# Chiral All-Dielectric Metasurface Based on Elliptic Resonators with Circular Dichroism Behavior

Authors: Ali Yahyaoui; Hatem Rmili
Journal: International Journal of Antennas and Propagation
 (2018)

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## Abstract

We present the design of a new microwave all-dielectric chiral metasurface with circular dichroism behavior based on elliptic dielectric resonators (EDRs). During the design procedure, we have first optimized numerically the effects of the main design parameters such as the resonator’s size and orientation, as well as the size of the slot within them, on the metasurface transmission over the frequency band 10–20 GHz. Measurements on the final metasurface prototype have shown a large circular dichroism (Δ=0.61 and Δ=0.5) over two bands (17.55–17.61 GHz and 17.91–18.05 GHz) with ellipticities close to 45° which means that the developed device can be used as a circular polarization filter and circular polarizer at microwave frequencies.


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## Body

## 1. Introduction

Metamaterials are artificially media characterized by exotic physical properties which do not exist in natural materials [1–4]. These structures are usually obtained by arranging a set of subwavelength-scattering elements in periodic structures to ensure the coupling between electric and magnetic components of the incident electromagnetic fields. This special arrangement offers to metamaterials original electromagnetic properties that can be tailored to a given application which is very useful for the design of innovative microwave devices such as cloaks, lens, absorbers, and polarizers.However, to overcome the main disadvantages of metamaterials such as high losses, bulkiness, and difficulty of fabrication, the scattering elements may be arranged in two-dimensional periodic structures, which are metasurfaces [5, 6]. These 2D version of metamaterials have permitted to control the amplitude, phase, and polarization of electromagnetic waves, giving many other potential applications such as controllable surfaces, miniaturized cavity resonators, novel wave-guiding structures, angular-independent surfaces, absorbers, biomedical devices, fast switches, and fluid-tunable frequency-agile materials [7].In addition, to further improve the performances of metasurfaces and avoid their ohmic losses, which may limit their use at higher frequencies, all-dielectric metasurfaces with low losses, high overall efficiency, and various functionalities [8–16] were developed for several microwave THz and optical applications. In all-dielectric metasurfaces, the main used scattering elements are dielectric resonators such as spheres, cubes, cylindrical/elliptical disks, and rods [7]. By using high dielectric constant dielectric resonators, we can excite both electric and magnetic resonant modes and reduce the metasurface size.On the other hand, chiral metamaterials [17, 18] have attracted much attention due to their interesting properties such as optical activity [19, 20], circular dichroism [21], and negative refractive index [20]. In these artificial media, the optical and circular dichroism properties are many orders of magnitude higher than those in natural chiral materials, whereas negative refractive index property can be achieved without combination of negative permeability and negative permittivity. In addition to these interesting properties, use of chiral metasurfaces instead of chiral metamaterials offers other original characteristics such as the asymmetric transmission of electromagnetic waves through the two opposite sides [22–24].Within this context, we propose the design of a new all-dielectric chiral metasurface with circular dichroism properties at microwave frequencies, based on elliptic dielectric resonators. Recently, we have used these resonators to design quarter-wave plate (QWP) and half-wave plate (HWP) metasurfaces operating at microwave frequencies [11, 15, 16].In this paper, we have studied numerically and experientially the electromagnetic response of an all-dielectric chiral metasurface over the band 10–20 GHz. The fabricated metasurface prototype showed large circular dichroism (Δ=0.61 and Δ=0.5) over two bands centered on 17.56 and 18 GHz, respectively, with ellipticities close to 45°, permitting it to be proposed as circular polarization filter and circular polarizer.


## 2. Theoretical Formulation of the Circular Dichroism

The circular dichroism (CD) is one main property characterizing chiral metasurfaces. This effect is due to the transmission difference, in terms of absorption and polarization state, of the metasurface when excited by incident right-hand circularly polarized (RCP) and left-hand circularly polarized (LCP) waves, respectively. The absorption (Δ) and polarization state (η) parameters are given by the following equations [25]:
(1)Δ=T++2−T−−2,η=12arcsinT++2−T−−2T++2+T−−2,where T++ and T−− are the transmitted coefficients of RCP and LCP waves, respectively.The coefficientsT++ and T−− are related to the linear transmission coefficients Txx, Txy, Tyx, and Tyy (the first and second subscripts denote transmitted and incident polarizations, resp.) through the following equation [25]:
(2)T++=12Txx+Tyy+iTxy−Tyx,T−−=12Txx+Tyy−iTxy−Tyx,where Txx=Ext/Exi, Txy=Ext/Eyi, Tyx=Eyt/Exi, and Tyy=Eyt/Eyi. For example, Exi is the x-polarized incident electric field and Eyt is the y-polarized transmitted electric field.


