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Abstract
Mimicking the quantum phenomena of electromagnetically induced transparency using metasurfaces has drawn continuous interest in recent years owing to its potential in realizing optical switching, slow-light, nonlinear enhancement, and sensing devices with much reduced working conditions. Various kinds of structures have been proposed through designing the internal coupling effect among the unit cell. In this work, we theoretically and experimentally propose a new type of coupled resonant structures composed of meanderline and U-shaped resonators in the terahertz regime, which can exhibit strong behavior of electromagnetically induced transparency. The introduction of the meanderline structure provides an effective manner for realizing electrically controlled electromagnetically induced transparency devices due to its continuous connection feature, making it convenient to serve as an integrated electrode. Such ability is verified by simulations where vanadium dioxide structures are further integrated. The proposed design opens new avenues to realize compact and tunable slow-light devices.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetically induced transparency (EIT) is an intriguing physical effect in quantum system, which exhibits phenomenon of tuning previously opaque medium to transparent one under external stimuli. Accompanying with the emergence of a narrow transmission window within a broad absorption band, significant modification happens in the dispersion properties around the transmission window, which could be used to slow down the group velocity of the passing light. EIT commonly occurs in three-level atomic systems, which can be theoretically explained by destructive quantum interference between different transition pathways [1–4]. Recently, such interference process have been well mimicked in classical systems, such as optical cavities, electric circuits, and plasmonic structures [5–11], where coupling plays an essential role in composing the interference “pathways” so as to generate the EIT-like spectra. These EIT analogs possess similar property of the quantum EIT but do not require the corresponding harsh working conditions, showing great potential in developing novel devices, including slow-light devices, optical switches, all-optical logic devices, nonlinear enhancement, and ultrasensitive sensors, etc. [12–24] In particular, plasmonic analogues of EIT based on subwavelength metasurface structures have aroused great interest. Various kinds of structures have been proposed, for example, coupled bar and double-bar resonators, bar and split-ring resonators, waveguide micro-resonators, and multi-layer structures [25–30].
In general, the essential rule for designing EIT metasurface is to select unit cell contains two coupled resonant modes with similar resonance frequencies but obviously different quality (Q) factors. One is bright mode which has a low quality (Q) factor and can be strongly excited by the external field, and the other is dark mode which has a high Q factor and can only be excited by the coupling near field of the bright mode or can be weakly excited by the external field at the same time [6–9,29,30]. Destructive interference between external excitation and dark mode coupling happen at the bright mode, suppressing the resonance of the bright mode and thus inducing a transparency window. The amplitude of the newly induced transparency window can be controlled by tuning the coupling strength, which could recover the resonance of the bright mode by reducing one interference pathway [31,32]. Another route is to increase the loss (or reduce the Q factor) of the dark mode. In this case, though the coupling field from the bright mode is still there, the dark mode could hardly be excited to affect the bright mode [6,33]. Such tuning way is quite suitable to realize active EIT by integrating functional materials into the dark mode. The above controlling ways could tune the EIT transmission well, however, such behavior seems not suitable in controlling the group delay in some applications as the amplitude of the transmission window also changes accordingly. Meanwhile, previous designs are usually based on isolate structures, which are suitable for optical and temperature control but hard for electric control. Graphene could be a good candidate for realizing electric control EIT metasurfaces [33], however, the performance is strongly determined by the graphene quality. Designing new type of EIT structures and the controlling manner to meet various application scenes is always in highly demanded.
In this paper, a novel EIT metasurface is theoretically and experimentally proposed in the terahertz regime. The metasurface is composed of meaderline resonator (MLR) as the bright mode and double U-shaped resonator (DUR) as dark mode. Strong EIT phenomenon is observed when putting them together to introduce coupling effect, which could also be interpreted by the constructive and destructive interference between the electric coupling and magnetic coupling pathways from the bright mode to the dark mode. As the meaderline structure is made of continuous metallic stripe, it could function as integrate electrode naturally for realizing electrically controlled EIT. To illustrate such ability, we theoretically design an active EIT device which could be electrically controlled, where we modulate the bright mode instead of the coupling or the dark mode using phase change material vanadium dioxide (VO2). A novel EIT modulation behavior is observed where the amplitude of the transmission window does not change, while the two resonance dips gradually shrink as the decrease of the VO2 conductivity. More importantly, the group delay at the transmission window frequency are changed accordingly. Such behavior is very promising in realizing active slow-light applications.
