Analog electromagnetically induced transparency for circularly polarized wave using three dimensional chiral metamaterials

In this paper, we theoretically and experimentally demonstrate a three dimensional metamaterial that can motivate electromagnetic induced transparency (EIT) by using circular polarized wave as stimulations. The unit cell consists of a pair of metallic strips printed on both sides of the printed circuit board (PCB), where a conductive cylinder junction is used to connect the metal strips by drilling a hole inside the substrate. When a right circularly polarized wave is incident, destructive interference is excited between meta-atoms of the 3D structure, the transmission spectrum demonstrates a sharp transparency window. A coupled oscillator model and an electrical equivalent circuit model are applied to quantitatively and qualitatively analyze the coupling mechanism in the EIT-like metamaterial. Analysis in detail shows the EIT window's amplitude and frequency are modulated by changing the degree of symmetry breaking. The proposed metamaterial may achieve potential applications in developing chiral slow light devices.


Introduction
Metamaterials are artificial materials that have fascinating properties [1]. Through carefully designing the structures and geometries of subwavelength unit cells, metamaterials have the ability to manipulate the propagation behavior of EM waves, including its amplitude, phase [2,3], polarization [4,5] and linear/angular momentum [6]. Many exceptional phenomena such as subwavelength imaging, hologram, beam shaper, invisible cloaks [7][8][9] have been demonstrated. Their applications have been expanded from the microwave band to the THz, IR and visible frequencies [10]. The attractive properties of various metamaterials rely on the interaction between incident EM waves and the meta-atoms. Due to the wave-particle duality, the underlying mechanism of coupling and interference between meta-atoms may also link the classic picture to quantum picture. In recent years, by means of manipulating the interaction between light and meta-atoms, there are lots of researches focused on using metamaterial to mimic the quantum phenomena such as Electromagnetic induced transparency (EIT), Fano resonance [11], spin-orbit interaction [12], Purcell effect [13], and so on. Among these phenomena, EIT has been considered as a possible means to realize slow light for future sensing and communication devices [14]. In most of the designs, the EIT response is implemented in the metamaterial by taking advantage of meta-atom's symmetry breaking [15]. The underlying mechanism of EIT in metamaterial system is interpreted by hybridization between the so called "dark mode" meta-atom and "bright mode" meta-atom [16]. Due to the excitation of the incident linear polarization light, subwavelength electric/magnetic dipolar or multipolar are induced in the meta-atoms. Destructive interference between the dipole/multipole will create a single transmission window that arises from an opaque background. This EIT-like spectra in metamaterial can perfectly mimic a three-level quantum system while the group velocity of incident light in these metamaterials will be greatly reduced or even stopped [17,18]. More complex dual EIT metamaterial is also studied in [19,20] to analog a four-level tripod quantum system.
In majority of the previous works, linearly polarized EM waves are used to excite metamaterial-based EIT. As a result, slow-light effects are limited to linearly polarized waves [21,22]. However, circularly polarized (CP) wave is also widely used in optical devices and experiments. In recent years, different kinds of chiral metamaterials have been proposed to manipulate handedness waves, various phenomenon such as negative index [23], asymmetry transmission [24], Berry phase [25], polarization rotation [26] for CP waves have been implemented. The realization of slowing down CP light may provide the possibility to construct handedness dependent optical storage and communication devices. However to the author's knowledge, the EIT-like metamaterial for circular polarization wave is not thoroughly studied. Only very recently, the authors demonstrate the EIT effect of circularly polarized waves using Born-Kuhn type resonators mixed with split ring resonators [27]. Meanwhile, most EIT-metamaterials make use of symmetry breaking "meta-atoms" on a planar to engineer the "dark mode" and "bright mode" interference [28,29]. These works give a clue that handedness sensitive EIT of CP light can be achieved in chiral metamaterials with symmetry breaking. Also recently, in our previous work [30,31], a unique threedimensional design was proposed to implement polarization-dependent EIT for linear polarization wave. The 3D structure brings in more design freedom for metamaterial excogitation. Inspired by these valuable works, we use LCP/RCP electromagnetic waves to excite EIT-like response in symmetry breaking 3D chiral metamaterial. The proposed structure shows circular dichroism (CD) and optical activity as conventional chiral metamaterials [32]. A typical EIT-like transparency window can be achieved under RCP incidence while it vanished at LCP incidence. The EIT response can be tailored through changing the asymmetry degree of the unit cells. The blueshift of EIT window can be explained by employing an equivalent circuit model. Both numericaly simulated and experimentally measured results verified these classic analog of EIT-like and related Fanolike resonance spectra. An analytical coupled oscillator model is applied to reproduce the transparency spectra that enhance the understanding of the underlying mechanism. Compared with previous work [27], the proposed structure provided an alternative simple and efficient solution to tailor the EIT-like phenomenon in metamaterial for CP waves.

