1. Introduction

Metamaterials with subwavelength unit geometries exhibit novel and intriguing electromagnetic properties, hardly accessible in the existing materials in nature [1]. Such artificial effective media can manipulate the electromagnetic wave in terms of amplitude, phase, polarization and wavelength arbitrarily. It will be highly desirable that metamaterials can modulate the terahertz (THz) wave effectively due to ultra-weak electromagnetic response of natural materials in the THz realm. On the basis of coupled micro-sized resonator, a large number of metamaterials and metadevices have been realized thus far, including ultra-high-refractive index [2], zero-refractive-index [3], hyperbolic [4], chiral metamaterials [5], as well as filters [6,7], perfect absorbers [8,9], polarization controllers [10–12], and super lenses [13]. Recently, much emphasis has been placed on the analogy of plasmon resonance with quantum phenomena, which opens up a new perspective toward verifying and visualizing solid-state physics and quantum optics effects in classical optics, such as quantum interference [14], P-T symmetry [15], spin-Hall effect [16], electromagnetically induced absorption (EIA) [17,18]. The most pivotal example is plasmon-induced transparency (PIT) mimicking the electromagnetic-induced-transparency (EIT) effect which results from destructive interference between two pathways in three-level atomic system [19–40]. Based on the phase delay effect and enhanced amplitude transmission effect within a broader absorption dip, EIT metamaterials reveal promising applications in optical networks and terahertz communications. Nevertheless, the practical implementation is strictly limited by low temperature and stable gas lasers, since the EIT effect is sensitive to broadening due to atomic motion [27,32]. Hence, PIT metamaterials are the best candidate to develop building blocks of the slow-light devices. In a general way, PIT effect can be realized via schemes of radiative-dark-coupling [19–31] and radiative-radiative-coupling [32–36]. The bright elements in the former case are directly excited by the external illumination, whereas the dark elements are purely excited by means of its coupling to the bright resonators. On the contrary, the bright and dark elements are excited simultaneously via the incident light in the latter case. The realization of the PIT effect associates with three principals, 1) frequency detuning between the corresponding resonators should be extremely finite. 2) Lifetime of the dark modes should be much longer than that of the bright modes and 3) quality factors of the bright and dark resonators are significantly different.

In this article, we present a systematic investigation on transmission properties of PIT metamaterials with respect to the relative distance, angle, and polarization in the THz regime. Quite different from the previously proposed radiative-dark-coupled mechanism, a radiative-radiative-coupled system consists of CRRs and SRRs is developed with the lowest order eigenmode excited. The destructive interference effect between the dipole resonance and LC resonance, in CRRs and SRRs respectively, leads to a sharp transparent window. Based on the detailed analysis of the coupling process in a unit cell, we predict and prove that the PIT phenomenon will be strongly modulated by varying the relative angle and vertical distance between the CRRs and SRRs, whereas, the transmission spectra remain the same with different horizontal distances. In the end, the polarization property of the proposed PIT metamaterial is considered. Polarization-independent metamaterials are designed, fabricated, and characterized, as well as the polarization-dependent metamaterials which generates an isolated PIT phenomenon in the frequency-domain, corresponding to the horizontal and vertical polarized incident THz beam.

2. Experiments and analysis

The functional unit cell, as is shown in Fig. 1(a), consists of a SRR and CRR, where the SRR is placed d = 5 µm from the CRR in the y-(vertical) direction and aligned in the x-(horizontal) direction. The THz beam is normal to the structure along the z-direction, with$\stackrel{\rightharpoonup }{E}$ and$\stackrel{\rightharpoonup }{H}$ along the x- and y-direction, respectively. Figure 1(b) shows the designed CRRs, SRRs, and PIT metamaterial with a period of P = 120 µm. Complementary optical microscopic image of the fabricated EIT sample is shown in Fig. 1(c). Microstructures of 200 nm-thick aluminum are fabricated on a silicon wafer using conventional photolithography and evaporation method. Utilizing photoconductive-antenna-based 8f confocal THz time-domain spectroscopy system (THz-TDS) [7,18,28,33,34,41–45], the transmission spectral response is achieved via the configuration shown in Fig. 1(d) with the THz beam travels through the PIT metamaterial and blank silicon wafer. The bare silicon which is identical to the sample substrate serves as a reference, and the transmission spectrum has been normalized in the frequency domain.

