Decisive role of the dielectric spacer on metamaterial hybridization

Vật lý<br /> <br /> <br /> DECISIVE ROLE OF THE DIELECTRIC SPACER ON<br /> METAMATERIAL HYBRIDIZATION<br /> PHAN THI DUYEN*, NGO DUC VIET*, NGUYEN THI HIEN**,<br /> NGUYEN THANH TUNG****, VU DINH LAM*<br /> <br /> Abstract: Since the first observation of the fascinating negative refractive-index<br /> property, meta-materials have been in the scientific spotlight. A typical interest has<br /> been paid for negative refractive meta-materials with a broad operating band,<br /> which are more useful for applications. In our recent work, we have theoretically<br /> shown that a broad negative permeability band can be achieved by introducing<br /> hybridized meta-materials [N. T. Tung et al., Appl. Phys. Express 5, 112001<br /> (2012)]. To step forward an experimental realization of the above proposal,<br /> evaluating the loss contribution at resonant frequencies is indispensable. In this<br /> report, we study the metallic and dielectric losses that directly influence the strength<br /> of permeability negativity at microwave regime. The results show that the dielectric<br /> loss plays a decisive role in forming the meta-material hybridization.<br /> Keywords: Meta-materials, Hybridization, Dielectric loss.<br /> <br /> 1. INTRODUCTION<br /> Recent development of science and technology investigates new materials with novel<br /> properties, which have large potential applications in science and engineering to replace<br /> conventional ones. In the last decade, meta-materials emerged as a completely new class<br /> of materials, attracted great attention of the scientific community by fascinating properties<br /> [1]. Meta-material is known to be a kind of artificial materials with sub-wavelength scaled<br /> unit cell. These unit cells function as the atoms in the material. A meta-material “atom” is<br /> generally composed of two main components: electric component creating negative<br /> permeability ε [see Fig. 1(a)]. In the asymmetric mode,<br /> the surface currents are antiparallel, generating an induced magnetic resonance (negative<br /> permeability). Meanwhile, the symmetric mode is consists of parallel surface currents<br /> which interact to the external electric field, creating an electric resonance. In this paper, we<br /> restrict our attention to the asymmetric mode with the magnetic resonance behavior.<br /> <br /> <br /> <br /> <br /> (a) (b)<br /> <br /> Fig. 1. Hybridization model of (a) the CWP monomer and (b) CWP dimer.<br /> <br /> It is known that a broad negative permeability band has been reported using CWP<br /> dimer metamaterials [2]. By controlling the internal-external coupling correlation along<br /> the k direction between two CWPs in a dimer, the original asymmetric mode |w-> can be<br /> split into two new asymmetric modes: |w--> and |w-+ > [see Fig. 1(b)]. A similar<br /> explanation as in case of CWP monomers can be used to understand the resonant split of<br /> CWP dimmers. When the distance between two identical CWP monomers is close enough,<br /> the charge interaction between two CWP monomers is getting stronger. Total energy of<br /> the CWP dimer system is now determined by the interaction energy between two CWs in a<br /> pair and the additional interaction energy between two CWPs in a dimer.<br /> Importantly, the asymmetric resonant split can only appear when the energy of the<br /> internal coupling and that of the external coupling are strong and comparable [2]. The<br /> lateral condition implies that the distance between two CWP monomers in a dimer must be<br /> well defined. This can be overcome by an intensive structural optimization. Meanwhile,<br /> the first condition suggests that loss factor in the asymmetric magnetic resonance should<br /> be small. One might know that the loss origin in materials, in general, can be divided into<br /> two parts: the Ohmic loss and the dielectric loss. In metamaterials, the major part of loss is<br /> often attributed to the dielectric materials while the Ohmic loss has almost no influence on<br /> the resonance [12]. Therefore, the key to keep the loss sufficient low is the dielectric<br /> <br /> <br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 35, 02 - 2015 107<br />  Vật lý<br /> <br /> spacer. By studying the loss contribution of the dielectric spacer, we might be able to<br /> estimate the loss threshold where the asymmetric resonant split does not exist.