In this paper, a three layered metamaterial composed of a ring-chain structure sandwiched between two layers of twisted sub-wavelength cut-wire arrays is proposed and investigated. The designed structure is optimized such that asymmetric transmission with an extremely broad bandwidth, sharp rejection stop-band and high transmittance is achieved. The physical mechanism is accounted for that the metallic layers form the Fabry-Perot-like resonance cavity, enhancing the polarization conversion efficiency between two orthogonal linearly polarized waves. To some extent, this approach offers a way to strengthen asymmetric transmission effect.
© 2014 Optical Society of America
Metamaterials, which is a rapidly developing research field, have attracted enormous attention owing to their unprecedented electromagnetic properties, such as negative refraction , invisibility cloak  and sub-diffraction imaging [3, 4]. During the past several years, lots of efforts have focused on the asymmetric transmission (AT) [5–17] in metamaterials. The AT is a new electromagnetic phenomenon for the metamaterial which results from different polarization conversion efficiencies [6, 14] between two orthogonal polarized states for waves propagating in opposite directions. This AT effect is irrelevant to the nonreciprocity of the Faraday effect, and can happen in the absence of magnetic media. The AT phenomenon, firstly observed and proposed by Fedotov et al. in 2006 , was reported only for circularly polarized waves before 2010 [6–9]. In 2010, Menzel et al.  presented the implement condition of AT for arbitrary base vector theoretically and achieved AT of both linearly and circularly polarized waves experimentally. Thereafter, an increasing number of structures [11–17] that could be used to achieve AT effects of linear polarization waves have been reported. More recently, several sophisticated structures for AT effects have been proposed. They could be used to enrich the functionality of the metamaterial such as: tuning , high polarization conversion efficiency , and multiband . However, most of these designed models do not have a broad bandwidth for AT. As a consequence, the transmissions with broad bandwidth and sharp rejection stop-band still remain unexplored for metamaterials in the AT field.
In this present paper, we report a three-layer metamaterial that consists of a ring-chain structure sandwiched by two layers of orthogonal cut-wire arrays with their dielectric layers. To begin with, we analyze the enhanced polarization conversion efficiency, which is a main reason for AT effect between two orthogonal linearly polarized waves. And then, we compare the electromagnetic responses of a single layer and stacking-type models. Fabry-Perot-like cavity is employed to analyze the enhancement mechanism. Furthermore, the AT with extremely broad bandwidth and sharp rejection stop-band for forward and backward propagating linearly waves is achieved using the composite three-layer metamaterial numerically and experimentally. In a way, this method (Fabry-Perot-like cavity) gives a new approach to enhance AT for the metamaterial.
2. Simulation and experiment method
The three-layer metamaterial consists of periodical arrays of identical unit cells, and it is sketched in Fig. 1 with a lattice periodicity of ax = ay = 8.6mm. Figures 1(a) and 1(b) are the front view of the ring-chain structure and sub-wavelength cut-wire arrays, respectively. Figure 1(c) is the perspective view of a unit cell. An ABC stacking scheme of the designed structure is constructed as shown in Fig. 1(d). Figure 1(e) depicts a photograph of the fabricated sample. Layer A is constructed by a substrate and sub-wavelength cut-wire arrays which are parallel to x-axis, while layer C is composed of the same substrate and the twisted 90° sub-wavelength cut-wire arrays which are parallel to y-axis. Layer B is a ring-chain structure whose principal axis coincides with off diagonal of the squared substrate. For layer B, the geometrical parameters are L = 11mm, W = 1mm, r1 = 1.5mm, r2 = 0.8mm. For layers A and C, the geometrical parameters are tw = 0.5mm, p = 1.2mm. As the substrates, FR-4 layers with a thickness of d = 4.1mm, relative dielectric constant of 4.4, and a loss tangent of 0.025 are utilized. The ring-chain and cut-wire are made of copper with a thickness of 17μm.
