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A wideband linear-to-circular polarizer is proposed, which consists of an array of dielectric slabs with double-sided parallel metallic strips. The polarization conversion is achieved by decomposing the linearly polarized incident plane wave into two orthogonal components of equal amplitude, which are subjected to an unequal phase shift such that the resultant phase difference between two components is 90° after an appropriate propagation path. The metallic strips are introduced to enhance the axial ratio bandwidth. Microwave experiment is performed to successfully realize these ideas and measured results are in good agreement with numerical simulations. The frequency range over which the measured transmission coefficient is higher than 0.95 is from 7 to 13.7 GHz, and the 3 dB axial ratio bandwidth under normal incidence ranges from 7 to 13 GHz, corresponding to a 60% fractional bandwidth. In addition, the proposed polarizer shows a good stability with respect to the oblique incidence.
© 2015 Optical Society of America
1. Introduction
Polarization is an important property of electromagnetic (EM) waves. Generally, there are three polarization states: linear, circular and elliptical polarizations; while the former two can be considered as special cases of the latter. Polarization can be commonly defined by three physical parameters: handedness, degree of ellipticity, and orientation of the ellipse’s major axis [1, 2]. In practical systems, it is often required to modify the polarization state of an incident plane wave. As an example, a circular polarizer [2, 3] can be used to convert a linearly polarized wave into a circularly polarized wave, which has been widely applied in optical communications and remote sensing [3–12]. Moreover, circular polarizer also behaves like a filter, which can pass an incident circularly polarized wave of the same handedness, while effectively rejects others of the opposite handedness.
According to existing studies reported in the open literature, circular polarizers can be realized by employing chiral [8–12] or photonic [4, 13, 14] metamaterials, metasurface [15], slots of various shapes [16, 17], meander-line [18], waveguide [19, 20], grating structures [21, 22], etc. Metamaterial-based polarizers [3–14] have a lot of advantages, such as subwavelength thickness, high conversion efficiency, angular tolerance, and scalability. Unfortunately, they share a common fatal flaw, which is the narrow operating bandwidth. On the other hand, ultrathin polarizers [15–17] often exhibit large insertion loss and relatively narrow bandwidth, with insertion loss of around 3 dB and not more than 20% axial ratio (AR) bandwidth for single-layer structures. Although multi-layer structures have been proposed to reduce the insertion loss, such as using stacked double-layer periodic array that are separated by dielectric spacers [16], they usually have narrow AR bandwidth. Although multi-layer meander-line polarizers [18] show excellent performance, their fabrication becomes challenging and expensive because they may employ up to eight layers. Moreover, attaching dielectric slabs along with the sidewalls of a waveguide [19] can effectively differentiate the phases between two orthogonally polarized waves. In comparison, it seems better if the dielectric slab could be placed at the center of a waveguide where the electric fields are strongest [20]. These waveguide polarizers show a broader operating bandwidth with AR < 3 dB. However, due to their relatively large thickness, they are not suitable for applications requiring miniaturized devices or systems. On the other hand, researchers suggested that removing heavy waveguide walls and only using two dimensional binary gratings can also realize circular polarizers [21, 22]. It is known that the thickness of these polarizers can be greatly reduced if a dielectric of high permittivity is employed though it may result in a narrow bandwidth.
In this paper, a wideband circular polarizer is presented based on dielectric gratings printed with periodic metallic strips. The proposed design employs the unequal phase shift to manipulate the polarization state of an incident plane wave of linear polarization, the concept of which is similar to those used in the field of optics and microwaves. However, the ingenious introduction of parallel metallic strips printed on both sides of the dielectric slab helps to significantly broaden the AR bandwidth and reduce the structural thickness by 28% compared with the design using pure dielectric gratings. Finally, a prototype is fabricated and measured at the microwave frequency as a proof of concept. Measured results are in very good agreement with simulated ones, which demonstrates that the proposed circular polarizer exhibits excellent performance in terms of low insertion loss and high conversion efficiency over a wide frequency band, and insensitivity to incidence angles.