2. Experiments and results
The proposed terahertz EIT metasurface is schematically illustrated in Fig. 1(a), the DUR is placed inside the MLR with the gaps facing to the top arm of the MLR. Both the contained MLRs and DURs are made from 0.2 µm-thickness aluminum on silicon substrate. The structure unit cell is schematically illustrated in Fig. 1(b), whose geometric parameters are L = 63 µm, l = 15 µm, D = 15.5 µm, d = 10 µm, w = 6 µm, g = 6 µm, s = 7 µm and period P = 100 µm, respectively. To demonstrate the EIT behavior, three metasurfaces made of sole MLRs, sole DURs, and the EIT structures were fabricated by conventional photolithography on a high-resistance silicon substrate of thickness h = 640 µm. The size of the fabricated metasurface was 1 cm × 1 cm in size. The amplitude transmission spectra of all the metasurfaces were measured by a photoconductive-antenna-based, broadband, 8f confocal terahertz time-domain spectroscopy (THz-TDS) system under normal incidence [34], as schematically illustrated in Fig. 1(c). The beam size at the sample position was 3.5 mm in diameter, which was focused by a parabolic mirror PM2. About 960 resonators were illuminated by the terahertz beams. The amplitude transmission spectra were extracted as $|{\widetilde t(\omega )} |= |{{{{{\widetilde E}_S}(\omega )} \mathord{\left/ {\vphantom {{{{\widetilde E}_S}(\omega )} {{{\widetilde E}_R}(\omega )}}} \right.} {{{\widetilde E}_R}(\omega )}}} |$, where ${\widetilde E_S}(\omega )$ and ${\widetilde E_R}(\omega )$ are the Fourier transformed results of the measured time-domain terahertz pulses transmitted through the samples and the reference (a bare silicon with same thickness), respectively.
Fig. 1. Schematic over view (a) and unit cell (b) of the proposed EIT metasurface. (c) Schematic of the experimental setup. PM: off-axis parabolic mirror.
Figures 2(a)–2(c) show the measured amplitude transmission spectra of the MLR, DUR, and EIT metasurfaces, respectively. Under y-polarized incidence, the MLR metasurface exhibits a typical broad localized surface plasmon resonance at around 0.615 THz with a Q factor of 6.1. Here, this resonance mode functions as bright mode. However, the DUR metasurface could not be excited around this frequency band under y-polarized incidence. Instead, a sharp inductive-capactive (LC) resonance with a higer Q factor of 12.6 can be excited at a similar frequency under x-polarized incidence, as shown in Fig. 2(b). This resonance mode functions as dark mode. Such features obey the EIT design rules of bright and dark resonance modes in previous studies. As a result, when putting these two resonators together in a single unit cell to ensure a strong near field coupling, an obvious EIT-like transmission spectrum is formed under y-polarized incidence, as shown in Fig. 2(c). A sharp and large transmission window occurs at 0.630 THz, just among the resonance dip of the bright mode. Here, the bright mode of the MLR is first exicted by external field, the resonance near field of it will then excite the dark LC mode of the DUR. Next, the resonance rear field of the excited dark mode will couple back to the bright mode, which destructively interfere with externally excited field to the bright mode. Finally, a remarkably transparent window is induced.
Fig. 2. Measured (a)-(c) and simulated (d)-(f) amplitude transmission spectra of the MLR, DUR and EIT metasurfaces, respectively. The insets and arrows in (a)-(c) illustrate the corresponding unit cells and the incident polarization states, respectively.
3. Analysis and discussion
For the purpose of gaining in-depth understanding of the EIT effect, we further carried out numerical simulations on the three metasurfaces using finite-element time-domain (FDTD) method. The silicon substrate was modeled as a lossless dielectric with a permitivity of ɛ = 11.78, while the aluminum structure was modeled as a lossy metal with a conductivity of σ = 3.72×107 S/m. Periodic boundary conditions were applied at both x and y directions, and a plane wave was used to excite the structures under normal incidences. The corresponding simulation results are shown in Figs. 2(d)–2(f), which are in good agreements with the measured results. Such consistence means that we could apply simulations to explore the inner mechanism of the proposed EIT structure.
