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Abstract
In this work, we theoretically investigate metal-substrate-enhanced magnetic dipole resonance in metamaterials for high-performance refractive index sensing. The metamaterials are composed of periodic arrays of vertical U-shaped split-ring resonators, dielectric spacer, and metal substrate. Because the metal substrate blocks the transmission channel of light, the radiative damping of magnetic dipole resonance is nearly completely suppressed and thus its quality factor is increased noticeably. Owing to the narrow bandwidth, nearly-zero reflectance, and huge enhancement of electromagnetic fields at the magnetic dipole resonance, our designed metamaterial sensor has very high sensitivity (S = 1308 nm/RIU, S* = 26/RIU) and figure of merit (FOM = 52, FOM* = 1187). The good sensing capability allows for a much more sensitive detection of small refractive index changes and suggests potential applications in biosensing.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As one type of the most important artificial magnetic “atoms”, subwavelength U-shaped split-ring resonators are capable of supporting a magnetic dipole resonance and thus counteracting the external magnetic field of the incident light, in spite of the saturation of the magnetic response beyond the THz regime in naturally occurring materials. Owing to their novel electromagnetic properties, U-shaped split-ring resonators have been widely employed as building blocks to engineer metamaterials with a negative refraction index [1, 2], electromagnetic cloak [3], metasurfaces [4, 5], perfect absorbers of electromagnetic waves [6, 7], toroidal metamaterials [8, 9], chiral metamaterials [10, 11], Fano resonances [12, 13], electromagnetic induced transparency (EIT) [14], polarization rotators [15, 16], and so on. They have also been utilized for second harmonic generation (SHG) [17, 18], magnetic dipole spontaneous emission [19, 20], surface-enhanced Raman spectroscopy (SERS) [21–25], and sensors [26–41]. All these applications depend strongly on the enhancement of electric or magnetic fields at the magnetic dipole resonance. Therefore, it is crucial to enhance as greatly as possible the magnetic response of U-shaped split-ring resonators for these applications. However, it is not an easy work because of the fast radiative damping of the magnetic dipole resonance.
In experiments, U-shaped split-ring resonators are usually designed to directly lie flat on a dielectric substrate (e.g. SiO2), due to the limitations of fabrication technology. For such planar U-shaped split-ring resonators, the “hotspots” of the electromagnetic fields produced by the magnetic dipole resonance will diffuse into the dielectric substrate. This is unfavorable to some applications like SERS and refractive index sensing, because the detected targets are not able to fully access to the electromagnetic field “hotspots”. To resolve this problem, some groups have overcome the difficulty in fabrication to successfully prepare vertical U-shaped split-ring resonators that stand on a dielectric substrate [42–45]. In this case, the “hotspots” of the electromagnetic fields can be exposed to the detected objects as much as possible [39, 40]. On the other hand, it is well known that the resonant wavelengths of plasmonic nanostructures are dependent of the refractive index of the surrounding dielectric environment, which has been studied extensively and intensively for sensing applications [46, 47]. But, it is challenging to simultaneously realize ultra-narrow band perfect absorption and electromagnetic field enhancement in plasmonic nanostructures, due to the intrinsic Ohmic dissipation of metals and the radiative damping of plasmon resonance modes, as pointed by a recent report [48].
In this work, we will study theoretically metal-substrate-enhanced magnetic dipole resonance in metamaterials composed of vertical U-shaped split-ring resonators for high-performance refractive index sensing. Because the metal substrate blocks the transmission channel of light, the radiative damping of magnetic dipole resonance is nearly completely suppressed and so its quality factor is increased noticeably. Thanks to the narrow bandwidth, nearly zero reflectance (or perfect absorption), and great enhancement of electromagnetic fields at the magnetic dipole resonance, our designed metamaterial sensor has very high sensitivity (S = 1308 nm/RIU, S* = 26/RIU) and figure of merit (FOM = 52, FOM* = 1187). Such a good sensing capability allows for a much more sensitive detection of small refractive index changes and may have potential applications in biosensing.