 

Fig. 1 (a) Schematic of the functional unit cell, with geometric parameters L = 70 µm, W = 5 µm, I = 31 µm, P = 120 µm, H = 2000 µm, g = 5 µm, d = 5 µm. (b) Top view for the design of RRs, SRRs, and R-SRRs. (c) Optical microscopic image of the fabricated sample. (d) Outline of the experimental measurement for THz electric field amplitude transmission. (e) Experimental and (f) simulation amplitude transmission of CRRs, SRRs, and PIT metamaterials.

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Figure 1(e) reveals the experimental transmission spectra$\left|T_{SRR\text{s}}\right|$, $\left|T_{CRR\text{s}}\right|$, and $\left|T_{PIT}\right|$ corresponding to SRRs, CRRs, and PIT metamaterials. $\left|T_{SRR\text{s}}\right|$and $\left|T_{CRR\text{s}}\right|$exhibit an evident resonance centered at 0.55 THz and 0.53 THz, respectively, with the amplitude transmission 0.73 and 0.12. Whereas, it should be noted that$\left|T_{SRR\text{s}}\right|$and$\left|T_{CRR\text{s}}\right|$behave as a remarkable deviating quality factor. When the SRRs and CRRs are combined into a simple structure, a sharply enhanced transmission occurs within the broad absorption band as shown in$\left|T_{PIT}\right|$. This enhanced transmission window attains a peak value exceeding 0.55 with the central frequency matching exactly with that of the$\left|T_{CRR\text{s}}\right|$dip, exhibiting a PIT effect. Complementary simulation has been carried out using commercially available software CST microwave studio, as shown in Fig. 1(f), showing a good agreement with the measured results in Fig. 1(e).

In the design, both SRRs and CRRs can be independently excited via the terahertz illumination with a polarization along the gap. CRRs purely support the even order eigenmode due to its symmetric structure. Thus its resonance which refers to the lowest even eigenmode can be interpreted as the electric dipole oscillation. The strong electric dipole moment enables CRRs strongly couple with the external THz radiation field, and its transmission property is characterized by broad linewidth, greater depth, and lower quality factor. On the other hand, only an odd order eigenmode can be stimulated in SRRs because of its asymmetric structure. Its fundamental eigenmode excited here behaves as a LC resonance, and the surface current is circular without dipole moment. Thus, SRRs weakly couple with the THz electric field, and its transmission spectra is featured by narrower linewidth, smaller depth, and higher quality factor, as shown in Fig. 1(e) and 1(f).