Figure 3 illustrates the simulated electric field and surface current distributions at the corresponding resonance frequencies of the MLR, DUR and EIT structure, respectively. It can be observed from Figs. 3(a) and 3(b) that the two vertical arms of the MLR support two symmetric dipole resonances under y-polarized incidence. At the corners of the arms, strong x-polarized near field components are generated inside the MLR, as illustrated in the Fig. 3(a), which could excite the DUR. Meanwhile, the surface currents along the two arms will also generate magnetic field [see the inset red marks in Fig. 3(b)] along the z direction inside the MLR, which could also excite the DUR according to the Faraday law of electromagnetic induction. Figures 3(c) and 3(d) confirm that the resonance mode of the DUR under x-polarized incidence is indeed LC resonance. The two U-shaped resonators are excited under same condition, thus the electric field distribution and the surface current distribution are anti-symmetric. When the MLR and DUR are assembled in a unit cell to form the EIT structure, it is seen from Figs. 3(e) and 3(f) that the resonant mode of the MLR is strongly suppressed as compared with that of the sole MLR case even though the incident terahertz wave is still y-polarized. However, the resonant mode of the DUR is strongly excited, whose resonant near field quenches the resonance of the MLR together with the incident field. Such features can be seen as a clear evidence of our above explanation on the proposed EIT. The quenched bright mode cannot bring too much influence on the incident wave at its resonance frequency, resulting in a transmission window. The configuration of the proposed EIT structure is actually similar to the previous EIT structure composed of bar and split-ring resonators, where the strong coupling effect is due to the fact that the electric coupling by the generated x-polarized resonance near field at the corners of the arms and the magnetic coupling by the generated z-polarized magnetic field from the MLR to the DUR are in-phase. It is interesting to see that the electric field and surface current distributions of the DUR in the EIT structure [see Figs. 3(e) and 3(f)] become opposite to those illustrated in Figs. 3(c) and 3(d). This can be explained by the corresponding distributions of the MLR in Figs. 3(a) and 3(b), the two U-shaped resonators are actually excited by the inside synchronously out-of-phase x-polarized electric field and z-polarized magnetic field components of the excited MLR, respectively. Though such resonance feature of the DUR changes, it is still typical LC resonance, so the corresponding resonance frequency of the DUR will not change a lot. More importantly, such resonance feature also indicates that there will not x-polarized output as the radiated x-polarized fields from the two U-shaped resonators are cancelled out with each other in the far field.
Fig. 3. Electric field (a, c, e) and surface current (b, d, f) distributions of the proposed structures. The black arrows in (b), (d) and (f) illustrate the surface current direction. The red marks in (b) illustrates the magnetic field direction derived from the present surface current.
To further elucidate the physical mechanism of the EIT behavior, a widely used coupled Lorentz oscillator model is applied. In this model, the resonance of the two aforementioned bright and dark modes can be described by the following equations:
Fig. 4. (a) Calculated (blue) and measured (red) amplitude transmission spectra of the EIT metasurface. (b) Group delays retrieved from calculated (blue) and measured (red) transmission spectra.
For the purpose of showing the slow-light capability of the EIT metasurface, the group delay tg of the terahertz wave passing through the sample is extracted, as shown in Fig. 4(b), which is calculated by taking difference between the group delay dψ/dω of the EIT metasurface where ψ is the transmission phase spectra with the contribution from the substrate, and the group delay dψ0/dω of vacuum with the same thickness where ψ0 = kh is propagation phase with k being the vacuum wave vector. Namely, tg = dψ/dω – dψ0/dω. It can be seen that the calculated and measured group delays match with each other very well. They both show a highest group delay of 6.94 ps at about 0.615 THz, which corresponds to the time delay induced by a 2.08-mm free-space distance. This slow-light capability is comparable with the previously reported works [6,35].
