Vật lý

DECISIVE ROLE OF THE DIELECTRIC SPACER ON METAMATERIAL HYBRIDIZATION PHAN THI DUYEN*, NGO DUC VIET*, NGUYEN THI HIEN**, NGUYEN THANH TUNG****, VU DINH LAM*

Abstract: Since the first observation of the fascinating negative refractive-index property, meta-materials have been in the scientific spotlight. A typical interest has been paid for negative refractive meta-materials with a broad operating band, which are more useful for applications. In our recent work, we have theoretically shown that a broad negative permeability band can be achieved by introducing hybridized meta-materials [N. T. Tung et al., Appl. Phys. Express 5, 112001 (2012)]. To step forward an experimental realization of the above proposal, evaluating the loss contribution at resonant frequencies is indispensable. In this report, we study the metallic and dielectric losses that directly influence the strength of permeability negativity at microwave regime. The results show that the dielectric loss plays a decisive role in forming the meta-material hybridization. Keywords: Meta-materials, Hybridization, Dielectric loss.

1. INTRODUCTION Recent development of science and technology investigates new materials with novel properties, which have large potential applications in science and engineering to replace conventional ones. In the last decade, meta-materials emerged as a completely new class of materials, attracted great attention of the scientific community by fascinating properties [1]. Meta-material is known to be a kind of artificial materials with sub-wavelength scaled unit cell. These unit cells function as the atoms in the material. A meta-material “atom” is generally composed of two main components: electric component creating negative permeability ε<0 and magnetic component providing negative permittivity μ<0. These “atoms” can be arranged either in a periodic or disordered lattice. By carefully designing the electric and magnetic components, one can create exotic properties using metamaterials, for instance, the negative refraction [2], the perfect absorption [3], the invisible cloak [4], or the electromagnetically-induced transparency [5]. The unusual properties of meta-materials have been theoretically and experimentally confirmed by numerous studies so far. However, to put the interesting properties of meta-materials towards real applications, in fact there are many issues that need to be studied and explained in a satisfactory manner. One of the longstanding issues is how to widen the operating frequency band of meta-materials [6]. While a wide negative permittivity band can be easily achieved using the plasma behavior of continuous wire medium, a broad negative permeability band is often narrow due to the nature of metamaterial resonances. Expanding the operating band of negative permeability metamaterials therefore has been a key challenge for scientists. Despite the fact that numerous efforts have been taken to overcome this question, most of them have been limited in applications by certain reasons, for examples, symmetric breaking and requirement of rigorous structural adjustments [7-10]. In our recent work, we proposed a simple but effective mechanism to extend the operating frequency band of a negative permeability by using hybridization metamaterials [2]. The underlying physics of this method is to have the original resonance split by

106

P. T. Duyen, …,V.D. Lam, “Decisive role of the dielectric spacer … hybridization.”

Nghiên cứu khoa học công nghệ

introducing a strong plasmonic hybridization. In this report, we evaluate the loss contribution to the plasmonic hybridization of a cut-wire-pair (CWP) dimer structure. 2. THEORETICAL MODEL We first consider the original magnetic resonance of a CWP monomer structure. When the structure is exposed to incoming electromagnetic waves, the plasmon effect induces surface currents in each CW. The total electromagnetic resonance total can be explained as a result from the plasmon hybridization between two CWs in a pair. Due to the coupling between two CWs, the original plasmon mode degenerates into two new plasmon ones: symmetric mode |w+> and asymmetric mode |w-> [see Fig. 1(a)]. In the asymmetric mode, the surface currents are antiparallel, generating an induced magnetic resonance (negative permeability). Meanwhile, the symmetric mode is consists of parallel surface currents which interact to the external electric field, creating an electric resonance. In this paper, we restrict our attention to the asymmetric mode with the magnetic resonance behavior.

(a)

(b)

Fig. 1. Hybridization model of (a) the CWP monomer and (b) CWP dimer. It is known that a broad negative permeability band has been reported using CWP dimer metamaterials [2]. By controlling the internal-external coupling correlation along the k direction between two CWPs in a dimer, the original asymmetric mode |w-> can be split into two new asymmetric modes: |w--> and |w-+ > [see Fig. 1(b)]. A similar explanation as in case of CWP monomers can be used to understand the resonant split of CWP dimmers. When the distance between two identical CWP monomers is close enough, the charge interaction between two CWP monomers is getting stronger. Total energy of the CWP dimer system is now determined by the interaction energy between two CWs in a pair and the additional interaction energy between two CWPs in a dimer. Importantly, the asymmetric resonant split can only appear when the energy of the internal coupling and that of the external coupling are strong and comparable [2]. The lateral condition implies that the distance between two CWP monomers in a dimer must be well defined. This can be overcome by an intensive structural optimization. Meanwhile, the first condition suggests that loss factor in the asymmetric magnetic resonance should be small. One might know that the loss origin in materials, in general, can be divided into two parts: the Ohmic loss and the dielectric loss. In metamaterials, the major part of loss is often attributed to the dielectric materials while the Ohmic loss has almost no influence on the resonance [12]. Therefore, the key to keep the loss sufficient low is the dielectric