Our simulation is based on a frequency-domain finite integration technology (FIT) method . In the simulations, the boundary conditions of the unit cell along the x and y directions are adopted to be periodic, whereas the Floquet ports are applied to the z direction. Two orthogonal linearly polarized incident plane waves propagating along the + z direction, are used for excitation. For the experiments, the transmission properties of this designed structure were conducted in Microwave Anechoic Chambers, which allow us to measure without any restrictions on the size of the structure. The experiment is performed using two horn antennas serving as the source and receiver which were connected to an Agilent E8362B network analyzer. The designed metamaterial with an overall size of 20 × 20 unit cells was placed in the middle between the antennas. It is worth noting that for an x-polarized incident wave (with x-polarized source antenna), linear transmission coefficients txx (with x-polarized receiver antenna) and tyx (with y-polarized receiver antenna) can be achieved. Similarly, the tyy and txy are also obtained when the incident wave is y-polarized (with y-polarized source antenna).
3. Results and discussions
As the first step, we studied the responses of the single layer B and bi-layered BC. Figures 2(a) and 2(b) show co-polarization and cross-polarization transmission coefficients of layer B and layer BC, respectively. We see from Fig. 2(a) that layer B is resonant at about 10 GHz, whereas the co-polarization transmission tyy is extremely low (not exceed 0.05) for layer BC across the whole simulated frequency. The numerical results of cross-polarization txy for layer B and BC are shown in Fig. 2(b). In BC case, two resonant peaks of 0.61 and 0.72 happen at 6.1 and 11.7 GHz, respectively. As to the layer B, the cross-polarization coefficient is much lower than layer BC from 3.2 to 14.3 GHz, indicating that polarization conversion efficiency between x and y polarization is enhanced when the layer B is accompanied by layer C. Now, we focus on the underlying mechanism that the ring-chain structure can convert incident polarization to its orthogonal counterpart. We choose the ring-chain structure is motivated by a double-ring-chain metamaterial proposed by L. Cong et al  that can enable efficient polarization conversion. Actually, when the incident y-polarized wave illuminates to the ring-chain structure, it excites a dipolar oscillation mainly along the principal axis of the ring-chain with two orthogonal components: one is along the x-direction, the other is along the y-direction. The y-direction dipolar oscillation determines the co-polarized transmission (tyy) and the x-direction one dominates cross-polarized transmission (txy), which can be well demonstrated by the red lines shown in Figs. 2(a) and 2(b).
In fact, this broad bandwidth polarization-conversion enhancement benefits from the Fabry-Perot-like resonance inside the two metallic layers. As illustrated in Fig. 3, when y-polarized incident wave illuminates to the ring-chain arrays, a portion of it will convert into x-polarized wave, which can be evidenced by txy, the red line shown in Fig. 2(b). And the converted x-polarized wave can penetrate through the cut-wire arrays, whereas the remaining y-polarized wave (red line shown in Fig. 2(a)), is reflected by the x-polarized selective cut-wire arrays, which is almost transparent to x-polarized wave while blocking y-polarized wave (the transmission and reflection coefficients of the layer C are not shown here), and goes back to interact with ring-chain arrays. Subsequently, the reflected x and y-polarized waves, which can be confirmed by the ryy and ryx as shown in Fig. 2(c), are also selected by the cut-wire arrays again. With the waves travelling back and forth between the two metallic layers, there is a Fabry-Perot-like cavity between them, which results in the enhanced transmitted x-polarized wave.
However, the maximum polarization conversion efficiency of the BC stacking-type is no more than 0.75. It may result from the reflection (shown in Fig. 2(d)) of the incident y-polarized wave when illuminates onto the ring-chain arrays. In order to further improve the polarization conversion efficiency, we add the y-polarization selective cut-wire arrays (transparent to y-polarized wave while blocking x-polarized wave) which are orthogonal to layer C in front of the ring-chain structure as shown in Figs. 1(c) and 1(d) as an ABC stacking. Two orthogonal linearly polarized normally incident plane waves are adopted to illuminate this composite structure.