Figure 2(a) and 2(b) demonstrate the outline of surface current${\stackrel{\rightharpoonup }{J}}_{SRR}^{THz}$,${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$,${\stackrel{\rightharpoonup }{J}}_{CRR}^{THz}$,${\stackrel{\rightharpoonup }{J}}_{CRR}^{Coupling}$corresponding to the inner and outer SRR configuration. ${\stackrel{\rightharpoonup }{J}}_{CRR}^{THz}$stimulated by THz radiation in the upper arm of CRR exhibits a strong dipole oscillation along the right direction, leading to an outward magnetic field within the SRR, as shown in Fig. 2(a). Predicted by the Faraday's law of induction, a clockwise circular current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$ on SRR should be activated. Particularly, it will be in phase with${\stackrel{\rightharpoonup }{J}}_{SRR}^{THz}$, which is directly excited by the THz field in SRR. Thus, the lifetime of SRR will be further extended. Vice versa, ${\stackrel{\rightharpoonup }{J}}_{SRR}^{THz}$will stimulate a current${\stackrel{\rightharpoonup }{J}}_{CRR}^{Coupling}$which in phase with${\stackrel{\rightharpoonup }{J}}_{CRR}^{THz}$on CRR via magnetic coupling simultaneously. These enhanced mutual coupling effects enable the electromagnetic field to couple back and forth between SRR and CRR, resulting in an interference destructive effect. It is evident that the absorption of CRR is strongly suppressed and a sharply transmission peak occurs. On the contrary, an anticlockwise circular current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$is activated by${\stackrel{\rightharpoonup }{J}}_{CRR}^{THz}$as presented in Fig. 2(b), whereas it out of phase with${\stackrel{\rightharpoonup }{J}}_{SRR}^{THz}$. The lifetime of the SRR LC resonance can be significantly minimized due to the counteraction between${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$and${\stackrel{\rightharpoonup }{J}}_{SRR}^{THz}$, thus the coupling effect is significantly suppressed. Since the coupling current${\stackrel{\rightharpoonup }{J}}_{CRR}^{Coupling}$is in phase with${\stackrel{\rightharpoonup }{J}}_{CRR}^{THz}$, CRR occupies a strengthen dipole resonance as well as that in Fig. 2(a). The above analysis is verified through measured and simulated spectra shown in Fig. 3.

 

Fig. 2 Outline of surface current stimulated by external THz radiation (${\stackrel{\rightharpoonup }{J}}_{SRR}^{THz}$and${\stackrel{\rightharpoonup }{J}}_{CRR}^{THz}$ represent by black solid line) and magnetic coupling regime (${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$and ${\stackrel{\rightharpoonup }{J}}_{CRR}^{Coupling}$represent by blue dash line). $\otimes$ and $\odot$ represent the inward and outward magnetic direction, respectively. (a) The aligned outer SRR in the horizontal direction is located 5 µm from CRR in the vertical direction, with the split gap towards the CRR arm. (b) The aligned inner SRR in horizontal direction is located 5 µm from CRR in the vertical direction, with the split gap against the CRR arm.

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Fig. 3 (a) Measured and (b) simulated transmission spectra with the separation Δy varying from 55.5 to −55.5 µm between the centre of SRR and CRR. (c) 2D plot of electric field distribution responding to Δy at 0.526 THz.

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Figure 3(a) depicts the dependence of the measured transmission spectra on Δy = 55.5, 9.5, −9.5, −55.5 µm, where Δy is the distance between the centre of SRR and CRR in the y-direction. It is evident that a PIT effect occurs with Δy = 55.5, −9.5 µm, and the enhanced transmission window attains the highest transmission value exceeding 0.717 at 0.526 THz. The destructive interference, which is resulted from enhanced mutual coupling between the SRR and CRR resonances, contributes to this EIT effect, as illustrated in Fig. 2(a). The corresponding electric field distribution in Fig. 3(c) shows that the CRR resonance is significantly suppressed and most of the energy is localized in the gap of SRRs. On the other hand, the resonance dip purely occurs for Δy = −9.5, 55.5 µm at 0.526 THz, with a transmission value as low as 0.188. The CRR resonance attains a considerable enhance, whereas the SRR resonance is strongly restricted due to current counteraction, as shown in Fig. 2(b). So, a little coupling between SRR and CRR is found. Compared to the significantly reduced electric distribution of SRRs in Fig. 3(c), CRRs attain considerably enhanced electric field intensity on the vertical arms. The simulation results in Fig. 3(b) match well with the measured results in Fig. 3(a).

3. Terahertz modulation and robust performance in the designed metamaterial

Further investigation on the influence of the PIT phenomenon due to destructive interference, is carried out by vertically, horizontally, and angularly modifying the arrangement of SRRs.