Tạp chí Nghiên cứu KH&CN quân sự, Số 35, 02 - 2015

107

Vật lý

spacer. By studying the loss contribution of the dielectric spacer, we might be able to estimate the loss threshold where the asymmetric resonant split does not exist. 3. NUMMERICAL MODEL AND NUMERIAL SIMULATION 3.1. Nummerical model A CWP monomer and its corresponding dimer structure are shown in geometric parameters in Fig. 2 with the electromagnetic polarization. A CWP dimer consists of two identical CWP monomer separated by a distance d. The CWP structure is composed of copper patterns (ts = 036mm thick) on both sides of a dielectric spacer (td = 0.4 mm thick) with a dielectric constant of 4.3. The length and width of CWs are l = 5.5 and w = 1.0 mm, respectively. The lattice constants of unit cell in the H-, E-, and k- direction are ax, ay, az, respectively. In this study, ax, ay are chosen to be 3.5 mm and 7.0 mm, respectively. These parameters are optimized to obtain a known magnetic resonance over the frequency range of 12-18 GHz [11]. The electromagnetic response of CWP metamaterials is simulated by using the commercial simulation software CST, based on the finite integration technique. For all calculations, the CWP metamaterial structure are illuminated by a normally incident plane wave where the magnetic field is polarized along to the x direction while the electric field is in the y axis.

Fig. 1. Schematic representing of (a) a CWP monomer and (b) a CWP dimer. 3.2. Numerial simulation For time dependent electromagnetic fields propagating through dielectric materials, the permittivity can have real and imaginary components as follows [13] ε = ε’ – jε” (1) where ε″ is the imaginary component of permittivity attributed to bound charge and dipole relaxation phenomena, which gives rise to energy loss that is indistinguishable from the loss due to the free charge conduction that is quantified by conductivity σ. The component ε′ represents the familiar lossless permittivity given by the product of the free space permittivity and the relative real permittivity, or ε′ = ε0 ε′r [14,15]. The loss tangent is then defined as tan = (ε” + σ)/ ε’

(2)

Equation (2) shows the total dielectric loss in a dielectric material. Based on that basis, we perform simulations to study the dependence of hybridization strength on the loss tangent of the dielectric layer. Table 1 indicates the loss tangents of most popular dielectric materials and their corresponding dielectric constants.

108

P. T. Duyen, …,V.D. Lam, “Decisive role of the dielectric spacer … hybridization.”

Nghiên cứu khoa học công nghệ

Table 1. Loss tangent and dielectric constant of dielectric materials [source: wikipedia.com]. Materials Loss tangent Dielectric constant Teflon 0.001 2.1 Mica 0.006 4.5 Borosilicate 0.02 5 Pyrex glass 0.05 4 Figure 3 presents the transmission spectra of hybridized CWP dimers according to the loss tangent suggested in Table I. For comparison, all calculations are done by taking an average dielectric constant of 4. It should be noted that different values of the dielectric constant does not change the loss contribution except for a resonant frequency shift. In case of low loss materials (Teflon), two resonances originated from the Plasmon hybridization are clearly observed. Nevertheless, the resonant strength decreases rapidly when the loss tangent goes from 0.006 to 0.05 (Mica to Pyrex glass). As can be seen that the resonant split is almost vanished when the loss tangent is 0.05 (Pyrex glass).

Fig. 3. Transmission spectra of hybridized CWP dimmers with different dielectric materials. A possible explanation is that when the loss tangent increases, a large amount of the resonant energy will be transferred to the dielectric loss. While the total energy absorbed at the resonant frequency is unchanged, increasing dielectric loss means the resonant energy decreases. The resonant energy can be qualitatively understood via the strength of the surface current density.

Fig. 4. Distribution of surface currents in hybridized CWP dimers at the frequency |w--> (f = 13.39 GHz) with different dielectric materials.

Tạp chí Nghiên cứu KH&CN quân sự, Số 35, 02 - 2015

109

Vật lý

For this purpose, we simulated the distribution of surface currents regarding to different dielectric materials, which is shown in Fig. 4. There are two points we can get from simulations in Fig. 4. Firstly, with all dielectric materials used, the surface current distribution is anti-parallel, indicating the nature of the magnetic resonance [16]. The second point, which is more important, is that the strength of surface currents significantly decreases as increasing the tangent loss from Teflon to Pyrex glass. With a weaker surface current density, the resonance turns out to be less pronounced. A similar phenomenon (not shown here) is observed at the second resonant frequency |w-+>. These results are in good agreement with our argument discussed in Fig. 3. 4. CONCLUSION In this report, we numerically studied the influence of the dielectric layer on the hybridization of metamaterials. It is shown that the broadband behavior of hybridized metamaterials is strongly sensitive to the dielectric loss of materials used for the spacer. Dielectric materials, such as Teflon, Mica, Borosilicate, and Pyrex glass, are employed in simulations to give a reliable evaluation on the data. It is suggested that to observe the metamaterial hybridization at microwave frequencies, a Teflon spacer must be utilized. These results would be useful for further experimental realizations of hybridized metamaterials and their applications. Acknowledgment: This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. “103.02-2013.54”.