The above analyses have fully shown the proposed EIT metasurface can support strong EIT effect and high group delay. To illustrate the ability of the EIT structure in realizing electrically controlled EIT, a new metasurface is theoretically designed by integrating VO2 structures into the EIT structures. VO2 is a well-known temperature-controlled phase change material [36,37]. At room temperature (23 °C), VO2 is in its dielectric phase whose conductivity is around 10 S/m. As temperature increases, VO2 gradually switches to its metallic phase with increasing conductivity to the order of 105 S/m. Recently, it has been experimentally demonstrated that besides direct temperature control by external heater [38,39], VO2-integrated structures could also be tuned by electric control [40,41]. By inserting build-in metallic wires into the metasurface structures with integrated VO2 and applying a current, the conductivity of the VO2 can be modulated by the Joule heat generated by these wires. Namely, one could control the conductivity of the VO2 by adjusting the current. In this case, the advantage of the proposed EIT structure is highlighted, as the bright resonators MLRs themselves could serve as the build-in metallic wires without having to insert and design new wires into the metasurfaces.
The designed electrically controlled EIT metasurface and the unit cell are schematically illustrated in Figs. 5(a) and 5(b), respectively. Two electrodes can be directly made on the two sides of the metasurface connecting the MLRs. Here, we design the VO2 structure with same cross-section dimensions to the MLR and place it just below the MLR. The thickness of the VO2 is set to be 150 nm. To allow the tuning, two gaps are designed in the middle of the two vertical arms of the MLR, the gap widths are gVO2 = 5 µm. The conductivity of VO2 is changed from 1 × 104 to 50 × 104 S/m, such setting is consistent with the previous experimental studies [42,43]. Figure 5(c) illustrates the corresponding simulated amplitude transmission spectra. A distinct EIT modulation behavior from previous reports is observed, where the amplitude at the transmission window almost does not change while those at the two resonance dips gradually change. At low VO2 conductivity, the charges cannot flow across the gaps, thus the resonance of the bright MLR cannot be excited. In this case, no resonance response can be observed. As the conductivity increases, more and more charges could flow across the gaps, thus the resonance of the bright MLR gradually establishes, resulting a gradually enhanced EIT effect. When the conductivity of VO2 is increased to 50 × 104 S/m, the modulation depths $|{{{({T_{{I_g}}} - {T_{{I_0}}})} \mathord{\left/ {\vphantom {{({T_{{I_g}}} - {T_{{I_0}}})} {{T_{{I_0}}}}}} \right.} {{T_{{I_0}}}}}} |$ at these two resonance dips reach 49% at 0.48 THz and 46% at 0.64 THz, respectively. Here, the TI0 and TIg are the transmission amplitudes when the VO2 conductivity is 1 × 104 and 50 × 104 S/m, respectively. Interesting thing happens when we check the group delay response of the proposed active EIT metasurface, as shown in Fig. 5(d). It is seen that the group delay at the EIT window frequency also changes accordingly. When the VO2 conductivity is 1 × 104 S/m, the group delay is about 5.65 ps. As the VO2 conductivity increases to 50 × 104 S/m, the group delay gradually increases to 7.18 ps.
Fig. 5. Schematic over view (a) and unit cell (b) of the electrically controlled EIT metasurface with integrated VO2 structures. Simulated amplitude transmission (c) and group delay (d) of the active EIT metasurface as a function of the VO2 conductivity.
4. Conclusion
In conclusion, a novel EIT structure composed of MLR and DUR is theoretically proposed and experimentally demonstrated in the terahertz regime. The near-field analysis shows that the EIT is induced by the constructive interference between the electric and magnetic coupling pathways. Besides, an electrically controlled active EIT metasurface based on VO2 is theoretically proposed. Owing to the continuous feature of the MLR, we modulate the strength of the bright mode instead of the dark mode in this active design. A distinct EIT modulation behavior is observed in simulations. At the two EIT resonance dips, the device functions as an active optical switch. At the EIT window, it functions as an active slow-light device with small changes in transmission amplitude. As the structure design and the modulation range of the VO2 conductivity here are all achievable in realistic, we believe our active device can be experimentally validated. Besides electric control, the EIT metasurface with integrated VO2 structures could also be tuned by placing it onto an external heater. This metasurface design would find broad applications in optical switches and slow-light devices.
Funding
National Natural Science Foundation of China (61705167, 61605143, 61505146); Tianjin University of Science and Technology (KJ1920, KYQD1907).
Disclosures
The authors declare no conflicts of interest.
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