1. Introduction

Terahertz (THz) metamaterials, consisting of artificially designed micrometer-scale arrays, can resonate with incident THz waves [1,2]. Their exotic optic response has not been achieved by a natural material [3,4]. Further, they may have applications in THz-communication [5], biosensing [6], and security inspection [7]. The discovery of EIT was made in atomic physics [8]. Owing to quantum interference, a window of transparency within a narrowband arises as electromagnetic waves can pass through an originally opaque medium [9]. This analog phenomenon was observed in metamaterials at room temperature [10]. The classical analog of EIT in metamaterials shows an exceedingly narrow reflection or transmission window, which comes from the coupling between a broadband ‘bright’ mode and a narrowband ‘dark’ mode [11,12]. As a result, EIT in metamaterials can be used for low-loss slow-light and ultra-sensitive biosensing [13,14]. However, the potential to detect vibrations has been limited by traditional THz metamaterials in the nanometer world. Device platforms with nanogap features are required to further expand the applications of THz metamaterials. Interest in metal-nanogap hybrid structures has been propelled primarily by significant requests in spectroscopy [15,16]. The study of THz spectroscopy demonstrates that THz waves with a fingerprint for molecules and low energy can be used to make a promising platform for the detection of biomolecular interactions [17–19]. Nevertheless, owing to the limitations of the size of the unit cell in the micrometer scale, more advanced applications have not been achieved by current THz metamaterials, such as the detection of vibration at the nanometer scale. It is strongly demanded that a novel THz metamaterial can detect the ultra-sensitive vibration of the nano-world by using the spectroscopic information of the THz response. The NDMMs-based platform potentially enables nano-vibration to be detected using the spectroscopic information of the THz response. By tuning the gap between two adjacent metal structures, a switch of EIT through the NDMMs was found. Potentially, this platform will enable the monitoring of a wide class of nano-assemblies, and nano-vibration, which enriches current nano-detection techniques.

2. Result and discussion

As shown in Fig. 1(a), the unit cell of the NDMMs consists of a rectangular bar resonator and a split-ring resonator; both are built up rectangular nano-gold bars and nanogap hybrid structures. The two resonators were placed on a PEG monolayer, serving as an extremely flexible substrate. The rectangular bar resonator can resonate with incident terahertz waves with an E-field oriented along the y-axis, which generates an electric dipole resonance (‘bright’ mode). The split-ring acts as a dark mode, which cannot be directly coupled with the incident terahertz waves. It can be excited by the bright mode. The simulations of the NDMMs were implemented using the finite-element time-domain solver in CST Microwave Studio. The switch depends strongly on the nanogap distance g which can determine the formation of the displacement current in the entire metal-nanogap hybrid unit cell. The displacement current usually can be considered as the flux integral of the time derivative of the displacement field and is not the actual current formed by the movement of charges in a conventional conductor, but it has the same properties as the actual current and is related to the surrounding magnetic field [20]. As g > gcv, there is no displacement current in nanogap, where gcv is the critical value of nanogap distance which is the displacement current formed in the entire metal-nanogap hybrid unit cell. As a result, the gold nano-bars are insulated by nanogaps into separate individuals. Since each individual is within the nanometer range, and a metamaterial that can modulate the THz wave must match the size of its unit cell in a micrometer-scale, the metamaterial decouples with incident THz waves.

 

Fig. 1. (a) Unit cell of the NDMMs with the geometric parameters: the period m = 150 µm, the gap g changes from 50 nm to 120 nm, the thickness of polyethylene glycol (PEG) monolayer serving as a substrate h =10 nm, the width of nano-gold bars l = 100 nm, the thickness of nano-gold bars a = 200 nm, other geometric parameters b = 70 µm, c = 5 µm, d = 5 µm, e = 32.5 µm, k = 50 µm, n = 17 µm; (b) the principle of a switch of electromagnetically induced transparent based on NDMMs identified as a function of the nanogap g. (c) Simulated transmittance spectra of the NDMMS as the nanogap g > gcv. (d) Simulated transmittance spectra of the NDMMS as the nanogap g < gcv. (e) The electric field distributions as the nanogap g > gcv. (f) The electric field distributions as the nanogap g < gcv.