REFERENCES [1]. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “ Composite Medium with Simultaneously Negative Permeability and Permittivity” Phys. Rev. Lett. 84, 4184 (2000). [2]. N. T. Tung, D. T. Viet, B. S. Tung, N. V. Hieu, P. Lievens, and V. D. Lam, “Broadband negative permeability by hybridized cut-wire pair metamaterials,” Appl. Phys. Exp. 5, 112001 (2012). [3]. J. B. Pendry, “ Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000). [4] N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Prop. Lett. 1, 10 (2002). [5]. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780 (2006). [6]. J. Bonache, I., Gil, J. García-García, and F. Martín, “Novel micro strip bandpass filters based on complementarysplit-ring resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1 (2006), pp. 265–271. [7]. C. Hu, L. Liu, X. N. Chen, and X. G. Luo, “Expanding the band of negative permeability of a composite structure with dual-band negative permeability,” Opt. Express. 16, 21544 (2008). [8]. Z. Wei, Y. Cao, J. Han, C. Wu, Y. Fan, and H. Li, “Broadband negative refraction in stacked fishnet metamaterial,” Appl. Phys. Lett. 97, 141901 (2010). [9]. C. Huang, Z. Zhao, Q. Feng, J. Cui, and X. Luo, “Metamaterial composed of wire pairs exhibiting dual band negative refraction,” Appl. Phys. B. 98, 365 (2010).

110

P. T. Duyen, …,V.D. Lam, “Decisive role of the dielectric spacer … hybridization.”

Nghiên cứu khoa học công nghệ

[10]. Y. Z. Cheng, Y. Niea, and R. Z. Gong, “Broadband 3D isotropic negative-index metamaterial based on fishnet structure,” Eur. Phys. J. B. 85, 62 (2012). [11]. N. T. Tung, P. Lievens,Y. P. Lee, and V. D. Lam, “Computational studies of a cutwire pair and combined metamaterials,” Adv.Nat.Sci.:Nanosci.Nanotechnol. 2, 033001 (2011). 12]. N. T. Tung, V. D. Lam, J. W. Park, M. H. Cho, J. Y. Rhee, W. H. Jang, and Y. P. Lee, “ Influence of lattice parameters on the resonance frequencies of a cut-wire pair medium,” J. Apply Phys. 106, 053109 (2009). [13]. L. F. Chen,C. K. Ong,C. P. Neo,V. V. Varadan, and V. K. Varada, “Microwave Electronics:Measurement and Materials Characterization” John Wiley & Sons (2004). [14]. D. M. Pozar, “Microwave Engineering, 3rd ed,” John Wiley & Sons (1998). [15]. J. A. Kong, “Electromagnetic Wave Theory,” EMW Publishing (2008). [16]. N. T. Tung, Y. P. Lee, and V. D. Lam, “ Transmission properties of electromagnetic metamaterials: From split-ring resonator to fishnet structure,” Opt. Rev. 16, 578 (2009). TÓM TẮT VAI TRÒ CỦA LỚP ĐIỆN MÔI LÊN SỰ LAI HÓA CỦA SIÊU VẬT LIỆU METAMATERIALS Kể từ khi hiện tượng khúc xạ âm được quan sát lần đầu tiên, siêu vật liệu Metamaterials đã được giới khoa học quan tâm nghiên cứu mạnh mẽ. Để đưa tính chất này vào ứng dụng thực tế, việc mở rộng vùng tần số có độ từ thẩm âm là một trong những vấn đề được ưu tiên nghiên cứu. Trong những nghiên cứu gần đây, chúng tôi đã đề xuất một cơ chế đơn giản nhưng hiệu quả để mở rộng vùng hoạt động có độ từ thẩm âm dựa trên mô hình lai hóa điện từ [Appl. Phys. Express 5, 112001 (2012)]. Tuy nhiên, để thu được vật liệu thực tế theo đề xuất dựa trên mô hình trên, một bước quan trọng và rất cần thiết đó là đánh giá sự tổn hao tại tần số cộng hưởng. Trong báo cáo này, chúng tôi nghiên cứu ảnh hưởng trực tiếp tổn hao của lớp kim loại và lớp điện môi đến cường độ của độ từ thẩm âm ở dải sóng GHz. Kết quả cho thấy rằng tổn hao của lớp điện môi đóng vai trò quyết định trong việc quá trình hình thành lai hóa điện từ của siêu vật liệu. Từ khóa: Metamaterials, Lai hóa, Tổn hao điện môi.

NhËn bµi ngµy 10 th¸ng 11 n¨m 2014 Hoµn thiÖn ngµy 15 th¸ng 01 n¨m 2014 ChÊp nhËn ®¨ng ngµy 10 th¸ng 02 n¨m 2015

Address: *Institute of Materials Science, Vietnam Academy of Science and Technology, Vietnam **Thainguyen university of sciences ***Institute of Engineering Physics, Academy of Military Science and Technology, Vietnam Corresponding author: [email protected]

Tạp chí Nghiên cứu KH&CN quân sự, Số 35, 02 - 2015

111