## 3 Results and Discussion  
To show the feasibility of the design, a prototype of the proposed polarization converter was assembled that incorporated a pair of confocal cylindrical lenses (LJ1878L1-A; LJ1960L1-A, THORLABS) with focal lengths of 10 mm and 20 mm, respectively, a pair of lateral displacement (polarizing and nonpolarizing) beamsplitters (PBS251; BS013; PS911, THORLABS), and two multiorder half-wave plates (MOWP-633-1/2-10, BVO). The dimensions of the device were 125 \(\times\) 50.8 \(\times\) 25.4 mm. A 632.8 nm helium-neon laser (AH100M, ONSET) was used as the light source, with an output power of 10 mW. The phase condition between each quadrant was maintained as in-phase through angle adjustments of the h-HWP on the \(y\)-axis. A positive IL with a focal length of 100 mm was used to generate the radially and azimuthally polarized beams in the far field. The donut-shaped patterns are shown in Figures 2 and 3. The size of the beams illustrated in Figures 2a and 3a was approximately 200 \(\upmu\)m. To verify the radial and azimuthal characteristic of these beams, an analyzer was applied with different azimuthal angles prior to the CCD camera (XCD-U100 CR, SONY) and a laser beam profiler (BP109-VIS, THORLABS). In Figure 2b-e, the beam profiles were observed with the transmitting axis of the analyzer being 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\) with respect to the \(x\)-axis. In Figure 3b-e, the beam profiles were observed with the transmitting axis of the analyzer being 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\) with respect to the \(-z\)-axis. To examine the polarization quality of these beams, an additional quarter-wave plate (WPQ05M-633, THORLABS) was inserted prior to the analyzer for the demonstration of the spatial distributions of Stokes parameters [14; 16], as shown in Figure 4. The Stokes parameter S\({}_{0}\) describes the total intensity of the optical beam, which was scaled between 0 and 2. The parameter S\({}_{1}\) is the intensity difference between horizontal and vertical polarization. The parameter S\({}_{2}\) represents the intensity difference between linear polarization oriented at 45\({}^{\circ}\) and 135\({}^{\circ}\). Therefore, the values of S\({}_{1}\) and S\({}_{2}\) were between \(+1\) and \(-1\). The parameter S\({}_{3}\) describes the intensity difference between right and left circular polarization, which was scaled between \(+0.5\) and \(-0.5\). Ideally, the values of S\({}_{3}\) should be much smaller than S\({}_{0}\), S\({}_{1}\), and S\({}_{2}\). Although the intensity distributions did not show a good cylindrical symmetry, they could be improved by applying highly accurate translation and rotation stages for alignment. These results successfully demonstrated the feasibility of the proposed design. Figure 2: Radially polarized lights in the transmission output converted from a linearly polarized light: (**a**) donut-shaped beam profile and intensity distribution in the \(x\)-direction observed without an analyzer, and beam profiles observed with the transmitting axis of an analyzer at (**b**) 0\({}^{\circ}\); (**c**) 45\({}^{\circ}\); (**d**) 90\({}^{\circ}\); and (**e**) 135\({}^{\circ}\) with respect to the \(x\)-axis. The proposed polarization converter has a simple and symmetric structure that facilitates the maintenance of the in-phase condition for the generation of radially and azimuthally polarized beams. In addition, the device can generate radially and azimuthally polarized beams simultaneously. In an application, a linear superposition of radially polarized mode and azimuthally polarized mode generates cylindrical vector (CV) beams [3], as shown in Figure 5. Because two beams are always produced simultaneously, it causes 50% losses if only one beam mode is needed. In this condition, an additional reflection prism (RP) could be applied to transform one mode into another.