Planar metamaterial analogue of electromagnetically induced transparency for a miniature refractive index sensor

Physics Letters A 383 (2019) 125947

Contents lists available at ScienceDirect

Physics Letters A www.elsevier.com/locate/pla

Planar metamaterial analogue of electromagnetically induced transparency for a miniature refractive index sensor Rong Li a,b , Xiang-kun Kong a , Shao-bin Liu a,∗ , Zhi-ming Liu a , Yu-meng Li a a b

Key Laboratory of Radar Imaging and Microwave Photonics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China Bin Zhou University, Binzhou, 256603, China

a r t i c l e

i n f o

Article history: Received 25 May 2019 Received in revised form 7 August 2019 Accepted 4 September 2019 Available online 9 September 2019 Communicated by M. Wu Keywords: Electromagnetically induced transparency Metamaterial Sensor Refractive index

a b s t r a c t A planar metamaterial of analogue of Electromagnetically Induced Transparency (EIT-like) is theoretically and experimentally investigated. The EIT-like metamaterial unit cell, whose electrical size is only 0.2λ0 , consists of a split ring resonator (SRR) and a folded-line pair resonator (FLPR). For the TM wave incidence, a sharp transmitted peak with high quality factor can be observed. The EIT-like metamaterial is fabricated and measured. Good agreement is obtained between the simulation and measurement results. A miniature refractive index sensor based on the proposed metamaterial is simulated and exhibits high sensitivity and Figure of Merit (FOM). © 2019 Elsevier B.V. All rights reserved.

1. Introduction Electromagnetically Induced Transparency (EIT) is a quantum interference phenomenon observed originally in the atomic system, and it can give rise to a sharp peak in the transmission spectrum because of the destructive interference between two different excited pathways [1,2]. So far, more and more researchers have been conscious that the EIT-like effect can be observed in metamaterials. Metamaterials are artificially engineered composites with subwavelength structures, being widely used in various functional devices due to their unique electromagnetic properties [3–9]. The EIT-like phenomenon observed in metamaterials usually can be realized by two modes: the “trapped modes” resonance [10–14] or the coupling of “bright mode” and “dark mode” [15–17]. The “trapped modes” are provided by the metamaterials with broken structural symmetry, and weakly coupled to free space [11]. The “bright mode” means the resonance can be excited directly by the incident electromagnetic wave, nevertheless the “dark mode” cannot be excited directly [17]. The characteristics of EIT-like based on metamaterials have many potential applications in coupled-resonators, ultra-high resolution sensors, slow-light devices and so on, while one of the fascinating applications is refractive index sensor [18–23].

*

Corresponding author. E-mail address: [email protected] (S.-b. Liu).

https://doi.org/10.1016/j.physleta.2019.125947 0375-9601/© 2019 Elsevier B.V. All rights reserved.

In this work, an EIT-like planar metamaterial structure is investigated theoretically and experimentally. The unit cell of the metamaterial structure is composed of a split ring resonator (SRR) and a folded-line pair resonator (FLPR). The SRR and the FLPR can be stimulated by the incident TM wave, respectively. However, the stimulation of the electromagnetic wave on the SRR is stronger than the one on the FLPR. Therefore, we define the SRR as “bright mode” and the FLPR as “quasi-dark mode” [24–28]. The electrical size of the proposed metamaterial unit cell is 0.2λ0 and smaller than the one of the most previously studied metamaterials in the same waveband [29–34]. Under the incident TM wave, a sharp transmitted peak with large angle consistency emerges in a transmission spectrum. Based on the properties of miniaturization and large angle consistency of the proposed planar metamaterial, the metamaterial can be utilized to design a miniature refractive index sensor. Numerical simulations are performed to verify the sensor exhibiting high sensitivity and Figure of Merit (FOM). All the simulated results are carried out using the full-wave numerical simulation tools (CST Microwave Studio). 2. Result and discussion Figs. 1(a)-(c) displays the geometry of the periodic metamaterial consisting of SRR and FLPR, and the periodic structure is symmetric around the y-axis. The SRR and the FLPR are copper, whose thickness is 0.018 mm, and patterned on the F4B substrate (εr = 2.55, tanδ = 0.001). The geometrical parameters of the EITlike structure unit cell are as follows: P x = P y = 6 mm, t = 1 mm,

2

R. Li et al. / Physics Letters A 383 (2019) 125947

Fig. 1. Schematic of the EIT-like metamaterial unit cell for (a) SRR only, (b) FLPR only, and (c) SRR+FLPR, and simulated transmission spectra for (d) SRR only, (e) FLPR only, and (f) SRR+FLPR.

