1. Introduction

Electromagnetically induced transparency (EIT) is a coherent optical nonlinearity which renders a medium transparent over a narrow spectral range within an absorption line [1]. EIT phenomenon gives rise to important effects such as ultraslow group velocity and enhancing nonlinear interactions between light and a medium, however, cumbersome experimental conditions are often involved in achieving EIT phenomenon, such as cryogenic temperatures and high intensity lasers.

During the past decade, metamaterials consisting of subwavelength electromagnetic resonators have attracted tremendous amount of interest [2–4], due to their unusual properties (e.g. negative refraction, invisibility and perfect lens). More recently, metamaterials are engineered to realize an intriguing classical analogy with famous quantum phenomenon such as EIT phenomenon [5] and Fano resonance [6]. The asymmetric Fano resonance, which has long been known as a characteristic feature of interacting quantum systems, has more recently been found in plasmonic nanostructures and metamaterials. Under certain conditions a Fano resonance can be regarded as the classical analogue of electromagnetically induced transparency. These conditions are: (i) sufficiently small frequency detuning between the two coupled resonances; (ii) strongly contrasting resonance linewidths; and (iii) appropriate resonance amplitudes [6]. When coherent coupling between the two resonances occurs, destructive interference can suppress the absorption of the broader resonance, resulting in an induced transparency window [7–9]. Subsequently, metamaterial analogy of EIT phenomenon has been widely investigated in a wide range of literatures [10–30]. The steep dispersion of EIT and Fano resonance profile promises applications in slow light, sensor, nonlinear and switching applications. The EIT phenomenon in metamaterials is generally realized by the bright-dark mode coupling [10–26] or the bright-bright mode coupling [7, 8, 27–30]. Classical analogy of EIT effect in metamaterials was initially observed in arrays of asymmetrically split rings (ASRs) [7], consisting of two wire arcs with a broken symmetry, serving as the bright modes for certain polarized wave. The asymmetric coupling between the bright modes can excite a high-Q mode formed by counter-propagating currents (i.e. a so-called trapped mode resonance that is associated with an asymmetric Fano-type line shape), revealing EIT transmission peak. The quality factor of such trapped-mode resonance is mainly limited by losses and attempts to compensate or eliminate Joule losses using optically-pumped gain media such as superconducting metamaterials [15, 27] and semiconductor quantum dots [31, 32] have been reported. The tunability of EIT effect is another key issue. Tuning of an EIT phenomenon was observed when crossing the superconducting transition temperature of a superconducting metamaterial [15, 27]. Most generally, the properties of EIT effect can mostly be controlled by the metamaterial design [7–13] or changing the location of one resonator [22]. However, it is extremely difficult to change the geometrical size of elements or move one resonator once they are fabricated. Therefore, a practical way of controlling EIT is desirable for developing EIT-type metamaterials for real applications. Active manipulation of plasmonic EIT was proposed and the tunability of EIT was only investigated theoretically in this scheme [17]. Even though the mechanical control has the disadvantage for high-speed applications, it is significant for active manipulation of EIT phenomenon.

In this paper, we report that high-dispersive EIT can be achieved in two types of planar single-layered metamaterials that consist of symmetrically split rings (SSR) and fish-scale (FS) pattern, respectively. The active tuning of EIT is demonstrated theoretically and experimentally and it can be efficiently switched and controlled via the angle of incidence. The local field enhancement is achieved through engaging so-called trapped modes, sub-radiant high-Q current modes. The local energy density enhancement can be adjusted from 80 to about 3000 times the incident wave’s energy density simply by tilting the metamaterial relative to the incident beam. Both metamaterials considered is single-layered and simple, offering an easy-to-implement way of achieving EIT tunability in metamaterials in the broad frequency domain.

2. Metamaterial samples

We investigated EIT tuning in two model meta-surfaces based on SSR and FS wire patterns, falling into the wallpaper symmetry groups pmm and pmg, respectively, see Fig. 1 . The SSRs consist of two identical wire arcs and the FS structure is assembled from pairs of identical “U”-shapes connected to form continuous wires, thus neither structure allows the excitation of anti-symmetric currents at normal incidence. Both metamaterials consist of square meta-molecule arrays with a period of 15 mm, rendering the structures non-diffracting at any angle of incidence for frequencies below 10 GHz. The metamaterial patterns with an overall size of about 200 × 200mm² were etched from 35 µm copper cladding covering FR4 PCB substrates of t = 1.6 mm thickness. The width of the metallic strips was 0.8mm. Detailed dimensions of the SSR and FS unit cells are given in Figs. 1(b) and 1(c), respectively. We note that the FS metamaterial had previously attracted attention for its invisibility, magnetic mirror properties [33, 34] and EIT phenomenon [8], where a bilayered FS metamaterial is necessary for the trapped-mode excitation.