2. Description of the structure
Figure 1(a) shows the perspective view of the proposed circular polarizer, which consists of an array of one dimensional dielectric slab printed with periodic metallic strips on both sides. A linearly polarized plane wave is excited from z < 0 and propagates along the direction of k. The incident wave has a polarization 45° titled away from the vertical direction (x-axis), and its electric field can be decomposed into two orthogonal components: one along the x-axis and the other along the y-axis. These two orthogonal linearly polarized field components propagate with different velocities through the polarizer such that the resultant field is circularly polarized at the other end of the polarizer. θ and ϕ denote the incidence and polarization angles of the incident plane wave respect to the z- and x- axes, respectively.
Fig. 1 Illustration of the proposed circular polarizer. (a) Perspective view of the structure, (b) View of a unit cell.
The unit cell of the proposed circular polarizer is shown in Fig. 1(b). It consists of a dielectric slab of thickness a and dielectric constant εr. Parallel metallic strips are printed on the top and bottom layers of the slab, where the bottom strip is represented in shadow. The unit cell periods along the x- and y- directions are denoted by px and py, respectively. The length and width of the metallic strips are ls and ws, respectively, while their thickness is assumed to be negligible compared to the operating wavelength. The thickness of the circular polarizer is denoted by l. The unit cell of the polarizer is simulated by the full-wave EM simulation software ANSYS HFSS. The periodic boundary conditions Master and Slave are adopted along the x- and y- directions to simulate the infinitely large periodic structure. Port 1and Port 2 are excited by Floquet modes with two orthogonal waves, which represent the horizontally (Ey) and vertically (Ex) polarized components of the incident plane wave, respectively. It may be mentioned that the proposed circular polarizer is very similar to the recently proposed three-dimensional frequency selective structures [23–25], which exhibit stable and quasi-elliptical filtering performance against the variation of the incident angle of an incoming EM wave.
3. Operating principle
In order to gain insight into the operating principle of the proposed circular polarizer, a linearly polarized incident plane wave with a polarization angle of ϕ = 45° relative to the x- axis is considered though the case of ϕ = −45° may be analyzed in the same way. The incident wave can be decomposed into two equal components of the same phase when entering the polarizer, which are parallel to the x- and y- axes, respectively, as depicted in Fig. 1. Different effective permittivity values in the x- and y- directions are obtained through the introduced gratings, which means that Ex and Ey components are propagating with different velocities. By properly adjusting the thickness of the circular polarizer and the loaded gratings, a 90° phase difference between these components can be achieved before the waves leave the polarizer and they begin to travel at the same velocity forming a circularly polarized wave in the other side of the polarizer.
3.1 Dielectric gratings
For a one-dimensional dielectric slab of thickness a in a periodic array with period px, the effective relative permittivity values along the x- and y- directions are εeff_x and εeff_y, respectively, and they can be estimated by their volumetric averages [26]
where a/px is the filling fraction. It can be seen from Eqs. (1) and (2) that the effect of dielectric gratings for Ex component can be ignored. However, the propagation constant of Ey component is effectively increased due to the existence of dielectric gratings. Thus, a phase difference occurs between Ex and Ey components after they pass through the circular polarizer, which can be calculated bywhere f and c denote the operating frequency and the speed of light, respectively. By adjusting the length l one can control the phase difference between Ex and Ey components. The AR of the transmitted circularly polarized wave formed by two linearly polarized waves of the same amplitude versus the phase difference can be derived asCircularly polarized wave can be obtained when the conditions of equal amplitude and Δθ = 90° between Ex and Ey components are met. The thickness of the polarizer at the center frequency can then be derived asAn example using pure dielectric gratings is simulated. In order to make sure that Ex and Ey components pass through the structure without much loss, the filling fraction should not be too large. Meanwhile, in order to obtain a minimum thickness for the polarizer, the filling fraction of 0.1 is chosen, which leads to a corresponding thickness of 19.45 mm. The phase difference between two orthogonal components is linearly proportional to the operatingfrequency. A 3 dB AR bandwidth of about 35% is obtained, which is similar to the one in [22]. It is certainly desirable to extend the AR bandwidth while retaining a small insertion loss for the conversion from linear polarization to circular polarization.
