorber can reach tunability. With different resonators being energized, different absorption states can be realized. When all the resonators are at excited state (state 1), the proposed TPIUA can reach an ultra-broadband absorption and the absorption region which is over 90% is from 7.18 THz to 14.29 THz. The corresponding relative bandwidth is 66.2%. If the middle and out resonators are energized (state 2), the proposed absorber can form an absorption region which is 8.42–12.81 THz (the absorptivity is above 90%), and its relative bandwidth is 41.4%. Besides, if all the resonators are nonenergized, the TPIUA can form four absorption frequency points whose absorptivities exceed 90%. And these absorption frequency points are 8.14 THz, 12.12 THz, 14.09 THz and 14.35 THz. Their absorptivities are 98.0%, 98.5%, 95.7% and 93.9%. If the incident angle is not larger than 20◦ , the absorber can achieve the stable absorption. The surface current distributions of such a TPIUA are shown to expound the physical mechanism. Besides, to analyzing the absorption mechanism of the TPIUA, we also give the electric fields and power loss densities. The reconfigurable device can be realized by tailoring the state of the solid state plasma.
1. Introduction Electromagnetic metamaterial (EM) is an artificially synthesized material. Because it has many fantastic characters that do not exist in the nature. EM has attracted many researchers’ attention [1,2]. In the past decades, EM had various of applications, such as negative index metamaterials [3–5], electromagnetic lens [6–8] and electromagnetic wave absorber [9–11]. EM is very important in THz region. Because there is no nature materials can act on the THz waves, it is hard to build THz devices [12]. The presence of EM solved this problem. And EM has very important applications in metamaterial modulators, detection, biomedical imaging, and so on. Generally, metamaterial absorber has attracted many researchers’ attention. Many people tried to broaden the absorption bandwidth [13–16]. In GHz regime, loading lumped components can broaden the absorption bandwidth [17–19]. Li et al. designed a frequency selective surface (SSF) by loading the resistors [19], and the SSF can reach an absorption which is from 1 GHz to 12 GHz (exceeding −10 dB). Besides, the multilayer structures also can widen the absorption bandwidth [20–22]. He et al. proposed a multilayer metamaterial absorber [22], and the absorber can form an absorption which is 0.76–0.96 THz.
In this article, we designed a TPIUA based on the plasma metamaterial. Because the state of solid state plasma can be changed by external voltage [23–25], such an absorber can reach a tunable absorption. However, the main challenge of the method proposed in the paper for future applications is how to control precisely [25]. The best absorption is from 7.18 THz to 14.29 THz (absorptivity is over 90%), whose relative absorption bandwidth is 66.2%, when the TPIUA is at state 1. However, the angular stability of the absorber is poor. Such an absorber only can achieve the stable absorption when the incident angle (IA) is less than 20◦ . 2. Modeling and simulation The top and side views are respectively shown in Fig. 1(a) and (b). The proposed TPIUA has three layers. From top to bottom, they are resonator units, dielectric and metal plate. The bottom layer is a metal plate. The metal plate is a whole gold plate and the electric conductivity of it is 4.561 × 107 s. It is a square plate and the side of the gold plate is 44.8 μm, and its thickness is 0.5 μm. The material of the middle layer is polyimide and it is loss free. The relative dielectric constant
∗ Corresponding author at: College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China. E-mail address: [email protected] (H.-F. Zhang).
https://doi.org/10.1016/j.optcom.2019.124435 Received 5 May 2019; Received in revised form 3 August 2019; Accepted 19 August 2019 Available online 21 August 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435
Fig. 1. The schematic diagrams for the TPIUA: (a) the top view of the TPIUA, (b) the side view of the TPIUA, (c) the schematic of state 1, (d) the schematic of state 2, (e) the schematic of state 3.
of polyimide is 3.5 [26]. The loss angle of it is 0. The material of the top layer is the solid state plasma, which is expressed as a Drude model. It is expressed as 𝜀𝑝 (𝜔) = 12.8 − 𝜔2𝑝 ∕(𝜔2 +𝑗𝜔𝜔𝑐 ). The solid state plasma can be controlled by external voltage. When the solid state plasma is at excited state, the frequency of solid state plasma is 𝜔𝑝 = 5 × 1014 rad/s and the collision frequency is 𝜔𝑐 = 5.903 × 1013 1/s. As Fig. 1(a) displayed, the top layer has three resonators, which are marked as R1 (the outside resonator), R2 (the middle resonator) and R3 (the inside resonator). The tunable absorption can be reached by controlling the state of three resonators. State 1 is the condition when R1 , R2 and R3 are all energized (as displayed in Fig. 1(c)). If R1 and R2 are at excited and R3 is at unexcited, the TPIUA is at state 2 (as shown in Fig. 1(d)). When three resonators are unenergized, such an absorber is at state
3 (as presented in Fig. 1(e)). The detailed parameters are shown in Table 1. The absorption of the TPIUA can be described as: 𝐴(𝜔) = 1 − 𝑅(𝜔) − 𝑇 (𝜔) And in the expression, 𝐴(𝜔) stands up absorptivity. 𝑅(𝜔) means reflectivity. 𝑇 (𝜔) is transmission. Because the bottom layer is a whole gold plate, 𝑇 (𝜔) = 0. Therefore, the formula can be simplified as: 𝐴(𝜔) = 1 − 𝑅(𝜔) = 1 − |𝑆11 (𝜔)|2 = 1 − |𝑆TMTE (𝜔)|2 − |𝑆TETE (𝜔)|2 |𝑆TMTE (𝜔)|2 and |𝑆TETE (𝜔)|2 respectively refer to cross-polarization reflectivity and co-polarization reflectivity. For this absorber, the crosspolarization is equal to zero. So the absorption of such an absorber can 2
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435 Table 1 The data for the TPIUA. Parameter Value (μm)
