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Abstract
We designed and fabricated terahertz toroidal dipole metasurfaces based on a C-shaped split ring resonator metallic pattern fabricated on a flexible dielectric material (mylar). The toroidal dipole moment (Ty) was demonstrated as the dominant contribution to two different resonances at low frequency (ω1) and at high frequency (ω2). Simulation and LC circuit model analysis offered a quantitative explanation to the blue shift of the resonant frequencies at ω1 and ω2 as the increase of the opening angle(θ). The resonant frequencies showed a red shift at ω1 and ω2 as the increase of the outer ring radius (QR). Furthermore, the enhancement of the Q factor was attributed to the increase of Ty and the decrease of radiative loss. It was further proven that the model provided a new scheme for designing the toroidal dipole metasurfaces under a terahertz band, which was expected to be used as terahertz functional devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The toroidal dipole (TD) was first considered in 1958 by Zel’dovich, in order to explain parity violation in nuclear physics [1]. The TD, magnetic dipole, and electric dipole were basic electromagnetic (EM) responses. The intensity of TD response was much weaker than that of the magnetic dipole and electric dipole, which was extremely hard to be observed in nature [2]. Due to the emergence of metamaterials (MMs), various structures were proposed to support the TD resonance. Many novel EM properties of TD broaden applicable prospects in designing high-performance EM devices and optical devices [3–5]. In addition, terahertz was a new radiation source with many unique advantages, such as strong complementary features, strong anti-interference, high temporal and spatial coherence. The combination of TD and terahertz waves would result in new EM features and new physical phenomena.
Nowadays, two-dimensional MMs, that is metasurfaces (MSs) [6–13], had attracted much attention from researchers due to their ability to control EM wave across their deeply subwavelength thickness and reduce the complexity of fabrication [14–20]. The MSs could realize effective manipulation of EM wave polarization, amplitude, phase, polarization mode, propagation mode and other characteristics [21]. In previous study, three-dimensional MMs had been widely employed to realize TD response first in microwave band [22], then in optical band [23], and last in terahertz band [24,25]. TD resonance was observed at terahertz frequencies via MSs fabricated on undoped and high-resistivity silicon wafer [26–29]. Strong TD could be achieved in MSs samples which were fabricated in a single lithography step [27]. The sensing with toroidal resonance was demonstrated in two-dimensional terahertz MSs [28,29].
In this paper, the EM characteristics of TD resonance at terahertz frequencies were studied by designing the TD MSs based on C- shaped split ring resonator (CSRR). We used a flexible substrate, mylar, to propose and fabricate the MSs. For the purpose of understanding the mechanism of TD, numerical simulations were performed in the time domain by using the commercially available software CST Microwave Studio. We had demonstrated that the CSRRs MSs structure had two distinct resonances at low frequency (ω1) and at high frequency (ω2), and both resonances were dominated by TD resonance at terahertz frequencies. We studied and discussed the effect of different parameters on the EM characteristics of MSs, such as the opening angle (θ), the outer ring radius (QR) and the distance between the two CSRRs (g). Under the parameters of θ, we had shown that the LC circuits model were well agreement with the measured results. Meanwhile, we also calculated the scattered powers of the multipoles to investigated TD in depth. In addition, we also investigated the relation among Ty, the Q factor and the figure of merit (FoM) under the parameters of QR. This planar structure TD MSs was easy to fabricate and had a stable resonance output. The TD MSs on a flexible substrate could be used as advanced terahertz functional devices.
2. Sample design and characterization
The unit cell of TD MSs consists of two CSRRs. The unit cell was periodically translated along the x and y axes to form a planar TD MSs. The Aluminum (Al) metallic layer (with the thickness of h = 400 nm) was fabricated on a mylar layer (with the thickness of t = 22 µm). Mylar flexible substrate was chosen as the substrate due to the perfect EM characteristics: low absorption, constant good compatibility with micromachining technology and isotropic at terahertz frequencies. The optimum parameters of TD MSs were as follows: the periodicity of the metamolecule (a × b) = 256 µm × 128 µm, QR = 38 µm, the inner ring radius (IR) = 33 µm, the width of the ring (w) = 5 µm, g = 4 µm, θ=90°. In this paper, the incident direction of the terahertz wave was along the z-axis direction, that is, the magnetic field was polarized along the y-axis, and the electric field was polarized along the x-axis.
