A broadband, circular-polarization selective surface Free

Frequency selective surfaces (FSSs) and spatial filters have a wide range of applications in many areas of science and engineering. If illuminated by an electromagnetic wave, these surfaces act as barriers for the propagating waves and can modify the spectral content of the waves as desired. For example, they can be designed to manipulate the magnitude and/or the phase of the transmitted or reflected waves in any desired fashion to obtain certain functionalities. FSSs have been employed in a wide range of applications in physics and engineering ranging from low radio frequencies¹ to infrared^2–5 and optical frequencies.⁶ These applications include spatial filtering, high-power microwave filters,^7,8 metamaterials,⁹ metasurfaces,¹⁰ chromatic aberration free lenses,^11–14 and true-time-delay reflectarrays.^15,16 The phase manipulation capability offered by FSSs can be exploited to design polarization selective surfaces. The function of such a device is to reflect one polarization of the wave while being transparent to the orthogonal polarization. A wire grid polarizer¹⁷ is the simplest implementation of such a device for linear polarization (LP). If properly designed, this device reflects the component of the wave whose polarization is parallel to the strips while allowing the orthogonal polarization component of the wave to pass through without any significant attenuation. Achieving similar functionality for circular polarization (CP), however, is not as straightforward. A number of different types of polarization selective surfaces for circular polarization have been reported in the past.^18–29 The structure based on Pierrot unit cell¹⁸ was among the first devices designed to perform as a circular-polarization selective surface (CPSS).^18–21 Pierrot unit cell is composed of two orthogonal monopoles connected by a vertical quarter-wavelength segment. Depending on the orientation of monopoles, it can act as left-hand circular-polarization (LHCP) or right-hand circular-polarization(RHCP) selective surfaces. In Ref. 22, a structure with similar functionality based on two orthogonal dipoles and a half-wavelength segment was presented. An improved design employing two closely-helices arranged in one unit cell was reported in Ref. 23. In Ref. 24, the segment between two monopoles was replaced by coupling elements. These structures generally use resonant constituting elements, and hence, they tend to be narrowband structures. Moreover, their performances degrade significantly when illuminated with obliquely incident waves.²⁵ These deficiencies are not desired in many applications for which broadband performance with a wide range angular stability is required.

The bandwidth issue has been mitigated to some extent using multilayer CPSSs.^26–29 These structures are generally composed of two linear to circular polarization (LP-to-CP) converters that are separated by a linear polarizer. In these CPSSs, the polarization converters and linear polarizers are realized by using arrays of strips or meander lines. The problem associated with them, however, is their large thicknesses when they are designed to provide large bandwidths. The reason for these large thicknesses is that they are composed of numerous layers that are all separated by relatively thick substrates. This large overall thickness generally deteriorates the performances of such CPSSs for obliquely incident electromagnetic waves.

Over the past few years, a new class of frequency selective surfaces with sub-wavelength unit cell dimensions—referred to as miniaturized-element frequency selective surfaces (MEFSSs)—has been extensively studied. Compared to the resonant-type traditional frequency selective surfaces, the main advantage of such a structure is its much smaller unit cell size and significantly reduced overall thickness. These advantages will in turn contribute to a much more stable frequency response as a function of incident angle. Recently, these structures have been employed to design spatial filters,^30–41 transmit arrays,^11–14 reflect arrays,^16,42 and polarization converters.⁴³ In this paper, we present a method for designing circular-polarization selective surfaces based on MEFSSs. The proposed CPSS is composed of two MEFSS-based LP-to-CP polarization converters⁴³ sandwiching a linear polarizer. Each polarization converter is composed of two-dimensional arrays of anisotropic sub-wavelength capacitive patches and inductive wire grids that are separated from each other by thin dielectric substrates. The linear polarizer is an array of sub-wavelength strips located in between two polarization converters. Using wideband low-profile polarization converters, the proposed polarization-selective surface is capable of offering a very broadband operation. In addition, due to the low profile nature of the structure as well as its small unit cell dimensions, the proposed structure can demonstrate a stable performance within a wide field of view. Using this approach, a circular-polarization selective surface operating in the 12–18 GHz was designed. The full-wave simulated results show that the structure operates over a bandwidth of more than 40% and can provide a very consistent frequency response with respect to the angle of incidence of the EM wave with a wide field of view of ±60°.