Fig. 2. Surface current distributions of the EIT-like metamaterial with normal incident wave at (a) f 1 = 9.54 GHz, (b) f 2 = 9.99 GHz and (c) f 3 = 10.36 GHz. (For interpretation of the colours in the figures, the reader is referred to the web version of this article.)

x1 = 5.4 mm, y 1 = 3.5 mm, m = 0.5 mm, y 2 = 4.2 mm, y 3 = 2.1 mm, w = 0.1 mm, s = 0.2 mm, x0 = 0.2 mm, y 0 = 0.2 mm. The SRR in Fig. 1(a) can couple with a normally incident electromagnetic wave with horizontal polarization, so does as the FLPR in Fig. 1(b). The SRR supports the “bright mode” and the FLPR supports the “quasi-dark mode”. The simulated transmission spectra with different Q-factor of the SRR and the FLPR are displayed in Figs. 1(d) and 1(e). When the SRR and the FLPR are put together [see Fig. 1(c)], the metamaterial exhibits EIT-like properties and a sharp transmitted peak appears in the transmission spectrum. As shown in Fig. 1(f), a sharp transmission peak ( f 2 = 9.99 GHz) locates between two transmission dips ( f 1 = 9.54 GHz, f 3 = 10.36 GHz). We calculate the Q-factor of the resonators from the transmission curves by Q = f 0 / f . Here, f 0 is the resonance frequency and  f is defined as the full width at half maximum (FWHM) of the transmission spectrum. The Q-factor of the curves in Figs. 1(d), 1(e), and 1(f) are about 1.4, 32.4 and 99.9, respectively. For further analyzing the underlying mechanism of the EIT-like effect, the surface current distributions of metamaterial structure at the peak ( f 2 = 9.99 GHz) [see Fig. 2(b)] and the two dips ( f 1 = 9.54 GHz, f 3 = 10.36 GHz) [see Figs. 2(a) and 2(c)] are simulated and compared. Fig. 2(a) illustrates that, at the first dip ( f 1 = 9.54

GHz), the surface currents of SRR and FLPR are distributed along the same direction, which is called antibonding mode in the EITlike phenomenon. At the second dip ( f 3 = 10.36 GHz), as shown in Fig. 2(c), the surface currents of SRR and FLPR are distributed along the opposite direction, which is called bonding mode [30]. At the peak ( f 2 = 9.99 GHz), there is almost no surface current on SRR, while the current is mainly distributed on FLPR as displayed in Fig. 2(b). This is because the surface current on SRR is nearly coupled to FLPR. Apparently, the destructive interference between the SRR and the FLPR suppresses the radiation loss [30,33], and a transmission peak emerges. The proposed metamaterial supports plane electromagnetic wave incidence with wide angles. As displayed in Fig. 3(a), when the TM wave is off the + z direction by the incident angle of θ , (e.g., θ = 0◦ , 15◦ , 30◦ , 45◦ ), the frequency responses of the EIT-like peak show no change nearly. The reason for this phenomenon is that the metamaterial structure is a compact array and symmetric around the y-axis. Especially, as shown in Fig. 2(b) and Fig. 4(b), the surface current distributions at EIT-like peaks keep constant with different incident angles, thus the transmission peak show no change nearly. Contrast to the transmission peak, the two dips appear slightly blue-shifted with the θ rising. When θ increases, for

R. Li et al. / Physics Letters A 383 (2019) 125947

3

Fig. 3. Simulated transmission spectra of the EIT-like metamaterial for: (a) TM polarized incident waves with incidence angles of 0◦ , 15◦ , 30◦ , and 45◦ , (b) The width of the FLPR w = 0.1 mm, 0.13 mm, 0.15 mm, (c) The loss tangent of F4B substrate from 0.001 to 0.011.

Fig. 4. Surface current distributions of the EIT-like metamaterial with θ = 45◦ at (a) f 1 = 9.65 GHz, (b) f 2 = 9.99 GHz and (c) f 3 = 10.47 GHz.

