Actively switchable terahertz metamaterial

Journal Pre-proofs Actively Switchable Terahertz Metamaterial Fangyuan Lu, Huiliang Ou, Yuhang Liao, Fengdi Zhu, Yu-Sheng Lin PII: DOI: Reference:

S2211-3797(19)32744-5 https://doi.org/10.1016/j.rinp.2019.102756 RINP 102756

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Results in Physics

Received Date: Revised Date: Accepted Date:

12 September 2019 12 October 2019 13 October 2019

Please cite this article as: Lu, F., Ou, H., Liao, Y., Zhu, F., Lin, Y-S., Actively Switchable Terahertz Metamaterial, Results in Physics (2019), doi: https://doi.org/10.1016/j.rinp.2019.102756

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Actively Switchable Terahertz Metamaterial Fangyuan Lu, Huiliang Ou, Yuhang Liao, Fengdi Zhu, and Yu-Sheng Lin* State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou 510275, China *E-mail: [email protected]

Abstract We present four designs of actively switchable terahertz metamaterials (ASTMs) to explore their extraordinary optical characteristics. They are denoted as ASTM_1, ASTM_2, ASTM_3, and ASTM_4, respectively. ASTM_1 and ASTM_2 are composed of asymmetrically single-layer L-shaped metamaterial and asymmetrically dual-layer L-shaped metamaterial with rotated 0° on Si substrate, respectively. ASTM_3 and ASTM_4 are composed of asymmetrically dual-layer L-shaped metamaterial with rotated 90° and asymmetrically connected L-shaped metamaterial on Si substrate, respectively. ASTM_1 shows three resonances at 0.19 THz, 0.33 THz, and 0.49 THz. The tuning range of first resonance is 0.06 THz by changing the gap between the L-shaped metamaterial. While ASTM_2 shows three resonances at 0.15 THz, 0.28 THz, and 0.42 THz. The tuning range of first resonance is 0.05 THz by changing the height between top and bottom L-shaped metamaterials. By changing the gap and height of L-shaped metamaterials, ASTM_3 and ASTM_4 exhibit the optical switching characteristic. The transmission spectra of four ASTMs show the polarization-independent characteristic. Such optical properties of ASTM designs provide the possibilities of THz metamaterial to be used in active switching optoelectronics applications, such as sensors, logic devices, programmable devices, and so on. Keywords: metamaterial, terahertz, modulator, resonator, switch

1. Introduction Recently, terahertz (THz) metamaterial is an emerging field owing to it has a great electromagnetic response in the THz frequency range, such as artificial magnetism, perfect absorption, electric field enhancement, and so on [1-4]. Therefore, many researches have been presented in various configurations of metamaterials to determine the unique electromagnetic properties [5]. The typical metamaterial design is the split-ring resonator (SRR). There have been reported many SRRs in literatures [6-9], such as U-shaped SRR [10], cross-shaped SRR [11], I-shaped SRR [12], flexible SRR [13], complementary SRR [14], electric SRR (eSRR) [15, 16], and three-dimensional (3D) SRR [17]. The extensive research efforts have been devoted to manipulate the electromagnetic characteristics using metamaterials to improve the flexibility in the THz frequency range [18], such as phase transition materials [19] and superconducting materials [20, 21]. These metamaterials are alternative solutions to obtain the excellent transmission characteristics. The active control of metamaterial plays an important role in obtaining various optical properties, which enables numerous practical applications. To date, there have been many