For the fabrication of the proposed planar MSs, lithography microfabrication process was carried out. The mylar film (22 µm) was too soft to be attached to the turntable and cannot be rotated at high speed. Firstly, we fixed the mylar film to the silicon wafer to keep the mylar film flat during rotation. Secondly, the metallic pattern layer was fabricated using conventional photolithography, followed by the deposition of 400 nm aluminum using vacuum coating equipment, then rinsing in acetone for several minutes. Finally, the MSs samples were removed from the silicon substrate. One of the microscope images of the sample with g = 4µm was shown in Fig. 1(b).
Fig. 1. (a) Schematic of the proposed metasurfaces metamolecule; (b) Microscope image of the fabricated sample with g = 4 µm.
In order to study the EM characteristics more in depth, we set the parameters θ (θ=30°,60°and 90°), QR (QR = 30, 35, 38, and 40µm), and g (g = 4,8 and 12µm), then the corresponding samples were fabricated. In previous research, we found that the distance between the two split ring resonators had a greater influence on the TD [30], however, we found that the change of the g parameter had almost no effect on the TD, as shown in the appendix A. We focused on the effect of θ and QR on the TD resonances. Only one parameter was changed at a time, and the remaining variables remain unchanged. The experimental data was measured via the THz time-domain spectroscopy system (THz-TDS system) [31,32].
In the simulation process, the material parameters of aluminum metal could be described by the Drude model, where the angular frequency dependent dielectric constant was given by ${\varepsilon }({\omega } )= {{\varepsilon }_\infty } - [{\omega_p^2/\omega ({\omega + i\varGamma } )} ]$, with the plasma frequency (22.43 × 1015rad s−1 for Al) and damping rate (124.34 $\times$ 1012 rad s−1)[29]. The permittivity of mylar substrate was 3.3 [33].
3. Results and discussion
Figure 2 showed the measured and simulated transmission spectra of the TD MSs with the different values of θ. We found that the measured results agreed well with the simulations. There were certain differences between measured and simulated results which attributed to the limited resolution of our measurements and the imperfections in the fabricated samples [34]. We found that there were two distinct resonances ω1 and ω2, and both resonances were proved to be TD resonances in later. The frequencies of TD resonances were both increased at ω1 and ω2 as θ increasing, and a blue shift were observed, respectively. When the values of θ increased from 30° to 90°, the frequency of ω1 was gradually blue shifted from 0.52 to 0.55 THz, meanwhile, the frequency of ω2 was gradually blue shifted from 1.11 to 1.17 THz. The transmission resonance achieves the maximum blue shift of 0.06 THz at ω2. Here, we could interpret the interacting mechanism using an effective LC circuit model. The CSRR provided the inductances (Lm and Le), which were the inductances of CSRR at ω1 and ω2, respectively. The split gap of CSRR provided the capacitance (Ce), and the coupling between two adjacent CSRRs provided the coupling capacitance (Cm). Lm, Le, Cm, Ce in the resonant circuit could be given by the following formula [35–36]:
Fig. 2. (a) Experimental, (b)Simulated amplitude transmission spectra for samples, surface current, and (c) Magnetic field distribution (on the XZ plane at Y = 0) at ω2 resonances of the design with different values of θ, (d) and (e) Schematics of the formation of head-to-tail arrangement correlating at ω1 and ω2, respectively.
Where μ0 was the permeability of vacuum, t was the thickness of the dielectric film, l was the length of the ring (can be approximated as the circumference of the ring), w was the width of the ring, G(x) was a function that for x$\to$0 behaves as -log(x), ɛ was the dielectric constant, c1 was the numerical factor (the ratio of the equivalent length to the true length of the metal ring) in the range $0.2 \le {c_1} \le 0.3$, h was the thickness of the metal, g was the distance between the two CSRRs, respectively.
As shown in the illustration of Fig. 2(b) θ=30°, the surface current formed a loop along CSRRs at ω1, which was the typical LC-induced resonance. The ω1 resonance can be expressed by an effective circuit shown in Fig. 3(a). Meanwhile, the surface currents flow opposite along CSRRs at ω2, which was the typical dipole-induced resonance. The ω2 resonance can be expressed by an effective circuit shown in Fig. 3(b). The red arrows indicate the directions of currents.