Fig. 5. (a) Photograph of the fabricated sample. (b) Photograph of the experimental setup.

instance, θ = 45◦ , the x-component electric field of the incident wave gradually declines, the resonance between the metamaterial and the incident wave becomes weaker. This makes the average surface currents at the two dips decrease. The corresponding surface current distributions at two transmission dips are shown in Figs. 4(a) and 4(c). Thus, the amplitudes of the two transmission dips increase with respect to the weaker resonance. Furthermore, the surface current no longer uniformly distributed in the unit cell due to the θ rising, which cause the effective length of the unit cell to be shortened. The two dips shift to higher frequency owing to the shorter effective length. Besides, we discuss the influence of the geometric parameters on the EIT-like effect. Fig. 3(b) depicts that the peak of the transparency window becomes smaller and removes to high frequency when the width of FLPR varies from w = 0.1 mm to w = 0.15 mm. With w = 0.1 mm, the EIT-like phenomenon is the most obvious one. It shows that the geometric parameters of the unit cell have an influence on the resonance frequency of the EIT-like effect. Especially, the change in the width of the FLPR causes resonance frequency to shift and the peak value √ to change. As we know, the resonance frequency is f = 1/(2π LC ). If w varies from 0.1 mm to 0.15 mm, but the interval between SRR and FLPR keeps invariant, then the equivalent capacitance of the unit cell is almost

unchanged. Nonetheless, the effective length of FLPR is shortened. As a result, the equivalent inductance of the FLPR declines, and thus the EIT-like peak shifts to a higher frequency. The dielectric loss of the substrate also is considered. Fig. 3(c) shows the transmission spectra with different loss tangent. When loss tangent of the substrate varies from 0.001 to 0.011 with the step of 0.002, the transparency peak shows no frequency-shift [see inset of Fig. 3(c)], but the peak value declines from about -0.7 dB to -5.6 dB. Apparently, the bigger dielectric loss of the substrate makes the FWHM of the transmission wider, and reduces the Qfactor of the EIT-like window. Therefore, using lossless or low-loss materials as substrates is ideal to propose metamaterial. To confirm the validity of the simulated results, the metamaterial sample is fabricated and measured. In consideration of the fabrication, the minimum machining accuracy is 0.15 mm, and the width of FLPR is w = 0.15 mm instead of w = 0.1 mm to verify the reliability of simulation results. The total sample size consists of 50×50 cells on a 300 mm×300 mm F4B substrate. A pair of standard horn antennas, serving as the transmitter and receiver, are connected to an Agilent 5245A network analyzer. The sample and the measurement scenario are shown in Figs. 5(a) and 5(b). The simulation results and experiment results are displayed in Figs. 6(a) and 6(b), respectively. It shows that experimental re-

4

R. Li et al. / Physics Letters A 383 (2019) 125947

Fig. 6. (a) Simulated transmission spectra and (b) Measured transmission spectra of the proposed EIT-like metamaterial with different incident angles of 0◦ , 15◦ , 30◦ , and 45◦ .

Fig. 7. (a) Simulated transmission spectra with the different refractive index. (b) Simulated EIT-like peak frequency with the different refractive index.

Fig. 8. (a) Simulated transmission spectra with different loss tangent. (b) The peak value of the transmission spectra with different loss tangent. Table 1 Comparison of various metamaterials with unit cell electrical sizes. Ref.

[21]

[29]

[30]

[31]

[34]

[35]

[37]

[39]

[40]

This work

Resonant Frequency (GHz) Unit Cell Electrical Size (mm)

5.2 0.40λ0

12.2 0.73λ0

8.6 0.46λ0

9.61 0.58λ0

5.8 0.30λ0

5.8 0.73λ0

9.10 0.43λ0

5.5 0.29λ0

6.0 0.40λ0

9.99 0.20λ0

sults are basically accordant to simulated results in the shape and resonance frequency, whereas the transmission peaks of the experimental results are lower than the ones of the simulated results. The difference between the measured results and the simulated ones is due to the manufacturing error, the deviation in dielectric properties of F4B substrate and the experimental environment. On the bases of the experimental results stated above, we can infer the validity of the proposed metamaterial when the width of FLPR is w = 0.1 mm. Due to the sharp transparency window, one appealing application of the proposed metamaterial is that it can be served as a refractive index sensor. Next, we simulated the sensitivity and FOM of the sensor with different tested dielectric materials. Here, sensitivity is defined as the shift in resonance wavelength per refractive index unit (RIU), and the FOM is the ratio of sensitivity to the resonance linewidth at half-maximum of the transmission peak [35]. The tested dielectric materials with a thickness of 1 mm