3.2 Effect of parallel metallic strips
From the discussions about the circular polarizer using pure dielectric gratings in the previous section, it can be seen from Eq. (3), the phase difference between two orthogonal components is linearly proportional to the operating frequency, which results in a relatively narrow AR bandwidth. In order to broaden the AR bandwidth of the transmitted wave, parallel metallic strips are introduced on the top and bottom layers of each dielectric slab, and they can significantly affect the transmission of the Ex component. The length of these metallic strips can be estimated by [27]
In order to understand the effect of the introduced metallic strips, the surface current distributions on the strips at two resonant (f1, f2) and center (fc) frequencies are investigated and shown in Fig. 2 by arrows lines and color patterns. It is seen from Figs. 2(a)-2(c) that there is hardly any surface current on the metallic strips under the excitation of Ey component for all three frequencies, which indicates that the strips do not have much influence on the Ey component. In comparison, for the excitation of Ex component, induction currents are generated along the strips because the electric field is perpendicular to the metallic surface resulting in a longitudinal surface current flowing along the strips. It is noted from Fig. 2(e) that the surface current is very weak at the center frequency, which implies that the effect is negligible. As the frequency moves away from the center frequency, the surface current gets stronger. It can also be seen that the surface current in Fig. 2(d) flows from the top strip to the bottom strip through the substrate. It is therefore expected that a transmission zero is provided by this resonator, which is formed between the parallel metallic strips. Moreover, the surface current in Fig. 2(f) shows that two current loops are obtained in the same strips, which produce another transmission zero. Resultantly, resonances can be produced if the length of the strips ls is integer multiples of half a guided wavelength. Therefore, we can determine that f2 = 2f1, and f1 can be estimated as
The effect of the metallic strips can be understood from the simulated results shown in Fig. 3. In the absence of metallic strips, Ex and Ey components can pass through the structure without much loss as long as the dielectric filling factor is sufficiently small. When metallic strips are introduced along the z-axis, it is expected that they do not have much influence on the Ey component, as shown in Fig. 3(a). However, the metallic strips can significantly affectthe propagation of the Ex component. Two resonant frequencies f1 = 6.7 GHz and f2 = 13.4 GHz are observed in the transmission coefficient for Ex component, which is consistent with the earlier discussions about the surface current. As shown in Fig. 3(b), the transmission coefficient is distorted near the resonant frequencies. Owing to the existence of two resonant frequencies f1 and f2, the phase trace of Ex component is disturbed and features a steeper slope, while that of Ey component is nearly uninfluenced. In this case, the phases of both Ex and Ey components become more parallel to each other and a more stable 90° phase difference between Ex and Ey components is obtained over a wide frequency band. Hence, the AR bandwidth of the outgoing wave can be significantly broadened.
Fig. 3 Transmission coefficient of the dielectric gratings with and without parallel metallic strips. (a) Ey component, (b) Ex component.
3.3 Electric field
Figure 4 depicts the electric field representation when a linearly polarized plane wave is normally incident upon the proposed polarizer with a polarization angle ϕ = + 45°. Due to the fact that Ex and Ey components are propagating with different velocities along the x- and y- directions, a phase difference between them is produced due to the existence of dielectric slabs and metallic strips. As shown in Fig. 4, the cluttered electric field represents that thepolarization state of the resultant wave going through polarizer is elliptically polarized. Moreover, the ellipticity of the elliptically polarized wave constantly decreases toward the direction of propagation benefiting from the continuous accumulation of the phase difference. When the ellipticity reduces to zero a perfect circularly polarized wave is achieved. It can also be seen that the electric field of a propagating wave is rotating along the direction of propagation after the wave emitting from the polarizer, which indicates that a circularly polarized wave is obtained. In addition, the field intensity exhibits a sinusoidal variation for linear polarization, while it has homogeneous distribution for circularly polarized wave. Figure 4 clearly verifies this point and indicates that a good conversion is achieved by the proposed structure.
