Dual-band Circular Polarizer Based on Simultaneous Anisotropy and Chirality in Planar Metamaterial

Metamaterial of dual-square array is proposed to design a dual-band circular polarizer. The novel design of asymmetric unit cell and layout of duplicate arrays significantly enhances the coupling between electric and magnetic fields. Simulation and measurement results show that the polarizer presents wide angle circular dichroism and circular birefringence. Moreover, the polarization conversion of the proposed metamaterial changes with frequency, incident angle, and polarization of incident waves. The fundamental mechanism behind is concluded to be the angle-dependent chirality and dispersion of our novel design.


Design Principle
Inspired by the original multiband chiral metamaterial of twisted arc structure 24 , a dual-band circular polarizer with two aligned identical square arrays of periodicity p separated by a dielectric slab of thickness h is proposed in this paper. Two aligned unit cells of the arrays are shown in Fig. 1 while the configuration of arrays is shown in Fig. 2. In each unit cell, a centered PEC circle of radius R and width w is broken into two arcs at angle φ 1 with an angle gap φ 2 .
The novel metamaterial highly asymmetric that results in is strong chirality. In addition, it is well known that helical-or spiral-like structure in most prominent metamaterial-based polarizers leads to the coupling of magnetic and electric field which is one of the fundamental mechanisms behind the circular dichroism and circular birefringence. To enhance the coupling, two aligned identical square arrays have been used. Consequently, circular dichroism and circular birefringence is achieved, as confirmed by numerical simulation and experiments.     The commercial software CST microwave studio is used to simulate the linear polarization transmission matrix τ of the metamaterial.
is the incident plane wave, k k k k sin cos x sin k , , The corresponding circularly polarized transmitted wave is where the subscripts + and − denote right-and left-handed circularly polarized waves respectively.

Measurements and Discussions
The dual-band circular polarizer has been fabricated as shown in Fig. 3. The two 25 × 25 square arrays of periodicity p = 13 mm are separated by a Rogers 5880 (relative permittivity 2 2 r ε = . and loss tangent tanδ = 0.0009) slab of thickness h = 1.524 mm. R = 5 mm, w = 0.5 mm, φ 1 = 10°, φ 2 = 40°. The experimental setup is shown in Fig. 4. The polarization transformation coefficient matrix τ of the fabricated polarizer has also been measured. The corresponding polarization transformation coefficient matrix T is subsequently obtained according to Eq. (2).
The simulated and measured transformation coefficients of the polarizer illuminated by ˆφ y( )-polarized incident wave of θ i = 50° and ϕ i = 0° is show in Fig. 5(a),(b). Simulation and measurement agree fairly well. Two resonant frequencies at 7.68 GHz and 8.82 GHz are observed in Fig. 5(a). The transmitted field at 7.68 GHz is LCP and RCP at 8.82 GHz which is evident from the large difference between − E t and + E t . LCP wave is observed at The simulated and measured transformation coefficients of the polarizer illuminated by φŷ( )-polarized incident wave of θ i = 50° and ϕ i = 180° is show in Fig. 5(c),(d). The same resonant frequencies as Fig. 5(a) are present in Fig. 5(c). Both of these two resonant frequencies are also slightly shift by about 0.1 GHz in Fig. 5(d). Unlike the case in Fig. 5(a),(b), at both resonant frequencies, the transmitted field in Fig. 5(c),(d) is all LCP. Although only circular dichroism can be confirmed at lower resonant frequency, both circular dichroism and circular birefringence are presented at higher frequency. This proves that our novel metamaterial is dispersive and chiral. Moreover the chirality is angle-dependent.
The surface current distributions at these two resonant frequencies are drawn in Fig. 6 to have a deeper understanding of the mechanism behind the observed circular dichroism and circular birefringence. As shown in Fig. 6(a),(c), at 7.68 GHz regardless of the incident azimuthal angle ϕ i , currents in the two arcs in each unit cell flow opposite to each other, while currents in the aligned arcs in the top and bottom arrays flow in the same direction. Therefore, there is no current loop in any unit cells. There is no current loop between the top and bottom arrays either. On the contrary as shown in Fig. 6(b),(d) at 8.82 GHz, currents in the two arcs in each and every unit cell form a loop. Current loops are also formed between the top and bottom arrays. In addition, the rotation of the current loops at ϕ i = 0° are opposite to the corresponding current loops at ϕ i = 180°.
Obviously, electric field couples differently with magnetic field in different frequencies and incident angles. For example, in Fig. 6(b), the induced magnetic field has a y-component that opposes the incident electric field, producing cross coupling between electric and magnetic fields in the metamaterial accordingly. However, in Fig. 6(d), the induced magnetic field has a y-component that coincides with the incident electric field. The The simulated and measured transformation coefficients of the polarizer illuminated by θˆ-polarized incident wave of θ i = 50° and ϕ i = 0° is show in Fig. 7(a),(b). Likewise the simulation and measurement agree fairly well. Three resonant frequencies at 7.63 GHz, 9.00 GHz, and 9.58 GHz are observed in Fig. 7(a). The transformed field at 9.0 GHz is LCP, while are RCP at 7.63 GHz and 9.58 GHz. It can be seen that transmitted wave is RCP at 7.80 GHz and 9.29 GHz, and LCP at 9.00 GHz in Fig. 7(b). All of these three resonant frequencies are shifted lower by about 0.3 GHz.
The simulated and measured transformation coefficients of the polarizer illuminated by θˆ-polarized incident wave of θ i = 50° and ϕ i = 180° is show in Fig. 7(c),(d). The structure also resonates at three frequencies, 7.63 GHz, 8.85 GHz, and 9.12 GHz by simulation, while 7.75 GHz, 8.96 GHz and 9.24 GHz by measurement. The difference between T θ − and θ + T at the highest resonant frequency is relatively smaller that no further discussion is made at this frequency. By comparing Fig. 7(a),(b) with Fig. 7(c),(d), once again only circular dichroism can be confirmed at lower resonant frequency while both circular dichroism and circular birefringence are presented at higher frequency. This feature proves that our novel metamaterial is dispersive and angle-dependent chiral.
More simulations have been performed to study the dependence of circular dichroism and circular birefringence of our metamaterial on the incident angle. Remarkable polarization transformation has been observed for elevation angles θ i larger than 30°. Beyond that, the difference between the LCP and RCP components in the transmitted wave becomes smaller and smaller as shown in Fig. 8.

Conclusion
A dual-band circular polarizer based on a novel metamaterial has been presented in this paper. The metamaterial implements a novel asymmetric unit cell and layout of duplicate arrays. Wide angle circular dichroism and circular birefringence have been observed in both numerical simulation and measurement. The fundamental mechanism behind is concluded to be the angle-dependent chirality and dispersion of our novel metamaterial. The multi-band metamaterial could be applied in microwave field and might be promising in terahertz and optical region.