are placed at the surface of the proposed metamaterial. Fig. 7(a) displays the performance of the metamaterial sensor with the different refractive index. It shows that the transmission peaks shift to a lower frequency when the refractive index n of the tested dielectric materials varies from 1.1 to 1.5. Fig. 7(b) presents the relations between the frequency and the refractive index. In this work, the sensitivity of the sensor is calculated as 10.3 mm/RIU, and the resonance linewidth at half-maximum of the transmission spectrum is about 0.3 mm, so the FOM is calculated to be 34.33. As shown in Fig. 7(a), the peak values of the transmission spectra with different refractive index n are nearly invariant. However, the peak values of the transmission spectra decline with the loss tangent of the tested dielectric materials increasing, as seen in Figs. 8(a) and 8(b), for the refractive index of the tested dielectric materials n = 1.1. Table 1 compares the unit cell electrical size for the same waveband. It is seen that the unit cell electrical size in this work is the

R. Li et al. / Physics Letters A 383 (2019) 125947

5

Table 2 Comparison of sensitivities and FOM values for sensing refractive index changes. Ref.

[36]

[37]

[38]

[39]

[40]

This work

Resonant Frequency (GHz) Sensitivity (mm/RIU) FOM

5.8 77.25 8.14

9.10 9.47 13.5

3.6 14.20 6.17

5.5 16.80 11.66

6.0 8.73

9.99 10.30 34.33

smallest one. Table 2 compares the sensitivities and the FOM values for different refractive index sensors. Although the sensitivity in this work is smaller, the FOM is better than the ones of the most refractive index sensors studied in previous literature. 3. Conclusion In summary, we have numerically and experimentally investigated the EIT-like effect and discussed the characteristics of the refractive index sensor. The unit cell electrical size of the proposed metamaterial structure is smaller than most of the others reported in previous works. The proposed metamaterial demonstrates sharp transparency window located in the two dips and is insensitive to the wide angles of the incident TM wave. Based on the above advantages, a miniature sensor is simulated. It shows high sensitivity and FOM when the refractive index of the tested dielectric media changes. To summarize, all the results benefit for much practical application in a variety of fields, such as biomedical and chemical devices. Acknowledgements This work was supported in part by Chinese Natural Science Foundation (Grant No. 61671238), China Postdoctoral Science Foundation (Grant No. 2016M601802), Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 1601009B), Equipment Advanced Research Foundation of China (Grant No. 61402090103). References [1] C.L.G. Alzar, M.A.G. Martinez, P. Nussenzveig, Am. J. Phys. 70 (2002) 37. [2] M. Fleischhauer, A. Imamoglu, J.P. Marangos, Rev. Mod. Phys. 77 (2005) 633. [3] S. Zhang, D.A. Genov, Y. Wang, M. Liu, X. Zhang, Phys. Rev. Lett. 101 (2008) 047401. [4] N. Liu, Nat. Mater. 8 (2009) 758. [5] V.T.T. Thuy, N.T. Tung, J.W. Park, V.D. Lam, Y.P. Lee, J.Y. Rhee, J. Opt. 12 (2010) 115102. [6] Y. Yang, Nat. Commun. 5 (2014) 5753. [7] J.S. Hwang, Y.J. Yoo, Y.J. Kim, K.W. Kim, L.Y. Chen, Y.P. Lee, Curr. Appl. Phys. 16 (2016) 469. [8] D. Wu, Sci. Rep. 7 (2017) 45210. [9] N. Liu, Nano Lett. 10 (2010) 1103.