2. Results and discussions
In Fig. 1, we schematically show the unit cell of the designed metamaterial sensor, which consists of a periodic array of vertical U-shaped split-ring resonators, a SiO2 spacer, and an Ag substrate. In this work, the absorption and reflection spectra, and the electric and magnetic field distributions are calculated by the commercial software package “EastFDTD, version 5.0”, which is based on finite-difference time-domain (FDTD) method [49]. In our numerical calculations, the refractive index of SiO2 is taken to be 1.45, and the optical constants of Ag are obtained from experimental data [50]. Our work mainly focuses on theoretical results, but the designed metamaterial sensor should be experimentally realized by the following fabrication process: the Ag substrate and the SiO2 spacer are firstly fabricated by the sputtering deposition method, and then the vertical U-shaped split-ring resonators are fabricated by the electron beam lithography with high precision alignment technology [42–44].
Fig. 1 Schematic diagram of metamaterials for high-performance refractive index sensing, which are composed of a periodic array of vertical U-shaped split-ring resonators, a SiO2 spacer, and an Ag substrate. Geometrical parameters: px and py are the array periods along the x and y directions, respectively; t is the thickness of the SiO2 spacer; l1, w and h1 are the length, width, and height of the vertical U-shaped split-ring resonators, respectively; l2 and h2 are the length and height of the gap, respectively. Light is normally incident in the negative direction of the z axis, with its electric field Ein and magnetic field Hin along the x and y axes, respectively.
In Fig. 2(b), we calculated the normal-incidence absorption and reflection spectra of the designed metamaterial sensor without the Ag substrate. A relatively broader absorption peak (or reflection dip) is observed, which is centered at the resonance wavelength of λ2 = 1446 nm. In the next paragraph, we will demonstrate that the relatively broader absorption peak results from the excitation of the magnetic dipole resonance mode supported in individual vertical U-shaped split-ring resonators. Figure 2(a) presents the corresponding results in the case with the Ag substrate. In this case, the magnetic dipole resonance mode is red-shifted to the resonance wavelength of λ1 = 1512 nm, due to the effect of the Ag substrate. More importantly, the corresponding absorption peak becomes very sharp, whose half-height width is only about 25 nm. This is because the Ag substrate blocks the transmission channel of light, and thus the radiative damping of the magnetic dipole resonance mode is suppressed and its quality factor is increased noticeably. In addition, the absorption at the resonance wavelength of λ1 exceeds 98%, very similar to extensively explored perfect absorbers of electromagnetic waves [7, 51–53]. The high absorption implies that the incident light is strongly concentrated in the gap region of the vertical U-shaped split-ring resonators, and therefore the great enhancement of electromagnetic fields is produced, which is very helpful for high-performance refractive index sensing [48].
Fig. 2 Normal-incidence absorption and reflection spectra in the wavelength range from 1200 to 2000 nm, with (a) and without (b) the Ag substrate. Geometrical parameters: px = 1000 nm, py = 400 nm, t = 30 nm, l1 = h1 = 200 nm, w = 50 nm, l2 = 100 nm, and h2 = 150 nm.
In order to prove that the absorption peaks (or reflection dips) discussed above arise from the excitation of the magnetic dipole resonance mode induced within the vertical U-shaped split-ring resonators. In Fig. 3, we plot the electromagnetic field distributions on the surface of the vertical U-shaped split-ring resonators, at the resonance wavelengths of λ1 and λ2. In Figs. 3(a) and 3(c), it is clearly seen that the electric field vectors form a loop current that induces a magnetic moment within the vertical U-shaped split-ring resonators. The induced magnetic moment can counteract the external magnetic field of the incident light, and so produce a magnetic dipole resonance mode [19, 54, 55]. At the same time, the electric field intensity near the top of two prongs [see Figs. 3(a) and 3(c)] and the magnetic field intensity at the bottom of the gap [see Figs. 3(b) and 3(d)] are hugely enhanced, which is a typical characteristic of a magnetic dipole resonance mode [43]. At the resonance wavelength of λ1, the maxima of the electric and magnetic field intensity reach more than 3500 and 5000 times of the incident field, and are 1.6 and 2.9 times stronger than those at the resonance wavelength of λ2, respectively, although the field patterns at the two resonance wavelengths are nearly the same. This further confirms that the Ag substrate is indeed able to suppress the radiative damping of the magnetic dipole resonance mode and thus increase its quality factor. Moreover, different conventional planar split-ring resonators directly lying on a dielectric substrate, the “hotspots” of electromagnetic fields no longer leak into the dielectric substrate but are fully exposed into air for the vertical U-shaped split-ring resonators. Such a field distribution property will help increase accessible sensing volume and achieve high sensitivity [39–41].