 

Fig. 1 Metamaterial structures. (a) The angle of incidence а is measured between the incident wave vector k and the metamaterial's surface normal n. Here metamaterial transmission is studied for y-polarized electromagnetic waves at oblique incidence which is realized by tilting the metamaterials around their y axis. (b) Symmetrically split ring (SSR) unit cell. (c) Fishscale (FS) unit cell.

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In metamaterials, trapped-mode resonances belonging to a family of Fano resonances are usually observed in structures with intrinsic symmetry breaking, for example in ASRs [7] or pairs of ring resonators of different size [28]. At normal incidence, such intrinsic symmetry breaking of the metamaterial structure is essential to allow the excitation of EIT phenomenon in metamaterials. Here we investigate transparency induced by extrinsic symmetry breaking provided by an oblique incidence. In contrast to normal incidence, where the incident wave excites the entire metamaterial interface in phase, at oblique incidence the wave fronts “roll across” the meta-surface, exciting different parts of the unit cell at different times. We will see that this phase lag allows and controls the excitation of the anti-symmetric currents underpinning EIT transmission peak.

3. Experimental and simulated results

The SSR and FS metamaterials were measured at angles of incidence from 0° to 50° in the 4-9 GHz frequency range. The experiments were carried out in an anechoic chamber using broadband horn antennas (Schwarzbeck BBHA9120D) equipped with dielectric lens concentrators and a vector network analyzer (Agilent E8364B). Corresponding transmission spectra and the associated modes of excitation were also simulated using the commercial software (CST Microwave Studio) in the frequency domain, where copper was treated as a perfect electric conductor and a relative permittivity ε = 4.05−i0.05 was assumed for the lossy dielectric substrate. For the results presented below, both the polarization of incident waves and the axis around which the metamaterial was tilted to achieve the oblique incidence were parallel to the SSR wires and the straight FS wires (i.e. the y axis), see Fig. 1.

Figure 2 shows the measured and simulated metamaterial transmission spectra as a function of the angle of incidence α. Apparently, EIT phenomenon can be switched and manipulated by angles of incidence. At normal incidence onto either metamaterial the y-polarization can only excite one resonance (III) at about 6.4 GHz, which we will later identify as a simple symmetric dipole resonance. However, when the metamaterial patterns are tilted around the y axis, a second transmission minimum I - which is not present at normal incidence - appears at a slightly lower frequency. Remarkably, a narrow pass band II discussed in terms of EIT [27, 28] forms in between the transmission minima I and III. This pass band has a strong dependence on the angle of incidence, which differs for the SSR and FS metamaterials. In case of SSRs [see Fig. 2(a)], the spectral separation of the transmission resonances I and III is independent of the angle of incidence α. However, with increasing α the pass band II at about f = 5.2 GHz becomes more pronounced and its quality factor measured as Q = f/Δf increases to about 23 at α = 50° (peak width Δf = 0.23 GHz at 3 dB below maximum). The FS metamaterial shows a remarkably different behavior, see Fig. 2(b). Its pass band II at 5.8 GHz broadens dramatically from Q = 27 to about 10 as the angle of incidence is increased from α = 10° to 50° and simultaneously the spectral separation of the surrounding transmission minima increases about 3-fold. There is a good agreement between the simulated and experimental results shown in Fig. 2, but the experimental results are a little worse than the simulated ones due to scattering losses during the experiment. Figure 2(c) and 2(d) illustrate that the maximum of the quality factor for SRR metamaterial is 30.4 at the angle of incidence α = 50° with the resonant frequency f = 5.17 GHz and the width Δf = 0.17 GHz while the maximum of the quality factor for FS metamaterial is about 50 at the angle of incidence α = 10° with the resonant frequency f = 6.11 GHz and the width Δf = 0.12 GHz, which are summarized in Fig. 3(c) .

 

Fig. 2 Transmission spectra. (a)-(b) Measured and (c)-(d) simulated transmission spectra of the SSR and FS metamaterials as a function of the angle of incidence α for incident y-polarized electromagnetic waves. The insets indicate types of metamaterials.