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Thus, THz waves pass through the NDMMs (the corresponding simulated transmission spectra of the NDMMs are shown in Fig. 1(c)). It can be seen from Fig. 1(c) that no resonance characteristic window is shown in the terahertz spectrum. Figure 1(d) shows that the typical resonance characteristic window of EIT appeared in the simulated transmittance spectra of the NDMMs as g < g_cv. Then, a link between the nanogap g and the spectroscopic information of the THz response is established. Therefore, the NDMMs can qualitatively read-out the change in Nanogap via a THz signal. Figure 1(e) shows the electric field distributions as g > gcv. Observation shows that the electric field strength is very weak, and no specific resonance mode is formed, indicating that NDMMs do not resonate with incident THz waves. On the other hand, Fig. 1(f) shows the classic resonance mode for EIT, g < gcv.

To understand the intrinsic principle of the switch of EIT based on NDMMs, when the electric field is perpendicular to the nanogap, different structures of NDMMs and corresponding transmission spectra are examined, as shown in Fig. 2. NDMMs are made up of a rectangular bar resonator with a nanogap feature and a split-ring resonator without nanogap features; the gold nano-bar is fixed at l = 100 nm; the nanogap g changes from 50 nm to 120 nm (see Fig. 2(a)). The simulations show that when the nanogap g is 50 nm, 80 nm, NDMMs present a distinct EIT-like peak that can be found at a frequency of 0.99 THz (II, III). In this case, the bright mode resonance can be excited and resonate with the incident THz waves. However, when the nanogap g is 100 nm and 120 nm, there is no appearance of a distinct EIT-like peak for NDMMs (IV, V). This indicates that as g > 100 nm, the dark mode cannot be directly excited by light at normal incidence, the dark mode is still dark. Thus, there is no appearance of a distinct EIT-like peak. As shown in Fig. 2(b), the electric field is perpendicular to the nanogap; NDMMs have a rectangular bar resonator without a nanogap feature and a split-ring resonator with nanogaps features. The gold nano-bar is fixed at l = 100 nm; the nanogap g changes from 50 nm to 120 nm. The simulation results show that when the nanogap g is 50 nm, 80 nm, NDMMs exhibit a distinct EIT-like peak that can be found at a frequency of 0.99 THz (II, III). This is because bright-mode resonance can be excited normally and resonate with incident terahertz waves. In addition, the dark mode exists in a ring resonator. In this case, the EIT-like peak emerges when the nanogap g is 50 nm and, 80 nm. However, when the nanogap g is 100 nm and 120 nm, there is only dipole resonance and no appearance of a distinct EIT-like peak for NDMMs (IV, V). In Fig. 2(c), the electric field is perpendicular to the nanogap; both the rectangular bar resonator and ring resonator acquire the nanogaps feature. It is verified by that NDMMs presents a distinct EIT-like peak at a frequency of 0.99 THz (Ó, Õ) and nanogap of 50 and 80 nm. When the nanogap g is 100 nm and 120 nm, there is no resonance mode for NDMMs at a frequency of 1.2 THz (Ô, Ö). For the electric field applied parallelly to the nanogap, the corresponding transmission spectra for different structures of NDMMs are shown in Fig. 3. In all cases, NDMMs exhibit a distinct EIT-like peak, implying that a switch of EIT based on NDMMs relies on the polarization direction of the electric field as well. As the electric field is perpendicular to the nanogap, the change in the nanogap can control the switch of electromagnetically induced transparency.

 

Fig. 2. Transmission spectra for the different structures of NDMMs as the direction of the electric field is perpendicular to nanogap. (a) A rectangular bar resonator with nanogap feature and a ring resonator (b) A rectangular bar resonator without nanogaps feature and ring resonator with nanogaps feature. (c) Both a rectangular bar resonator and a ring resonator with nanogaps feature.

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Fig. 3. Transmission spectra for the different structures of NDMMs as the direction of the electric field is parallel to nanogap. (a) A rectangular bar resonator with nanogap feature and a ring resonator without nanogaps feature. (b) A rectangular bar resonator without nanogaps feature and ring resonator with nanogaps feature. (c) Both a rectangular bar resonator and a ring resonator with nanogaps feature.

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3. Conclusion

In summary, we propose a potential application of the nano-discretized metamaterial, which may enable the monitoring of a wide class of nano-assemblies and nano-vibrations. Additionally, the switch of EIT is linked to the polarization of the electric field. The proposed NDMMs have potential for applications in probing the binding characteristics of biomolecular interactions and detecting ultra-sensitive vibrations of the nano-world.