𝑑 1.5
ℎ 0.5
𝑙1 39.2
𝑙2 28
𝑙3 16.8
𝑚 1.12
𝑝 44.8
𝑡 3
In this paper, the results are calculated by the commercial programme HFSS. As shown in Fig. 3, the Master–Slave boundary conditions are set to simulate such a infinite periodic structure. The upper and lower surfaces are set as the Floquet ports to represent the ports for emitting and receiving electromagnetic wave, respectively. Besides, the electric field and magnetic field of TE wave are respectively parallel to y axis and x axis. And if the electric field and magnetic field are parallel to y axis and x axis respectively, it is TM wave. The absorption of the presented absorber is described in Fig. 2. Such an absorber is polarization insensitive, which means that the absorption for TE and TM waves are the same. From Fig. 2 we can see that when the TPIUA is at state 1, it has the best absorption (the absorptivity is over 90%) which is from 7.18 THz to 14.29 THz. And the corresponding relative absorption bandwidth is 66.2%. When the TPIUA is at state 2, the absorption region which is above 90% of such an absorber is 8.42–12.81 THz and the relative absorption bandwidth is 41.4%. If three resonators are at unexcited state (state 3), the proposed absorber only has four absorption frequency points whose absorptivities are over 90%. They are 8.14 THz, 12.12 THz, 14.09 THz and 14.35 THz and their absorptivities are 98.0%, 98.5%, 95.7% and 93.9%, respectively.
Fig. 2. The absorption spectra of the TPIUA under normal incidence under different states.
3. Theoretical analysis The electric fields and surface current distributions of the presented absorber for TE and TM waves at 11.5 THz when the TPIUA is at state 1 are separately plotted in Figs. 4 and 5. From Fig. 4 we can see that the main electric fields focus on the top and bottom of each resonators (marked by ‘‘#’’) at 11.5 THz for TE wave. As the arrow shown, the surface current distributions are mainly along −𝑦 direction at 11.5 THz for TE wave. Where electric fields concentrate on at 11.5 THz are the left and right sides of each resonator (marked by ‘‘#’’) for TM wave. The main surface current distributions are along −𝑥 direction (as arrow shown). The main surface current distributions for TE wave concentrates on the center and each side of the unit cell (marked by ‘‘#’’), it is the same for TM wave. Where the electric fields concentrated can be equally seen as positive charges and some negative charges can be equally placed on the region where the surface current distributions focus on. As Figs. 4 and 5 displayed, we can see that the main region where the electric fields and surface current distributions focus on are the same. However, there are some areas where the surface current distributions and electric fields concentrated on are different. In other words, when the incident electromagnetic waves pass through such
Fig. 3. The boundary conditions and port setting of simulation model.
come down to: 𝐴(𝜔) = 1 − 𝑅(𝜔) = 1 − |𝑆11 (𝜔)|2 = 1 − |𝑆TETE (𝜔)|2
Fig. 4. The electric fields and surface current distributions of the TPIUA for TE wave at 11.5 THz when such an absorber is at state 1: (a) the electric fields at 11.5 THz, (b) the surface current distributions at 11.5 THz. 3
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435
Fig. 5. The electric fields and surface current distributions of the TPIUA for TM wave at 11.5 THz when such an absorber is at state 1: (a) the electric fields at 11.5 THz, (b) the surface current distributions at 11.5 THz.
Fig. 6. The energy loss densities of the TPIUA for TE wave at 11.5 THz on different layers when such an absorber is at state 1: (a) the energy loss densities on the resonators, (b) the energy loss densities on the gold plate.
Fig. 7. The absorption region of the TPIUA with different IAs for TE wave when the absorber is at state 1: (a) the absorption with different IAs, (b) the contours of absorbance with different IAs.
an absorber, the energy will be loss by the magnetic resonances and electric resonances. Therefore, the magnetic resonances and electric resonances are the physical mechanism for absorption of the proposed TPIUA. In Fig. 6, when the absorber is at state 1, the energy loss densities on the resonators and gold layer at 11.5 THz are given. From Fig. 6(a) we can know that most energy loss densities are on the solid state plasma are concentrated on the R1 and R2 . There are almost no power loss densities on the gold plate. Besides, because the loss angle of dielectric is 0, the energy loss densities on the dielectric layer are almost nonexistent. Therefore, when the electromagnetic waves pass through the TPIUA, the main power loss densities are on the solid state plasma.
As Figs. 7 and 8 shown are the absorption areas of the TPIUA with different IA for TE and TM waves when the absorber is at state 1. From Fig. 7(a) we can see that when IAs are 0◦ , 10◦ , 20◦ and 30◦ , for TE wave, the absorption region whose absorptivities (AB) are above 90% are 7.18–14.29 THz, 7.15–14.44 THz, 7.06–15.20 THz and 10.31– 14.97 THz. Their responding relative bandwidths are 66.2%, 67.5%, 73.1% and 36.9%. But when IA is equal to or larger than 40◦ , there are no absorption spectra (𝐴𝐵 > 90%) in 0–20 THz. The contours of absorbance with different angles of this absorber are displayed in Fig. 7(b). Therefore, such an absorber can stably absorb incident electromagnetic waves for TE wave when 𝐼𝐴 < 20◦ . From Fig. 8(a) we can know that when IAs are 0◦ , 10◦ , 20◦ , 30◦ , 40◦ , 50◦ and 60◦ , the absorption spectra (𝐴𝐵 > 90%) for TM 4
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435
Fig. 8. The absorption spectra of the TPIUA with different IAs for TM wave when the absorber is at state 1: (a) the absorption with different IAs, (b) the contours of absorbance with different IAs.