## 3. Metasurface Design Procedure

The all-dielectric chiral metasurface of thickness 5.12 mm is composed of two layers of EDRs of thicknessh = 2.56 mm made of Rogers RO3210 (relative permittivity 10.2, loss tangent 0.0027) as shown in Figure 1. Each layer is composed with an infinite array of connected EDRs.Figure 1
Perspective view of the all-dielectric metasurfaces with connected dielectric resonators along thex-direction.The dielectric ring resonator composing the unit cell was obtained by subtracting an elliptic volume (slot) of minor radiusas, major radius bs, and ellipticity τs = bs/as from elliptic dielectric resonators of minor radius a, major radius b, and ellipticity τ = b/a. Both the elliptic resonator and slot are concentric. The resonators composing the upper and lower layers are rotated around their z-axis with angles +ϕ and −ϕ, respectively, as shown in Figure 2, and connected along the x-direction with thin strips of length Lc = (Lx/2) − a and width W = 1.25 mm.Figure 2
CST model for the unit cell: (a) upper layer; (b) lower layer.
(a)
(b)The unit cell (Figure2) is modelled by a box of dimensions Lx × Ly × Lz (Lx = 14.9 mm, Ly = 14.9 mm, and Lz = 160 mm), where the longitudinal dimension Lz along the propagation direction z is greater than the wavelength (Lz = 16λ), and the transverse dimensions Lx and Ly along x- and y-directions, respectively, are lower than the wavelength (Lx < λ and Ly < λ), with λ = 15 mm being the free-space wavelength associated to the upper frequency of the band 10–20 GHz.We have used the electromagnetic simulator CST Microwave Studio to perform numerical simulation. The structure was excited under normal incidence with periodic boundary conditions along thex- and y-directions.We have studied the effect of the main design parameters such as the resonator ellipticityτ, the slot ellipticity τs, and the orientation of the resonators described by the azimuth angle ϕ on the metasurface properties (see Figure 3). These parameters were optimized to improve the metasurface circular dichroism by analyzing the variation of the absorption Δ and the polarization state η variation over the frequency band 10–20 GHz. The main data related to this study are regrouped in Table 1.Figure 3
Variation of the absorptionΔ and ellipticity angle η, over the frequency band 10–20 GHz, for different values of the resonator ellipticity ((a) and (b)) and orientation ((c) and (d)) and the slot ellipticity ((e) and (f)).
(a)
(b)
(c)
(d)
(e)
(f)Table 1
Main data related to the effects of the resonator ellipticity (a), orientation (b), and slot ellipticity (c), on the metasurface circular dichroism.
(a)
Resonator ellipticity,τ
1.33
1.66
2
2.33
Frequency bandwidth for |Δ| > 0.5
—
—
12.72–12.97
19.41–19.6
12.18–13.14
19.22–19.48
Bw (%)
—
—
1.9
0.9
7.5
1.3
Absorption for |Δ| > 0.5
—
—
0.52
0.73
0.9
0.76
Peak frequency,f (GHz)
—
—
12.85
19.53
12.62
19.32
Ellipticity angle,η (°)
—
—
15.42
−41
38.13
36.29
(b)
Rotation angle,ϕ
ϕ = 15°
ϕ = 25°
ϕ = 35°
ϕ = 45°
Frequency bandwidth for |Δ| > 0.5
12.05–12.82
17.2–17.63
12.18–13.14
19.22–19.48
12.59–13.21
19.42–19.66
19.83–20
Bw (%)
6.1
2.4
7.5
1.3
4.8
1.2
0.8
Absorption for |Δ| > 0.5
0.84
0.65
0.9
0.76
0.65
0.71
0.67
Peak frequency,f (GHz)
12.42
17.41
12.62
19.32
12.87
19.54
19.93
Ellipticity angle,η (°)
36.95
39.51
38.13
36.29
23.85
34.27
39.5
(c)
Slot ellipticity,τs
1.5
2
2.5
3
Frequency bandwidth for |Δ| > 0.5
14.83–15.3
15.92–17.45
15.21–15.58
16.82–18.76
15.56–15.69
17.54–18.92
16.35–16.37
18.1–18.62
Bw (%)
3.1
9.1
