We propose and demonstrate two designs of complementary spiral-shape metamaterials (CSSM) with square and hexagonal meta-atom arrangements in the terahertz (THz) frequency range. For convenience, they are denoted as CSSM-S and CSSM-H for CSSM with square and hexagonal meta-atom arrangements, respectively. The electromagnetic responses are investigated for CSSM with different spiral angle (θ). CSSM-S exhibits dual-, triple-, and quad-resonance for θ = 360°, θ = 540° and θ = 720°, respectively in transverse electric (TE) mode and exhibits single-, dual-, and triple-resonance for θ = 360°, θ = 540° and θ = 720°, respectively in transverse magnetic (TM) mode. By applying a direct-current (dc) bias voltage on CSSM-S, it shows the actively tunable resonance with a tuning range of 0.12 THz and switching polarization characteristics. Furthermore, to facilitate the flexibility and applicability of CSSM, the unit cell of CSSM with different θ is superimposed to form CSSM-H. CSSM-H possesses the combination of electromagnetic behaviors generated by each unit cell of CSSM with different θ. This study provides a design of complementary THz metamaterials to have electromagnetically induced transparency (EIT) analog characteristics, which shows single-digital and multi-digital signals for the programmable metamaterial application. It paves a way to the possibility of THz metamaterials with great tunability and good polarization-dependence.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Terahertz (THz) wave is the transition spectrum from microwave to infrared (IR) wavelength which occupies the spectrum in the frequency range of 0.1 THz to 10 THz [1–3]. Among the entire electromagnetic spectrum, THz optics in spectroscopy and imaging systems is imperative to THz wave applications, such as quality control, security check, physics study, and molecule identification [4–6]. Moreover, the integration of THz optics constituted by miniaturized optical components is expected to express higher signal transportation . It allows more compact systems and enables the integration with other systems for increasing flexibility and applicability. For instance, THz device can be compacted into semiconductor integrated circuits and integrated photonic circuits [8,9]. Such miniaturized THz optical components are required new approaches and techniques for the realization of active manipulation to possess multi-functionalities.
Over the past two decades, the artificially electromagnetic material, termed metamaterial, has attracted a tremendous amount of attention for researchers owing to their exotic and extraordinary optical properties to manipulate the amplitude, direction, polarization, wavelength, and phase of electromagnetic waves [10–14]. By properly tailoring the geometrical dimension of metamaterial, it can be realized electro-optic devices spanning the frequency range from microwave, THz, IR, visible to ultraviolet caused from the transformation optics theory . Therefore, many literatures have been reported unique electromagetic metamaterials which have largely improved many classic devices, such as switch, resonator, waveguide, filter and so on [16–23]. The unprecedented advantages of metamaterial come from its extreme scalability and ultrathin feature. Metamaterial has led to the demonstration of even exotic THz properties such as artificial magnetism, negative refractive index, wavelength perfect absorption, chirality, and electromagnetically induced transparency (EIT) [24–29]. Recently, the EIT analog using planar metamaterials have been demonstrated to enable the realization of slow light effect and high nonlinearity in THz frequency range, which are reported and performed through near-field coupling between the resonators at bright and dark modes by implanting extra materials into the unit cell of metamaterial [30,31]. The controllable methods are through dynamic modulation of resonator at dark mode  or the intercoupling distance , including optical pumping of photoconductive materials , or thermally controlled superconducting materials as the part of coupled resonator system . Such tunability in coupled resonator system adds a new dimension to the design and functionality of metamaterial and possible applications .
In this study, we propose a design to control the EIT analog without implanted any extra material into the metamaterial structures. We design and utilize two types of THz complementary spiral-shape metamaterial (CSSM) with square and hexagonal meta-atom arrangements, which are denoted as CSSM-S and CSSM-H, respectively. The proposed devices possess EIT analog characteristics by controlling bright and dark modes within resonators. CSSM-S with different spiral angle (θ) exhibits dual-, triple-, and quad-resonance at transverse electric (TE) mode, while that shows single-, dual-, and triple-resonance at transverse magnetic (TM) mode, respectively. Furthermore, CSSM-H indicates the characteristics of tunable and switchable single-band and dual-band EIT analog. These electromagnetic characteristics provide the possibilities for the realization of programmable metamaterial in THz wave applications.