Fig. 9. The absorption region of the TPIUA when it is at state 1 with different parameters for TE wave: (a) the absorption region with different 𝑙1 , (b) the absorption region with different 𝑙2 , (c) the absorption region with different 𝑙3 .
wave are 7.18–14.29 THz, 7.26–14.75 THz, 7.71–15.42 THz, 7.97– 16.04 THz, 8.37–16.87 THz, 8.79–17.94 THz and 9.27–18.91 THz. The corresponding relative bandwidths are 66.2%, 68.1%, 66.7%, 67.2%, 67.4%, 67.1% and 68.4%, respectively. However, when IAs are 70◦ and 80◦ , the proposed absorber has no absorption region (𝐴𝐵 > 90%) in 0– 20 THz. So, the TPIUA can reach the best absorption for TM wave when 𝐼𝐴 = 10◦ . When 𝐼𝐴 < 30◦ , the absorption of such an absorber for TM wave is stable. Besides, the TPIUA has an ultra broadband absorption for TM wave when the incident is less than 60◦ . From above we can
see that the angular stability of such an absorber for TE wave is better for TM wave. The absorption region of the TPIUA with different structure parameters for TE wave when such an absorber is at state 1 are displayed in Fig. 9. As Fig. 9(a) shown is the absorption region with different values of 𝑙1 . When 𝑙1 = 36.4 μm, 37.8 μm, 39.2 μm and 40.6 μm, the corresponding absorption regions (𝐴𝐵 > 90%) are 7.11–8.04 THz and 9.71– 15.10 THz, 7.15–14.94 THz, 7.18–14.29 THz and 7.17–14.43 THz. Their relative absorption bandwidths are 12.3% and 43.5%, 70.5%, 66.2% and 67.2%. From Fig. 9(b) we can know that when 𝑙2 = 5
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435
25.2 μm, 26.6 μm, 28.0 μm, 29.4 μm and 30.8 μm, the absorption whose absorptivities are above 90% of the TPIUA are 7.26–8.71 THz and 9.91–14.59 THz, 7.24–14.46 THz, 7.18–14.29 THz, 7.09–15.11 THz and 8.45–15.72 THz. The corresponding relative bandwidths are 18.2% and 38.2%, 66.5%, 66.2%, 72.2% and 60.2%. The absorption spectra with different values of 𝑙3 are shown in Fig. 9(c). The absorption regions are 7.24–14.14 THz, 7.21–13.88 THz, 7.18–14.29 THz, 7.13–14.48 THz and 9.68–14.59 THz when 𝑙3 = 14.0 μm, 15.4 μm, 16.8 μm, 18.2 μm and 19.6 μm. And their relative bandwidths are 64.5%, 63.3%, 66.2%, 68.0% and 40.5%, respectively.
[5] C. Argyropoulos, E. Kallos, Y. Zhao, Y. Hao, Manipulating the loss in electromagnetic cloaks for perfect wave absorption, Opt. Express 17 (10) (2009) 8467–8475. [6] K. Aydin, I. Bulu, E. Ozbay, Focusing of electromagnetic waves by a left-handed metamaterial flat lens, Opt. Express 13 (22) (2005) 8753–8759. [7] E. Verney, B. Sauviac, C.R. Simovski, Isotropic metamaterial electromagnetic lens, Phys. Lett. A. 331 (3–4) (2004) 244–247. [8] X.Q. Lin, T.J. Cui, J.Y. Chin, X.M. Yang, Q. Cheng, R. Liu, Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens, Appl. Phys. Lett. 92 (13) (2008) 131904. [9] C.M. Watts, X. Liu, W.J. Padilla, Metamaterial electromagnetic wave absorbers, Adv. Mater. 24 (23) (2012) OP98–OP120. [10] J. Zhu, Z. Ma, W. Sun, F. Ding, Q. He, L. Zhou, Y. Ma, Ultra-broadband terahertz metamaterial absorber, Appl. Phys. Lett. 105 (2) (2014) 021102. [11] L.L. Spada, L. Vegni, Metamaterial-based wideband electromagnetic wave absorber, Opt. Express 24 (6) (2016) 5763–5772. [12] H.T. Chen, J.F. O’hara, A.K. Azad, A.J. Taylor, R.D. Averitt, D.B. Shrekenhamer, W.J. Padilla, Experimental demonstration of frequency-agile terahertz metamaterials, Nat. Photonics 2 (5) (2008) 295. [13] B.X. Wang, L.L. Wang, G.Z. Wang, W.Q. Huang, X.F. Li, X. Zhai, Metamaterialbased low-conductivity alloy perfect absorber, J. Lightwave Technol. 32 (12) (2014) 2293–2298. [14] S. He, T. Chen, Broadband THz absorbers with graphene-based anisotropic metamaterial films, IEEE Trans. Terahertz Sci. Technol. 