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The three-dimensional (3D) and two-dimensional (2D) chiral metamaterials (CMMs) have been proved to exhibit circular dichroism and circular conversion dichroism, respectively. The layer-by-layer chiral metamaterials, as a category of 3D CMMs, are expected to show the same properties as bulk 3D structures (e.g. helices). However, in this paper, we demonstrated that the layer-by-layer CMMs exhibit circular dichroism and circular conversion dichroism simultaneously by using both theoretical and experimental methods. This work showed that asymmetric transmissions of circular polarizations can also be observed in layer-by-layer CMMs. Moreover, we provided some necessary requirements for the existing of asymmetric transmissions in layer-by-layer CMMs.
©2013 Optical Society of America
1. Introduction
Metamaterials are periodical artificial media with pitches smaller than the wavelength of interest and can exhibit unusual properties not found in nature or in their constituent materials. Over the past decade years, chirality in metamaterials has attracted much attention in the field of metamaterials[1,2]. The concept of chirality is defined as the lack of mirror image symmetry, which widely exists in nature such as DNA, carbohydrates and proteins. Compared with the materials in nature, the chiral metamaterials (CMMs) can exhibit much stronger optical activities [3]. Generally, there are two categories of CMMs: 3D and 2D chiral metamaterials [4–6]. 3D chirality leads to circular birefringence and circular dichroism as manifestations of optical activity (see Fig. 1(a) ). The perceived twist of 3D chiral objects (e.g. helices) is the same for opposite directions of observation, so optical activity is the same for the opposite propagating directions. 2D chirality leads to circular conversion dichroism as a manifestation of asymmetric transmission [7–9] (see Fig. 1(b)). The asymmetric transmission is defined as the partial conversion of the incident wave into the opposite handedness is asymmetric for the opposite propagating directions. This phenomenon can be understood by regarding that the sense of twist of 2D CMM is reversed for opposite directions of observation. In 3D CMMs, the layer-by-layer chiral metamaterials show advantages in fabrications [10–12]. The structures are first suggested by Svirko et al. [13] and it has been demonstrated that they can exhibit circular birefringence [14] and circular dichroism [3–10]. So it’s widely believed that the layer-by-layer CMMs exhibit the same properties as other 3D CMMs (e.g. helices) do. But according to this work, the layer-by-layer CMMs can exhibit not only optical activity due to 3D chirality but also some properties of 2D chirality.
Fig. 1 Electromagnetic manifestations of chirality in (a) 3D chiral metamaterials; (b) 2D chiral metamaterials; (c) layer-by-layer chiral metamaterials.
In this paper, the twisted layer-by-layer CMMs were classified into two cases according to their constitutions: one is consisting of planar non-chiral structures, the other one is consisting of planar chiral structures. It was found that both structures can exhibit circular dichroism and circular conversion dichroism simultaneously (see Fig. 1(c)). But in one case, for the layer-by-layer CMMs stacked with planar chiral structures, when the two layers are mirror image of each other, there will be only circular dichroism exhibited. The Jones matrices were used to confirm the fact that asymmetric transmission is a generic property of circular conversion dichroism [15]. By analyzing these phenomena, we gave necessary conditions for the existing of asymmetric transmission in layer-by-layer CMMs.
2. Method
Figure 2 shows the schematic diagram of our experiment setups. We fabricated the structures with overall size of 30 × 30 cm2 etched from a 35-μm-thick layer of cooper on a 1.6 mm thick FR-4 substrate with the relative dielectric constant εr = 4.2 and the loss tangent tan tδ = 0.02 (measured by experiments). The linearly x and y polarized microwaves irradiated the samples. On the other side of the samples, we measured the transmitted waves of x and y polarizations using an Agilent N5244A network analyzer. All the measurements were performed in an anechoic chamber. We used Finite-Difference Time-Domain (FDTD) to simulate the transmissions of layer-by-layer CMMs. The periodic boundary conditions were applied to the x and y directions, and the absorbing boundary conditions were applied to the z direction. The metal was regarded as Perfect Electric Conductor (PEC) at microwave regime. The transmission of circularly polarized waves can be converted from the linear transmission coefficients using Jones matrix method as below [16]:
In the equations, the transmission coefficients are expressed as Tij, where indices i and j correspond to polarization states of the transmitted and incident waves, which could be linear polarizations, right-handed (RCP, + ) or left-handed (LCP, –) circular polarizations.3. Results and discussions
3.1 Layer-by-layer CMMs stacked with planar non-chiral structures
By stacking planar non-chiral structures with a twist angle between them, the new constructed materials can achieve chirality. These structures are especially attractive at optical regime because they are easy to fabricate and integrate within nanophotonic systems due to low-profile [12]. Here, the layer-by-layer CMMs stacked with wires were studied at microwave regime. Figure 3(a) shows the schematic diagram of one unit cell of the CMMs along with the structure parameters. And the photographs of the slabs of the first and second layer are showed in Fig. 3(b) and 3(c), respectively. The two layers are with a twist angle of 60° in counter clockwise between them. Figure 4(a) and 4(b) show the simulation results of their transmission coefficients for forward and backward propagations, respectively. Figure 4(c) and 4(d) show the corresponding experiment results. It’s clear that the simulations and experiments deliver consistent results.