Fig. 3 Normalized electric field intensity (E/Ein)2 and magnetic field intensity (H/Hin)2 on the surface of the vertical U-shaped split-ring resonators, at the resonance wavelengths of λ1 and λ2 labeled in Fig. 2. The red arrows and the colors stand for the directions and the strengths of the electromagnetic fields, respectively.
The resonance wavelength of the magnetic dipole mode is very sensitive to the refractive index n of the surrounding dielectric environment, which can be utilized for sensing applications. To overall evaluate the sensing capability of the designed metamaterial sensor, we have calculated the physical quantities of sensitivity (S) and figure of merit (FOM), whose definitions are expressed in the following equations [48, 56–59]:
where Δλ is the spectral shift caused by a certain refractive index change Δn in the environment medium, FWHW is the full width at half maximum of the magnetic dipole mode, ΔI is the detected intensity variation of the reflected light for a given refractive index change Δn, and I is the absolute intensity of the reflected light at the resonance wavelength of the magnetic dipole mode. Thanks to the narrow bandwidth and the nearly zero reflectance around the resonance wavelength, our designed metamaterial sensor is expected to have good sensing performance. In Fig. 4, we give the normal-incidence absorption and reflection spectra of the metamaterial sensor immersed in different environment media. It is clearly seen that the resonance wavelength of the magnetic dipole mode will have a very large red-shift, when the refractive index n is increased slightly. Figure 5 exhibits the dependence of the resonance wavelength on the refractive index n of the environment medium. By linearly fitting the data in Fig. 5, we can obtain the sensitivity S = 1308 nm/RIU (as shown by the slope of the curve), and the figure of merit FOM = 52, when considering that FWHW is about 25 nm. Moreover, a small spectral shift will also lead to a very large intensity variation of the reflected light. Using the above definitions, we can also obtain S* = 26/RIU and FOM* = 1187 around the resonance wavelength of λ1 = 1512 nm.Fig. 4 Normal-incidence absorption (a) and reflection (b) spectra of the metamaterial sensor immersed in different environment media, whose refractive index n is supposed to be varied from 1.0 to 1.1 in steps of 0.025. The geometrical parameters are the same as those in Fig. 2.
Fig. 5 The dependence of the resonance wavelength on the refractive index n of the environment medium, which is obtained by the calculated data in Fig. 4.
Finally, we would like to investigate the effects of some geometrical parameters on the magnetic dipole mode. In Fig. 6, we show the calculated reflection spectra in the wavelength range from 1440 to 1580 nm for the different thickness t of the SiO2 spacer and the different array periods px and py. It is clearly seen in Fig. 6(a) that, the magnetic dipole mode will have an obvious blue-shift for the thickness t to vary from 20 to 50 nm, and the reflection will increase. When t is 20 or 30 nm, the reflection is nearly zero, and the correspondingly electromagnetic fields at the resonance wavelength of the magnetic dipole mode are greatly enhanced, which is favorable for sensing application. The magnetic dipole mode will have a slight blue-shift when the array period px is changed from 800 to 1100 nm, but it will have a red-shift when the array period py is changed from 300 to 600 nm [please seen Figs. 6(b) and 6(c)]. Such a shift of the resonance wavelength can be well explained by the electromagnetic interactions between closely spaced metal nanoparticles [60]. For the array period px to be increased, the attractive force along the x direction between the nearest neighbor split-ring resonators is weakened, and so the repulsive force within each split-ring resonator becomes stronger, leading to a higher resonance frequency (or blue-shift). However, for the array period py to be increased, the situation is reverse. In addition, when the array period px (py) exceeds 1000 (400) nm, the reflection approaches to zero. For smaller periods, the reflection becomes stronger and the correspondingly electromagnetic fields become weaker, which is disadvantageous to sensing application.
