A generalized schematic diagram of the CPC metasurface is depicted in Fig. 1(a).

Fig. 1.

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	Fig. 1. (color online) (a) Schematic diagram of the proposed metasurface. (b) Unit cell. (c) 3D schematic of the unit cell. (d) Photograph of the real fabricated metasurface sample.

It consists of a two-dimensional periodic array of metallic split-ring-resonator (SRR) unit cells inside which a square metallic loop is placed co-centrically, as shown in the unit cell depiction of Fig. 1(b). The SRRs have two equal gap slits placed in the middle of the perpendicular sides. The two-dimensional periodic array of the SRRs and loops is designed over a dielectric substrate backed by a metallic ground plane. The unit cells are repeated in the x and y directions with the same periodicity of 7 mm. A 3D schematic of the unit cell is shown in Fig. 1(c). Figure 1(d) shows a photograph of the fabricated prototype which consisted of 44 × 44 unit cells.

CPC implies that an incident x-polarized electromagnetic wave is converted into a y-polarized wave, and vice versa, upon reflection from the metasurface. The reflected field generally consists of both the x and y components, even when the incident field has only one component. The co-polarized reflection coefficients are defined as: R_xx = |E_rx|/|E_ix| and R_yy = |E_ry|/|E_iy| while the cross-polarized reflection coefficients are: R_yx = |E_ry|/|E_ix| and R_xy = |E_rx|/|E_iy|. R_yx is the reflection coefficient when the incident field E_i is x-polarized while the reflected field E_r is y-polarized, and R_xy is the reflection coefficient when the incident field is y-polarized while the reflected field is x-polarized.

The metasurface consists of a repetition of sub-wavelength unit cells which can be polarized electrically or magnetically; therefore, an arbitrary metasurface can be modeled as a surface consisting of polarizable particles or artificial atoms.^[31] Each particle can be characterized by its electric and magnetic polarizability (α_e,m). The electric and magnetic polarizability of the particles is the ratio of the electric and magnetic dipole moments to the respective local average electric and magnetic fields. The electric and magnetic dipole moments can be related to the average electric and magnetic fields via 1 where p = [p_x, p_y]^T is the electric dipole moment, m = [m_x, m_y]^T is the magnetic dipole moment, and E = [E_x, E_y]^T and H = [H_x, H_y]^T represent the average tangential electric and magnetic fields at the metasurface, respectively. The time changing electric and magnetic polarization will cause electric and magnetic surface currents on the metasurface given by 2 where J = [J_x, J_y]^T and M = [M_x, M_y]^T are the electric and magnetic surface current densities, respectively, and ω is the angular frequency of the incident electromagnetic wave. A time harmonic form of e^iωt is considered here. The electric and magnetic response determines the impedance of the metasurface given by , where η(ω) is the frequency-dependent impedance, μ(ω) and ε(ω) are the frequency-dependent magnetic and electric permittivities, respectively. The reflection coefficient at normal incidence is given by 3 where R(ω) is the frequency dependent complex reflection coefficient consisting of both real and imaginary parts, η_o is the impedance of free space and is 377 Ω. The reflection coefficient can be expressed in its magnitude and phase form as |R(ω)|e^iϕ(ω), where ϕ(ω) is the phase of the reflection coefficient which also depends upon the frequency of the incident electromagnetic wave.

Equation (3) shows that if the impedance of the metasurface in an electromagnetic spectrum is much larger than the free space impedance η_o, then the magnitude of the reflection coefficient is unity and its phase is 0°. In such an electromagnetic spectrum, the metasurface behaves as a high-impedance surface (HIS),^[32] also called an artificial magnetic conductor (AMC), which ideally reflects the electromagnetic wave with a magnitude of unity and zero phase. To understand the CPC upon reflection from the metasurface, consider a y-polarized plane electromagnetic wave incident normally on the metasurface as shown in Fig. 2.

Fig. 2.

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	Fig. 2. (color online) Incident electric field along the y-axis is decomposed into two orthogonal components along the u- and v-axes and reflected along the x-axis.

As can be seen from Fig. 2, the unit cell is anisotropic along the u- and v-axes which are at ±45° to the x- and y-axes. The unit cell also has mirror symmetry along the v-axis making the structure achiral.^[33] The incident electric field can be decomposed into u and v components and . The reflected electric field can be expressed as: where R_u = |R_u|e^iϕ_u = E_ru/E_iu and R_v = |R_v|e^iϕ_v = E_rv/E_iv are the complex reflection coefficients. If in a certain frequency range |R_u| ≈ |R_v| ≈ 1 and one component of the incident wave is reflected in phase (a phase difference of Δϕ ≈ 0°) with the component of the incident electric field along the same axis, while the other orthogonal component is reflected out of phase (Δϕ ≈ 180°) then the electric field of the reflected wave is rotated 90° with respect to the electric field of the incident wave. In other words, CPC is achieved and the incident y-polarized wave is reflected as the x-polarized wave as shown in Fig. 2.