From Eqs. (1)–(4), we can obtain equations as following [35–36]:
Table 1. The frequencies calculated at ω1 and ω2.
In order to understand the mechanism of the two resonances, the magnetic field distribution on x–z plane (y = 0) was obtained at both resonances. As shown in the illustration of Fig. 2(b) θ=90°, the magnetic field vectors were connected in a head-to-tail way, demonstrating the existence of TD along y-axis at ω1 [37]. The same phenomena were also observed in Fig. 2(c), and the intensity at ω2 was much stronger than that at ω1. The Q factor was an important parameter for MSs, which defined as the ratio of resonance frequency to the full width at half maximum [27]. When TD was enhanced, and the radiation loss was reduced, thus the Q factor was dramatically enhanced. For the TD resonance at ω2 (1.17 THz), the Q (∼5.56) was almost three times stronger than that of the TD resonance at ω1(0.55THz) with Q (∼1.87).
In order to prove generation of TD, the scattering powers of various multipoles were calculated by using the multipole scattering theory according to the volume current density distribution [29,38,39]. At THz normal incidence, the electric dipole vector (Px) was along the x-axis, and the magnetic dipole vector (Mz) was parallel to the z-axis, and the TD vector (Ty) was parallel to the y-axis. The Px, Mz, Ty were calculated according to the optimum parameters in Fig. 1(a). The scattered powers as a function of frequency were displayed in Fig. 4. The intensity of Ty at ω1 had the largest intensity, which was 8 times order larger than that of Mz. Similarly, the intensity of Ty at ω2 also had the largest intensity, which was 9 times order larger than that of Mz. The largest intensity of Ty determined that TD resonance dominated at the resonant frequencies.
The effect of QR was also investigated further. Figure 5 showed measured and simulated transmission spectra of the TD MSs with the different values of QR. The third resonances were occurred around 1.6THz in the simulation; however, it was not detected in the measurement. In the paper, we only focus on the first two resonances. We found that when the values of QR increased from 30µm to 40µm, the frequency of ω1 was gradually red shifted from 0.69 to 0.5 THz, meanwhile, the frequency of ω2 was gradually red shifted from 1.37 to 1.13 THz.
Fig. 5. (a) Experimental and (b) Simulated amplitude transmission spectra for samples with different values of QR, when the E field was parallel to the x-axis.
The nature of the high Q factor in the TD response was helpful to make efficient resonant MSs devices. As shown in Fig. 6(a), we found that the simulated Q factor at ω1/ω2 was decreased as QR increased, where the Q factor at ω2 was higher than that at ω1 in the same MSs. The reason for the decrease of Q factor with the increase of QR could be explained as following: Firstly, as the value of QR increases, the self-coupling region of the CSRRs became bigger, and the coupling between CSRRs was weaken, resulting in weakening of the TD response and increasing radiation loss. Secondly, the magnetic field was confined in the bigger circular region as the value of QR increases, hence the field confinement per unit volume was decreased, and Q factor decreases, accordingly.
The FoM was the product of Q factor and the resonant intensity ($FoM = Q \times \Delta I$), which quantifies the strength of toroidal coupling [28,29,40]. The FoM parameter was crucial as it considered the trade-off between the quality factor and the intensity of the toroidal resonance [40]. Figure 6(b) depicted FoM of simulated results with different values of QR at ω1 and ω2. The peak FoM (1.21) of toroidal resonance at ω2 was more than twice the peak FoM (0.6) value at ω1, indicating that the EM coupling of ω2 was stronger than ω1. Hence, the intensity of TD at ω2 was stronger than that at ω1, which is demonstrated by Fig. 7. Figure 7 showed scattering power of Ty as a function of QR at ω1 and ω2. The Ty at ω1 was largest when QR = 35µm, and the Ty at ω2 was largest when QR = 38µm, which were consistent with the FoM results. The FoM at ω2 is bigger than that at ω1, indicating the decrease of radiative loss and the enhancement of TD, which results in the increase of Q factor at ω2.