3 (6) (2013) 757–763. [15] W. Pan, X. Yu, J. Zhang, W. Zeng, A novel design of broadband terahertz metamaterial absorber based on nested circle rings, IEEE Photonics Technol. Lett. 28 (21) (2016) 2335–2338. [16] Y. Peng, X.F. Zang, Y.M. Zhu, C. Shi, L. Chen, B. Cai, S.L. Zhuang, Ultrabroadband terahertz perfect absorber by exciting multi-order diffractions in a double-layered grating structure, Opt. Express 23 (3) (2015) 2032–2039. [17] A.K. Rashid, Z. Shen, S. Aditya, Wideband microwave absorber based on a two-dimensional periodic array of microstrip lines, IEEE Trans. Antennas and Propagation 58 (12) (2010) 3913–3922. [18] H. Zhai, C. Zhan, L. Liu, Y. Zang, Reconfigurable wideband metamaterial absorber with wide angle and polarisation stability, Electron. Lett. 51 (21) (2015) 1624–1626. [19] J. Li, J. Jiang, Y. He, W. Xu, M. Chen, L. Miao, S. Bie, Design of a tunable low-frequency and broadband radar absorber based on active frequency selective surface, IEEE Antennas Wirel. Propag. 15 (2016) 774–777. [20] Z. Su, J. Yin, X. Zhao, Terahertz dual-band metamaterial absorber based on graphene/MgF2 multilayer structures, Opt. Express 23 (2) (2015) 1679–1690. [21] Y. Danlée, I. Huynen, C. Bailly, Thin smart multilayer microwave absorber based on hybrid structure of polymer and carbon nanotubes, Appl. Phys. Lett. 100 (21) (2012) 213105. [22] X. He, S. Yan, Q. Ma, Q. Zhang, P. Jia, F. Wu, J. Jiang, Broadband and polarization-insensitive terahertz absorber based on multilayer metamaterials, Opt. Commun. 340 (2015) 44–49. [23] X.K. Kong, H. Li, B. Bian, F. Xue, G. Ding, S. Yu, S. Liu, Microwave tunneling in heterostructures with electromagnetically induced transparency-like metamaterials based on solid state plasma, Eur. Phys. J. Appl. Phys. 74 (3) (2016) 30801. [24] X.K. Kong, J.J. Mo, Z.Y. Yu, W. Shi, H.M. Li, Reconfigurable designs for electromagnetically induced transparency in solid state plasma metamaterials with multiple transmission windows, Internat. J. Modern Phys. B 30 (14) (2016) 1650070. [25] F. Xue, S.B. Liu, H.F. Zhang, Y.D. Wen, X.K. Kong, A novel reconfigurable electromagnetically induced transparency based on S-PINs, Internat. J. Modern Phys. B 32 (04) (2018) 1850030. [26] Y. Ren, D.C.C. Lam, Properties and microstructures of low-temperatureprocessable ultralow-dielectric porous polyimide films, J. Electron. Mater. 37 (7) (2008) 955.
4. Conclusion In conclusion, a tunable polarization insensitive ultra-broadband absorber based on the solid state plasma has been designed. We can change the foments of solid state plasma by external voltage. Therefore, the TPIUA can reach tenability by controlling the foments of solid state plasma. When the absorber is at state 1 (all the resonators are excited), the absorption spectra (𝐴𝐵 > 90%) is from 7.18 THz to 14.29 THz and the corresponding relative bandwidth is 66.2%. Such an absorber can form an absorption region (𝐴𝐵 > 90%) which is 8.42–12.81 THz when it is at state 2 (the middle and out resonators are energized). Its corresponding relative bandwidth is 41.4%. If all the resonators are unenergized (state 3), the absorber has four absorption frequency points (𝐴𝐵 > 90%), which are 8.14 THz, 12.12 THz, 14.09 THz and 14.35 THz. And the corresponding absorptivities are 98.0%, 98.5%, 95.7% and 93.9%. The angular stability of the TPIUA is worse. The performance of this absorber can maintain stable when 𝐼𝐴 < 20◦ . By analyzing the electric fields, surface current distributions and power loss densities of the TPIUA, we can know that when the incident electromagnetic waves pass through such an absorber, the energy will be loss by the magnetic resonances and electric resonances. Acknowledgments This work was supported by the Open Research Program in China’s State Key Laboratory of Millimeter Waves (Grant No. K201927), and Jiangsu Overseas Visiting Scholar Program for the University prominent Young & Middle-aged Teachers and Presidents. References [1] W.F. Bahret, The beginnings of stealth technology, IEEE Trans. Aerosp. Electron. Syst. 29 (4) (1993) 1377–1385. [2] R.L. Fante, M.T. McCormack, Reflection properties of the Salisbury screen, IEEE Trans. Antennas and Propagation 36 (10) (1988) 1443–1454. [3] Y. Cheng, H. Yang, Z. Cheng, N. Wu, Perfect metamaterial absorber based on a split-ring-cross resonator, Appl. Phys. A 102 (1) (2011) 99–103. [4] N.I. Landy, S. Sajuyigbe, J.J. Mock, D.R. Smith, W.J. Padilla, Perfect metamaterial absorber, Phys. Rev. Lett. 100 (20) (2008) 207402.