<br /> <br /> 3. NUMMERICAL MODEL AND NUMERIAL SIMULATION<br /> 3.1. Nummerical model<br /> A CWP monomer and its corresponding dimer structure are shown in geometric<br /> parameters in Fig. 2 with the electromagnetic polarization. A CWP dimer consists of two<br /> identical CWP monomer separated by a distance d. The CWP structure is composed of<br /> copper patterns (ts = 036mm thick) on both sides of a dielectric spacer (td = 0.4 mm thick)<br /> with a dielectric constant of 4.3. The length and width of CWs are l = 5.5 and w = 1.0 mm,<br /> respectively. The lattice constants of unit cell in the H-, E-, and k- direction are ax, ay, az,<br /> respectively. In this study, ax, ay are chosen to be 3.5 mm and 7.0 mm, respectively. These<br /> parameters are optimized to obtain a known magnetic resonance over the frequency range<br /> of 12-18 GHz [11].<br /> The electromagnetic response of CWP metamaterials is simulated by using the<br /> commercial simulation software CST, based on the finite integration technique. For all<br /> calculations, the CWP metamaterial structure are illuminated by a normally incident plane<br /> wave where the magnetic field is polarized along to the x direction while the electric field<br /> is in the y axis.<br /> <br /> <br /> <br /> <br /> Fig. 1. Schematic representing of (a) a CWP monomer and (b) a CWP dimer.<br /> <br /> 3.2. Numerial simulation<br /> For time dependent electromagnetic fields propagating through dielectric materials, the<br /> permittivity can have real and imaginary components as follows [13]<br /> ε = ε’ – jε” (1)<br /> where ε″ is the imaginary component of permittivity attributed to bound charge and dipole<br /> relaxation phenomena, which gives rise to energy loss that is indistinguishable from the<br /> loss due to the free charge conduction that is quantified by conductivity σ. The<br /> component ε′ represents the familiar lossless permittivity given by the product of the free<br /> space permittivity and the relative real permittivity, or ε′ = ε0 ε′r [14,15]. The loss<br /> tangent is then defined as<br /> tan = (ε” + σ)/ ε’ (2)<br /> Equation (2) shows the total dielectric loss in a dielectric material. Based on that basis, we<br /> perform simulations to study the dependence of hybridization strength on the loss tangent<br /> of the dielectric layer. Table 1 indicates the loss tangents of most popular dielectric<br /> materials and their corresponding dielectric constants.<br /> <br /> <br /> 108 P. T. Duyen, …,V.D. Lam, “Decisive role of the dielectric spacer … hybridization.”<br /> Nghiên cứu khoa học công nghệ<br /> <br /> Table 1. Loss tangent and dielectric constant of dielectric materials<br /> [source: wikipedia.com].<br /> Materials Loss tangent Dielectric constant<br /> Teflon 0.001 2.1<br /> Mica 0.006 4.5<br /> Borosilicate 0.02 5<br /> Pyrex glass 0.05 4<br /> Figure 3 presents the transmission spectra of hybridized CWP dimers according to the<br /> loss tangent suggested in Table I. For comparison, all calculations are done by taking an<br /> average dielectric constant of 4. It should be noted that different values of the dielectric<br /> constant does not change the loss contribution except for a resonant frequency shift. In<br /> case of low loss materials (Teflon), two resonances originated from the Plasmon<br /> hybridization are clearly observed. Nevertheless, the resonant strength decreases rapidly<br /> when the loss tangent goes from 0.006 to 0.05 (Mica to Pyrex glass). As can be seen that<br /> the resonant split is almost vanished when the loss tangent is 0.05 (Pyrex glass).<br /> <br /> <br /> <br /> <br /> Fig. 3. Transmission spectra of hybridized CWP dimmers<br /> with different dielectric materials.<br /> <br /> A possible explanation is that when the loss tangent increases, a large amount of the<br /> resonant energy will be transferred to the dielectric loss. While the total energy absorbed at<br /> the resonant frequency is unchanged, increasing dielectric loss means the resonant energy<br /> decreases. The resonant energy can be qualitatively understood via the strength of the<br /> surface current density.<br /> <br /> <br /> <br /> <br /> Fig. 4. Distribution of surface currents in hybridized CWP dimers at the frequency |w--><br /> (f = 13.39 GHz) with different dielectric materials.<br /> <br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 35, 02 - 2015 109<br />  Vật lý<br /> <br /> <br /> For this purpose, we simulated the distribution of surface currents regarding to different<br /> dielectric materials, which is shown in Fig. 4. There are two points we can get from<br /> simulations in Fig. 4. Firstly, with all dielectric materials used, the surface current<br /> distribution is anti-parallel, indicating the nature of the magnetic resonance [16]. The<br /> second point, which is more important, is that the strength of surface currents significantly<br /> decreases as increasing the tangent loss from Teflon to Pyrex glass. With a weaker surface<br /> current density, the resonance turns out to be less pronounced. A similar phenomenon (not<br /> shown here) is observed at the second resonant frequency |w-+>. These results are in good<br /> agreement with our argument discussed in Fig. 3.