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Department of Electrical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen, 40002, Thailand

Author to whom correspondence should be addressed: nantakan@kku.ac.th

Chirality Control in Metamaterials by Geometrical Manipulation

W. Panpradit 1 , A. Sonsilphong 1 and N. Wongkasem1,2

Abstract- Chirality index of chiral structures can be controlled by adjusting the structure geometry. Bi-layer structures are modified to break symmetry of the structure pair, aiming to generate cross coupling terms between electric and magnetic fields. As the bi-layer structures are twisted, in both normal and mirror orientations, chirality index can be then generated, while the number of axes and the angle between the main axis and the connected arm also play a significant role. The most interesting case is the non twisted mirror bi-layer where the resonance indices are envisioned. The results have shown several possibilities of effectively controlling chirality index in metamaterial structures, which will be beneficial in wave controlling devices.

1 INTRODUCTION

As any arbitrary electromagnetic wave propagates through lossy chiral materials, the wave splits into two waves with different phase velocities. These two waves travel with opposite polarized rotation, defined by left- and right- circular polarization, respectively. This effect is referred to as optical activity, or optical rotary dispersion (ORD).Furthermore, due to circular dischroism (CD), the two eigenwaves will experience an unequal attenuation, resulting in a change of wave ellipticity. These two unique features in chiral material are beneficial to optoelectronic devices, especially for polarization control and splitting light applications [1].

Chirality( ) is found in bi-isotropic and bi-anisotropic materials in the cross-polarization or magnetoelectriccoupling terms, and [2]. In connection with negative index metamaterials [3-4], artificial chiral structures such as helices [5], Gammadion [6], Y structure [7], chiral SRR [8-10], [11], Cross-wire [12], and Rosette [13-14], have been designed to generate chirality in both microwave frequencies and optical regimes [15].

This paper discusses how to geometrically manipulate the chirality index in chiral metamaterial structures by focusing on structures, the chiral structures with supplementary geometrical parameters. Based on their well adjustable orientation, e.g., number of axes, number of arms, different angles, etc., structures, - , shown in figure 1, are selected to observe the chirality index( ).Transmission properties are obtained by CST Microwave Studio® and then are used to extract [13] the chirality index.

2 CHIRALITY CONTROL IN CN STRUCTURES

(a) (b)

(c) (d)

(e) (f)

Figure 1: structures: (a-f) - structures

Figure 1 (a) presents the structure with its dimensions, which can also apply to other structures. H1 and H2, respectively, are the main axis and the arm of the structure. w is the linewidth (of all lines), A° is the angle between the main axis, H1, and the connected arm, H2, and B° is the angle between the two adjacent main axes.

To study how the geometry can direct chirality index of structures, four different bi-layer formats, shown in

figure 2 (a-d) are observed. Case A presents two identical structures (bi-structure), fabricated on each side of a substrate (with the thickness s). The two structures are located on top of each other, with the substrate inserted in between. On the other hand, the two structures are twisted with an angle in Case B. Case C, shown in figure 2(c), also presents the twisted structures with an angle

but the arms of each structure lay in oppositedirection. Here, we call it “the mirror” twist. Last, in Case D(figure 2(d)), the two structures with opposite arms are

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placed on top of each other; however, there is no twisted angle. These bi-layer structures in all cases are set using a periodic boundary (or a unit cell in CST simulations).Propagation direction, k, electric field, E, and magnetic field, H, are referenced in figure 2(a).

A double copper-clad Arlon Di 880 (lossy) board is used as a substrate in all studies. The dielectric constant , of the substrate board is 2.2. The dimension parameters are given as follows: = = 5.5 mm, H1/H2 = 2, H1 = 5 mm, H2 = 2.5 mm, w = 0.4 mm, s = 0.254 mm, A = 60° andB = . The copper thickness, mt , is 0.03 mm. These

parameters will be used in all simulations.

(a)(b)

(c) (d)

Figure 2: Four different cases used to observed chirality index of structures: (a) Case A: non-twisted structure ( 0 ) with

the same arm orientation, (b) Case B: twisted structure ( 15 )

with the same arm orientation, (c) Case C: twisted structure with the opposite arm orientation and (d) Case D: non-twisted structure with the opposite arm orientation.

Case A: This is the simplest model, where the structures are not twisted; therefore the angle = 0 . The two structures are set with the same arm orientation. The example of structure is illustrated in Figure 2(a). Since the two structures of this bi-layer case are identical, there is no inductive coupling [14, 16] so that chirality index is zero.This is true for all structures, - . Case B: The orientation of this bi-layer structure is similar to Case A, except that the top structure is twisted (normal twist) with an angle 15 . Case B is a usual method to create κ in bi-layer structures [12-14]. Chirality index(κ) of

- structures from Case B is shown in Fig. 3. The

chirality resonances of all structures are located in the same region, where a peak of the index of structureswith more arms is generated at a lower frequency. The indices of - structures are quite high, in the range of (-)25 to (+)35.

Figure 3: Chirality indices (κ) of - structures from Case B.