The metasurface shown in Fig. 1 was demonstrated with electromagnetic modeling and full-wave numerical simulations using Ansys HFSS. The optimized physical dimensions (in millimeters) of the final design are: w = 7, L = 6, s = 1, p = 0.5, d = 1, m = 3, and h = 2.4. The dielectric substrate was FR4 with a relative permittivity of 4.4 and loss tangent of 0.02. Copper with a conductivity of 5.8 × 10⁷ S/m was used for the SRRs and metallic ground plane.

The co- and cross-polarized reflection coefficients under normal incidence when the incident wave was x-polarized (TM polarization) are shown in Fig. 3(a). As can be seen from Fig. 3(a), resonances occurr at 5.4, 7.6, and 12.4 GHz, where the cross-polarized reflection approaches 0 dB (unity magnitude) while the co-polarized reflection coefficient reaches to a minimum value of −27 dB. Therefore, at resonance frequencies, an incident x-polarized wave is completely converted into a y-polarized wave upon reflection from the metasurface.

Fig. 3.

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	Fig. 3. (color online) Co- and cross-polarized reflection coefficients when the incident field is (a) x-polarized and (b) y-polarized.

Figure 3(b) shows the co- and cross-polarized reflection coefficients for normal incidence when the incident field is y-polarized (TE polarization). Similar to the case of the x-polarized waves, the co-polarized reflection is minimized to −18, −26, and −28 dB at the three resonances 5.4, 7.6, and 12.4 GHz, respectively, while the cross-polarized reflection approaches 0 dB. It can be seen from Figs. 3(a) and 3(b) that the cross-polarized reflection coefficient is larger than −3 dB over a wide frequency range 5–15 GHz leading to a fractional bandwidth of 100%. It is also clear from Fig. 3 that the response of the metasurface is the same for both the x- and y-polarized waves. Both of these polarizations are converted into their respective cross-polarized waves in a similar fashion. Moreover, the resonances are achieved at the same three distinct frequencies for both polarizations. This same polarization conversion behavior for both the x- and y-polarization results from the mirror symmetry of the unit cell along the v-axis, in which the structure appears the same to both the x- and y-polarizations (both of these encounter the split-bearing and no-split sides of the SRR).

In order for the CPC metasurface to be useful in a variety of applications, the response of the metasurface must be stable against variations in the incidence angle. A metasurface based on a relatively thin dielectric substrate has a higher angular stability compared with one employing a thick substrate, however, thin substrates result in a narrower bandwidth.^[34,35] Dielectric substrates with large dielectric constants can be used to enhance angular stability, however, this also reduces the bandwidth.^[34,35] A possible way to achieve both broad bandwidth and an angularly stable response is to design a unit cell with a sub-wavelength size and unique structural configuration so that it can produce multiple plasmonic resonances. The co- and cross-polarized reflection coefficients for different incidence angles when the incident field is x-polarized (TM polarization are shown in Figs. 4(a) and 4(b). As it can be seen from Fig. 4(b), the cross-polarized reflection is quite stable against variations in the incidence angle. The incidence angles had little effect on both the performance and bandwidth of the metasurface. The co- and cross-polarized reflection coefficients when the incident wave is y-polarized (TE polarization) for different incidence angles, are presented in Figs. 4(c) and 4(d), respectively. As the incident waves are transverse magnetic (TM) polarized, the small variations in the cross-polarized reflection are due to the electric field which started passing into the SRR and loop at large incidence angles and disturbes the current flow. However, these variations remain in an acceptable range due to the surface currents on the SRR and the loop which counteract against the effects induced by the oblique incidence, and hence stabilized the response. Generally, the stability of the response of the metasurface against variations in the incidence angle results from the unique optimized design of the unit cell, thin dielectric substrate (0.12λ at 15 GHz), and sub-wavelength unit cell size which are 0.11λ at 5 GHz and 0.35λ at 15 GHz. As in most applications, the incoming wave can have any arbitrary incidence angle; therefore, the incidence angle insensitivity makes the proposed metasurface a potential candidate for many practical applications.

Fig. 4.

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	Fig. 4. (color online) Reflection coefficient when the incident and reflected fields are y-polarized: (a) Co-polarized and (b) cross-polarized.