6
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
A tunable polarization insensitive ultra-broadband absorber based on the plasma metamaterial Xin-Ru Kong a , Hai-Feng Zhang a,b,c ,∗, Ri-Na Dao a , Guo-Biao Liu a a
College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China State Key Laboratory of Millimeter Waves of Southeast University, Nanjing, 210096, China c Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA b
ARTICLE
INFO
Keywords: Plasma metamaterial Polarization insensitive absorber Ultra-broadband Tunability
ABSTRACT In this article, we proposed a tunable polarization insensitive ultra-broadband absorber (TPIUA) in THz band make use of the plasma metamaterial, which is the solid state plasma. Because the foments of solid state plasma can be controlled by the external voltage, such an absorber can reach tunability. With different resonators being energized, different absorption states can be realized. When all the resonators are at excited state (state 1), the proposed TPIUA can reach an ultra-broadband absorption and the absorption region which is over 90% is from 7.18 THz to 14.29 THz. The corresponding relative bandwidth is 66.2%. If the middle and out resonators are energized (state 2), the proposed absorber can form an absorption region which is 8.42–12.81 THz (the absorptivity is above 90%), and its relative bandwidth is 41.4%. Besides, if all the resonators are nonenergized, the TPIUA can form four absorption frequency points whose absorptivities exceed 90%. And these absorption frequency points are 8.14 THz, 12.12 THz, 14.09 THz and 14.35 THz. Their absorptivities are 98.0%, 98.5%, 95.7% and 93.9%. If the incident angle is not larger than 20◦ , the absorber can achieve the stable absorption. The surface current distributions of such a TPIUA are shown to expound the physical mechanism. Besides, to analyzing the absorption mechanism of the TPIUA, we also give the electric fields and power loss densities. The reconfigurable device can be realized by tailoring the state of the solid state plasma.
1. Introduction Electromagnetic metamaterial (EM) is an artificially synthesized material. Because it has many fantastic characters that do not exist in the nature. EM has attracted many researchers’ attention [1,2]. In the past decades, EM had various of applications, such as negative index metamaterials [3–5], electromagnetic lens [6–8] and electromagnetic wave absorber [9–11]. EM is very important in THz region. Because there is no nature materials can act on the THz waves, it is hard to build THz devices [12]. The presence of EM solved this problem. And EM has very important applications in metamaterial modulators, detection, biomedical imaging, and so on. Generally, metamaterial absorber has attracted many researchers’ attention. Many people tried to broaden the absorption bandwidth [13–16]. In GHz regime, loading lumped components can broaden the absorption bandwidth [17–19]. Li et al. designed a frequency selective surface (SSF) by loading the resistors [19], and the SSF can reach an absorption which is from 1 GHz to 12 GHz (exceeding −10 dB). Besides, the multilayer structures also can widen the absorption bandwidth [20–22]. He et al. proposed a multilayer metamaterial absorber [22], and the absorber can form an absorption which is 0.76–0.96 THz.
In this article, we designed a TPIUA based on the plasma metamaterial. Because the state of solid state plasma can be changed by external voltage [23–25], such an absorber can reach a tunable absorption. However, the main challenge of the method proposed in the paper for future applications is how to control precisely [25]. The best absorption is from 7.18 THz to 14.29 THz (absorptivity is over 90%), whose relative absorption bandwidth is 66.2%, when the TPIUA is at state 1. However, the angular stability of the absorber is poor. Such an absorber only can achieve the stable absorption when the incident angle (IA) is less than 20◦ . 2. Modeling and simulation The top and side views are respectively shown in Fig. 1(a) and (b). The proposed TPIUA has three layers. From top to bottom, they are resonator units, dielectric and metal plate. The bottom layer is a metal plate. The metal plate is a whole gold plate and the electric conductivity of it is 4.561 × 107 s. It is a square plate and the side of the gold plate is 44.8 μm, and its thickness is 0.5 μm. The material of the middle layer is polyimide and it is loss free. The relative dielectric constant
∗ Corresponding author at: College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China. E-mail address: [email protected] (H.-F. Zhang).
https://doi.org/10.1016/j.optcom.2019.124435 Received 5 May 2019; Received in revised form 3 August 2019; Accepted 19 August 2019 Available online 21 August 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435
Fig. 1. The schematic diagrams for the TPIUA: (a) the top view of the TPIUA, (b) the side view of the TPIUA, (c) the schematic of state 1, (d) the schematic of state 2, (e) the schematic of state 3.
of polyimide is 3.5 [26]. The loss angle of it is 0. The material of the top layer is the solid state plasma, which is expressed as a Drude model. It is expressed as 𝜀𝑝 (𝜔) = 12.8 − 𝜔2𝑝 ∕(𝜔2 +𝑗𝜔𝜔𝑐 ). The solid state plasma can be controlled by external voltage. When the solid state plasma is at excited state, the frequency of solid state plasma is 𝜔𝑝 = 5 × 1014 rad/s and the collision frequency is 𝜔𝑐 = 5.903 × 1013 1/s. As Fig. 1(a) displayed, the top layer has three resonators, which are marked as R1 (the outside resonator), R2 (the middle resonator) and R3 (the inside resonator). The tunable absorption can be reached by controlling the state of three resonators. State 1 is the condition when R1 , R2 and R3 are all energized (as displayed in Fig. 1(c)). If R1 and R2 are at excited and R3 is at unexcited, the TPIUA is at state 2 (as shown in Fig. 1(d)). When three resonators are unenergized, such an absorber is at state
3 (as presented in Fig. 1(e)). The detailed parameters are shown in Table 1. The absorption of the TPIUA can be described as: 𝐴(𝜔) = 1 − 𝑅(𝜔) − 𝑇 (𝜔) And in the expression, 𝐴(𝜔) stands up absorptivity. 𝑅(𝜔) means reflectivity. 𝑇 (𝜔) is transmission. Because the bottom layer is a whole gold plate, 𝑇 (𝜔) = 0. Therefore, the formula can be simplified as: 𝐴(𝜔) = 1 − 𝑅(𝜔) = 1 − |𝑆11 (𝜔)|2 = 1 − |𝑆TMTE (𝜔)|2 − |𝑆TETE (𝜔)|2 |𝑆TMTE (𝜔)|2 and |𝑆TETE (𝜔)|2 respectively refer to cross-polarization reflectivity and co-polarization reflectivity. For this absorber, the crosspolarization is equal to zero. So the absorption of such an absorber can 2
X.-R. Kong, H.-F. Zhang, R.-N. Dao et al.