Case C: In this case, the bi-layer structure is also twistedwith the angle 15 , but the two structures are set with opposite arm orientation (mirror twist). Here, the chirality value increases when more arms are added, as shown in Fig. 4. Note that the indices of - structures are quite small, in the range of (-)6.5 to (+)6.5.

Figure 4: Chirality indices (κ) of - structures from Case

C.

Case D: The opposite arm orientation is still maintained in Case D but the structures are not twisted, i.e. = 0 .Similar to case C, the index increases as more arms are added, as shown in Fig. 5. Nevertheless, unlike other cases, the dominant (or first) resonance index of each structure is not located in the same frequency range. The indices of

bi-layer structures with more arms appear at lower frequencies, i.e. 7.13 GHz, 7.78 GHz, 8.80 GHz, 9.23 GHz, 9.24 GHz and 9.40 GHz for to , respectively. It is important to state that a mirror resonance (or the second) index peak of the structures with less arms is located closer to the first resonance, e.g., the 1st and 2nd peak of

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structure are at 9.24 GHz and 9.73 GHz. The summary of the resonance locations is presented in Table 1.

Figure 5: Chirality indices (κ) of - structures from Case

D.

Table 1. Summary of chirality indices resonance location of - structures of Case D within 6-12 GHz frequency

range. Structure 1st Index

Resonance (GHz)

2nd Index Resonance

(GHz)

Bandwidth between the Resonances

(GHz)9.40 9.54 0.149.24 9.73 0.499.23 9.77 0.548.80 9.74 0.947.78 10.27 2.497.13 10.34 3.21

The chirality index found in Cases B, C and D are due to the asymmetric geometry of the pairs (bi-layer), causing the cross coupling terms between electric and magnetic field [8, 12, 17] occurrence within chiral resonance regimes.

The angle (A°) between the main axis and the connected arm also plays a significant role in controlling the chirality index of structures [11]. Since the index of structure does not fluctuate with the orientation, the structure is selected to observe the index trend when the angle A for Cases B, C and D is varied in 6 different values: 15°, 30°, 45°, 60°, 75° and 90°.

(a)

(b)

(c)

Figure 6: Chirality index(κ) of structure from (a) Case B, (b) Case C and (c) Case D, where the angle A between the main axis

and the arm is varied.

Fig.6 (a-c) illustrates chirality indices for Case B, C and D of the bi-layer structure, where the six angles are varied. For Case B, there is no chirality in the resonance interval, if the angle A° is small (15° and 30°). The chirality of the structures with A=75° and A=90° peaks at 8.23 GHz and 8.77 GHz, respectively. The chirality of with A=90°is quite broad. The bandwidth between the two resonances is 0.54 GHz. In Case C, the structure with A=30°, A=60°, and A=75° generate similar chirality shape, except

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that appear at a different location. The chirality from A=45°and A=90° shows more resonances but smaller values. Last, in Case D, as the angle is adjusted, the bandwidth between the two resonances is varied. With larger angle (A=60° andA=90°), the interval becomes narrower. However, if the angle is smaller, there are more index resonances in the same observated frequency range.

3 DISCUSSION AND CONCLUSIONS

It is shown that chirality index of bi-layer chiral structures can be controlled by adjusting the structure geometry. Three of four orientations are proved to have a chirality index. All

structures with normal or conventional twist (Case B) can create chirality indices. However, as the two bi-layer arms lay in opposite direction (Case C), only structures with more arms can generate a significant index value. The most interesting results come from Case D, where the two bi-layer structures are not twisted. There are two index resonances within the given frequency range. These two resonances can be controlled by the number of arms i.e. 1) the indices of the structures with more arms appear at lower frequency, and 2) a mirror or the second index peak of the structures with less arms is located closer to the first resonance.

We have also studied the effect of an angle between the main axis and the connected arm on chirality index. The structure was selected for a case study. We have found that in Case B, there is no chirality in the observed resonance interval, if the angle A° is small. In Case C, the some angles’ indices are similar in shape, but appear at different location. Finally, in Case D, the index is more predictable. The first index resonances are likely in the same interval, but the second peaks are varied, depending on the number of arms. There are at least two index peaks in our range of interest.

Based on all results, we can conclude that chirality in chiral bi-layer structures can be optimized by manipulating the structure geometry. Three orientations are our preferred choices to control the index; yet, the mirror twist or Case D provides the best controllable tool, for both number of arms, and angle manipulation. We recommend this orientation in order to effectively design chirality index from any bi-layer chiral structures.

Acknowledgments

This project is financially supported by the Industry/University Cooperative Research Center (I/UCRC) in HDD Component, Faculty of Engineering, Khon Kaen University, Thailand, and National Electronics and Computer Technology Center, National Science and Technology Development Agency (CPN-R&D 01-10-53IF). We also wish to thank TRIDI, the Telecommunications Research and Industrial Development Institute for funding the Optical and Wireless Communications Research

Laboratory, particularly for the CST Microwave Studio® software used in the simulations (TARG 2553/001).

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