Transmission control of electromagnetic waves by using quarter-wave plate and half-wave plate all-dielectric metasurfaces based on elliptic dielectric resonators

. We present the design of all-dielectric Quarter-Wave Plate (QWP) and Half-Wave Plate (HWP) metasurfaces based on elliptic dielectric resonators (EDRs) for the transmission control of electromagnetic waves over the frequency band 20–30GHz. First, an extensive numerical analysis was realized by studying the effect of the resonators geometry (thickness and ellipticity) on the transmission of both 𝑥 - and 𝑦 -polarized waves. Then, based on the numerical analysis, we have realized and characterized experimentally both QWP and HWP all-dielectric metasurfaces.


Introduction
Metamaterials are artificial structures typically engineered by arranging a set of scattering elements in a regular pattern throughout a volumetric region of space.This arrangement allows for desirable bulk electromagnetic responses that are typically not found naturally.The extraordinary metamaterial control of electromagnetic waves is due to the possibility of engineering effective negative refractive index, near-zero index, cloaking materials, and so forth.Over the past several years, metamaterials have evolved from a theoretical concept to a mature and groundbreaking technology with real-world applications [1][2][3][4][5].However, three-dimensional metamaterials suffer from major issues, such as high losses, bulkiness, and difficulty of fabrication.Most of these disadvantages may be eliminated by reducing their dimensionality by arranging electrically small scattering elements into a two-dimensional pattern at a surface or interface.This two-dimensional version of a metamaterial has been given the name metasurface [6,7].For many applications, metasurfacescanbeusedinplaceofmetamaterialswiththe advantageoftakinguplessphysicalspaceandhavinglower losses.
When the electric and magnetic resonance frequencies of the dielectric resonators are different, the phase variation of the transmission coefficient is limited to ,whereasthisvalue can reach 2 by superposition of both resonances at the same frequency [8].
Metasurfaces have a wide range of potential applications in electromagnetics including, but not limited to, controllable surfaces, miniaturized cavity resonators, novel waveguiding structures, angular-independent surfaces, absorbers, biomedical devices, fast switches, and fluid-tunable frequency-agile materials.Recently, several experimental research works have been published on the realization of metasurfaces with such novel functionalities [9].

International Journal of Antennas and Propagation
The spatial distribution of the subwavelength elements composing the metasurface acts on the incident wave in terms of amplitude, phase, and polarization, which may affect its electromagnetic response, and offers the possibility of obtaining specific functionalities.
However, the majority of metasurfaces were designed by using metallic elements with Ohmic losses, which may limit their performances especially at optical frequencies.In order to overcome these limitations, all-dielectric metasurfaces have attracted particular interest recently; and some successful designs with low-losses, high overall efficiency, and various functionalities [10][11][12][13][14][15] were obtained in microwave and optical frequencies.
Dielectric resonators are the main structure used in alldielectric metasurfaces because they can excite both electric and magnetic resonant modes, in addition to the possibility of reducing the size by using high dielectric constant   .Several resonators shapes such as spheres, cubes, cylindrical/elliptical disks, and rods were investigated in order to design alldielectric metasurfaces especially at THz and optical frequencies [12][13][14][15].
Therefore, in all-dielectric metasurfaces based on dielectric resonators, the geometrical parameters of the resonators and the spacing between them are the main factors affecting the phase variation as well as the metasurface performances [16][17][18].
Recently, we are interested in the design of all-dielectric metasurfaces based on EDRs operating at microwave frequencies.The main design parameters of these resonators are their ellipticity, orientation, and thickness.In the first study [18], we have investigated numerically the effect of the resonators ellipticity and orientation on the metasurface transmission.In this paper, we propose a complementary study to first determine numerically, by using the Ansys-HFSS software, the effect of the resonators thickness.Then, we realize and characterize experimentally the optimized prototypes of the QWP and HWP metasurfaces.

