## Circular Polarizer and Circularly Polarized Patch Antenna Design  
### Design of Circular Polarizer  
A circular polarizer consisting of the DSSRs is investigated. DSSRs mainly consist of two face-to-face placed semicircular split-rings (SSRs) that are printed on the substrate of a Rogers Duroid 4350B (\(\epsilon_{\mathrm{r}}\) = 3.48, tan\(\delta\) = 0.0037, with dimensions 132 mm \(\times\) 132 mm \(\times\) 1 mm), as shown in Figure 2. The polarizer is excited by a LP incident wave with x-polarization, which is converted into a CP transmitted one as it passes through the polarizer. For the single semicircular split-ring, it was obtained by bending a conventional circular split ring into a semicircular one so that the resulting compact structure could assemble more electromagnetic energy as it was constituted into a circular polarizer. Then, most of the work was directed at the design and optimization of the inner part. Here, one important step is that double bottom strips are horizontally inserted along its diameter edge. Also, a short stub segment is inserted at the top of the inner side of the arc-shaped film for enhancing and tuning the CP radiation. Dual inner arc-shaped strips are separated by a split located between their ends and are connected to the outer arc-shaped film through bottom strips. An arc-shaped slot is formed between them. Also, a bottom split is generated due to the separated bottom strips. The dual SSRs are in a similar structure, as previously illustrated, but mainly differ in their bottom split, which inversely offsets an equal distance from the semicircular center. Moreover, the structures are slightly different in dimensions. In detail, the SSR (with outer radius R\({}_{5}\)) in the upper half-plane is smaller than the one (with R\({}_{1}\)) in the lower half-plane. In addition, the dual SRRs present an approximate elliptical shape on the whole, which can generate orthogonal modes when excited properly and thus result in a circularly polarized radiation [26]. According to the circular polarizer proposed above, a cavity model containing it was constructed in HFSS using an eigenmode solution [27]. Then, the surface current distributions of the DSSRs were obtained, as shown in Figure 3. It was found that a pair of degenerate orthogonal modes (mode #1 and #2) with adjacent eigenfrequencies of 2.5189 GHz and 2.5190 GHz, respectively, was generated, related to the orthogonal modes of the CP radiation of the polarizer. Also, it can be seen that the surface currents have a considerable intensity on the edge of the slots and mainly flow on the outer films and the thin inner strips (though relatively small) of DSSRs along the 45\({}^{\circ}\) titled direction. This is partly because the outer films and the inner strips contribute to the inductive effect of DSSRs, and the corresponding  
Figure 2: Configuration of the proposed circular polarizer. capacitive ones are mainly attributed to the slots in the eigenmode model, where both result in considerable resonance. Note that while the polarizer integrated into the antennas is considered in this paper, the resulting currents would be primarily distributed on the edge of the slots and the inner strips due to the center-placed elliptical radiator's excitation making electromagnetic energy accumulate on the inner part of DSSRs. In this case, the outer films still operate for the impedance matching and the inner part plays an important role in achieving the circular polarization and can easily be adjusted to control the CP performance. Also, it can be observed that the surface currents vary in magnitude by close to a half wavelength when flowing along the 45\({}^{\circ}\) titled direction of the DSSRs and corresponding to its orthogonal direction, the current is non-uniform due to the outer films and inner strips of different configuration but approximately symmetrical. Alternatively, the current intensity for both modes appears to make a small difference.