We present a reconfigurable terahertz (THz) resonator using double C-shape metamaterials (DCM) that can be used as filter and single-/dual-resonance switch. By changing the position of the C-shape metamaterial along x-axis and y-axis directions, the resonances can be modulated from single-resonance to dual-resonance in TE mode and the corresponding free spectrum range (FSR) can be changed from 0.19 THz to 0.09 THz. These results indicate the proposed DCM can be used as a single-/dual-resonance switch and polarization switch. To increase the tunability, flexibility, and applicability of DCM, the resonant frequency could be tuned by changing the gap between DCM with the dual-layer. The resonances are blue-shifted 0.04 THz from 0.22 THz to 0.26 THz (1st resonance) and 0.11 THz from 0.36 THz to 0.47 THz (2nd resonance) in TE mode. The relationship of resonance and gap variation is quite stable and linear. This design of DCM provides a potential possibility of feasible opto-electronics applications in the THz frequency range.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Metamaterial is an artificial material with extraordinary electromagnetic properties that cannot found in natural materials. Metamaterial has the advantages of reducing the size and weight of optical devices compared to conventional materials. Among terahertz (THz) metamaterial designs, the classic metamaterial structure is considered as a ring with a common split, i.e. split-ring resonator (SRR), which was first theoretically proposed in 1999 and then experimentally verified in 2000 [1,2]. After that, some derivative designs such as U-shaped SRR, complementary SRR (cSRR), I-shaped SRR, V-shaped SRR, electric SRR (eSRR), and 3D SRR, etc. are presented and demonstrated [3–6]. The metamaterials are commonly used but not limited to metallic materials, e.g. gold (Au), silver (Ag), copper (Cu), and aluminum (Al) and 2D materials, e.g. graphene [7,8], molybdenum disulfide (MoS2) , barium strontium titanate [10,11], perovskite [12,13], vanadium dioxide (VO2) [14–17], isotropic silicon , germanium antimony telluride (GST) , and so on. Among these materials, Ag and Au are the two most often used for metamaterial applications than other materials due to their relatively small ohmic losses or high conductivity in THz frequency range. Although Ag has the lowest loss, it will suffer the degradation in the fabrication process. Furthermore, the losses of Ag are strongly dependent on the surface roughness. Au has predominately been the materials for metamaterial applications . Additionally, Au is anti-oxidative and chemically stable in many environments. It is unlike Ag, Al and Cu materials, which are easily oxidized and very rapidly come into being a metallic oxide layer under atmospheric conditions. Therefore, Au becomes the usual material of choice for most applications, especially for biological and chemical sensing applications [21,22].
Recently, tunable metamaterial is a hot research topic owing to its flexibility and applicability in real applications. The tuning approaches of metamaterial can be used to manipulate the amplitude, frequency and polarization of incident electromagnetic wave [23–27], which are including thermal, ferroelectric materials, semiconductor materials or diodes, laser pumping, liquid crystal, electrostatic force, and so on . Among these tuning approaches, reconfigurable metamaterial becomes feasible in many applications, which are other than the use of liquid crystal , ferroelectric materials [30,31], and semiconductor diodes [32–34] are highly dependent on the nonlinear properties of nature material and limited the tuning range [35–38].
In this study, we propose a THz resonator by using double C-shape metamaterial (DCM) microstructures. The C-shape structure is kept as the same as a semicircle. By changing the space configuration of DCM, the electromagnetic response can be modified from single-resonance to dual-resonance and the corresponding free spectrum range (FSR) can be also modified. To increase the flexibility of DCM device, two stacked DCM layers with a gap between top and bottom DCM is presented. The sophisticated parameter changes can be utilized micro-electro-mechanical systems (MEMS) technique to tune the electromagnetic response of DCM. This design can be realized the reconfigurable DCM to possess tunable resonance, transmission intensity, FSR, and single-/dual-resonance switch characteristics.