Fig. 4 Electric field representation of an incident wave propagating through a unit cell of the circular polarizer.
4. Simulated and measured results
A prototype of the proposed circular polarizer is fabricated to verify its conversion performance. The fabrication is carried out through standard printed circuit board technology and involves two types of structures in general. The first is the main dielectric slabs printed with periodic parallel strips with a total length of 168 mm. The metallic strips are made of copper with a thickness of 0.017-mm. The second part is the comb-structure with a total length of 166.6 mm, which is employed to support all the dielectric slabs at an equal spacing along the x- direction. The depth of these periodic slots is 3.5 mm in the comb with a width of 7 mm. The assembled sample is shown in Fig. 5, which consists of a 40 × 34 unit cells. The substrate Rogers RO 3010 (εr = 10.2, tan δ = 0.0035) is used in this design. Due to the introduction of parallel metallic strips, the filling fraction is slightly increased from 0.1 to 0.13, while the thickness of the proposed circular polarizer is 15.5 mm (0.51λ0 at the center frequency of 10 GHz). In order to obtain a center frequency of 10 GHz, the optimized length of 7 mm is selected for the metallic strips. Other geometrical parameters are designed as a = 0.64 mm, px = 4.9 mm, py = 4 mm, l = 15.5 mm, d = 2.13 mm, ls = 7 mm, and ws = 0.8 mm.
Fig. 5 Photographs of the fabricated circular polarizer. Two types of structures: one is dielectric strip with periodic parallel strips; the other is comb-structure made of FR-4.
The fabricated sample is measured in a microwave anechoic chamber by the free-space method using two horn antennas and a vector network analyzer. Two horn antennas are separated by a distance of 1 m so as to meet the far-field condition.
4.1 Normal incidence
Figure 6 shows the measured and simulated results for both the reflection and transmission coefficients of the proposed circular polarizer under the normal incidence (θ = 0°). It is seen that measured results show good agreement with simulated ones; while some small differences are attributed to manufacturing and experimental errors. It can be seen in Fig. 6(a) that the reflection coefficient Rx of the Ex component is below 0.32 (the reflected power less than 10%) from 7 to 13.7 GHz, which corresponds to a fractional bandwidth of 67% at thecenter frequency. Moreover, Fig. 6(b) shows a 100% bandwidth for the reflection coefficient Ry of the Ey component less than 0.32. The transmission coefficients for both Ex and Ey components are shown in Figs. 6(a) and 6(b), respectively. It is observed that the transmission coefficient of more than 0.95 for both Ex and Ey components is obtained from 7 to 13.7 GHz, which indicates that almost the same amplitude for both components is achieved over a wide frequency band. Furthermore, as predicted by simulations, two transmission zeros are observed at f1 = 6.9 GHz and f2 = 13.8 GHz, respectively. It should be mentioned that f1 = 6.7 GHz and f2 = 13.4 GHz are the results calculated by Eq. (7), which are in good agreement with measured results. The slight shift in these resonant frequencies may be due to the assembly errors.
Fig. 6 Performance of the circular polarizer under normal incidence. (a) Reflection and transmission coefficients of Ex component, (b) Reflection and transmission coefficients of Ey component, (c) Phase delayed and phase difference between Ex and Ey components, (d) Axial ratio of transmitted wave.