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Fig. 3 Energy density enhancement and quality factor at the resonant modes. (a)-(b) Magnitude of the electromagnetic energy density 0.1 mm above the surface, relative to the energy density of the incident y-polarized wave at α = 50° for the SSR metamaterial and at α = 10° for the FS metamaterial. The modes shown here correspond to the resonances I, II, and III marked in Fig. 2. (c)-(d) Quality factor and peak energy density enhancement for the pass band II as a function of the angle of incidence. Square and triangle symbols correspond to the SSR and FS metamaterials, respectively (dashed lines - simulations, solid lines - experiments).

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For metamaterials with symmetric patterns like those discussed here anti-symmetric current configurations are forbidden, but only at normal incidence. The origin of EIT-type resonances appearing at oblique incidence can be traced to the excitation of trapped modes [7, 28]. Remarkably, strong magnetic dipole generated by anti-parallel propagating surface currents confines most electromagnetic energy near the surface of the planar metamaterial, which gives rise to giant local field energy density enhancement. The factor of near-field energy density enhancement is calculated as the ratio of the magnitude of the electromagnetic energy density 0.1mm above the SSR and FS metamaterial relative to the energy density of incident y-polarized wave. The energy distribution maps of the SSR metamaterial at α = 50° and FS metamaterial at α = 10° are shown in Fig. 3(a) and 3(b). In case of the SSR metamaterial, this trapped mode consists of currents of equal magnitude oscillating in anti-phase in the two wire arcs, while in the FS pattern the currents in neighboring bends have the same magnitude but oscillate in opposite directions. In either case, radiation losses are very weak, as emission from opposite arcs/bends would destructively interfere in the far-field and therefore electromagnetic energy is trapped at the meta-surface. As a consequence, the magnitude of the excited currents can become very large, ensuring a high quality factor of the pass band, see Fig. 3(c). In particular this results in a remarkably large local energy density enhancement relative to the incident wave, which can be tuned from 80 to 2900 for the FS metamaterial and from 170 to 3700 in case of the SSR metamaterial, see Fig. 3(d). This tunable trapping of electromagnetic energy is of interest for various sensing applications and achieving strong optical nonlinearities.

The transmission phase changes of the FS and SRR metamaterials at α = 50° are illustrated in Fig. 4(a) and 4(c). The transmission window studied here is accompanied by a very sharp normal phase dispersion that, as was recently pointed out in Refs. 8 and 9, renders the response of the structure a metamaterial analog of EIT. Despite the metamaterials vanishing thickness of ~λ/35, it can potentially be used for achieving long pulse delays. In fact, the phase dispersion of the FS metamaterial at α = 10° is much stronger (not shown here). The group index is roughly estimated according to n_g = c₀ dk/dω = - (c₀/t) dΦ /dω [17, 24, 35], where c₀ is the speed of light in vacuum, Φ is the transmission phase, ω is the angular frequency and t is the thickness of metamaterials. In Fig. 4(b) and 4(d), the group indices are the same order as those in Ref. 35 [35]. The high group index corresponds to an increased traversing time of light through the entire structure. There is a good agreement between the simulated and measured results despite the fabrication error and random error in experiments.

 

Fig. 4 Phase change and group index across the FS and SSR metamaterial as a function of frequency at an incident angle of α = 50° (dashed lines-simulations, solid lines-experiments). Gray boxes indicate areas of sharp normal phase dispersion.

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4. Spectral splitting of the SSR and FS metamaterials

It is difficult to produce a simple and accurate estimate for the resonant frequency for the polarized incident radiation considered here at the normal incidence [33], however, the resonances appear when the wavelength of excitation in the strip is approximately equal to the full length of the metallic wire within the unit cell. Under the oblique incidence, the resonant frequencies seem more sophisticated to be estimated. Asymmetric shifts of SRR and FS metamaterials are used to describe the hybridization strength of the dipolar-active and dipolar-inactive modes quantitatively [29], defined as ${\omega }^{+}-{\omega }^{-}$, where ${\omega }^{+}$and ${\omega }^{-}$ correspond to the resonant frequencies of the resonances III and I. ${\omega }_{{}^{FS}}^{+}$ and${\omega }_{{}^{FS}}^{-}$ shift progressively to blue and red with increasing angles of incidence, respectively, while ${\omega }_{{}^{SSR}}^{+}$ and ${\omega }_{{}^{SSR}}^{-}$ are kept nearly unchanged in Fig. 5(a) . The asymmetric shifts describe the resonant feature straightforwardly shown in Fig. 5(b). It is obvious that the asymmetric coupling of SRR metamaterial is much weaker than that of FS metamaterial when the angle of incidence increases.