2. Designs and methods
Figure 1(a) shows the schematic drawing of proposed dual-layer DCM. The polarization configurations of transverse electric (TE) mode and transverse magnetic (TM) mode are also denoted in Fig. 1(a). The proposed dual-layer DCM device is composed of two stacked Au layers with 220 nm in thickness on Si substrate. There is a gap between top and bottom tailored Au layers. The height of gap is 1500 nm. The geometrical dimensions of dual-layer DCM device are the period along x-axis direction (Px = 120 µm) and y-axis direction (Py = 100 µm), diameter of C-shape microstructure (d), and metallic line width (w), respectively. The electromagnetic responses are investigated by changing x and y values along x-axis direction and y-axis direction, respectively. The merits of this design are that dual-layer DCM device exhibits polarization-dependence, single-/dual-resonance switch, and tunable FSR characteristics owing to the geometry of DCM is asymmetrical with different x and y values as shown in Fig. 1(b). To increase the flexibility of dual-layer DCM, the g value could be tuned along z-axis direction. Such approach makes dual-layer DCM showing actively tunable resonance by changing g value.
The electromagnetic responses of dual-layer DCM are adopted by Lumerical Solution’s finite difference time domain (FDTD) based simulations to study the optical properties. The direction of incident light is set to be perpendicular to the x-y plane in the numerical simulations. Periodic boundary conditions are adopted in the x and y directions and perfectly matched layer (PML) boundaries conditions are assumed in the z direction. The mesh precision is 1 nm and the minimum clearance size is 0.1 µm. The transmission of incident electromagnetic waves is set a monitor on the bottom side of device. First, the single-layer DCM is presented to figure out the optimized geometrical parameters and discussed the interactions of incident THz wave and DCM. Second, according to the results of single-layer DCM, we can choose the suitable geometrical parameters to design dual-layer DCM with active tunability.
3. Results and discussions
Figure 2 shows the transmission spectra of single-layer DCM by changing x value at TE mode (Fig. 2(a)) and TM mode (Fig. 2(b)). The geometrical dimensions are kept as constant as d = 55 µm, w = 5 µm, and y = 0 µm, respectively. In Fig. 2(a), by changing x value from initial state (x = 0 µm) to x = 30 µm, the resonances are modulated from single resonance at 0.213 THz to dual-resonance at 0.306 THz to 0.494 THz at TE mode. When x value is increased to 40 µm, two resonances becomes closer and then merged gradually. It can be seen there will be an electromagnetically induced transparency (EIT) characteristic at 0.369 THz. By continuously increasing x value to 60 µm, there are two resonances at 0.236 THz and 0.602 THz. The corresponding FSR could be modified from 0.188 THz to 0.366 THz by changing x = 30 µm to 60 µm. At TM mode, there is only one resonance at 0.21 THz at initial state (x = 0 µm). By increasing x value to 30 µm, 40 µm, and 60 µm, the resonance is shift to 0.233 THz, 0.219 THz, and 0.178 THz, respectively as shown in Fig. 2(b).
In order to better understand the interaction of incident THz wave to DCM microstructures, the electric (E) and magnetic (H) fields distributions of single-layer DCM with different x value are monitored at TE mode as shown in Fig. 3. In Fig. 3(a), single-layer DCM with x = 0 µm shows a dipole resonance at 0.213 THz caused from the E-field and H-field energies concentrated on the arc-shape structures. When x = 30 µm, E- and H-fields energies are distributed on the arc-shape structure and vertices of the DCM. There will generate dipole resonances are 0.306 THz and 0.494 THz as shown in Fig. 3(b) and (c), respectively. By increasing x = 40 µm, two resonances are merged together at 0.369 THz as E- and H-fields distribution shown in Fig. 3(d). When x = 60 µm, there are two dipole resonances caused from fields energies distributed on the vertices of the DCM at 0.236 THz and 0.602 THz as shown in Fig. 3(e) and (f), respectively. At TM mode, the E- and H-fields distributions of single-layer DCM with different x value are shown in Fig. 4. It is clearly observed that E-field energies are concentrated on top and bottom side of DCM while H-field energies are concentrated on the arc-shape structures of DCM. Therefore, the resonance is single-resonance at 0.213 THz (Fig. 4(a)), 0.233 THz (Fig. 4(b)), 0.219 THz (Fig. 4(c)), and 0.178 THz (Fig. 4(d)) for single-layer DCM with x = 0 µm, 30 µm, 40 µm, and 60 µm, respectively.