The influence of coupling by manipulating SRRs within CRRs in the vertical direction is explored firstly. The measured transmission spectra in Fig. 4(a) illustrate that the enhanced transparency window undergoes a complete modulation with Δy varying from −9.5 to 9.5 µm. For the configuration of Δy = −9.5 µm, a prominent PIT effect occurs with a transmission of 0.717 at 0.526 THz. The corresponding 2D field plot in Fig. 4(c) reveals that most of the electric field is localized in the SRRs gap and the CRRs resonance is extensively suppressed due to destructive interference in a manner of mutually reinforcing coupling, and the in-phase coupling current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$dominates this situation. As Δy is gradually increased to 0 µm, a considerably modified PIT window is observed, leading to an amplitude transmission as low as 0.447 at 0.526 THz. Almost uniformly electric field distribution on SRRs and CRRs is found as shown in Fig. 4(c), since the in-phase coupling current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$on SRR is decreased with increasing Δy, and the out-phase coupling current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$is increased at the same time. With further increasing Δy to 9.5 µm, the transmission spectra become a resonance dip at 0.526 THz. The 2D field plot in Fig. 4(c) reveals that most of the electric field localized on the vertical arms of CRRs and CRRs resonance is nearly quenched, and the out-phase coupling current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$is dominating, such that the PIT phenomenon vanishes. The measured transmission spectra in Fig. 4(a) are well supported by the simulation results in Fig. 4(b).

 

Fig. 4 Measured (a) and simulated (b) transmission spectra for different vertical separation distances Δy. (c) Corresponding 2D field plot at transparency frequency 0.526 THz.

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In addition, we perform a study on the evolution of coupling by rotating the angle of SRRs with a fixed Δy = −3 µm, and a modified I = 31 µm. The experimental results in Fig. 5(a) demonstrate that the PIT window experiences a dramatic modification with the rotation angle α varying from 0 °to 90°. When there is no rotation, a fully resolved PIT phenomenon occurs as described before in Fig. 4. As we gradually rotating SRRs from α = 0° to 60°, the PIT window reflects a sharp decline with an amplitude transmission 0.370 at 0.526 THz. The electric field distributes uniformly on SRRs and CRRs, as shown in Fig. 5(c), because the in-phase coupling current on SRR is declining with increasing α, whereas the out-phase coupling current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$is increasing simultaneously. Finally, only a resonance dip can be observed as α = 90°. The field distribution plot in Fig. 5(c) reveals that most of the electric field is localized in the vertical arms of CRRs and SRRs and the resonance is nearly disappears. At this time the out-phase coupling current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$is dominating, such that the PIT phenomenon vanishes. Qualitative matching between the measured and simulated results in Fig. 5(b) is achieved.

 

Fig. 5 (a) Measured and (b) simulated transmission spectra with various twist angles α = 0°, 30°, 45°, 60°, 90° for SRRs. (c) Corresponding 2D field plot at transparency frequency 0.526 THz.

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Further on, dependence of transmission spectra on the horizontal separation distance Δx is studied. The measured results in Fig. 6(a) manifest that the transmission response remains the same as Δx is varying from 0 to 18 µm (or 0 to 8 µm for the inner SRRs). The transparency windows for Δy = −9.5 and 55.5 µm are nearly undisturbed, as well as the resonance dips for Δy = 9.5 and −55.5 µm. When CRRs are varied in the horizontal direction with fixed Δy, the magnetic field distribution and excited surface current${\stackrel{\rightharpoonup }{J}}_{SRR}^{Coupling}$remain almost the same, thus the transmission spectra hinged on the magnetic coupling between SRRs and CRRs exhibit little difference. The interesting results indicate a robust performance in the designed metamaterial, which opens several fascinating applications, such as to elimination of the influence of fabrication errors.

 

Fig. 6 (a) Measured and simulated (b) transmission spectra for different horizontal separation distance Δx, with Δy = 9.5 µm (Fig. 6 A), −9.5 µm (Fig. 6 B), 55.5 µm (Fig. 6 C), −55.5 µm (Fig. 6 D) as a parameter. (c) Corresponding schematic of the configuration.