2. Designs and methods
The schematic drawing of CSSM-S is shown in Fig. 1(a). The unit cell and corresponding denotations of CSSM-S are indicated in Fig. 1(b). They are spiral angle (θ) and spiral width (w). Here, the spiral widths are 6 µm and the periods of devices are kept as constant as 100 × 100 µm2 and 160 × 160 µm2 for CSSM-S and CSSM-H, respectively. The proposed CSSM device was fabricated using maskless photolithography and lift-off techniques. First, the lift-off resistance was spin coated, which was polymethylmethacrylate (PMMA) spun on the device and baked at 180 °C for 2 min. Second, the metamaterial pattern was defined on the resist layer using a maskless photography technique. Third, the 10/200 nm thick Cr/Au layer was deposited on an unintentional doping Si substrate using a sputtering system. After development of the resist in 3:1 isopropyl alcohol (IPA)/deionized water (DI) solution for 5 min, the CSSM pattern was performed by removing the resist. Figure 1(c-e) are optical microscopy images of spiral-shape array of CSSM-S with θ = 360°, θ = 540°, and θ = 720°, respectively. The corresponding unit cells are shown in the inserted images of Fig. 1(c-e), respectively. The patterns are easily fabricated, high portability, applicability, and cost-effectiveness. The electromagnetic characteristics of CSSM-S and CSSM-H are performed by using Lumerical Solution’s finite difference time-domain (FDTD) based simulations to study the optical properties of devices. The propagation direction of incident THz wave is perpendicular to the x-y plane in the numerical simulations. Periodic boundary conditions are also adopted in the x and y directions and perfectly matched layer (PML) boundaries conditions are assumed in the z direction. The mesh precision is 0.5 nm with the minimum clearance size of 0.1 µm. The transmission THz wave is calculated by setting monitor on the bottom side of device.
3. Results and discussions
Fig. 2 shows the transmission spectra of CSSM-S with different θ at TE and TM modes. In Fig. 2(a), there is no any resonance in the frequency range of 0.1-0.5 THz at TM mode. It can be seen there is a sharp transmission peak at 0.26 THz within the broad frequency range of 0.1-0.5 THz for CSSM-S with θ = 360°. This is a signature of the strong plasmonic hybridization in the resonator system. It is the resonance of bright mode in EIT analog. It can be explained by the strong E-field energy focused on the spiral-shape of CSSM-S as shown in Fig. 3(a). The induced transmission intensity is switched from 0.11 to 0.65 by rotating incident polarization angle from TM mode to TE mode. Simultaneously, there is a dark mode at 0.27 THz. The transmission intensity could be switched from 0 (TM mode) to 0.11 (TE mode). Figure 2(b) shows the transmission spectra of CSSM-S with θ = 540°. The transmission intensity of 0.28 at TM mode can be switched to 0.65 at TE mode to form the bright mode in EIT analog. The resonance is at 0.30 THz. While it can be also switched to the dark mode at 0.33 THz. For the case of CSSM-S with θ = 720° as shown in Fig. 2(c), there are bright modes at 0.17 THz (TE mode) and 0.45 THz (TM mode). While there are dark modes at 0.18 THz (TE mode) and 0.44 THz (TE mode). That can be switched between bright mode and dark mode by changing incident polarization light. To better understand the interactions of THz wave to the proposed CSSM-S, the electromagnetic field monitors are simulated and set into CSSM-S. The corresponding electric (E) field and magnetic (H) field distributions are represented in Fig. 3(a-f). The resonant frequency of the circuit model of CSSM-S can be expressed by 
To further enhance the flexibility of proposed CSSM, it is designed to be controlled by applying a direct-current (dc) bias voltage to heating up the temperature of surrounding ambient. CSSM-S with θ = 720° is chosen to be an example for the realization of tunable CSSM. The schematic drawing of proposed tunable CSSM-S is shown in Fig. 4(a). The experimental results are shown in Fig. 4(b). The electromagnetic responses of CSSM-S at TM and TE modes without applying a dc bias voltage are identical to the results of Fig. 2. By increasing the dc bias voltage from 0 V to 30 V, the resonance is red-shift from 0.46 THz to 0.34 THz with a tuning range of 0.12 THz. The surrounding temperature is increased by applying a dc bias voltage on device, which can be expressed by 