2.4
10.9
0.8
7.5
0.1
2.8
Absorption for |Δ| > 0.5
0.92
0.77
0.75
0.91
0.52
0.93
0.54
0.75
Peak frequency,f (GHz)
15.02
16.3
15.39
17.24
15.63
17.91
16.36
18.27
Ellipticity angle,η (°)
39.5
−44.44
33.6
−44.6
26.87
36.96
25.67
−21.1First, the effect of the resonator (without slot) ellipticity on the chiral metasurface transmission (see Figures3(a) and 3(b)) was studied by fixing the resonator minor radius a to 3 mm (λ/5) and by varying the ellipticity τ (variation of the major radius b) without affecting the cell size. The azimuth angle ϕ defining the resonator orientation was fixed to 25°. In Figures 3(a) and 3(b), we have illustrated the variation of the absorption Δ and ellipticity angle η, over the frequency band 10–20 GHz, for different values of the ellipticity τ (τ = 1.33, 1.66, 2, and 2.33), respectively.Next, we tried to ameliorate the metasurface performances (absorption, bandwidth, and polarization of transmitted waves) by taking the previous optimized configuration (τ = 2.33, ϕ = 25°) and by varying the resonators’ orientation; the resonators were rotated around their z-axis with an angle ϕ (5° < ϕ < 45°). Figures 3(c) and 3(d) show the variation of both the absorption Δ and ellipticity angle η for the rotation angles ϕ = 15°, 25°, 35°, and 45°.Finally, to further improve the metasurface properties in terms of absorption, bandwidth, and ellipticity, we have added elliptic slots of ellipticityτs to the resonators (τ = 2.33 and ϕ = 25°). Figures 3(e) and 3(f) illustrate the parametric study realized for the slot ellipticities τs = 1.5, 2, 2.5, and 3.As it can be noticed from Table1, from the four studied resonator ellipticities (τ = 1.33, 1.66, 2, and 2.33), only the values τ = 2 and 2.33 showed high absorption levels (more than 50%). The best configuration (with ϕ = 25°) corresponds to τ = 2.33 with an absorption peak of 0.9 at 12.62 GHz and ellipticity η = 38.13°.On the other hand, the rotation of the elliptic resonators without slots may not improve their performances. For the circular dichroism, the best configuration remains atϕ = 25° where absorption is high over the band 12.18–13.14 GHz with a maximum of 0.9 at 12.62 GHz. Similarly, the ellipticity (η = 38.13°) also was not improved significantly by varying the rotation angle ϕ.However, the addition of the slots has shifted all the resonating frequencies and improved the metasurface performances. For example, with a slot ellipticityτs = 2, we obtain the best metasurface operating over the frequency band 16.82–18.76 GHz (10.9%), with maximum values of absorption (Δ = 0.91) and ellipticity (−44.6°) at 17.24 GHz. Nevertheless, for the slot ellipticity τs = 2.5, we obtain stronger circular dichroism (Δ = 0.93 at 17.91 GHz) but lower values of bandwidth (7.5%) and ellipticity (η = 36.96°). We can also notice a large ellipticity (η = −44.4°) for the metasurface designed with τs = 1.5, but again, the other performances are lower (Δ = 0.77 with bandwidth equal to 9.1%).From the previous results, we can conclude that the optimized metasurface designed with resonator ellipticityτ = 2.33, and orientation ϕ = 25°, and with slots of ellipticity τs = 2 showed high circular dichroism over the wide frequency range 16.82–18.76 GHz (10.9%) with a peak of Δ = 0.91 at 17.24 GHz and a large ellipticity close to −45° (η = −44.6°), which offers to the proposed microwave device the possibility to transmit circularly polarized waves and thus the capability to work as a circular polarization filter and/or circular polarizer.