 

Fig. 5 Resonant frequency and asymmetric shift. (a) ${\omega }^{+}$ and${\omega }^{-}$ of SSR and FS metamaterials. ${\omega }^{+}$and ${\omega }^{+}$ correspond to the resonant frequencies of the resonances I and III marked in Fig. 2. (b) Asymmetric shifts ${\omega }^{+}-{\omega }^{-}$ of SSR and FS metamaterials. Square and triangle symbols correspond to the SSR and FS metamaterials, respectively.

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Next, it is necessary to explicate why the resonant frequencies of the resonances III and I in the FS metamaterial shift progressively to blue and red with increasing angles of incidence, while the resonant frequencies of the resonances III and I in the SSR metamaterial are almost kept unmoved. Oblique incidence leads to a small delay between the excitation of the two arcs of the SSR or halves of the FS-wire, meanwhile a small portion of magnetic component propagates across the surface of the metamaterial, rendering the whole system symmetry broken. This delay is sufficient to allow the excitation of an anti-symmetric trapped current mode associated with transmission minimum I and maximum II. Different from the SSR metamaterial with two separated arms, the “U” elements are being physically connected. The conductive coupling contributes to spectral separation [36]. For the connected structures, the spectral splitting that is directly correlated with the electromagnetic coupling strength is substantially enhanced. In particular, the redshift of the anti-symmetric modes (lower frequency resonance I) is weaker than the blueshift of the symmetric modes (higher frequency resonance III), which is contrary to the result in Ref. 36 [36]. On the other hand, the large spectral splitting of the FS metamaterial is linked to the surface current distribution variation due to the oblique incidence, illustrated in Fig. 6 . It is clearly seen in Fig. 6(a) and 6(c) or Fig. 6(b) and 6(d) that the surface current distribution in two adjacent unit cells is greatly influenced by phase φ₀ of incident waves. Whatever angles of incidence and phase of incident waves are, the response of the resonances I and II in the FS metamaterial is mostly dominated by anti-phase surface currents in the FS bends while in-phase surface currents contribute to the response of the resonance III. At α = 10°, there are four nodes of the surface current for each resonance in Fig. 6(a), marked by the dashed circles. At α = 50°, the resonance II still has four nodes, however, three nodes for the resonance I and five nodes for the resonance III due to large surface current distribution variation. The variation of nodes never occurs in the SSR metamaterial with two separated arcs. The additional current nodes require higher energies of the electromagnetic field to excite the particular surface current modes [37]. Therefore, the resonant frequencies of the resonances III and I in the FS metamaterial shift progressively to blue and red with increasing angles of incidence, much stronger than that of the SSR metamaterial.

 

Fig. 6 Normalized absolute surface current distribution of resonant modes I, II and III in the FS metamaterial at α = 10° and α = 50°. (a)-(b) Absolute surface current of the FS metamaterial at φ₀ = 0°. φ₀ denotes initial phase of incident waves. (c)-(d) Absolute surface current of the FS metamaterial at φ₀ = 90°. Arrows qualitatively indicate the instantaneous directions and magnitudes of the current flows. The dashed circles indicate the locations of the nodes in the surface current maps.

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5. Conclusions

In summary, we experimentally and numerically demonstrated that highly-dispersive EIT-type transmission band can be switched and controlled via angles of incidence. In particular, we have realized (i) trapped mode on/off switching, (ii) tuning of highly-dispersive EIT transmission band, (iii) tuning of the resonance quality factor and (iv) a controlled 35-fold increase of local energy density enhancement via the angle of incidence for simple, planar model structures based on SSRs and a FS wire pattern. These structures are well-suited for existing microfabrication and nanofabrication technologies and tuning via the angle of incidence can be easily applied anywhere in the electromagnetic spectrum. The variation of surface current nodes provides an insight into large spectral splitting of the FS metamaterial and explains the reason that the resonant frequencies of the resonances III and I in the FS metamaterial shift progressively to blue and red with increasing angles of incidence. The EIT-like behavior of the SSR and FS metamaterials makes them promising candidates for “slow light” applications, while local energy density enhancement provides in interesting platform for nonlinear, gain metamaterials and the lasing spaser.