1. Introduction

Metamaterials have excited increasing interest over the past decade due to its ability for scientists to develop novel artificial structures with fantastic electromagnetic responses, which have many potential applications, such as negative refractive index, sub-diffraction imaging and invisibility cloaks [1–6]. Metamaterials with chirality can also be designed to achieve giant circular dichroism and optical activity [7]. Plenty of polarization devices have been designed and reported based on chiral metamaterials, such as polarization rotators [8–10], circular polarizers [11–13], and polarization spectrum filters [14,15]. Moreover, metamaterials can exhibit some properties that go beyond natural materials, such as symmetries and topologies [16–18] and may introduce entirely new physical effects and electromagnetic phenomena [19].

Recently, it was found that metamaterials with strong symmetry breaking can exhibit the propagation direction-dependent polarization sensitive transmission effect, known as asymmetric transmission (AT), for both circular [20–28] and linear polarizations [19,29–35]. This effect resembles the famous Faraday Effect, however the latter is a nonreciprocal effect, and can be used to design isolators, while normal AT is a reciprocal effect that cannot be used to make isolators [28,36]. Since the concept of AT was proposed, it is always associated with chirality, including single layer [20,23,26], double layers [29,30,35], and multi layers [31], intrinsic and extrinsic [37]. After systematically reviewing the research history of the AT effect, one tends to have an impression that, chirality is the precondition for designing AT devices. Actually in many important and famous works, the chirality based on symmetry breaking was always taken as a key factor responsible for the AT effect. In this paper, we demonstrate that using 3D symmetric (achiral) structure, at least circular AT effect can be obtained. The AT mechanism of this mirror symmetric metamaterials is discussed later in detail. With further optimizing the parameters, a broadband (>80% of the central wavelength), high circular polarization converting efficiency (~80% modal conversion efficiency) and almost flat top AT effect is obtained. The idea shown here can be proven with the working frequency from GHz, THz, or even optical frequency, although further optimization for each frequency band is needed. Since devices working at THz frequency are badly in need because of the THz gap, we present the result in THz region for demonstration.

2. Metamaterial structure

The unit cell of the metamaterial is illustrated in Fig. 1(a). It is consisted of a pair of joined mirror symmetric helices. Along the z axis, the metallic helices form a square array in the x-y plane with a lattice constant of a = 130 μm. Each unit cell has a pitch of p = 150 μm, the wire radius r = 10 μm, and radius of the helix R = 50 μm. The metamaterial structure is located from -L to L along the z axis with a substrate thickness d. The substrate is indicated by the grey layer, and should be optimized for different operating frequency. In this paper, we just treat it as the air as a demo. The metamaterial shown in Fig. 1(b) is formed by the 2D periodic array of the unit cell. Obviously, this structure is anisotropic. A single helix structure, which is obvious chiral, has been deeply investigated and many devices were reported or suggested [11,38,39]. However, the metamaterial shown in Fig. 1(b) is mirror symmetric, i. e., achiral, which is essentially different from most of the reported results. Besides, this is a 3D metamaterial, not a planar 2D metamaterial. The helix structure usually has a wide working bandwidth, due to the combination of internal and Bragg resonance [11].

 

Fig. 1 Schematic diagram of the mirror symmetric metamaterial. (a) Unit cell and (b) the array of unit cell to form a 3D metamaterial. The grey layer indicates the substrate, which is air in this paper.

Download Full Size | PDF

In the following discussion, t represents the amplitude transmission coefficient, which directly shows the relation of the incident and transmitted electric fields and T is the transmission in terms of the power density, which equals ${\left|t\right|}^2$. The top arrows indicate the wave propagation direction: ‘$\to$’ for z direction and ‘$\leftarrow$’ for –z, the opposite direction. The indices ‘ + ’ and ‘-’ denote the handedness of the circularly polarized component: ‘ + ’ for RCP and ‘-’ for LCP. When two indices form a pair, the first index means the incident wave handedness and the second indicates the output wave handedness, for example, ${\overrightarrow{t}}_{+-}$represents the circular polarization transmission coefficient of output LCP component when the RCP wave is incident from the left. The total transmission of the metamaterial is defined in this form:${\overleftarrow{T}}_{-}={\left|{\overleftarrow{t}}_{--}\right|}^2+{\left|{\overleftarrow{t}}_{-+}\right|}^2$. We define the transmission difference $\Delta \overrightarrow{T}={\overrightarrow{T}}_{+}-{\overrightarrow{T}}_{-}$for right-handed and left-handed circularly polarized waves striking on left side of the metamaterial sample, $\Delta \overleftarrow{T}$for the opposite side.