## 4. Experimental Results and Discussion

The fabricated all-dielectric metasurface of length 74.5 mm and width 74.5 mm is composed of 5 × 5-unit cells made of Rogers RO3210 as shown in Figure4(a). The total thickness of 5.12 mm was obtained by superposing 4 identical dielectric layers of thickness 1.28 mm. Each unit cell of size Lx × Ly (Lx = 14.9 mm, Ly = 14.9 mm) contains two connected dielectric resonators with slots. We have considered the metasurface configuration with optimized design parameters. Therefore, the minor and major radii of the elliptic resonator of ellipticity τ = 2.33 are a = 3 mm (≈λ/5) and b = 7 mm (≈λ/2.14), respectively, whereas the minor and major radii of the elliptic slot of ellipticity τs = 2 are as = 2 mm (≈λ/7.5) and bs = 4 mm (≈λ/3.75), respectively. The dielectric strips ensuring the connection between resonators along the x-direction are of width W = 1.25 mm (≈λ/12). The rotation angles are ϕ = −25° and ϕ = +25° for all the resonators composing the upper and lower metasurface layers, respectively.Figure 4
Photos of the realized prototype (a) and measurement setup (b).
(a)
(b)We have measured the transmission coefficients in terms of amplitude and phase by using the home-made measurement setup (developed by Dr. Christophe Caloz’s research team at the University of Montreal in Canada) shown in Figure4(b). This setup is composed with a rotating arm used to attach the exciting horn antenna, which can rotate from −90° to +90° around the center where the metasurface is placed. This arm is with sufficient length to ensure far-field measurements. On the other side of the setup, a moving scanning probe was placed to measure the transmitted power through the metasurface. The distance between the horn antenna and the device under test is chosen equal to 80 mm, to perform measurement in the far-field region.In Figure5, we have superposed moduli of both simulated and measured RCP and LCP transmitted coefficients for the realized prototype over the frequency band 10–20 GHz. As it can be remarked, the agreement between simulation and measurement is acceptable over the majority part of the band 10–20 GHz, except the frequency range 14-15.8 GHz where repetitive experiments fail to retrieve the predicted peak around 15.38 GHz. Analysis of the measured curves presented in Figure 5 shows that the RCP and LCP moduli are equal up to 14.1 GHz, whereas for higher frequencies, a visible difference between them is observed, which means that the circular dichroism of the proposed all-dielectric metasurface appears for frequencies higher than 14.1 GHz with a tendency to transmit LCP waves more than RCP ones.Figure 5
Variation of the simulated and measured RCP and LCP transmission coefficients over the frequency band 10–20 GHz.To better analyze the circular dichroism behavior, we have represented in Figure6 both simulated and measured constitutive parameters, Δ and η versus the frequency. Again, the predicted peak around 15.38 GHz is not retrieved experimentally. However, we can notice that, for an absorption difference Δ > 0.5 between measured RCP and LCP waves with ellipticity close to 45°, the metasurface presents two operating bands 17.55–17.61 GHz (0.34%) and 17.91–18.05 GHz (0.77%) with maximum absorptions Δ = 0.61 and Δ = 0.5 and the maximum of ellipticities η ≈ −44.9° and η ≈ −44.9° at the peak frequencies 17.56 and 18 GHz, respectively. However, in the simulations (see Table 1), we have obtained a unique wide band extending from 16.82 to 18.76 GHz (10.9%) with a maximum of absorption Δ = 0.91 and ellipticity η ≈ −44.6° at the resonant frequency 17.24 GHz. We estimate that the simulations are in acceptable agreement with the experiments. Finally, we can notice that the particular values (close to 45°) of the large ellipticities (η ≈ −44.9° at 17.56 GHz and η ≈ −44.9° at 18 GHz) mean that the transmitted waves through the all-dielectric metasurface are circularly polarized, which may offer to the metadevice the possibility to be used as a circular polarization filter and circular polarizer at microwave frequencies.Figure 6
Variation of the simulated and measured absorptionΔ (a) and ellipticity angle η (b) over the frequency band 10–20 GHz.
(a)
(b)


## 5. Conclusion

An all-dielectric chiral metasurface with circular dichroism behavior was designed to operate at microwave frequencies. The structure based on elliptic dielectric resonators was first optimized numerically by studying the effects of the main design parameters on its transmission within the band 10–20 GHz. The optimized design was fabricated and tested experimentally, and the measured results were compared with simulations. It is found that the fabricated prototype is characterized by a large circular dichroism over two bands with ellipticities close to 45°.



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*Source: 6352418-2018-04-19.xml*