To understand the physical mechanism responsible for the CPC, the proposed design is analyzed under u and v polarizations to study the magnitude and phase of the reflection coefficient, as well as surface current distribution. The magnitude and phase of the reflection coefficient for the u and v-polarized waves are shown in Figs. 5(a) and 5(b) respectively. As it can be seen from Fig. 5(a), the magnitude of the reflection coefficient both for the u- and v-polarized waves is greater than ȡ2.2 dB, while the phase difference between the u- and v-polarized reflected fields is 180° within the operating frequency band 5–15 GHz. Owing to the phase difference of 180° between the u and v components of the reflected electric field, an incident x-polarized wave is reflected as a y-polarized wave and vice versa (the principle is already explained using Fig. 2).

Fig. 5.

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	Fig. 5. (color online) Reflection coefficients: (a) magnitude and (b) phase, for u and v-polarized waves.

It is clear from Fig. 5 that the two resonances (dips in the reflection coefficient magnitude) occurring at 5.4 GHz and 12.4 GHz are due to the u-polarized incident wave, while the third resonance occurring at 7.6 GHz is due to the v-polarized incident wave. At resonance frequencies, the structure behave as an HIS for one component and a perfect electric conductor (PEC) for the other. The structural anisotropy along the u- and v-axes is an essential part of the design as it helps to provide a different electromagnetic response to the u- and v-polarized incident electric fields at the same frequency. The physical mechanism responsible for the CPC can be further understood by considering the surface current distribution on the top and bottom metallic surfaces for both the u- and v-polarized incident waves, as shown in Fig. 6. It is well known that, according to Faraday’s law, a time changing magnetic field sandwiched between the two metals produces surface currents on the top and bottom metallic layers in opposite directions. As depicted in Fig. 6, the net current on the top and bottom layers (the ground plane) are directed in opposite directions at resonance frequencies. The vector sum of the currents is represented by the large black arrow and symbol J in Fig. 6. These oppositely directed currents on the top and bottom layers lead to a large value of magnetization producing high values for the anisotropic permeabilities and . Owing to the large impedance , the surface behaved as an HIS at 5.4 and 12.4 GHz for the u-component of the electric field. Conversely, it acts as a normal electric conductor for the v-component at these frequencies. Similarly, the structure obtains magnetic resonance (large ) at 7.6 GHz only for the v-component of the incident electric field, behaving as a simple metallic reflector for the u-component.

Fig. 6.

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	Fig. 6. (color online) Surface current distribution at resonant eigen-modes: 5.4 GHz ((a), (b)), 7.6 GHz ((c), (d)), 12.4 GHz ((e), (f)), on the top layer ((a), (c), (e)), and on ground plane ((b), (d), (f)).

At all three resonances, the metasurface acts as an HIS (reflecting with a 0° phase) for one component and as a normal metallic reflector (reflecting with a 180° phase) for the other, producing a 180° phase difference between the reflected field components leading to CPC.

Parametric analysis was carried out to investigate the effect of the geometrical dimensions on the response of the metasurface. Figure 7(a) presents the effect of varying the substrate thickness on the cross-polarized reflection coefficient. As it can be seen from Fig. 7(a), the cross-polarized reflection coefficient is small when the dielectric thickness is small. Furthermore, the bandwidth is also small for a small dielectric thickness. It can also be inferred from Fig. 7(a) that the optimum value for the substrate thickness is 2.4 mm.

Fig. 7.

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	Fig. 7. (color online) Variation of the cross-polarized reflection coefficient when the (a) substrate thickness (h in mm) is varied and (b) geometrical dimensions in the xy-plane are scaled with a fixed substrate thickness of 2.4 mm.

The effect of changing the dimensions of the unit cell in the xy-plane on the cross-polarized reflection coefficient is also presented in Fig. 7(b). The geometrical dimensions of the unit cell are changed by scaling them in the xy-plane and keeping the substrate thickness fixed at 2.4 mm. All lengths and widths of the different parts of the unit cell in the xy-plane (given in section C) are halved, due to the scaling by 0.5. It can be seen from Fig. 7(b) that the response of the metasurface is shifted towards higher frequencies (blue shift) when the dimensions of the unit cell are reduced. Similarly, when the dimensions of the unit cell are increased by scaling with a number greater than one, the response is shifted towards lower frequencies (red shift). It is important to note that the periodicity of the unit cell must be far less than the operating wavelength to produce only specular reflections and avoid the scattering lobes. The ability to shift the response of the metasurface towards lower or higher frequencies by properly scaling the unit cell makes the proposed design a potential candidate for numerous applications in different frequency regimes.