<br /> <br /> 4. CONCLUSION<br /> In this report, we numerically studied the influence of the dielectric layer on the<br /> hybridization of metamaterials. It is shown that the broadband behavior of hybridized<br /> metamaterials is strongly sensitive to the dielectric loss of materials used for the spacer.<br /> Dielectric materials, such as Teflon, Mica, Borosilicate, and Pyrex glass, are employed in<br /> simulations to give a reliable evaluation on the data. It is suggested that to observe the<br /> metamaterial hybridization at microwave frequencies, a Teflon spacer must be utilized.<br /> These results would be useful for further experimental realizations of hybridized<br /> metamaterials and their applications.<br /> Acknowledgment: This work is supported by Vietnam National Foundation for Science<br /> and Technology Development (NAFOSTED) under Grant No. “103.02-2013.54”.<br /> <br /> <br /> <br /> REFERENCES<br /> [1]. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “<br /> Composite Medium with Simultaneously Negative Permeability and Permittivity”<br /> Phys. Rev. Lett. 84, 4184 (2000).<br /> [2]. N. T. Tung, D. T. Viet, B. S. Tung, N. V. Hieu, P. Lievens, and V. D. Lam,<br /> “Broadband negative permeability by hybridized cut-wire pair metamaterials,”<br /> Appl. Phys. Exp. 5, 112001 (2012).<br /> [3]. J. B. Pendry, “ Negative Refraction Makes a Perfect Lens,” Phys. Rev. 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Cui, and X. Luo, “Metamaterial composed of wire<br /> pairs exhibiting dual band negative refraction,” Appl. Phys. B. 98, 365 (2010).<br /> <br /> <br /> 110 P. T. Duyen, …,V.D. Lam, “Decisive role of the dielectric spacer … hybridization.”<br /> Nghiên cứu khoa học công nghệ<br /> <br /> [10]. Y. Z. Cheng, Y. Niea, and R. Z. Gong, “Broadband 3D isotropic negative-index<br /> metamaterial based on fishnet structure,” Eur. Phys. J. B. 85, 62 (2012).<br /> [11]. N. T. Tung, P. Lievens,Y. P. Lee, and V. D. Lam, “Computational studies of a cut-<br /> wire pair and combined metamaterials,” Adv.Nat.Sci.:Nanosci.Nanotechnol. 2,<br /> 033001 (2011).<br /> 12]. N. T. Tung, V. D. Lam, J. W. Park, M. H. Cho, J. Y. Rhee, W. H. Jang, and Y. P. Lee,<br /> “ Influence of lattice parameters on the resonance frequencies of a cut-wire pair<br /> medium,” J. Apply Phys. 106, 053109 (2009).<br /> [13]. L. F. Chen,C. K. Ong,C. P. Neo,V. V. Varadan, and V. K. Varada, “Microwave<br /> Electronics:Measurement and Materials Characterization” John Wiley & Sons<br /> (2004).<br /> [14]. D. M. Pozar, “Microwave Engineering, 3rd ed,” John Wiley & Sons (1998).<br /> [15]. J. A. Kong, “Electromagnetic Wave Theory,” EMW Publishing (2008).<br /> [16]. N. T. Tung, Y. P. Lee, and V. D. Lam, “ Transmission properties of electromagnetic<br /> metamaterials: From split-ring resonator to fishnet structure,” Opt. Rev. 16, 578<br /> (2009).<br /> <br /> <br /> TÓM TẮT<br /> VAI TRÒ CỦA LỚP ĐIỆN MÔI LÊN SỰ LAI HÓA<br /> CỦA SIÊU VẬT LIỆU METAMATERIALS<br /> <br /> Kể từ khi hiện tượng khúc xạ âm được quan sát lần đầu tiên, siêu vật liệu<br /> Metamaterials đã được giới khoa học quan tâm nghiên cứu mạnh mẽ. Để đưa tính<br /> chất này vào ứng dụng thực tế, việc mở rộng vùng tần số có độ từ thẩm âm là một<br /> trong những vấn đề được ưu tiên nghiên cứu. Trong những nghiên cứu gần đây,<br /> chúng tôi đã đề xuất một cơ chế đơn giản nhưng hiệu quả để mở rộng vùng hoạt<br /> động có độ từ thẩm âm dựa trên mô hình lai hóa điện từ [Appl. Phys. Express 5,<br /> 112001 (2012)]. Tuy nhiên, để thu được vật liệu thực tế theo đề xuất dựa trên mô<br /> hình trên, một bước quan trọng và rất cần thiết đó là đánh giá sự tổn hao tại tần số<br /> cộng hưởng. Trong báo cáo này, chúng tôi nghiên cứu ảnh hưởng trực tiếp tổn hao<br /> của lớp kim loại và lớp điện môi đến cường độ của độ từ thẩm âm ở dải sóng GHz.<br /> Kết quả cho thấy rằng tổn hao của lớp điện môi đóng vai trò quyết định trong việc<br /> quá trình hình thành lai hóa điện từ của siêu vật liệu.<br /> Từ khóa: Metamaterials, Lai hóa, Tổn hao điện môi.<br /> <br /> <br /> <br /> NhËn bµi ngµy 10 th¸ng 11 n¨m 2014<br /> Hoµn thiÖn ngµy 15 th¸ng 01 n¨m 2014<br /> ChÊp nhËn ®¨ng ngµy 10 th¸ng 02 n¨m 2015<br /> <br /> <br /> Address: *Institute of Materials Science, Vietnam Academy of Science and<br /> Technology, Vietnam<br /> **Thainguyen university of sciences<br /> ***Institute of Engineering Physics, Academy of Military Science and<br /> Technology, Vietnam<br /> Corresponding author: lamvd@ims.vast.ac.vn<br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 35, 02 - 2015 111<br />