Optics Communications 453 (2019) 124435 Table 1 The data for the TPIUA. Parameter Value (μm)
𝑑 1.5
ℎ 0.5
𝑙1 39.2
𝑙2 28
𝑙3 16.8
𝑚 1.12
𝑝 44.8
𝑡 3
In this paper, the results are calculated by the commercial programme HFSS. As shown in Fig. 3, the Master–Slave boundary conditions are set to simulate such a infinite periodic structure. The upper and lower surfaces are set as the Floquet ports to represent the ports for emitting and receiving electromagnetic wave, respectively. Besides, the electric field and magnetic field of TE wave are respectively parallel to y axis and x axis. And if the electric field and magnetic field are parallel to y axis and x axis respectively, it is TM wave. The absorption of the presented absorber is described in Fig. 2. Such an absorber is polarization insensitive, which means that the absorption for TE and TM waves are the same. From Fig. 2 we can see that when the TPIUA is at state 1, it has the best absorption (the absorptivity is over 90%) which is from 7.18 THz to 14.29 THz. And the corresponding relative absorption bandwidth is 66.2%. When the TPIUA is at state 2, the absorption region which is above 90% of such an absorber is 8.42–12.81 THz and the relative absorption bandwidth is 41.4%. If three resonators are at unexcited state (state 3), the proposed absorber only has four absorption frequency points whose absorptivities are over 90%. They are 8.14 THz, 12.12 THz, 14.09 THz and 14.35 THz and their absorptivities are 98.0%, 98.5%, 95.7% and 93.9%, respectively.
Fig. 2. The absorption spectra of the TPIUA under normal incidence under different states.
3. Theoretical analysis The electric fields and surface current distributions of the presented absorber for TE and TM waves at 11.5 THz when the TPIUA is at state 1 are separately plotted in Figs. 4 and 5. From Fig. 4 we can see that the main electric fields focus on the top and bottom of each resonators (marked by ‘‘#’’) at 11.5 THz for TE wave. As the arrow shown, the surface current distributions are mainly along −𝑦 direction at 11.5 THz for TE wave. Where electric fields concentrate on at 11.5 THz are the left and right sides of each resonator (marked by ‘‘#’’) for TM wave. The main surface current distributions are along −𝑥 direction (as arrow shown). The main surface current distributions for TE wave concentrates on the center and each side of the unit cell (marked by ‘‘#’’), it is the same for TM wave. Where the electric fields concentrated can be equally seen as positive charges and some negative charges can be equally placed on the region where the surface current distributions focus on. As Figs. 4 and 5 displayed, we can see that the main region where the electric fields and surface current distributions focus on are the same. However, there are some areas where the surface current distributions and electric fields concentrated on are different. In other words, when the incident electromagnetic waves pass through such
Fig. 3. The boundary conditions and port setting of simulation model.
come down to: 𝐴(𝜔) = 1 − 𝑅(𝜔) = 1 − |𝑆11 (𝜔)|2 = 1 − |𝑆TETE (𝜔)|2
Fig. 4. The electric fields and surface current distributions of the TPIUA for TE wave at 11.5 THz when such an absorber is at state 1: (a) the electric fields at 11.5 THz, (b) the surface current distributions at 11.5 THz. 3
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Optics Communications 453 (2019) 124435
Fig. 5. The electric fields and surface current distributions of the TPIUA for TM wave at 11.5 THz when such an absorber is at state 1: (a) the electric fields at 11.5 THz, (b) the surface current distributions at 11.5 THz.
Fig. 6. The energy loss densities of the TPIUA for TE wave at 11.5 THz on different layers when such an absorber is at state 1: (a) the energy loss densities on the resonators, (b) the energy loss densities on the gold plate.
Fig. 7. The absorption region of the TPIUA with different IAs for TE wave when the absorber is at state 1: (a) the absorption with different IAs, (b) the contours of absorbance with different IAs.
an absorber, the energy will be loss by the magnetic resonances and electric resonances. Therefore, the magnetic resonances and electric resonances are the physical mechanism for absorption of the proposed TPIUA. In Fig. 6, when the absorber is at state 1, the energy loss densities on the resonators and gold layer at 11.5 THz are given. From Fig. 6(a) we can know that most energy loss densities are on the solid state plasma are concentrated on the R1 and R2 . There are almost no power loss densities on the gold plate. Besides, because the loss angle of dielectric is 0, the energy loss densities on the dielectric layer are almost nonexistent. Therefore, when the electromagnetic waves pass through the TPIUA, the main power loss densities are on the solid state plasma.