Figure 5 shows the transmission spectra of single-layer DCM by changing y value at TE mode (Fig. 5(a)) and TM mode (Fig. 5(b)). The geometrical dimensions are kept as constant as d = 55 µm, w = 5 µm, and x = 30 µm, respectively. In the initial state (y = 0 µm), the resonances are at 0.306 THz and 0.494 THz. When y value is changed to 5 µm, the resonances are modulated at 0.306 THz and 0.448 THz. By increasing y value to 10 µm, the resonances are at 0.311 THz and 0.430 THz. Continuously increasing y value to 15 µm, the resonances are at 0.323 THz and 0.419 THz. It can be observed the first resonance is blue-shift 0.02 THz and second resonance is red-shift 0.08 THz. The corresponding FSR becomes narrower from 0.19 THz to 0.09 THz from y = 0 µm to 15 µm. At TM mode, the resonant frequencies are single resonances for y value changing from 0 µm to 15 µm, which are 0.233 THz, 0.227 THz, 0.215 THz, and 0.196 THz, respectively as shown in Fig. 5(b). The single-resonance is shift from 0.233 THz to 0.196 THz. The corresponding relationships of resonances and y value are plotted in Fig. 5(c) and (d) for TE and TM modes, respectively. It can be clearly seen that FSR is decreased gradually by increasing y value as shown in Fig. 5(c).
The interaction of incident THz wave to DCM microstructures could be observed by E- and H-fields distributions of single-layer DCM with different y value monitored at TE mode as shown in Fig. 6. Single-layer DCM with y = 0 µm shows resonances are dipole resonances at 0.306 THz and 0.494 THz caused from the E-field and H-field energies concentrated on the arc-shape structures and apexes of DCM as shown in Fig. 6(a) and (b), respectively. When y = 5 µm, E- and H-fields energies are distributed on the arc-shape structure and vertices of the DCM. The dipole resonances are shift to 0.306 THz and 0.448 THz as shown in Fig. 6(c) and (d), respectively. By increasing y = 10 µm, dipole resonances are shift to 0.311 THz and 0.430 THz as shown in Fig. 6(e) and (f), respectively. E-field and H-field energies of second resonance are concentrated on the apexes and central arc-shape structures of DCM. When y = 15 µm, there are two dipole resonances caused from fields energies distributed on the vertices of the DCM at 0.323 THz and 0.419 THz as shown in Fig. 6(g) and (h), respectively. At TM mode, the E- and H-fields distributions of single-layer DCM with different y value are shown in Fig. 7. It is clearly observed that E-field energies are concentrated on top and bottom side of DCM while H-field energies are concentrated on the arc-shape structures of DCM. Therefore, the resonance is single-resonance at 0.233 THz (Fig. 7(a)), 0.227 THz (Fig. 7(b)), 0.215 THz (Fig. 7(c)), and 0.196 THz (Fig. 7(d)) for single-layer DCM with y = 0 µm, 5 µm, 10 µm, and 15 µm, respectively.