Design, Model and Simulation
The proposed 3-D metamaterial with a unit cell is shown in Fig. 1(a), where the meta-atom has a continuous metallic strip in both the top and the bottom side. In order to connect the top and bottom arms, one vertical metallic cylindrical junction was fabricated to pierce through dielectric layer to form a three-dimensional structure. The bottom strip is parallel to the x-axis while the top strip is rotated with an angle 15    from the x axis. The whole length of both strips is 8.2mm. In order to break the symmetry of the structure, the copper via hole is not placed at the center of each metal strip. The distance between the left end of the top side strip and the via hole's center is a=3.5mm while for the case of the bottom strip is c=4.7mm. The radius of the hole is r=0.7mm, and the thickness of the substrate is 0.81mm which is made up with Rogers RO4003 material with a relative permittivity 3.38. The full-wave numerical simulation software CST microwave studio was employed to analyze the spectral response of our proposed design. Open boundary conditions were set along the light propagating direction (z-direction), and unit cell boundary conditions were applied at the x-y plane. The input and output Floquet ports are excited with circular polarized wave. After optimizing the parameters in simulations, experimental samples with overall dimension of 180×180 mm 2 were fabricated using the printed circuit board (PCB) technique, whose images of top and bottom panel are shown in Fig. 1(b) and Fig.1(c). The spectral responses were measured by circular polarized antennas used as emitter and receiver respectively. A vector network analyzer (Agilent N8362B) was employed to calibrate, store and retrieve data.
Our specific design breaks the symmetry of the 3D volumetric meta-molecular, the proposed structure has no mirror symmetry plane which can be regarded as 3D chiral metamaterial. The chirality in chiral metamaterials offers great possibilities in the control of light polarizations, optical activity and circular dichroism which can exceed the effects obtained in natural chiral materials. In this work, the chirality of the proposed metamaterial provide distinct transmission spectral for left-and right handed circularly polarized incident waves as shown in the Fig.2(a) and Fig.2  The most important feature of EIT-like metamaterial is slow wave propagation. To demonstrate this property in the proposed design, we simulate a RCP wave carrying Gaussian shape pulse that is transmitted normally through the infinite monolayer of the metamaterial. The Gaussian pulse is centered at 11.7GHz with a 1.5GHz bandwidth. In simulation the distance between the source plane and the transmission probe plane is 10mm. From Fig.2 (d), it shows that the peak of the incident Gaussian pulse appears at 1.2ns, when the propose metaatom (metallic part of the unit cell) exists, the peak of the transmitted pulse emerges at 1.6685ns. If we remove the meta-atom, the peak of the transmitted pulse shows at 1.26ns. This means the transmitted pulse experience a much longer delay time. Due to the strong dispersion characteristics of the metamaterial, the transmitted pulse through the metamaterial becomes much wider than the incident pulse.
In order to understanding the resonance and coupling mechanism between the metaatoms, we plot the simulated surface current distributions under LCP/RCP light incidence in Fig.3 respectively. The frequencies are chosen as two transmission dip and transparency peak frequency for RCP incidence: 10.77GHz, 13.85GHz and 11.70GHz. For both RCP/LCP incidence case, at the lower frequency of the transmission dips, the surface currents run on the metallic structure following two loop paths due to the existence of the metal via as shown in Fig.3 (a) and Fig.3 (b). The role of each twisted loop current plays equivalent to a magnetic dipole. The direction of both magnetic dipole are antiparallel. Since the current intensity on the left loop and the right loop are comparable, the interaction between the magnetic dipoles can be regarded as strong constructive interference. At another transmission dip frequency 13.85GHz, the resonance is caused by the interaction between a twisted electric dipole and two antiparallel electric dipoles as shown in Fig.4(e) and Fig.4(f). Thus the system can be viewed to work in a symmetric mode. These working modes are quite similar to that described in [14]. However, in [14] the currents flow on a planar 2D unit cell and the stimulation wave are linear polarized.
The transparency peaks at 11.70GHz for the RCP incidence case can also be well explained using the surface current distribution. In Fig.3(d), it shows that the induced circular currents on the left and right part of the proposed structure are still antiparallel to each other. But differs from that shown in Fig.3 (b), the current density on the right path is much weaker than that of the left one. This can be regarded as an evidence of the destructive interference. On the other hand, when 11.7GHz LCP wave incidents, the loop currents runs parallel to each other, their strength are also comparable as shown in Fig.3(c), which means both twisted asymmetry U-shape resonator works at quasi-bright mode, thus, typical EIT response vanished in this case. The current distributions plots illustrate that the loop currents flow along twisted-U shape paths. The coupling mechanism of the two twisted U shape resonator might have an electric analog using RLC equivalent circuit. An electrical analogy model [33] for the EIT-like phenomenon in metamaterial is considered as plotted in Fig.4 (b). The resonance atom is modeled using resonant circuit formed by coupled RLC circuit. The resistance, inductance, and capacitance of each loop are represented by R i , L i , C i , respectively. The coupling capacitor C models the coupling between the two loop shape meta-atoms. The induced transparency is investigated by analyzing the power transfer from the voltage source to the resonant circuit R 2 L 2 C 2 . When geometric parameters of the structure change, the value of lumped elements in the electrical analogy model will change accordingly as well as the amplitude and frequency of transparency window. This intuitive analogy model inspire us to study tunable EIT-like phenomena based on the proposed structure which will be discussed in the subsequent section of this article. A known theoretical model for quantitatively interpreting the EIT phenomenon is the twooscillator model [34]. The interaction between both oscillator (bright ( 1 x ) and quasi-dark ( 2 x