As Figs. 7 and 8 shown are the absorption areas of the TPIUA with different IA for TE and TM waves when the absorber is at state 1. From Fig. 7(a) we can see that when IAs are 0◦ , 10◦ , 20◦ and 30◦ , for TE wave, the absorption region whose absorptivities (AB) are above 90% are 7.18–14.29 THz, 7.15–14.44 THz, 7.06–15.20 THz and 10.31– 14.97 THz. Their responding relative bandwidths are 66.2%, 67.5%, 73.1% and 36.9%. But when IA is equal to or larger than 40◦ , there are no absorption spectra (𝐴𝐵 > 90%) in 0–20 THz. The contours of absorbance with different angles of this absorber are displayed in Fig. 7(b). Therefore, such an absorber can stably absorb incident electromagnetic waves for TE wave when 𝐼𝐴 < 20◦ . From Fig. 8(a) we can know that when IAs are 0◦ , 10◦ , 20◦ , 30◦ , 40◦ , 50◦ and 60◦ , the absorption spectra (𝐴𝐵 > 90%) for TM 4
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Optics Communications 453 (2019) 124435
Fig. 8. The absorption spectra of the TPIUA with different IAs for TM wave when the absorber is at state 1: (a) the absorption with different IAs, (b) the contours of absorbance with different IAs.
Fig. 9. The absorption region of the TPIUA when it is at state 1 with different parameters for TE wave: (a) the absorption region with different 𝑙1 , (b) the absorption region with different 𝑙2 , (c) the absorption region with different 𝑙3 .
wave are 7.18–14.29 THz, 7.26–14.75 THz, 7.71–15.42 THz, 7.97– 16.04 THz, 8.37–16.87 THz, 8.79–17.94 THz and 9.27–18.91 THz. The corresponding relative bandwidths are 66.2%, 68.1%, 66.7%, 67.2%, 67.4%, 67.1% and 68.4%, respectively. However, when IAs are 70◦ and 80◦ , the proposed absorber has no absorption region (𝐴𝐵 > 90%) in 0– 20 THz. So, the TPIUA can reach the best absorption for TM wave when 𝐼𝐴 = 10◦ . When 𝐼𝐴 < 30◦ , the absorption of such an absorber for TM wave is stable. Besides, the TPIUA has an ultra broadband absorption for TM wave when the incident is less than 60◦ . From above we can
see that the angular stability of such an absorber for TE wave is better for TM wave. The absorption region of the TPIUA with different structure parameters for TE wave when such an absorber is at state 1 are displayed in Fig. 9. As Fig. 9(a) shown is the absorption region with different values of 𝑙1 . When 𝑙1 = 36.4 μm, 37.8 μm, 39.2 μm and 40.6 μm, the corresponding absorption regions (𝐴𝐵 > 90%) are 7.11–8.04 THz and 9.71– 15.10 THz, 7.15–14.94 THz, 7.18–14.29 THz and 7.17–14.43 THz. Their relative absorption bandwidths are 12.3% and 43.5%, 70.5%, 66.2% and 67.2%. From Fig. 9(b) we can know that when 𝑙2 = 5
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Optics Communications 453 (2019) 124435
25.2 μm, 26.6 μm, 28.0 μm, 29.4 μm and 30.8 μm, the absorption whose absorptivities are above 90% of the TPIUA are 7.26–8.71 THz and 9.91–14.59 THz, 7.24–14.46 THz, 7.18–14.29 THz, 7.09–15.11 THz and 8.45–15.72 THz. The corresponding relative bandwidths are 18.2% and 38.2%, 66.5%, 66.2%, 72.2% and 60.2%. The absorption spectra with different values of 𝑙3 are shown in Fig. 9(c). The absorption regions are 7.24–14.14 THz, 7.21–13.88 THz, 7.18–14.29 THz, 7.13–14.48 THz and 9.68–14.59 THz when 𝑙3 = 14.0 μm, 15.4 μm, 16.8 μm, 18.2 μm and 19.6 μm. And their relative bandwidths are 64.5%, 63.3%, 66.2%, 68.0% and 40.5%, respectively.
[5] C. Argyropoulos, E. Kallos, Y. Zhao, Y. Hao, Manipulating the loss in electromagnetic cloaks for perfect wave absorption, Opt. Express 17 (10) (2009) 8467–8475. [6] K. Aydin, I. Bulu, E. Ozbay, Focusing of electromagnetic waves by a left-handed metamaterial flat lens, Opt. Express 13 (22) (2005) 8753–8759. [7] E. Verney, B. Sauviac, C.R. Simovski, Isotropic metamaterial electromagnetic lens, Phys. Lett. A. 331 (3–4) (2004) 244–247. [8] X.Q. Lin, T.J. Cui, J.Y. Chin, X.M. Yang, Q. Cheng, R. Liu, Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens, Appl. Phys. Lett. 92 (13) (2008) 131904. [9] C.M. Watts, X. Liu, W.J. Padilla, Metamaterial electromagnetic wave absorbers, Adv. Mater. 24 (23) (2012) OP98–OP120. [10] J. Zhu, Z. Ma, W. Sun, F. Ding, Q. He, L. Zhou, Y. Ma, Ultra-broadband terahertz metamaterial absorber, Appl. Phys. Lett. 105 (2) (2014) 021102. [11] L.L. Spada, L. Vegni, Metamaterial-based wideband electromagnetic wave absorber, Opt. Express 24 (6) (2016) 5763–5772. [12] H.T. Chen, J.F. O’hara, A.K. Azad, A.J. Taylor, R.D. Averitt, D.B. Shrekenhamer, W.J. Padilla, Experimental demonstration of frequency-agile terahertz metamaterials, Nat. Photonics 2 (5) (2008) 295. [13] B.X. Wang, L.L. Wang, G.Z. Wang, W.Q. Huang, X.F. Li, X. Zhai, Metamaterialbased low-conductivity alloy perfect absorber, J. Lightwave Technol. 