Figure 8 shows the transmission spectra of single-layer DCM by changing w value at TE mode (Fig. 8(a)) and TM mode (Fig. 8(b)). The geometrical dimensions are kept as constant as x = 60 µm, y = 0 µm, and d = 55 µm, respectively. In Fig. 8(a), by changing w value from 5 µm to 10 µm, there are dual-resonances with a linear blue-shift at TE mode. In the initial state (w = 5 µm), there is dual-resonance at 0.236 THz and 0.602 THz. When w is 7.5 µm, the dual-resonance is at 0.274 THz and 0.680 THz. By increasing w to 10 µm, the dual-resonance is at 0.303 THz and 0.750 THz. The corresponding FSR is varied from 0.36 THz to 0.45 THz by changing w from 5 µm to 10 µm at TE mode. At TM mode, the resonances are 0.178 THz, 0.195 THz, and 0.213 THz for w = 5 µm, 7.5 µm, and 10 µm, respectively. The single-resonance is a linear blue-shift at TM mode as shown in Fig. 8(b). The corresponding relationships of resonances and w value are summarized in Fig. 8(c) and (d) for TE and TM modes, respectively. It can be clearly seen from Fig. 8(c) that the FSR is increased slightly by changing the w value. The interactions of incident THz wave and DCM with different w value are plotted in Fig. 9 and Fig. 10 for TE and TM modes, respectively. Single-layer DCM with w = 5 µm shows resonances are dipole resonances at 0.236 THz and 0.602 THz as shown in Fig. 9(a) and (b), respectively. When w = 7.5 µm, the dipole resonances are shift to 0.274 THz and 0.680 THz as shown in Fig. 9(c) and (d), respectively. By increasing w = 10 µm, dipole resonances are shift to 0.303 THz and 0.750 THz as shown in Fig. 9(e) and (f), respectively. These resonances are caused from the E- and H-field energies concentrated on the apexes of DCM (first resonance) while those concentrated along the arc-shape of DCM (second resonance), respectively. At TM mode, the E- and H-fields distributions of single-layer DCM with different w value are shown in Fig. 10. The resonance is single-resonance at 0.178 THz (Fig. 10(a)), 0.195 THz (Fig. 10(b)), and 0.213 THz (Fig. 10(c)) for single-layer DCM with w = 5 µm, 7.5 µm, and 10 µm, respectively. These resonances are caused from the E-field energies concentrated on the apexes of DCM while the H-field energies concentrated on the arc-shape of DCM, respectively.
To increase the flexibility of DCM device, two stacked DCM layers with a gap between top and bottom DCM is presented. The transmission spectra of DCM with dual-layer by changing g value at TE mode are shown in Fig. 11(a). The geometrical dimensions are kept as constant as d = 55 µm, x = 30 µm, y = 0 µm, and w = 5 µm, respectively. There are two resonances blue-shift by changing g value from 0 nm to 1500 nm. The tuning mechanism can be realized by using MEMS technique to modify the g value. By increasing g value from 0 nm to 1500 nm, the tuning ranges of two resonances are 0.04 THz and 0.11 THz for first resonance and second resonance, respectively. The corresponding relationships of resonances and g value are summarized in Fig. 11(b). The tuning electromagnetic responses are quite stable and linear. In view of above-mentioned, the proposed DCM device exhibits tunable filter, single-/dual-resonance switch, tunable FSR, and polarization-dependent characteristics in THz frequency range. Such results pave a way to the devices used in THz spectroscopy, THz imaging, and THz sensor applications.
In conclusion, we present a high-efficiency THz resonator by using DCM microstructures and investigate the electromagnetic characterizations. By changing x value from initial state (x = 0 µm) to x = 30 µm, the resonances are modulated from single-resonance at 0.22 THz to dual-resonance at 0.31 THz to 0.50 THz at TE mode. When x value is changed to 40 µm, two resonance will be merged together. Continuously increasing x value to 60 µm, FSR is modulated from 0.188 THz to 0.366 THz. By changing the y value from 0 µm to 15 µm, the second resonance is red-shift 0.08 THz and the first resonance is almost kept as constant. To achieve tuning capabilities, the distance between two DCM layers can be adjusted to achieve efficient tuning capabilities. The tuning range of second resonance is 0.11 THz, while the corresponding FSR can be tuned from 0.14 THz to 0.21 THz. By tailoring the geometrical dimensions, proposed device can be the filter, switch, and polarize in THz frequency range. It provides the capabilities for the use in widespread THz applications.
Sun Yat-sen University (76120-18841202).
The authors acknowledge the State Key Laboratory of Optoelectronic Materials and Technologies of Sun Yat-Sen University for the use of simulation codes.
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