literatures to present the actively tunable metamaterials, including electrical [22], optical pumping [23], magnetic [24], thermal [25, 26], and mechanical [27] approaches. Among these approaches, the reconfigurable tunability is a straightforward method to deform the metamaterial by rearranging, rotating, and reshaping the unit cell of metamaterial. There are many controllable electromagnetic properties, such as multiband switching [28], electrical response [29] and electromagnetic induced transparency (EIT) analogue [14, 27] by using metamaterials. Therefore, the incident electromagnetic wave could be actively controlled and then used in widespread applications [30-35], especially in the switchable THz metamaterial absorbers [36-39]. In this study, we present four designs of actively switchable terahertz metamaterials (ASTMs). They are composed of asymmetrically single-layer L-shaped metamaterial (ASTM_1), asymmetrically dual-layer rotated 0° L-shaped metamaterial (ASTM_2), asymmetrically dual-layer rotated 90° L-shaped metamaterial (ASTM_3) and asymmetrically connected L-shaped metamaterial (ASTM_4), respectively. These ASTM designs can be realized the active control of electromagnetic behaviors not only the filter function but also the switching function, which are potentially used in widespread THz-wave applications.

2. Materials and methods Fig. 1 shows the schematic drawings of ASTM_1 (Fig. 1(a)), ASTM_2 (Fig. 1(b)), ASTM_3 (Fig. 1(c)), ASTM_4 (Fig. 1(d)), and corresponding denotations, respectively. They are composed of asymmetrically L-shaped Au layers on Si substrate. The permittivities of Au and Si materials are simulated as constant in this study. They are 104 for Au layer and 10 for Si substrate, respectively [40]. The thickness of Au layer is kept as constant as 300 nm. The variations of g1, g2, and h values are defined as the gaps between two L-shaped metamaterials along y-axis direction (g1), x-axis direction (g2), and top and bottom L-shaped metamaterials (h), which are modified to figure out the unique performances in the THz frequency range. The geometrical parameters of g1, g2, a, b and h are kept as constant as g1 = 50 μm, g2 = 70 μm, a = 60 μm, b = 65 μm, h = 0.5 μm, respectively. The periods of devices are kept at 100 μm × 100 μm. It is because the configurations of ASTM_2, ASTM_3, and ASTM_4 are basically composed of the ASTM_1, their corresponding equivalent circuits are identical to that of ASTM_1. To explain the mechanism of electromagnetic responses of ASTM, the equivalent circuit is plotted in Fig. 1(e). First, the parameters of ASTM are kept at a = 60 μm and b = 65 μm to investigate the electromagnetic responses by changing g1 values from 50 μm to 74 μm (g2 is kept as constant as 70 μm) and changing g2 values from 66 μm to 90 μm (g1 is kept as constant as 50 μm). Second, the relationships of resonances and h values for ASTM_2 and ASTM_4 will be discussed to possess flexible tunability. Finally, the influence of polarization angle of four ASTM designs will be investigated and compared. These electromagnetic behaviors of ASTMs are simulated by using Lumerical Solution’s finite difference time-domain (FDTD) based simulations. The propagation direction of incident THz wavelength is perpendicular to the x-y plane in the numerical simulations. Periodic boundary conditions are assumed in the x- and y- directions, and the perfectly matched layer (PML) boundary conditions are applied in the z-direction.

Fig. 1. Schematic drawings of (a) ASTM_1, (b) ASTM_2, (c) ASTM_3, (d) ASTM_4, and (e) the equivalent circuit of ASTM_1, respectively.

3. Results and discussions Fig. 2(a) and (b) show the transmission spectra of ASTM_1 by changing g1 values from 50 μm to 74 μm with constants of g2 = 70 μm, a = 60 μm, b = 65 μm, h = 0.5 μm at TE mode and TM mode, respectively. There are three resonances at 0.18 THz, 0.34 THz, and 0.49 THz. These resonances are identical at TE and TM modes, which can be explained by the equivalent circuit models of L-shaped metamaterial being the same for both modes as plotted in Fig. 1(e). Fig. 2(c) and (d) show the transmission spectra of ASTM_1 by changing g2 values from 66 μm to 90 μm at TE mode and TM mode, respectively, while keeping g1 values as constant as 50 μm. There are three resonances at 0.19 THz, 0.33 THz, and 0.49 THz. The corresponding tuning ranges are 0.05 THz, 0.04 THz, and 0.04 THz, sequentially. These resonances are identical compared to those at TM mode as shown in Fig. 2(d). The reason is the same as the explanation in Fig. 2(a) and (b). These tuning ranges of resonances are larger than those shown in Fig. 2(a) and (b) owing to the electromagnetic response of ASTM_1 is more sensitive by changing g2 values. According to the quasi-static formulas for a parallel plate capacitor and a solenoid, it can be expressed by [41] 𝜔𝐿𝐶 =