Thereafter, we simulated and measured the response of the composite structure with the ABC stacking-type. Figure 4 shows the calculated and experimental transmission coefficients in this ABC stacking-type for the forward and backward propagating waves. As illustrated in Fig. 4, the co-polarization transmission coefficient tyy of y-polarized wave coincides with txx of x-polarized wave since an orthogonal arrangement of the ABC stacking-type ensuring that the whole structure is isotropic when the wave is normal incidence. However, in contrast to co-polarization transmission, the cross-polarization transmission txy is extremely different from tyx. Compared to the cross-polarization txy of BC stacking-type in Fig. 2(b), txy of ABC shown in Fig. 4(a) has a broader bandwidth and a higher value confirming that the polarization conversion efficiency is significantly enhanced. In fact, the composite structure forms two Fabry-Perot like cavities: one consists of AB stacking-type, the other includes B and C layers. The incident energy is first coupled efficiently into the AB stacking-type which services as in-coupler; broad bandwidth and high polarization conversion efficiency are obtained by releasing the previously coupled energy which is confined to the former cavity after passing the BC stacking-type which amounts to out-coupler, and this mechanism is similar to the reference of . Besides, the cross-polarization transmission shows a good sharp rejection stop-band performance that attenuates in a specific range to very low levels, which can be characterized by the transition width (a bandwidth that signal increases from 10% to 90% or drops from 90% to 10% in transmission). Obviously, the transition width in both simulation and experiment is about 1.4GHz, which is much less than the 3dB bandwidth of about 11GHz.
Seen from Fig. 4(a), the cross-polarized transmission reaches three resonant peaks of 0.92, 0.91, 0.86 at 3.9, 8.1, 12.0GHz, respectively. The cross-polarized coefficient txy is larger than 0.5 from 2.8 to 14.3 GHz while tyy is no more than 0.05 across the interest frequency. It indicates that the incident y-polarized wave is almost completely converted into x-polarized wave. When the incident direction is reversed, txy and tyx interchange with each other as shown in Fig. 4(b). The measured cross-polarized transmissions in Figs. 4(c) and 4(d) are in good agreement with the simulated ones shown in Figs. 4(a) and 4(b). The measured and simulated co-polarized transmission txx and tyy agree with each other. Small discrepancy can be explained by the fabrication error in experiments. It should be noted that since txx is exactly equal to tyy, the AT of this designed structure is only available for linearly polarized waves, and not for the circular ones [11, 14, 18].
The AT parameter Δ, defined as difference transmittance in two opposite directions [10, 11], can represent the degree of AT. The Δ for the linearly polarized wave can be defined as. Figure 5 presents the simulated and measured Δ for forward propagating x- and y-polarized waves. Clearly, both the AT parameter and hold a broad bandwidth (from 3.5 to 14 GHz) with high value. The measured AT parameters in Fig. 5(b) agree well with the simulated ones. It is clearly demonstrated that two curves of and are exactly contrary to each other in Fig. 5. Apparently, the composite three-layer structure reveals a broad-bandwidth one-way transmission of linearly polarized waves.
In summary, we have proposed a three layered metamaterial that is composed of a ring-chain structure sandwiched between two layers of sub-wavelength cut-wire arrays. Fabry-Perot-like resonance cavity is formed between metallic layers to enhance the AT. As a result, a broad bandwidth (from 2 to 15GHz), sharp rejection stop-band and high polarization conversion for AT has been achieved theoretically and experimentally. To some extent, this approach (Fabry-Perot-like resonance cavity) provides a new way to strengthen AT. Our study exhibits a broad bandwidth AT in the metamaterial and allows the manipulation of electromagnetic waves through a metamaterial design. The same functionality can be achieved in optical frequencies by scaling down the proposed metamaterial structure to a proper scale. We believe our findings are beneficial in designing broad bandwidth one-way transmission devices.
This work is supported by the National Natural Science Foundation of China (61078060), Ningbo Optoelectronic Materials and Devices Creative Team (2009B21007), the Outstanding (Postgraduate) Dissertation Growth Foundation of Ningbo University (grant PY2013012), the Scientific Research Foundation of Graduate School of Ningbo University, and is partially sponsored by K. C. Wong Magna Fund in Ningbo University.
References and links
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