The phase delay of Ex and Ey components going through the polarizer versus frequency from 5 to 15 GHz is shown in Fig. 6(c). It can be seen that two mutations exist in the phase curve of Ex component, which correspond to the resonant frequencies f1 and f2, respectively. Due to the existence of parallel metallic strips, the phase curve of Ex component becomes more parallel to the one of Ey component, which in turn results in a more constant 90° phase difference between them over a wide frequency band. Figure 6(d) shows that the minimum AR is 0 dB around the center frequency of 10 GHz, which indicates that a perfect circularly polarized wave is obtained at that frequency. It is also shown that 3 dB AR bandwidth is from 7 to 13 GHz, corresponding to a fractional bandwidth of 60%, which is about 81% improvement relative to pure dielectric gratings.
4.2 Oblique incidence
The performance of our proposed circular polarizer under oblique incidence is also investigated, and Figs. 7(a) and 7(b) plot the transmission coefficients of Ex and Eycomponents, respectively. It can be seen that there is little change with increasing the incident angle and this implies that the proposed circular polarizer exhibits stable transmission characteristics under the oblique incidence. The simulated and measured transmission coefficients for various incident angles are still above 0.9 between 7 to 13 GHz, which indicates that the proposed polarizer is very stable to the oblique incidence, and the incident wave can pass through the structure without much loss. In addition, it is noted that two transmission zeros still exist in Ex component and their positions do not change when increasing the incident angle. They are entirely dependent upon the parameters of the metallic strips and dielectric slabs.
Fig. 7 Performance of the circular polarizer under oblique incidence (θ = 0°, 20°, 40°). (a) Transmission coefficient of Ex component, (b) Transmission coefficient of Ey component, (c) Phase difference between Ex and Ey components, (d) Axial ratio of transmitted wave.
The phase difference between Ex and Ey components versus frequency under different incident angles is shown in Fig. 7(c). It can be seen that the 90° phase difference shifts toward a lower frequency; this is because the filling fraction will increase when viewed from the oblique incident angle. From Eqs. (1) and (2) one can notice that the effective permittivity in the x- direction does not change, while the effective permittivity in the y- direction increases with the increasing angle of incident plane wave. Resultantly, the 90° phase difference appears at a lower frequency. Figure 7(d) shows the axial ratio of the transmitted wave under different angles of the incident plane wave. It is observed that the same minimum AR about 0 dB can be obtained for different incident angles. When the incident angle increases to 40°, the 3 dB AR bandwidth is from 7 to 10.8 GHz, which is about 42% of the center frequency of 8.9 GHz. Overall, the performance of our circular polarizer shows a good stability under the oblique incidence.
4.3 Conversion coefficient and efficiency
When the conditions of |Ex| |Ey| and 90° are satisfied simultaneously, the outgoing wave at the output interface is left-hand circularly polarized (LCP) and right-hand circularly polarized (RCP) assuming that the structure is illuminated by a linearly polarized wave with a polarization angle of ϕ = 45° and ϕ = −45°, respectively. In order to assess the performance of the proposed circular polarizer, the circular polarization conversion coefficient and efficiency results for 45° polarization angle under different incident angles are plotted in Fig. 8. As shown in Fig. 8(a), the conversion coefficients exceed 0.95 and are stable for LCP wave from 6.7 to 13 GHz, meanwhile insensitive to the incidence angle. Besides, the cross-polarization component (RCP wave) is extremely small, with conversion coefficient less than 5% of the LCP wave.
Fig. 8 Numerical results for (a) conversion coefficient and (b) conversion efficiency spectrum under different incident angles (θ = 0°, 20°, 40°).
According to [21], the conversion efficiency can be described as follows
where C- and C+ are circular conversion coefficients of LCP and RCP wave, respectively. It is obvious from Fig. 8 (b) that the conversion efficiency is larger than 90% over a wide frequency band from 6.7 GHz to 13 GHz under the normal incidence, which corresponds to a fractional bandwidth of 63%. In addition, the conversion efficiency is relatively stable for different incident angles, although there is a small degradation at higher frequency for large- oblique incident angle.Overall, the proposed structure produces approximately the same amplitude for Ex and Ey components and a phase difference of about 90°, which indicates that an excellent circular polarization is obtained. Moreover, the proposed polarizer also features low AR and high conversion efficiency over a broad frequency band as well as insensitivity to incident angle. It may also be mentioned that our proposed design can be scaled to optical frequency using silicon lithography and metal deposit processing [21, 28] due to its relatively simple structure.