[10] C. Antonopoulos, R. Cahill, E.A. Parker, I.M. Sturland, Proc. IEEE Microw. Antennas Propag. 144 (1997) 415. [11] V.A. Fedotov, M. Rose, S.L. Prosvirnin, N. Papasimakis, N.I. Zheludev, Phys. Rev. Lett. 99 (2007) 147401. [12] N. Papasimakis, V.A. Fedotov, N.I. Zheludev, S.L. Prosvirnin, Phys. Rev. Lett. 101 (2008) 253903. [13] N. Papasimakis, Y.H. Fu, V.A. Fedotov, S.L. Prosvirnin, D.P. Tsai, N.I. Zheludey, Appl. Phys. Lett. 94 (2009) 211902. [14] W. Cao, R. Singh, I.A.I. Al-Naib, M. He, A.J. Taylor, W. Zhang, Opt. Lett. 37 (2012) 3366. [15] Z.Y. Li, Y.F. Ma, R. Huang, R. Singh, J.Q. Gu, Z. Tian, J.G. Han, W.L. Zhang, Opt. Express 19 (2011) 8912. [16] F.L. Zhang, Q. Zhao, C.W. Lan, X. He, W.H. Zhang, J. Zhou, K.P. Qiu, Appl. Phys. Lett. 104 (2014) 131907. [17] D.J. Meng, S.Y. Wang, X.L. Sun, R.Z. Gong, C.H. Chen, Appl. Phys. Lett. 104 (2014) 261902. [18] X.Q. Lin, J. Peng, Z. Chen, J.W. Yu, X.F. Yang, IEEE Sens. J. 18 (2018) 9251. [19] X.J. He, L. Wang, J.M. Wang, X.H. Tian, J.X. Jiang, Z.X. Geng, J. Phys. D, Appl. Phys. 46 (2013) 510. [20] J. Hu, T.T. Lang, Z. Hong, C.Y. Shen, G.H. Shi, J. Lightwave Technol. 36 (2018) 2083. [21] X.Q. Lin, IEEE Sens. J. 16 (2016) 293. [22] Z.C. Wei, Plasmonics 12 (2017) 641. [23] P.Y. Wang, T. Jin, F.Y. Meng, Opt. Express 26 (2018) 12318. [24] F.Y. Meng, F. Zhang, K. Zhang, Q. Wu, J.Y. Kim, J.J. Choi, B. Lee, J.C. Lee, IEEE Trans. Magn. 47 (2011) 3347. [25] S. Hu, H.L. Yang, S. Han, X.J. Huang, B.X. Xiao, J. Appl. Phys. 117 (2015) 043107. [26] Y. Wang, Opt. Eng. 55 (2016) 027108. [27] M. Manjappa, Opt. Lett. 42 (2017) 2106. [28] X. Liu, J.Q. Gu, Appl. Phys. Lett. 100 (2013) 36. [29] H.L. Yang, S. Hu, D. Liu, H. Lin, B.L. Xiao, Appl. Phys. A 122 (2016) 54. [30] H.M. Li, F. Xue, Phys. Lett. A 381 (2017) 3000. [31] L. Zhu, F.Y. Meng, L. Dong, J. Appl. Phys. 117 (2015) 146. [32] S. Han, L.Q. Cong, H. Lin, B.X. Xiao, H.L. Yang, R.J. Singh, Sci. Rep. 6 (2016) 20801. [33] H.M. Li, S.B. Liu, S.Y. Wang, S.Y. Liu, Y. Hu, H.B. Li, Sci. Rep. 6 (2016) 21457. [34] S. Hu, D. Liu, H. Lin, J. Chen, Y.Y. Yi, H.L. Yang, J. Appl. Phys. 121 (2017) 123103. [35] C.Y. Chen, I.W. Un, N.H. Tai, T.J. Yen, Opt. Express 17 (2009) 15372. [36] F.Y. Meng, Q. Wu, Daniel Erni, K. Wu, J.C. Lee, IEEE Trans. Microw. Theory Tech. 60 (2012) 3013. [37] L. Zhu, L. Dong, F.Y. Meng, J.H. Fu, Q. Wu, Appl. Opt. 51 (2012) 7794. [38] L. Zhu, J.H. Fu, F.Y. Meng, X.M. Ding, L. Dong, Q. Wu, IEEE Trans. Magn. 50 (2014) 4000604. [39] Y. Tian, S. Hu, X.J. Huang, Z.T. Yu, H. Lin, H.L. Yang, J. Phys. D: Appl. Phys. 50 (2017) 113518. [40] L. Zhu, L. Dong, J. Guo, F.Y. Meng, X.J. He, T.H. Wu, J. Phys. D: Appl. Phys. 51 (2018) 265101.