4. Conclusions
We had created a terahertz TD resonance by properly design of the CSRRs MSs. Then, the samples were fabricated and measured via THz-TDS system. And with terahertz transmission measurements, comprehensive model calculation, and a full-wave simulation, we demonstrated that the structure exhibits TD resonance at ω1 and ω2. It was found that θ and QR would affect the resonance frequency, Q factor, FoM and the EM characteristics of the TD resonances. The resonant frequencies were blue shift at ω1 and ω2 with the increase of θ; meanwhile, the resonant frequencies were red shift at ω1 and ω2 with the increase of QR. According to the LC circuit model, the calculation of the frequency was good agreement with the measured results. In addition, multipole vector was calculated using the multipole scattering theory, we found that the intensity of TD dominated at two resonances. The FoM at ω2 is bigger than that at ω1, indicating the decrease of radiative loss and the enhancement of TD, which results in the increase of Q factor at ω2. TD MSs could develop a more advanced, better performing, and lower cost terahertz functional device.
Appendix A
Figure 8 showed the measured and simulated transmission spectra of the TD MSs with the different values of g. And there were two distinct resonances in all samples: the ω1 resonance was around 0.6 THz, and ω2 resonance was around 1.2THz. And the resonance frequency was slightly blue-shifted as the distance between the g increases. However, we believed that the value of g had little effect on the resonant frequency, suggesting that for this model, the g parameter was negligible.
Funding
National Natural Science Foundation of China (61505146, 61705167); the Science Development Foundation of Tianjin University of Technology and Education (KJ1920, RC14-33); the Application Foundation and Advanced Technology Research Program of Tianjin Science and Technology Committee (15JCYBJC52200); the Scientific Research Project of Tianjin Municipal Education Commission (JWK1608, 20140714).
References
1. I. B. Zel’Dovich, “The Relation Between Decay Asymmetry and Dipole Moment of Fundamental Particles,” SoV. Phys. JETP 6(6), 1148–1155 (1958).
2. Y. Bao, X. Zhu, and Z. Fang, “Plasmonic Toroidal Dipolar Response under Radially Polarized Excitation,” Sci. Rep. 5(1), 11793 (2015). [CrossRef]
3. N. Papasimakis, V. A. Fedotov, and V. Savinov, “Electromagnetic Toroidal Excitations in Matter and Free Space,” Nat. Mater. 15(3), 263–271 (2016). [CrossRef]
4. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405 (2018). [CrossRef]
5. L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017). [CrossRef]
6. C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011). [CrossRef]
7. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012). [CrossRef]
8. Y. Fan, F. Zhang, N. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018). [CrossRef]
9. Y. Fan, T. Qiao, F. Zhang, Q. Fu, J. Dong, B. Kong, and H. Li, “An electromagnetic modulator based on electrically controllable metamaterial analogue to electromagnetically induced transparency,” Sci. Rep. 7(1), 40441 (2017). [CrossRef]
10. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef]
11. A. J. Burrow, R. Yahiaoui, A. Sarangan, J. Mathews, I. Agha, and A. T. Searles, “Eigenmode hybridization enables lattice-induced transparency in symmetric terahertz metasurfaces for slow light applications,” Opt. Lett. 44(11), 2705 (2019). [CrossRef]
12. R. Yahiaoui, A. J. Burrow, A. Sarangan, J. Mathews, I. Agha, and A. T. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97(15), 155403 (2018). [CrossRef]
13. A. J. Burrow, R. Yahiaoui, A. Sarangan, J. Mathews, I. Agha, and A. T. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25(26), 32540 (2017). [CrossRef]
14. M. Papaioannou, E. Plum, J. Valente, E. T. Rogers, and N. I. Zheludev, “Two-dimensional control of light with light on metasurfaces,” Light: Sci. Appl. 5(4), e16070 (2016). [CrossRef]
15. O. Tsilipakos, A. C. Tasolamprou, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Pairing Toroidal and Magnetic Dipole Resonances in Elliptic Dielectric Rod Metasurfaces for Reconfigurable Wavefront Manipulation in Reflection,” Adv. Opt. Mater. 6(22), 1800633 (2018). [CrossRef]