4.4 Performance comparison
In order to clearly illustrate the performance of our circular polarizer, a detailed comparison between the proposed design and other transmission polarizers is made in Table 1. It can be observed that our circular polarizer based on dielectric gratings with periodic strips has a very low insertion loss of 0.1 dB and bandwidths of 67%, 60%, and 63% for reflection coefficient less than 0.32, 3 dB AR, and at least 0.9 conversion efficiency, respectively.
Table 1. Performance Comparison of Typical Circular Polarizers
As shown in Table 1, the gold helix structure shows the broadest bandwidth for circular polarization conversion efficiency, while the designs based on chiral, metasurface, and slot-type structures exhibit very small thickness. Although the meander-line polarizers showsimilar performance to our design, their fabrication is more complicated because they use up to eight layers. It is seen that in our design both insertion loss and operating bandwidth can be significantly improved when parallel metallic strips are introduced in the conventional dielectric grating structure. Compared to many existing designs, our circular polarizer exhibits overall excellent performance, in terms of low insertion loss, broad operating bandwidth, high conversion efficiency as well as a reasonable thickness, which makes the proposed polarizer potentially useful in many practical systems.
5. Conclusion
A simple and wideband circular polarizer has been experimentally demonstrated in this paper. The polarizer consists of an array of dielectric slabs printed with parallel metallic strips. It can convert a linearly polarized incident wave into circularly polarized plane wave. Measured and simulated results are in good agreement, and the polarizer exhibits more than 60% bandwidth for axial ratio less than 3 dB. It has also experimentally verified that the polarizer features stable performance under the oblique incidence up to 40°. Although it requires a fixed incident polarization angle, the proposed circular polarizer exhibits very good performance and can be potentially very useful in optical communications, spectroscopy, liquid crystal display, and instrumentations.
References and links
1. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef] [PubMed]
2. Wikipedia, “Polarizer,” http://en.wikipedia.org/wiki/Polarizer.
3. Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3(870), 870 (2012). [CrossRef] [PubMed]
4. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]
5. J. J. Wang, W. Zhang, X. Deng, J. Deng, F. Liu, P. Sciortino, and L. Chen, “High-performance nanowire-grid polarizers,” Opt. Lett. 30(2), 195–197 (2005). [CrossRef] [PubMed]
6. L. Yang, L. L. Xue, C. Li, J. Su, and J. R. Qian, “Adiabatic circular polarizer based on chiral fiber grating,” Opt. Express 19(3), 2251–2256 (2011). [CrossRef] [PubMed]
7. H. F. Ma, G. Z. Wang, G. S. Kong, and T. J. Cui, “Broadband circular and linear polarization conversions realized by thin birefringent reflective metasurfaces,” Opt. Mater. Express 4(8), 1717–1724 (2014). [CrossRef]
8. X. J. Huang, D. Yang, and H. L. Yang, “Multiple-band reflective polarization converter using U-shaped metamaterial,” J. Appl. Phys. 115(10), 103505 (2014). [CrossRef]
9. Y. Huang, Y. Zhou, and S. T. Wu, “Broadband circular polarizer using stacked chiral polymer films,” Opt. Express 15(10), 6414–6419 (2007). [CrossRef] [PubMed]