1 𝐿𝐶

=

( ) 𝑐0

𝑔

𝑙 𝜀𝑐

𝑤

(1)

where c0 is the light velocity in vacuum, C = ε0εcwt/g and L = μ0l2/t referring to the respective capacitance and inductance, ε0 is the free space permittivity, and εc is the relative permittivity of the materials within ASTM_1, w is the metallic width, g is the gap width (i.e. g in this study), l is the size of models (i.e. Px and Py in this study), t is the metallic thickness. Therefore, the resonances of ASTM_1 can be actively tuned when the gap width are changed. In order to better understand the physic mechanism of electromagnetic response, the corresponding electric (E) field and magnetic (H) field distributions of ASTM_1 with g1 = 50 μm and g2 = 70 μm at TE mode are shown in Fig. 3. At the first resonance (0.18 THz), the E-field energy is distributed around two “L-shaped” conductor bars, while the H-field energy is distributed around the two corners of “L-shaped”. The E-field energy is distributed around the both ends of the “L-shaped” while the H-field is distributed around the middle of conductor bars.

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66 74 82 86 90

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0.5

Fig. 2. Transmission spectra of ASTM_1 with different g1 values at (a) TE mode, (b) TM mode, and g2 values at (c) TE mode, and (d) TM mode, respectively.

Fig. 3. (a-c) E-field and (d-f) H-field distributions of ASTM_1 with g1 = 50 μm and g2 = 70 μm at TE mode. Fig. 4 shows the transmission spectra of ASTM_2 by changing g1 values from 50 μm to 74 μm and g2 values from 66 μm to 90 μm at TE and TM modes, respectively. ASTM_2 exhibits polarization-independence because the corresponding equivalent circuit models are the same at TE and TM modes. The resonances are at 0.15 THz, 0.28 THz, and 0.42 THz. By changing g2 values from 66 μm to 86 μm, there are three resonances at 0.15 THz, 0.28 THz, and 0.42 THz. The resonances are kept as constant at TE and TM modes. When g2 = 90 μm,

1.0

0.9

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transmission(a.u.)

1.0 0.8 0.7 0.6

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at TE mode

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g1 (unit: μm)

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50 56 62 68 74

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at TE mode g2 (unit: μm)

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transmission(a.u.)

transmission(a.u.)

there is a resonance at 0.23 THz generated by the L-shaped metamaterial coupling to the adjacent L-shaped metamaterial. The first and second resonant intensities at TE mode are stronger than those at TM mode. It can be explained by the electromagnetic responses within the ASTM_2, the corresponding E- and H-field distributions of ASTM_2 at TE mode are summarized in Fig. 5. The E-field energy is distributed within the four conductor bars of ASTM_2 and the H-field energy is distributed around two corners of “L-shaped” of ASTM_2 at 0.15 THz. While the E-field energy is distributed within the both ends and corners of “L-shaped” of ASTM_2 at 0.28 THz and 0.42 THz. The H-field energy is distributed within four conductor bars and distributed within left and right bars of ASTM_2 at 0.28 THz and 0.42 THz, respectively. The intensity of E-field and H-field energies in ASTM_2 are focused on the conductors which are stronger than those in ASTM_1 owning to the ASTM_2 is composed of double ASTM_1. The coupling efficiency can be enhanced between the top and bottom asymmetrically L-shaped metamaterials. Owing to the stronger capacitance coupling within the asymmetrically dual-layer L-shaped metamaterial [42], the Fano resonances appear at 0.42 THz shown in Fig. 4 and Fig. 6. Fig. 6 shows the transmission spectra of ASTM_2 with different h values at TE and TM modes. The parameters of a, b, g1 and g2 are kept at 60 μm, 65 μm, 50 μm and 70 μm, respectively. By changing h values from 0.1 μm to 1.5 μm, the first resonance is modified within 0.15 THz to 0.20 THz with a tuning range of 0.05 THz. When h value is changed from 0.1 μm to 1.5 μm, the resonances are in the range of 0.28 THz to 0.34 THz at TE and TM modes. It is clearly observed that ASTM_2 exhibits a switching on/off in the range of 0.28 THz to 0.34 THz at TE and TM modes.