32 (12) (2014) 2293–2298. [14] S. He, T. Chen, Broadband THz absorbers with graphene-based anisotropic metamaterial films, IEEE Trans. Terahertz Sci. Technol. 3 (6) (2013) 757–763. [15] W. Pan, X. Yu, J. Zhang, W. Zeng, A novel design of broadband terahertz metamaterial absorber based on nested circle rings, IEEE Photonics Technol. Lett. 28 (21) (2016) 2335–2338. [16] Y. Peng, X.F. Zang, Y.M. Zhu, C. Shi, L. Chen, B. Cai, S.L. Zhuang, Ultrabroadband terahertz perfect absorber by exciting multi-order diffractions in a double-layered grating structure, Opt. Express 23 (3) (2015) 2032–2039. [17] A.K. Rashid, Z. Shen, S. Aditya, Wideband microwave absorber based on a two-dimensional periodic array of microstrip lines, IEEE Trans. Antennas and Propagation 58 (12) (2010) 3913–3922. [18] H. Zhai, C. Zhan, L. Liu, Y. Zang, Reconfigurable wideband metamaterial absorber with wide angle and polarisation stability, Electron. Lett. 51 (21) (2015) 1624–1626. [19] J. Li, J. Jiang, Y. He, W. Xu, M. Chen, L. Miao, S. Bie, Design of a tunable low-frequency and broadband radar absorber based on active frequency selective surface, IEEE Antennas Wirel. Propag. 15 (2016) 774–777. [20] Z. Su, J. Yin, X. Zhao, Terahertz dual-band metamaterial absorber based on graphene/MgF2 multilayer structures, Opt. Express 23 (2) (2015) 1679–1690. [21] Y. Danlée, I. Huynen, C. Bailly, Thin smart multilayer microwave absorber based on hybrid structure of polymer and carbon nanotubes, Appl. Phys. Lett. 100 (21) (2012) 213105. [22] X. He, S. Yan, Q. Ma, Q. Zhang, P. Jia, F. Wu, J. Jiang, Broadband and polarization-insensitive terahertz absorber based on multilayer metamaterials, Opt. Commun. 340 (2015) 44–49. [23] X.K. Kong, H. Li, B. Bian, F. Xue, G. Ding, S. Yu, S. Liu, Microwave tunneling in heterostructures with electromagnetically induced transparency-like metamaterials based on solid state plasma, Eur. Phys. J. Appl. Phys. 74 (3) (2016) 30801. [24] X.K. Kong, J.J. Mo, Z.Y. Yu, W. Shi, H.M. Li, Reconfigurable designs for electromagnetically induced transparency in solid state plasma metamaterials with multiple transmission windows, Internat. J. Modern Phys. B 30 (14) (2016) 1650070. [25] F. Xue, S.B. Liu, H.F. Zhang, Y.D. Wen, X.K. Kong, A novel reconfigurable electromagnetically induced transparency based on S-PINs, Internat. J. Modern Phys. B 32 (04) (2018) 1850030. [26] Y. Ren, D.C.C. Lam, Properties and microstructures of low-temperatureprocessable ultralow-dielectric porous polyimide films, J. Electron. Mater. 37 (7) (2008) 955.
4. Conclusion In conclusion, a tunable polarization insensitive ultra-broadband absorber based on the solid state plasma has been designed. We can change the foments of solid state plasma by external voltage. Therefore, the TPIUA can reach tenability by controlling the foments of solid state plasma. When the absorber is at state 1 (all the resonators are excited), the absorption spectra (𝐴𝐵 > 90%) is from 7.18 THz to 14.29 THz and the corresponding relative bandwidth is 66.2%. Such an absorber can form an absorption region (𝐴𝐵 > 90%) which is 8.42–12.81 THz when it is at state 2 (the middle and out resonators are energized). Its corresponding relative bandwidth is 41.4%. If all the resonators are unenergized (state 3), the absorber has four absorption frequency points (𝐴𝐵 > 90%), which are 8.14 THz, 12.12 THz, 14.09 THz and 14.35 THz. And the corresponding absorptivities are 98.0%, 98.5%, 95.7% and 93.9%. The angular stability of the TPIUA is worse. The performance of this absorber can maintain stable when 𝐼𝐴 < 20◦ . By analyzing the electric fields, surface current distributions and power loss densities of the TPIUA, we can know that when the incident electromagnetic waves pass through such an absorber, the energy will be loss by the magnetic resonances and electric resonances. Acknowledgments This work was supported by the Open Research Program in China’s State Key Laboratory of Millimeter Waves (Grant No. K201927), and Jiangsu Overseas Visiting Scholar Program for the University prominent Young & Middle-aged Teachers and Presidents. References [1] W.F. Bahret, The beginnings of stealth technology, IEEE Trans. Aerosp. Electron. Syst. 29 (4) (1993) 1377–1385. [2] R.L. Fante, M.T. McCormack, Reflection properties of the Salisbury screen, IEEE Trans. Antennas and Propagation 36 (10) (1988) 1443–1454. [3] Y. Cheng, H. Yang, Z. Cheng, N. Wu, Perfect metamaterial absorber based on a split-ring-cross resonator, Appl. Phys. A 102 (1) (2011) 99–103. [4] N.I. Landy, S. Sajuyigbe, J.J. Mock, D.R. Smith, W.J. Padilla, Perfect metamaterial absorber, Phys. Rev. Lett. 100 (20) (2008) 207402.
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