Metasurface Design
The proposed all-dielectric metasurface consists of an infinite two-dimensional array of connected EDRs, as shown in Figure 1(a), made of dielectric (Rogers RO3210) of relative permittivity 10.2, loss tangent 0.003, and thickness ℎ.
The minor (along ) and major radii (along )oftheEDR are denoted as  and , respectively, whereas its ellipticity is  = /.Th es i z eo ft h eu n i tc e l li s  ×  ×  .I nt h i s regard,   =9 .9m m(   < ),   =9 .9m m(   < ), and   =16,where = 10 mm is the wavelength associated with the upper frequency limit 30 GHz, and the longitudinal dimension   is great compared to the wavelength  (  = 160 mm).The resonators are connected along -direction with thin connection of length   =(   /2) −  and width   = 1.25 mm.We have excited the structure with normal incidence (Floquet ports) along -direction.
The ellipticity of the resonator was studied by varying the ratio  of EDRs while fixing the minor radius at  =2m m (/5), without affecting the cell size ( isboundedwithinthe ranges: 1 ≤≤2.47with a step of 0.01).Finally, the height ℎ of both the EDRs and the connections is varied from 0.64 to 2.56 mm with a step of 0.64 mm.

Simulated Results
The simulation of the metasurface was performed by using the commercial software Ansys-HFSS.In Figure 1(b), we present the simulation model where the unit cell boundary condition was used along -and-directions.The model is excited under normal incidence with Floquet ports along direction in the frequency range 20-30 GHz.
In order to study the transmission of the designed alldielectric metasurface, we have analyzed its response when excited under normal incidence with two orthogonal polarization parallel to -and-axes as shown in Figure 1(a).
We define then the module transmission ratio of -and-linear polarization of the electric field, respectively, and Δ =   −  as the phase difference between the -a n d-components of the transmitted electromagnetic fields.Consequently, the moduli   and   will vary from 0 to 1, and the phase difference Δ varies from −360 ∘ to +360 ∘ .Th eQ W Pa n d HWP metasurfaces are obtained when the moduli are equal (  =  ) and the phase difference is Δ = ±90 ∘ and ±180 ∘ , respectively.
3.1.Effect of the Resonator Geometry.We have investigated the effect of the main design parameters affecting the transmission of the all-dielectric metasurface, in particular the resonators thickness ℎ,s i z e ,a n ds h a p e( e l l i p t i c i t y).The effect of the resonator size on the metasurface transmission was studied mainly by varying the EDR major axis .Results for radius  = /5 are illustrated in Figure 2. The effect of the EDR ellipticity on the metasurface transmission was analyzed from moduli (  and   ), phases (  and   ), the ratio between moduli (we take log(  /  ) for better visualization), and the phase shift Δ, for four considered resonator thicknesses ℎ 1 = 0.64 mm, ℎ 2 = 1.28 mm, ℎ 3 = 1.92 mm, and ℎ 4 = 2.56 mm.In Figure 2, we have studied, over the frequency band 20-30 GHz, the effect of the resonator ellipticity  and thickness ℎ, on the metasurface transmission.We can remark easily that the exciting frequency and the resonators geometry (ellipticity and thickness) affect deeply the metasurface transmission behavior.We can notice also that ellipticity of the resonators affects more moduli and phases of -polarized incident waves (  )th a n-polarized waves (  )d u et oth e orientation of the resonators along the -axis.
However, by analysis of colors distribution in Figure 2(a), wecannotethattheredcolor ,whichrepresentshightransmission moduli (  and   ), is more dominant in graphs corresponding to metasurfaces excited with -polarized waves.This result can be explained by the connection extension along the -axis which reduces slightly the transmission along this direction.
From Figure 2(b), we can notice the equality between moduli represented with green color.
On the other hand, we can note that the phases   and   (Figure 2(c)) as well as the phase shift Δ (Figure 2(d)) variations are increased for higher values of the metasurface thickness ℎ, which means that the phase difference Δ spans a wider range of values for thick metasurfaces.
3.2.Application: QWP and HWP Metasurfaces.In order, to design all-dielectric QWP and HWP metasurfaces, we have considered the previous results of the parametric study (Section 3.1).Both of QWP and HWP metasurfaces require high transmission and particular phase shift (|Δ| =9 0 ∘ for QWP and |Δ| =1 8 0 ∘ f o rH W P ) .I nT a b l e1 ,w eh a v e regrouped main data, deduced from Figure 2, related to the design of QWP and HWP devices.For each metasurface of thickness ℎ (0.64 mm, 1.28 mm, 1.92 mm, and 2.56 mm), we have presented the bandwidths (column 2) associated with QWP and HWP metasurfaces where the transmissions moduli   and   (columns 3 and 4) are considered to be greater than 0.7 and the phase shift is |Δ| =90 ∘ ± 5 ∘ for QWP (column 5) and |Δ| =180 ∘ ± 5 ∘ for HWP (column 6); these results are obtained for ellipticity ranges given in column 7.
F romT able1,wecandeducetha tthetransmissionlevel of the -and-polarization (  and   )isincreasedwith the thickness ℎ;c a s e s( w h e r em o d u l i> 0.9) are obtained with the thickness 2.56 mm.We can note also that, except for the thickness 1.28 mm, we can design QWP and HWP metasurfaces with good performances; however, only the thickness 2.56 mm allows us to design both QWP and HWP operating in different frequency ranges.