Fig. 6 Normal-incidence reflection spectra in the wavelength range from 1440 to 1580 nm. (a) The thickness t of the SiO2 spacer is varied from 20 to 50 nm in steps of 10 nm. (b) The array period px along the x direction is varied from 800 to 1100 nm in steps of 100 nm. (c) The array period py along the y direction is varied from 300 to 600 nm in steps of 100 nm. The geometrical parameters are the same as those in Fig. 2.
3. Conclusion
In summary, we have theoretically studied metal-substrate-enhanced magnetic dipole resonance in metamaterials composed of vertical U-shaped split-ring resonators for high-performance refractive index sensing. Because the metal substrate blocks the transmission channel of light, the radiative damping of magnetic dipole resonance is nearly completely suppressed and its quality factor is increased noticeably. Thanks to the narrow bandwidth, nearly zero reflectance, and huge enhancement of electromagnetic fields at the magnetic dipole resonance, our designed metamaterial sensor has very high sensitivity (S = 1308 nm/RIU, S* = 26/RIU) and figure of merit (FOM = 52, FOM* = 1187). Such a good sensing capability allows for a much more sensitive detection of small refractive index changes and may have potential applications in biosensing.
Funding
National Natural Science Foundation of China (NSFC) (11304159 and 11104136); Natural Science Foundation of Jiangsu Province (BK20161512); Natural Science Foundation of Zhejiang Province (LY14A040004); Project funded by China Postdoctoral Science Foundation (2018M632345); Qing Lan Project of Jiangsu Province; Specialized Research Fund for the Doctoral Program of Higher Education of China (20133223120006); NUPTSF (NY217045 and NY218022); Open Project of State Key Laboratory of Millimeter Waves (K201821); National Research Foundation of Korea under “Korea-China Young Scientist Exchange Program”.
References and links
1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]
4. C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013). [CrossRef] [PubMed]
5. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef] [PubMed]
6. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]
7. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120 (2012). [PubMed]
8. N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016). [CrossRef] [PubMed]
9. N. Talebi, S. Guo, and P. A. van Aken, “Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance,” Nanophotonics 7(1), 93–110 (2018). [CrossRef]
10. Z. F. Li, R. K. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, “Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. 97(8), 081901 (2010). [CrossRef]
11. Z. F. Li, M. Mutlu, and E. Ozbay, “Chiral metamaterials: from optical activity and negative refractive index to asymmetric transmission,” J. Opt. 15(2), 023001 (2013). [CrossRef]
12. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]
13. A. B. Khanikaev, C. H. Wu, and G. Shvets, “Fano-resonant metamaterials and their applications,” Nanophotonics 2(4), 247–264 (2014).
14. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]
15. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial,” Opt. Express 19(15), 14290–14299 (2011). [CrossRef] [PubMed]
16. M. Kang, T. Feng, H. T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express 20(14), 15882–15890 (2012). [CrossRef] [PubMed]
17. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006). [CrossRef] [PubMed]
18. N. M. Litchinitser and J. Sun, “Optical meta-atoms: going nonlinear,” Science 350(6264), 1033–1034 (2015). [CrossRef] [PubMed]
19. S. M. Hein and H. Giessen, “Tailoring magnetic dipole emission with plasmonic split-ring resonators,” Phys. Rev. Lett. 111(2), 026803 (2013). [CrossRef] [PubMed]
20. D. G. Baranov, R. S. Savelev, S. V. Li, A. E. Krasnok, and A. Alù, “Modifying magnetic dipole spontaneous emission with nanophotonic structures,” Laser Photonics Rev. 11(3), 1600268 (2017). [CrossRef]
21. C. Cao, J. Zhang, X. Wen, S. L. Dodson, N. T. Dao, L. M. Wong, S. Wang, S. Li, A. T. Phan, and Q. Xiong, “Metamaterials-based label-free nanosensor for conformation and affinity biosensing,” ACS Nano 7(9), 7583–7591 (2013). [CrossRef] [PubMed]
22. G. Sarau, B. Lahiri, P. Banzer, P. Gupta, A. Bhattacharya, F. Vollmer, and S. Christiansen, “Enhanced Raman scattering of graphene using arrays of split ring resonators,” Adv. Opt. Mater. 1(2), 151–157 (2013). [CrossRef]
23. W. S. Yue, Y. Yang, Z. H. Wang, L. Q. Chen, and X. B. Wang, “Gold split-ring resonators (SRRs) as substrates for surface- enhanced Raman scattering,” J. Phys. Chem. C 117(42), 21908–21915 (2013). [CrossRef]
24. X. Wen, G. Li, J. Zhang, Q. Zhang, B. Peng, L. M. Wong, S. Wang, and Q. Xiong, “Transparent free-standing metamaterials and their applications in surface-enhanced Raman scattering,” Nanoscale 6(1), 132–139 (2014). [CrossRef] [PubMed]
25. C. Cao, J. Zhang, S. Li, and Q. Xiong, “Intelligent and ultrasensitive analysis of mercury trace contaminants via plasmonic metamaterial-based surface-enhanced Raman spectroscopy,” Small 10(16), 3252–3256 (2014). [CrossRef] [PubMed]
26. J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16(3), 1786–1795 (2008). [CrossRef] [PubMed]
27. C. Y. Chen, I. W. Un, N. H. Tai, and T. J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17(17), 15372–15380 (2009). [CrossRef] [PubMed]
28. Y. T. Chang, Y. C. Lai, C. T. Li, C. K. Chen, and T. J. Yen, “A multi-functional plasmonic biosensor,” Opt. Express 18(9), 9561–9569 (2010). [CrossRef] [PubMed]
29. X. Xu, B. Peng, D. Li, J. Zhang, L. M. Wong, Q. Zhang, S. Wang, and Q. Xiong, “Flexible visible-infrared metamaterials and their applications in highly sensitive chemical and biological sensing,” Nano Lett. 11(8), 3232–3238 (2011). [CrossRef] [PubMed]
30. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012). [CrossRef] [PubMed]
31. Y. C. Lai, H. C. Lee, S. W. Kuo, C. K. Chen, H. T. Wu, O. K. Lee, and T. J. Yen, “Label-free, coupler-free, scalable and intracellular bio-imaging by multimode plasmonic resonances in split-ring resonators,” Adv. Mater. 24(23), OP148–OP152 (2012). [CrossRef] [PubMed]
32. T. Chen, S. Li, and H. Sun, “Metamaterials application in sensing,” Sensors (Basel) 12(3), 2742–2765 (2012). [CrossRef] [PubMed]
33. X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013). [CrossRef] [PubMed]
34. R. J. Singh, W. Cao, I. Al-Naib, L. Q. Cong, W. Withayachumnankul, and W. L. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014). [CrossRef]
35. J. Chen, W. Fan, T. Zhang, C. Tang, X. Chen, J. Wu, D. Li, and Y. Yu, “Engineering the magnetic plasmon resonances of metamaterials for high-quality sensing,” Opt. Express 25(4), 3675–3681 (2017). [CrossRef] [PubMed]