0.8 0.7 0.6 0.5

g2 (unit: μm) 66 74 82 86 90

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at TM mode

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0.0 0.1

(d) 0.2

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frequency(THz) Fig. 4. Transmission spectra of ASTM_2 with different g1 values at (a) TE mode, (b) TM

mode, and g2 values at (c) TE mode, and (d) TM mode, respectively.

Fig. 5. (a-c) E-field and (d-f) H-field distributions of ASTM_2 with g1 = 50 μm and g2 = 70 μm at TE mode.

Fig. 6. Transmission spectra of ASTM_2 with different h values at (a) TE mode and (b) TM mode. Fig. 7(a) shows the transmission spectra of ASTM_3 by changing g1 values from 50 μm to 70 μm at TE mode and keeping other parameters as constant. There are five resonances at 0.17 THz, 0.27 THz, 0.32 THz, 0.39 THz and 0.52 THz. These resonances are quite stable by changing g1 values. In Fig. 7(b), the resonances of ASTM_3 with different g1 values at TM mode are weaker than those in Fig.7 (a), especially the resonances of 0.52 THz and 0.54 THz. By changing the g2 values of ASTM_3 at TE mode (Fig.7(c)) and TM mode (Fig.7(d)) and keeping g1 and h values as constant as 50 μm and 0.5 μm, respectively, the transmission spectra are almost identical except the transmission intensities are different. To compare the results of ASTM_1 and ASTM_2, ASTM_3 exhibits two extra resonances at 0.27 THz and 0.39 THz. It indicates that the electromagnetic behaviors between ASTM_1 and ASTM_3, and ASTM_2 and ASTM_3 possess the switching characteristics. It provides a suitable design for the switching function in the THz-wave applications. Fig. 8 shows the E- and H-field

distributions of ASTM_3. The E-field energy is distributed within the bottom of the left bar and the top of the right bar while the H-field energy is distributed around the “L-shaped” conductor bars at 0.17 THz. When the resonance is at 0.32 THz, the E-field energy is distributed within the end of “L-shaped” bar and the H-field energy is distributed around the top-left corner and bottom-right corner of ASTM structures. To compare the electromagnetic energies distributions of ASTM_1, the E-field energy of ASTM_3 is focused within the “L-shaped” bars and the H-field energy is around the “L-shaped” conductor bars obviously. To investigate the active switching characteristic of ASTM_3, the h value between top and bottom L-shaped metamaterial of ASTM_3 is modified from 0.1 μm to 2.0 μm. The transmission spectra of ASTM_3 with different h values at TE and TM modes are shown in Fig. 9(a) and (b), respectively. It is clearly observed that ASTM_3 exhibits actively switching function at the resonances of 0.27 THz and 0.39 THz by changing h values from 0.1 μm to 0.5 μm and 0.5 μm to 2.0 μm. These two resonances of 0.27 THz and 0.39 THz are very sharp with ultrahigh Q-factors. The calculated Q-factors are 130 and 133 for the resonances of 0.27 THz and 0.39 THz, respectively. In Fig. 7 and Fig. 9, the Fano resonances are at 0.27 THz which generated from the stronger capacitance coupling between the asymmetrically dual-layer rotated 90° L-shaped metamaterial. This rotation angle makes the asymmetric degree of ASTM_3 stronger. The Fano resonance will be broader caused by the higher radiative losses in this asymmetric regime. Fig. 10(a) and (b) show the transmission spectra of ASTM_4 by changing g1 values from 50 μm to 74 μm and keeping g2 value as 70 μm at TE and TM modes, respectively. There are six resonances at 0.18 THz, 0.23 THz, 0.37 THz, 0.42 THz, 0.53 THz and 0.60 THz. These resonances are identical at TE and TM modes because of the corresponding equivalent circuit models are the same for both modes. Fig. 10(c) and (d) show the transmission spectra of ASTM_4 by changing g2 values from 66 μm to 86 μm at TE and TM modes, respectively. There are six resonances at 0.18 THz, 0.23 THz, 0.37 THz, 0.42 THz, 0.53 THz and 0.60 THz. These resonances are identical at TE and TM mode except the resonant intensities. The corresponding E- and H-filed distributions of ASTM_4 with g1 = 50 μm and g2 = 70 μm at TE mode are shown in Fig. 11. The most E-field and H-field energies are distributed within the L-shaped conductor bars and around the L-shaped bars, respectively. The Fano resonances at 0.18 THz are generated from the asymmetrically connected L-shaped metamaterial from the LC coupling between layers. These Fano resonances are extremely sensitive to the conducting properties of the resonators.