Fig. 3 The schematic diagram and photographs of the layer-by-layer CMMs stacked with planar non-chiral structures with the structure parameters of l = 12.5 mm, w = 3 mm and d = 6 mm.
Fig. 4 The simulation and experiment results of transmission coefficients of the layer-by-layer CMMs stacked with planar non-chiral structures for forward and backward propagations.
From the figures, it can be seen that the layer-by-layer CMMs show both circular dichroism and circular conversion dichroism, which is unexpected according to previous researches. Circular dichroism can be told from the co-polarized transmissions (solid lines), the LCP and RCP each has one resonance at different frequencies due to the chiral nature of twisted layer-by-layer structures. And the co-polarized transmissions are propagating direction independent. Circular conversion dichroism can be told from the cross-polarized transmissions (dash lines), the two conversions aren’t identical, and their magnitudes are reversed as the alteration of propagation directions. The phenomena verify the fact that asymmetric transmission is a generic and peculiar property of circular conversion dichroism.
The asymmetry of opposite transmissions is given by the difference between conversions:
As the planar structures are very thin, ΔTs of 2D CMMs are very small, for example, ΔTs are less than 0.2 in Ref. [8] and [15]. While in this bilayered structure, the largest ΔT is 0.24 at 7.44 GHz (experiment result in Fig. 4(d)). As the each layer in the studied structures barely has 2D chirality, with further design, the layer-by-layer CMMs can be expected to enhance the asymmetric transmissions greatly.According to other works, by stacking the planar structures with a twist angle between them, 3D chirality will achieve, so the appearance of circular dichroism is easy to understand. So we will mainly analyze the cause of circular conversion dichroism. For planar chiral structures, the cause is that the sense of twist is reversed for opposing directions of observation. While for these twisted layer-by-layer structures, when they are observed from opposite sides, the sense of perceived rotation remains unchanged (counter clockwise in this case), but the orientations of the structures change. On the one hand, the electric field components of circular polarizations are symmetric around x- and y-axis, so the orientations of the structures don’t influence the co-polarized transmissions. On the other hand, the structures aren’t symmetric around x- or y-axis, so the conversions of electric fields are affected by the orientations of the structures. Therefore, the cross-polarized transmissions aren’t exactly the same for opposing propagations as it’s shown in Fig. 4. Here, the Jones matrix is used to analyze the relationship between asymmetric transmission and circular conversion dichroism. The Jones matrix connects the generally complex amplitudes of the incident and transmitted fields [16]:
The Jones matrix for backward propagation describes the light propagating through the structure rotated by 180° with respect to the y-axis. Therefore, we have [17]:Then the Jones matrix of circular states for backward propagation is:By comparing Eq. (1) and (5), it is found that the diagonal elements (representing the co-polarized transmissions) stand the same, while the off-diagonal elements (representing the cross-polarized transmissions) are reversed. It indicates that the cross-polarized transmissions will be reversed when waves propagate from opposing directions. Therefore, the asymmetric transmission is a generic and peculiar property of circular conversion dichroism, which is also shown in Refs [7–9,15].After these analyses, it can be concluded that asymmetric transmissions of circular polarizations can also be observed in layer-by-layer CMMs. And it can be understood by that the layer-by-layer twisting CMMs have characteristics of 3D chirality and different orientations for opposite directions of observation, which gives rise to circular conversion and circular conversion dichroism, respectively.