10. H. X. Xu, G. M. Wang, M. Q. Qi, T. Cai, and T. J. Cui, “Compact dual-band circular polarizer using twisted Hilbert-shaped chiral metamaterial,” Opt. Express 21(21), 24912–24921 (2013). [CrossRef] [PubMed]
11. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric chiral metamaterial circular polarizer based on four U-shaped split ring resonators,” Opt. Lett. 36(9), 1653–1655 (2011). [CrossRef] [PubMed]
12. S. Yan and G. A. E. Vandenbosch, “Compact circular polarizer based on chiral twist double split-ring resonator,” Appl. Phys. Lett. 102(10), 103503 (2013). [CrossRef]
13. J. Kaschke, J. K. Gansel, and M. Wegener, “On metamaterial circular polarizers based on metal N-helices,” Opt. Express 20(23), 26012–26020 (2012). [CrossRef] [PubMed]
14. Y. F. Li, J. Q. Zhang, S. B. Qu, J. F. Wang, H. Y. Chen, Z. Xu, and A. X. Zhang, “Wideband selective polarization conversion mediated by three-dimensional metamaterials,” J. Appl. Phys. 115(23), 234506 (2014). [CrossRef]
15. H. L. Zhu, S. W. Cheung, K. L. Chung, and T. I. Yuk, “Linear-to-circular polarization conversion using metasurface,” IEEE Trans. Antenn. Propag. 61(9), 4615–4623 (2013). [CrossRef]
16. M. Euler, V. Fusco, R. Dickie, and R. Cahill, “Comparison of frequency-selective screen-based linear to circular split-ring polarization convertors,” IET Microwave Antennas Propag. 4(11), 1764–1772 (2010). [CrossRef]
17. J. Wang and Z. Shen, “Improved polarization converter using symmetrical semi-ring slots,” IEEE Antennas Propag. Society Int. Symp. 2052–2053 (2014). [CrossRef]
18. R. S. Chu and K. M. Lee, “Analytical model of a multilayered meander-line polarizer plate with normal and oblique plane-wave incidence,” IEEE Trans. Antenn. Propag. 35(6), 652–661 (1987). [CrossRef]
19. E. Lier and T. S. Pettersen, “A novel type of waveguide polarizer with large cross-polar bandwidth,” IEEE Trans. Microw. Theory Tech. 36(11), 1531–1534 (1988). [CrossRef]
20. S. W. Wang, C. H. Chien, C. L. Wang, and R. B. Wu, “A circular polarizer designed with a dielectric septum loading,” IEEE Trans. Microw. Theory Tech. 52(7), 1719–1723 (2004). [CrossRef]
21. M. Mutlu, A. E. Akosman, and E. Ozbay, “Broadband circular polarizer based on high-contrast gratings,” Opt. Lett. 37(11), 2094–2096 (2012). [CrossRef] [PubMed]
22. M. Mutlu, A. E. Akosman, G. Kurt, M. Gokkavas, and E. Ozbay, “Experimental realization of a high-contrast grating based broadband quarter-wave plate,” Opt. Express 20(25), 27966–27973 (2012). [CrossRef] [PubMed]
23. A. K. Rashid, B. Li, and Z. Shen, “An overview of three-dimensional frequency-selective structures,” IEEE Antennas Propag. Magazine 56(3), 43–67 (2014). [CrossRef]
24. B. Li and Z. Shen, “Three-dimensional bandpass frequency-selective structures with multiple transmission zeros,” IEEE Microwave Theory Tech. 61(10), 3578–3589 (2013). [CrossRef]
25. B. Li and Z. Shen, “Angular-stable and polarization-independent frequency selective structure with high selectively,” Appl. Phys. Lett. 103(17), 171607 (2013). [CrossRef]
26. J. D. Shumpert, Modeling of Periodic Dielectric Structures. A Dissertation in the University of Michigan, (2001).
27. B. A. Munk, Frequency Selective Surface: Theory and Design (John Wiley & Sons, 2000).
28. J. Mu, X. Li, and W. P. Huang, “Compact Bragg grating with embedded metallic nano-structures,” Opt. Express 18(15), 15893–15900 (2010). [CrossRef] [PubMed]