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Fig. 7. Transmission spectra of ASTM_3 with different g1 values at (a) TE mode, (b) TM mode, and g2 values at (c) TE mode, and (d) TM mode, respectively.

Fig. 8. (a-e) E-field and (g-k) H-field distributions of ASTM_3 with g1 = 50 μm and g2 = 70 μm at TE mode.

Fig. 9. Transmission spectra of ASTM_3 with different h values at (a) TE mode and (b) TM mode.

Fig. 10. Transmission spectra of ASTM_4 with different g1 values at (a) TE mode, (b) TM mode, and g2 values at (c) TE mode, and (d) TM mode, respectively.

Fig. 11. (a-f) E-field and (g-o) H-field distributions of ASTM_4 with g1 = 50 μm and g2 = 70 μm at TE mode.

4. Conclusions In conclusion, we present four designs of ASTM devices by modifying the relative parameters to investigate their superior optical properties in the THz frequency range. ASTM_1 exhibits triple-resonance, which can be tuned to be red-shift or blue-shift depending on the g2 values. ASTM_2 shows the active switching function from triple-resonance to quad-resonance by changing g2 values and triple-resonance to dual-resonance by changing h values, respectively. Furthermore, ASTM_3 can be realized active switching resonance at 0.27 THz and 0.39 THz by changing h values. For the ASTM_4 design, the resonances are quite stable by changing g1 values. By changing g2 values of ASTM_4, the resonant intensities can be modified to possess the variable optical attenuator (VOA) characteristic. These four ASTM designs provide the possibilities of THz metamaterial to be used in active switching optoelectronics applications, such as filter, sensor, VOA, logic device, programmable device, and so on.

Acknowledgment: The authors acknowledge the financial support from research grants of 100 Talents Program of Sun Yat-Sen University (grant number 76120-18831103) and the State Key Laboratory of Optoelectronic Materials and Technologies of Sun Yat-Sen University for the use of experimental equipment.

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Highlights   

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Four actively switchable terahertz metamaterials (ASTMs) are presented. ASTM_1 exhibits triple-resonance, which can be tuned to be red-shift or blue-shift depending on the g2 value. ASTM_2 shows the active switching function from triple-resonance to quad-resonance by changing g2 value and triple-resonance to dual-resonance by changing h value, respectively. ASTM_3 can be realized active switching resonance at 0.27 THz and 0.39 THz by changing h value. ASTM_4 exhibits the variable optical attenuator characteristic. The transmission spectra of four ASTMs are investigated to possess polarization-independence.