36. W. Xu, L. Xie, and Y. Ying, “Mechanisms and applications of terahertz metamaterial sensing: a review,” Nanoscale 9(37), 13864–13878 (2017). [CrossRef] [PubMed]
37. Y. Lee, S. J. Kim, H. Park, and B. Lee, “Metamaterials and metasurfaces for sensor applications,” Sensors (Basel) 17(8), 1726 (2017). [CrossRef] [PubMed]
38. A. Salim and S. Lim, “Review of recent metamaterial microfluidic sensors,” Sensors (Basel) 18(1), 232 (2018). [CrossRef] [PubMed]
39. P. C. Wu, G. Sun, W. T. Chen, K. Y. Yang, Y. W. Huang, Y. H. Chen, H. L. Huang, W. L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014). [CrossRef]
40. P. C. Wu, C. Y. Liao, J. W. Chen, and D. P. Tsai, “Isotropic absorption and sensor of vertical split-ring resonator,” Adv. Opt. Mater. 5(2), 1600581 (2017). [CrossRef]
41. W. Wang, F. Yan, S. Tan, H. Zhou, and Y. Hou, “Ultrasensitive terahertz metamaterial sensor based on vertical split ring resonators,” Photon. Res. 5(6), 571–577 (2017). [CrossRef]
42. P. C. Wu, W. T. Chen, K. Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012). [CrossRef]
43. P. C. Wu, W. L. Hsu, W. T. Chen, Y. W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D. P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015). [CrossRef] [PubMed]
44. W. L. Hsu, P. C. Wu, J. W. Chen, T. Y. Chen, B. H. Cheng, W. T. Chen, Y. W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5(1), 11226 (2015). [CrossRef] [PubMed]
45. Z. Liu, Z. Liu, J. Li, W. Li, J. Li, C. Gu, and Z. Y. Li, “3D conductive coupling for efficient generation of prominent Fano resonances in metamaterials,” Sci. Rep. 6(1), 27817 (2016). [CrossRef] [PubMed]
46. J. Yuan, Y. Y. Xie, Z. X. Geng, C. X. Wang, H. M. Chen, Q. Kan, and H. D. Chen, “Enhanced sensitivity of gold elliptic nanohole array biosensor with the surface plasmon polaritons coupling,” Opt. Mater. Express 5(4), 818–826 (2015). [CrossRef]
47. J. Chen, J. Yuan, Q. Zhang, H. M. Ge, C. J. Tang, Y. Liu, and B. N. Guo, “Dielectric waveguide-enhanced localized surface plasmon resonance refractive index sensing,” Opt. Mater. Express 8(2), 342–345 (2018). [CrossRef]
48. Z. Yong, S. Zhang, C. Gong, and S. He, “Narrow band perfect absorber for maximum localized magnetic and electric field enhancement and sensing applications,” Sci. Rep. 6(1), 24063 (2016). [CrossRef] [PubMed]
49. Website, www.eastfdtd.com.
50. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
51. Y. X. Cui, Y. R. He, Y. Jin, F. Ding, L. Yang, Y. Q. Ye, S. M. Zhong, Y. Y. Lin, and S. L. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014). [CrossRef]
52. Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015). [CrossRef]
53. P. Wang, N. Chen, C. Tang, J. Chen, F. Liu, S. Sheng, B. Yan, and C. Sui, “Engineering the complex-valued constitutive parameters of metamaterials for perfect absorption,” Nanoscale Res. Lett. 12(1), 276 (2017). [CrossRef] [PubMed]
54. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
55. C. Tang, Q. Wang, F. Liu, Z. Chen, and Z. Wang, “Optical forces in twisted split-ring-resonator dimer stereometamaterials,” Opt. Express 21(10), 11783–11793 (2013). [CrossRef] [PubMed]
56. R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97(25), 253116 (2010). [CrossRef]
57. A. E. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6(11), 9989–9995 (2012). [CrossRef] [PubMed]
58. X. Lu, L. Zhang, and T. Zhang, “Nanoslit-microcavity-based narrow band absorber for sensing applications,” Opt. Express 23(16), 20715–20720 (2015). [CrossRef] [PubMed]
59. Y. Zhu, H. Zhang, D. Li, Z. Zhang, S. Zhang, J. Yi, and W. Wang, “Magnetic plasmons in a simple metallic nanogroove array for refractive index sensing,” Opt. Express 26(7), 9148–9154 (2018). [CrossRef] [PubMed]
60. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1–3), 137–141 (2003). [CrossRef]