The asymmetric transmission can be assessed by deriving and analyzing the corresponding scattering matrix. We treat the LCP and RCP, for both forward and backward propagation, as a four-port system with the two ends of the device as input and output. The equation can be expressed using the following electric field equation:

3. Results and discussions

The calculated transmission spectra of the left and right incidence are outlined in Fig. 2. Figure 2(a) schematically demonstrates the magnitudes of transmission coefficients with RCP wave incident from z and –z direction. The respective spectrum of the transmission coefficients are presented in Fig. 2(b). It is found that there is huge difference between the cross transmission coefficients ${\overrightarrow{t}}_{+-}$and ${\overleftarrow{t}}_{+-}$. Besides, the direct transmission coefficients are independent of the incident direction:${\overrightarrow{t}}_{++}={\overleftarrow{t}}_{++}$. The case of LCP incidence is almost identical, but the incident direction should be interchanged. The total transmission of the THz metamaterial is shown in Fig. 2(c). A broadband AT effect can be seen and the conversion efficiency is as high as 80% [Fig. 2(d)].

 

Fig. 2 Schematic (a) and calculated (b) transmission coefficient of the metamaterial. (c) Total transmission and total absorption with different incident polarization and direction. (d) Transmission difference.

Download Full Size | PDF

Our numerical results also show that the scattering matrix S [Eq. (2)] is strictly symmetric, i.e., the forward and backward propagation reflection coefficients${\overrightarrow{r}}_{-+}={\overleftarrow{r}}_{-+}={\overrightarrow{r}}_{+-}={\overleftarrow{r}}_{+-}$, the direct transmission coefficients${\overrightarrow{t}}_{++}={\overleftarrow{t}}_{++}={\overrightarrow{t}}_{--}={\overleftarrow{t}}_{--}$ and the conversion transmission coefficients${\overrightarrow{t}}_{+-}={\overleftarrow{t}}_{-+}$,${\overrightarrow{t}}_{-+}={\overleftarrow{t}}_{+-}$. These results imply that the asymmetric response is strictly reciprocal and satisfies the general conditions of Lorentz reciprocity theorem. However, because${\overrightarrow{t}}_{+-}/{\overrightarrow{t}}_{-+}\ne {\overleftarrow{t}}_{+-}/{\overleftarrow{t}}_{-+}$, the device demonstrated in Fig. 2 converts one mode (RCP/LCP) to the cross polarization mode (LCP/RCP) only in one way, leading to the asymmetric transmission effect. For example, in case of RCP entering from the left side, the metamaterial’s total transmission${\overrightarrow{T}}_{+}={\left|{\overrightarrow{t}}_{++}\right|}^2+{\left|{\overrightarrow{t}}_{+-}\right|}^2$, is asymmetric with respect to opposite direction of wave propagation${\overleftarrow{T}}_{+}={\left|{\overleftarrow{t}}_{++}\right|}^2+{\left|{\overleftarrow{t}}_{+-}\right|}^2={\left|{\overrightarrow{t}}_{-+}\right|}^2+{\left|{\overrightarrow{t}}_{--}\right|}^2=\text{}{\overrightarrow{T}}_{-}$. Compared with the previous work, the AT effect shown here is much stronger and broader due to the significant different conversion efficiencies for the same mode incident on the structure from opposite directions.

The reflection coefficient ref and reflectance Ref are almost complementary to t and T, since the metal is almost PEC to THz and GHz wave [11] and the absorption is negligible, as can be seen in Fig. 2(c). It indicates that, ref and Ref have the inverted AT effect with respect to t and T, and this is useful in some cases, for example, the substrate is opaque. It also indicates that the operation frequency may vary from GHz, THz to infrared, depending on the plasmonic frequency of the material.