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4. Polarization-independent and polarization-dependent PIT meta-materials

The proposed polarization-independent PIT structure, as shown in Fig. 7(a), comprises of a CRR and four identical SRRs, where two faced SRRs aligned with CRR in horizontal direction with a separation distance d = 5 µm, and the other two show a similar configuration in the vertical direction. Figure 7(b) reveals the microscopic image of the fabricated EIT sample. Figure 7(c) demonstrates the measured transmission spectra of the polarization-independent PIT sample with an angle difference θ at 0°, 30°, 45°, 60°, and 90°, where each spectrum has been offset vertically by progressively adding 0.15 or −0.15 for the sake of clarity. It is interesting to note that the PIT window with transmission of 0.713 at 0.526 THz is almost unchanged for all polarization angles. The four-fold symmetric PIT metamaterial possesses a polarization-independent feature, exhibiting the same response to vertical and horizontal incident electric field. The PIT spectra present no difference varying θ due to the fact that the effective electric field is the superposition of horizontally and vertically polarized fields. The simulation results in Fig. 7(d) match well with the measured spectra in Fig. 7(c).

 

Fig. 7 (a) Schematic of the polarization-independent PIT unit cell with geometric parameters L = 71 µm, W = 5 µm, I = 30 µm, P = 150 µm, H = 2000 µm, g = 5 µm, d = 5 µm. (b) Microscopic image of the fabricated sample. (c) Measured and (d) simulated amplitude transmission with the angle difference θ varying from 0°to 90°between the electric field polarization and the x-axis, where the angle difference θ is illustrated in the inset.

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Figure 8(a) shows that CRR is surrounded by two pairs of SRRs, where a bar along the y-axis located in the middle of CRR. It is evident to see that these two faced SRRs aligned with CRR in the x-axis have a different design compared to the other two faced SRRs aligned with CRR in the y-axis. The displacement length d between CRRs and SRRs is 5 µm. Figure 8(b) displays the microscopic image of the fabricated EIT sample. Figure 8(c) depicts the experimental transmission spectra of the x-polarized and y-polarized incident THz wave. It can be observed that the electric field polarization plays a critical role in tuning the PIT effect. These two isolated PIT windows exhibit transmission of 0.682 at 0.418 THz and 0.785 at 0.575 THz for the x-polarization and y-polarization, respectively. Most importantly, the bar within CRRs can significantly increase the resonance frequency for the y-polarization case, since the resonance arm has been split into three parts. However, a little influence on the resonance frequency can be observed with the x-polarization situation. Because of the two-fold symmetric structure, the polarization-related PIT metamaterial achieves an isolated response in the frequency domain for the x-polarized and y-polarized incident THz electric field, thus it capable to control the PIT effect via polarization rotation.

 

Fig. 8 (a) Schematic of the polarization-related PIT unit cell, with geometric parameters P_x = 150 µm, P_y = 120 µm, L_x = 130 µm, L_y = 60 µm, I_xx = 29 µm, I_xy = 28 µm, I_yx = 54 µm, I_yy = 20 µm, W = 5 µm, H = 2000 µm, g = 5 µm, d = 5 µm. (b) Microscopic image of the fabricated sample. (c)Measured and (d) simulated amplitude transmission for the x-polarized (red) and y-polarized (blue) incident electric field.

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5. Summary

We experimentally investigate a PIT metamaterial consisting of two independent excited elements at THz frequencies. Coupling analysis between the high quality factor and low quality factor entities indicates that mutual magnetic induction leads to the PIT phenomenon in a manner of destructive interference. It is inspiring to observe that a considerable modulation of the PIT effect can be realized via physically moving SRRs in the vertical direction or rotating the inner SRRs. Meanwhile, very little disturbance on the transmission is revealed when we alter SRRs in the horizontal direction, exhibiting an excellent robust performance. Finally, the proposed polarization-independent PIT metamaterial displays an identical transmission response for arbitrary polarization of the incident THz electric field. The polarization-dependent PIT metamaterial is capable to identify the polarization via the isolated enhanced transmission peak, which reveals a tuning functionality by rotating the sample. Such PIT metamaterials reveal a number of promising applications, such as slow light, optical buffers, and ultra-sensitive sensors.