The electromagnetic responses of CSSM-H with θ = 360°, θ = 540°, θ = 720°, and corresponding superimposed conditions are shown in Fig. 5. The simulated results of CSSM-H with θ = 360°, θ = 540°, and θ = 720° are shown in Fig. 5(a-c), respectively. In Fig. 5(a), CSSM-H with θ = 360° exhibits the bright-mode at 0.26 THz and dark-mode at 0.27 THz. The corresponding E-field and H-field distributions are shown in the inserted images of Fig. 5(a). In the design of CSSM-H with θ = 540°, it exhibits the bright-mode at 0.30 THz and dark-mode at 0.33 THz as shown in Fig. 5(b). The corresponding E- and H-fields distributions are shown in the inserted images of Fig. 5(b). Moreover, CSSM-H with θ = 540° exhibits a polarization switch at 0.55 THz, which can be switched the transmission intensity from 0.05 at TM mode to 0.60 at TE mode. Figure 5(c) shows the results for the case of CSSM-H with θ = 720°, which exhibits the bright-mode at 0.17 THz and dark-mode at 0.18 THz. The corresponding E-field and H-field distributions are shown in the inserted images of Fig. 5(c). For the cases of CSSM-H with superimposed different θ, the transmission spectra of CSSM-H with θ = 360°+540°, θ = 360°+720°, and θ = 540°+720° are shown in Fig. 5(d-f), respectively. Figure 5(d) shows the resonances of CSSM-H with θ = 360°+540° at 0.26 THz and 0.30 THz for bright-modes while at 0.27 THz and 0.32 THz for dark-modes, which are the superimposed results of Fig. 5(a) and Fig. 5(b). There is a little variation of 0.01 THz for dark-mode resonance caused from the continuous superimposed spectra. It is worth to noted that there are two polarization switching functions at 0.52 THz and 0.55 THz, respectively. In Fig. 5(e), there are two bright-modes at 0.17 THz and 0.26 THz and two dark-modes at 0.18 THz and 0.27 THz, respectively for the case of CSSM-H with θ = 360°+720°. The corresponding E-field and H-field distributions are shown in the inserted images of Fig. 5(e). Figure 5(f) shows the transmission spectra of CSSM-H with θ = 540°+720°. There are two bright-modes at 0.17 THz and 0.30 THz and two dark-modes at 0.18 THz and 0.33 THz, respectively. The corresponding E-field and H-field distributions are shown in the inserted images of Fig. 5(f). These results indicate that the EIT analog can be controlled by hexagonal meta-atom arrangement of CSSM to possess single-digital and multi-digital signals to increase the flexibility and capability for the realization of programmable metamaterials in THz frequency range.
In conclusion, we present two CSSM designs with square and hexagonal meta-atom arrangements (CSSM-S and CSSM-H) which exhibit EIT analog characteristics. CSSM-S shows dual-, triple-, and quad-resonance for θ = 360°, θ = 540°, and θ = 720°, respectively at TE mode and shows single-, dual-, and triple-resonance for θ = 360°, θ = 540° and θ = 720°, respectively at TM mode. These electromagnetic behaviors are polarization-dependence and EIT switch at different polarization state. CSSM-H indicates single-digital and multi-digital signals to lay the foundation for the realization of programmable metamaterials in THz frequency range. CSSM-S performs the tunable THz filter by applying a dc bias voltage on device. The tuning range is 0.12 THz compared to that without and with a dc bias voltage of 30 V. With the investigation of CSSM being fully understood, the design of CSSM exhibits the multi-functionalities of single-band and dual-band switch and polarization switch. It potentially provides a new direction for future THz device applications and a flexible platform for developing the next generation randomly accessible, digital and programmable metamaterials for precise tailoring of electromagnetic properties and multi-channel data processing at higher bit rates.
Research grants of the 100 Talents Program of Sun Yat-sen University (SYSU) (76120-18841202).
The authors acknowledge the State Key Laboratory of Optoelectronic Materials and Technologies of Sun Yat-Sen University for the uses of simulation codes and experimental equipment.
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