After phenomenologically analyzing the AT effect, we further studied the physical mechanism of the mode conversion by slowly varying the unit cell. Firstly, the unit cell is broken from the junction and separated apart to a distance 20 μm (one helix wire size), see top of Fig. 3(a). It is known that the propagation of EM wave through the helical metamaterials will induce the current on the surface of helix metal wire. The mirror symmetry is maintained during the separation, but now the coupling between the two helices is through the air (field) other than directly induced current. The comparison of the new transmission difference ($\Delta T$) spectrum with the original one is depicted in Fig. 3(a). It can be seen clearly that with just a small spacing in the junction, the performance of AT effect drops down quickly, though it is still obvious. Secondly, the junction is changed from a single spot to a bar, as illustrated at the top of Fig. 3(b). In this case, the mirror symmetry is broken, while the central symmetry is built, which ensures that it is still an achiral structure. The helix pair is still connected, but in a different manner. The comparison of the$\Delta T$spectra of the second case and the original one is shown in Fig. 3(b).Obviously, the new $\Delta T$ spectrum is very similar to the original one, but blue shifted. As the last case, the bar of the unit cell in the second case is removed (top of Fig. 3(c)). The central symmetry is reserved, but the coupling is again through the air. The third $\Delta T$spectrum compared with the original one is shown in Fig. 3(c). The performance again becomes worse, but in a different way with respect to the first case. From these studies we can see that, first, AT effect is obtained in all achiral structures; second, modal conversion efficiency plays a more important role to get high performance (broader, higher), which is one important research goal in this field. In supporting material Visualization 1, Visualization 2, Visualization 3, and Visualization 4, the induced current distributions at 1.15 THz of all cases are illustrated. The induced currents of both the original unit cell (directly connected) and the second example (bar connected, central symmetric) are very strong, while that of the first and third examples (separated from center) are much weaker, which are in consistent with the strength of the AT effects and verify that the improved modal conversion gives better result.

 

Fig. 3 The $\Delta T$spectrum of three different examples (solid line) compared with the original structure (dotted line). (a) Separated from the center, (b) bar connected, (c) bar removed from (b). All the dashed lines represent the spectrum of the original structure, while the solid lines correspond to that of the modified structures separately (see Visualization 1, Visualization 2, Visualization 3, and Visualization 4).

Download Full Size | PDF

4. Optimization

Although the AT effect shown in Fig. 2 is already much better than that previously reported, there is still some oscillation in the AT spectrum. Therefore, we further modify the metamaterial to improve the performance. The helix pair to form the unit cell is changed from fixed radius$R_1$to a gradually varying radius$R(z)=R_1-z\ast (R_1-R_2)/(N*p),$$z>0$, in which N is the number of turns on the helix, p is the pitch of the helix. The upgraded helix with a Christmas tree shape is schematically depicted in Fig. 4(a) [40]. The slowly increase of the radius from $R_2$to $R_1$makes it possible to couple more incident power into the metamaterial, leading to the enhancement of the light transmittance. At the output end, the small radius $R_2$can decrease the duty ratio, reduce the interaction between nearby current, and hence keep the output wave more circular [41]. The transmission spectrum and the comparison with that of the original metamaterial are shown in Fig. 4(b). The spectrum is smoother, and average transmission ratio ${\overrightarrow{T}}_{+}/{\overleftarrow{T}}_{+}$change from 19.33 to 74.05 (maximum 150.83 at 1.02 THz), greatly improved than before (notice the log coordinate). The extremely high transmission ratio strongly shows that the modified structure can be used for practical application. In the previous structures, the substrates are air. For real device fabrication, we also calculated the AT effect with substrate refraction n = 1.5 (see Visualization 5 and Visualization 6). The operation frequency is red-shifted due to substrate index change as expected [28], while the bandwidth will be a little narrower. However, when the structure is immersed in the substrate similar to Ref [11], the spectrum will be just red-shifted while keeping the same relative bandwidth.

 

Fig. 4 Comparison of total transmission (a) and transmission ratio (b) between the modified structure (solid line) and the original structure (dashed line). Substrate effect is also considered (see Visualization 5 and Visualization 6).

Download Full Size | PDF

5. Conclusions

In conclusion, we show that AT effect can be achieved in any structure that has modal conversion by careful design. Although most of the AT effect was realized using chiral metamaterials, it is shown that the chirality of the structure is not the essential requirement. To realize a practical metamaterial with AT effect, scientists should focus on the structure design to obtain high modal conversion efficiency and transmission ratio. In particular, we proposed a mirror symmetric metamaterial generating the AT effect with giant bandwidth (>80% of central operation frequency) and high modal conversion efficiency (~80%) in THz region. After optimization, the super high average transmission ratio can reach 74.05 (maximum 150.83 at 1.02 THz), making it possible for practical application. The idea shown in this paper can be transplanted to microwave region. For optical region, similar structure can also show AT effect, however, because the loss in metal become predominant at the nanometer scale, the AT effect will be worse. Circular polarization device is demonstrated in this paper, with the combination of other techniques, like external or substrate field modulation, nonlinear effect or time-dependent modulation [42], new AT devices or even nonreciprocal devices can be realized.