16. A. V. Kildishev, B. Alexandra, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
17. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]
18. Y. Yang, L. Jing, B. Zheng, R. Hao, W. Yin, E. Li, C. M. Soukoulis, and H. Chen, “Full-Polarization 3D Metasurface Cloak with Preserved Amplitude and Phase,” Adv. Mater. 28(32), 6866–6871 (2016). [CrossRef]
19. Y. Yang, H. Wang, F. Yu, Z. Xu, and H. Chen, “A metasurface carpet cloak for electromagnetic, acoustic and water waves,” Sci. Rep. 6(1), 20219 (2016). [CrossRef]
20. Y. Yang, L. Jing, L. Shen, Z. Wang, B. Zheng, H. Wang, E. Li, N. Shen, T. Koschny, C. M. Soukoulis, and H. Chen, “Hyperbolic spoof plasmonic metasurfaces,” NPG Asia Mater. 9(8), e428 (2017). [CrossRef]
21. K. D. Donda and R. S. Hegde, “Bilayered nanoantenna design improves the performance of silicon metasurfaces in the visible-wavelength region,” Nanophotonics 11(4), 046002 (2017). [CrossRef]
22. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010). [CrossRef]
23. A. Ahmadivand and B. Gerislioglu, “Directional Toroidal Dipoles Driven by Oblique Poloidal and Loop Currents Flows in Plasmonic Meta-Atoms,” J. Phys. Chem. C 122(42), 24304–24308 (2018). [CrossRef]
24. Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017). [CrossRef]
25. A. Ahmadivand, B. Gerislioglu, P. Manickam, A. Kaushik, S. Bhansali, M. Nair, and N. Pala, “Rapid Detection of Infectious Envelope Proteins by Magnetoplasmonic Toroidal Metasensors,” ACS Sens. 2(9), 1359–1368 (2017). [CrossRef]
26. A. Ahmadivand, B. Gerislioglu, and N. Pala, “Large-Modulation-Depth Polarization-Sensitive Plasmonic Toroidal Terahertz Metamaterial,” IEEE Photonics Technol. Lett. 29(21), 1860–1863 (2017). [CrossRef]
27. M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp Toroidal Resonances in Planar Terahertz Metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016). [CrossRef]
28. M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017). [CrossRef]
29. M. Gupta and R. Singh, “Toroidal versus Fano Resonances in High-Q-planar THz Metamaterials,” Adv. Opt. Mater. 4(12), 2119–2125 (2016). [CrossRef]
30. S. Wang, S. Wang, Q. Li, X. Zhao, and J. Zhu, “Dual Toroidal Dipole Resonance Metamaterials under a Terahertz Domain,” Materials 11(10), 2036 (2018). [CrossRef]
31. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). [CrossRef]
32. A. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31(5), 634–636 (2006). [CrossRef]
33. N. Wongkasem, A. Akyurtlu, K. A. Marx, W. D. Goodhue, J. Li, Q. Dong, and E. T. Ada, “Fabrication of a novel micron scale Y-structure-based chiral metamaterial: Simulation and experimental analysis of its chiral and negative index properties in the terahertz and microwave regimes,” Microsc. Res. Tech. 70(6), 497–505 (2007). [CrossRef]
34. V. Torres, N. Sanchez, D. Etayo, R. Ortuno, M. Navarro-Cia, A. Martinez, and M. Beruete, “Compact Dual-Band Terahertz Quarter-Wave Plate Metasurface,” IEEE Photonics Technol. Lett. 26(16), 1679–1682 (2014). [CrossRef]
35. Q. Li, L. Cong, R. Singh, N. Xu, W. Cao, X. Zhang, Z. Tian, L. Du, J. Han, and W. Zhang, “Monolayer graphene sensing enabled by the strong Fano-resonant metasurface,” Nanoscale 8(39), 17278–17284 (2016). [CrossRef]
36. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef]
37. A. Ahmadivand, B. Gerislioglu, A. Tomitaka, P. Manickam, A. Kaushik, S. Bhansali, M. Nair, and N. Pala, “Extreme sensitive metasensor for targeted biomarkers identification using colloidal nanoparticles-integrated plasmonic unit cells,” Biomed. Opt. Express 9(2), 373–386 (2018). [CrossRef]
38. Z. Dong, J. Zhu, J. Rho, J. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012). [CrossRef]
39. Y. Huang, W. Chen, P. Wu, V. Fedotov, V. Savinov, Y. Ho, Y. Chau, N. I. Zheludev, and D. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012). [CrossRef]
40. L. Cong, M. Manjappa, N. Xu, I. Al-Naib, W. Zhang, and R. Singh, “Fano Resonances in Terahertz Metasurfaces: A Figure of Merit Optimization,” Adv. Opt. Mater. 3(11), 1537–1543 (2015). [CrossRef]