3.2 Layer-by-layer CMMs stacked with planar chiral structures
In this section, the planar chiral structures consisting of wire dimers are used to construct layer-by-layer CMMs. Due to the special arrangements of two wires, these wire dimers can exhibit 2D chirality with quite simple configurations [18,19]. Figure 5(a) shows the schematic diagram of one unit cell of the CMMs along with the structure parameters. And the photographs of the slabs of the first and second layer are showed in Fig. 5(b) and 5(c), respectively. The bilayered structure is also with a twist angle of 60° in counter clockwise. Figure 6(a) and 6(b) show the simulation results of their transmission coefficients for forward and backward propagations, respectively. Figure 6(c) and 6(d) show the corresponding experiment results.
Fig. 5 The schematic diagram and photographs of the layer-by-layer CMMs stacked with planar chiral structures with the structure parameters of l1 = 10 mm, l2 = 12 mm, θ = 45°, w = 0.7 mm and d = 6 mm.
Fig. 6 The simulation and experiment results of transmission coefficients of the layer-by-layer CMMs stacked with planar chiral structures for forward and backward propagations.
We should note that there exist discrepancies between experiments and simulations, we conjecture that they are mainly due to the tolerances in the fabrication and the imperfection in measurements. However, we still can get the same conclusion from simulations and experiments: the layer-by-layer CMMs stacked with planar chiral structures can exhibit both circular dichroism and circular conversion dichroism. Similarly, the co-polarized transmissions are propagation direction independent, while the cross-polarized transmissions are reversed as changing the propagation directions. The largest asymmetry ΔT is 0.21 at 6.96 GHz (experiment results in Fig. 6(d)). This magnitude is much bigger than that of each layer in this structure, and by using 2D CMMs with large ΔT, the asymmetric transmissions of layer-by-layer CMMs can be predicated to be highly improved.
Furthermore, we reconfigured the bilayered metamaterials consisting of wire dimers. One layer is arranged as the mirror image of the other. Their schematic diagram and photographs are shown in Fig. 7 . The structure parameters of wire dimers are consistent with that in Fig. 5. The results of simulations and experiments are shown in Fig. 8 . It can be seen that this structure exhibit only circular dichroism. It was because that the 2D chirality of the two layers of opposite handedness cancels, leading to absence of circular conversion dichroism in the whole structure.
Fig. 7 The schematic diagram and photographs of the layer-by-layer CMMs stacked with planar chiral structures.
Fig. 8 The simulation and experiment results of transmission coefficients of the reconfigured layer-by-layer CMMs stacked with planar chiral structures for forward and backward propagations.
Comparing the geometric features of the structures in Fig. 5(a) and Fig. 7(a), the structure in Fig. 7(a) looks the same for opposite directions of observations under the precondition of ignoring the substrates, while the structure in Fig. 5(a) doesn’t. This characteristic in geometry can be used to judge the appearance of circular conversion dichroism in layer-by-layer CMMs.
In a word, a necessary condition for the appearances of asymmetric transmissions in layer-by-layer CMMs can be concluded: by ignoring the substrate, shape features from opposite directions of observation are different. Meanwhile, like that in 2D CMMs, this effect is forbidden in isotropic chiral arrays of high symmetry such as CMMs with 4-fold rotational symmetry [7].
4. Conclusions
In this paper, we investigated the layer-by-layer CMMs using both simulations and experiments. It was found that the twisting bilayered CMMs can exhibit both circular dichroism and circular conversion dichroism, which is quite different from other 3D CMMs (e.g. helices). Particularly, for bilayered CMMs stacked with planar chiral structures, when the two layers are mirror images of each other, the structures exhibit only circular dichroism. We also proposed some necessary conditions for the appearances of asymmetric transmissions in layer-by-layer CMMs: One is that by ignoring the substrate, shape features from opposite directions of observation are different; the other is that the structure presents anisotropy. Besides, a generalized definition of 2D chirality for layer-by-layer structures is needed and expected to be proposed in further studies. In addition, the layer-by-layer CMMs can be expected to enhance the asymmetric transmissions of circular polarizations.
Acknowledgment
We acknowledge support by the Natural Science Foundation of China (NSFC) (Nos. 11104094, 61007019, and 91123035), the National Basic Research Program of China (973 Program) (No. 2011CB013003), the Fundamental Research Funds for the Central Universities (HUST: Nos. 2011TS060, and 2012QN092), the Fok Ying Tung Education Foundation (No. 132034), and the Open Fund of The State Key Laboratory of High Performance Complex Manufacturing (No. KL12-9).
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