Experimental Validation
Two metasurface prototypes, each one composed of 7 × 7 cells, were fabricated with Rogers RO3210 substrates of thickness ℎ =2 .5 6m m( ≈/3.8),relative permittivity   = 10.2, and loss tangent tan  = 0.0027.The total thickness 2.56 mm was obtained by superposition of 4 identical layers, each one of thickness 0.64 mm.The unit cell size is 9.9 mm (≈).The dielectric connections are oriented along -direction as illustrated in Figure 3.The two devices were characterized by measuring their -and-polarized transmission coefficients in an anechoic room over the frequency band 20-30 GHz.
We have regrouped in Table 2 both simulated and measured results for the designed QWP and HWP metasurfaces.We can notice, from these results, that we have good agreement between simulation and measurement in terms of moduli and phase difference of the transmitted power, with a certain frequency shift attributed mainly to fabrication imperfections and error measurements.
We can notice, from Figure 4, that, at the frequency of 28.2 GHz, both -a n d-polarized transmission moduli are equal (≈−1.5 dB, which correspond to 70% of the transmitted power), whereas the phase difference is close to 90 ∘ .Therefore, the designed QWP metasurface acts as a polarization converter at 28.2 GHz and permits converting linear to circular polarization.
The second metasurface presented in Figure 3(b) is a HWP device designed to transmit both -polarization and -polarization with equal moduli and phase shift difference |Δ| ≈ 180 ∘ .With minor radius,  =2m m( ≈/5), and major radius  =2.26mm(≈/4.4),the resonators ellipticity  is 1.13 (≈/8.7).Observing the transmitted power over the frequency band 21-28 GHz (see Figure 5) shows that the two transmission curves, corresponding to -and-polarization, overlap at the frequency 21.9 GHz with a transmission level close to −2.2 dB (which correspond to 60% of the transmitted power) and a phase difference of 180 ∘ .Therefore, at 21.9 GHz, the proposed HWP metasurface can change the handedness of circularly polarized wave or rotates a linear polarization by 90 ∘ .
We can explain the behavior difference between the two transmitted coefficients (  and   )b yt h ee ff e c to ft h e asymmetric geometry of the elliptic resonators and with the nonnegligible effect of the connections.The operation bandwidths deduced from measured values extend from 25.9 GHz to 28.68 for the QWP metasurface, from 21.78 GHz to 22.15 GHz, and from 23 GHz to 23.12 GHz for the HWP metasurface.Due to losses in the structure, we have considered limits for the -a nd-transmissions coefficients modulus and phases less restrictive than simulated o n e s .W ee s t i m a t et h a tt h eo b t a i n e dt r a n s m i s s i o nl e v e l sa r e still acceptable for operation of the structure as QWP/HWP in the mentioned bands above.
Note that the transmission coefficients presented in F i g u r e s4a n d5h a v eb e e nn o r m a l i z e dw i t hr e s p e c tt ot h e exciting horn antenna reference transmission coefficients in the presented band.

Conclusion
In this paper, we have investigated numerically and experimentally the design of all-dielectric QWP and HWP metasurface operating in the microwave band 20-30 GHz.First, we have studied the effect of the resonators thickness and ellipticity on the transmission.Then we have realized the structures and measured their transmissions for both and -polarized incident waves.Good agreement is obtained between simulation and measurement.It is found that the realized QWP and HWP metasurfaces operate at the frequencies 28.2 GHz and 21.9 GHz, respectively, with transmission rates of 70% and 60% of the incident power, respectively.

Figure 1 :
Figure 1: Schema of the proposed all-dielectric metasurface: (a) 2D connected EDR array with -and-polarization of the electric field and (b) HFSS-model for the unit cell.

Table 2 :
Simulated and experimental results for the designed QWP and HWP metasurface.