Fig. 1 presents the topology of a circular-polarization selective surface. This device is a slab of anisotropic medium and treats waves with left-hand circular polarization (LHCP) and right hand circular polarization (RHCP) in different ways. In this paper, the polarization is defined from the point of view of the source. Therefore, RHCP and LHCP waves can be regarded as clockwise and counter-clockwise, respectively. Depending on the polarization, two types of CPSSs can be envisioned. A left-handed circular-polarization selective surface (LH-CPSS) reflects an LHCP wave while transmitting an RHCP wave without changing its polarization and magnitude over the frequency band of operation. A right-handed circular-polarization selective surface (RH-CPSS), on the other hand, is transparent to LHCP waves and completely reflects RHCP waves within its operating frequency range. Similar to LH-CPSS, the polarization and magnitude of the LHCP incident wave remains unchanged after passing through the RH-CPSS. Figs. 1(a) and 1(b) show the schematic models for RH-CPSS and LH-CPSS, respectively. In both cases, the structure is reciprocal and symmetrical. Thus, the operating mechanism remains unchanged for wave propagation in $ẑ$ or $−ẑ$ directions. Therefore, a CPSS can be considered as a four-port network. Such a network can be described using a scattering parameter (S-parameter) matrix. An S-parameter matrix shows the relation between the incident power waves, a_n, and reflected power waves, b_n, in a network. Each element of this matrix is defined as $Sij=bjai$⁠, where a_k = 0 for k ≠ i. The S-parameter matrix for a CPSS can be defined as follows:

where $bjR$ and $bjL$ denote the reflected power wave amplitudes for right- and left-handed circularly polarized power waves from port j, respectively. Also, $ajR$ and $ajL$ are, respectively, the incident power wave amplitudes for right- and left-handed circularly polarized power waves on port j. In addition, $sijLL$ and $sijRR$ denote the co-polarized components and $sijLR$ and $sijRL$ shows the cross-polarized components. The ideal S-parameter matrices for RH-CPSS and LH-CPSS are as follows:

For the ideal cases, the level of the cross-polarized components is considered to be zero. For a realistic design, however, this level is not zero but needs to be sufficiently low.

The CPSS shown in Fig. 1 is a combination of three planar structures. Fig. 2(a) shows the composition of the proposed CPSS which consists of two LP-to-CP polarization converters that are separated by a linear polarizer. The polarization converters are designed to transform a circularly polarized wave to a linearly polarized wave and vice versa. The linear polarizer is designed to completely reflect one linear polarization while maintaining its transparency for the orthogonal one. Knowing the functionalities of different stages of the proposed structure, we can examine the behavior of the structure for an incident circularly polarized wave with a given polarization. The examined CPSS in this section is considered to be an RH-CPSS. The same mechanism is transferable to LH-CPSS by a simple geometry transformation. In Figs. 2(b) and 2(c), the operating mechanism of the RH-CPSS is examined for the incoming LHCP and RHCP waves, respectively. As shown in Figs. 2(b) and 2(c), the structure is, respectively, illuminated with an LHCP and an RHCP wave with the electric field component of Eⁱ. As discussed in Ref. 43, the operating mechanism of a polarization converter is based on behaving differently for two orthogonal components of the incident wave. Within the operational band, this device passes both components very efficiently with little or no attenuation while these components experience two distinct phase shifts with the phase difference of 90° Therefore, after passing through the first polarization converter, the transmitted signal is a linearly polarized wave with the electric field vector, E^u or E^v, depending on the polarization of the incoming wave. $û$ and $v̂$ are both tilted 45° relative to $x̂$ and $ŷ$ directions, respectively. This transmitted linearly polarized wave, then, passes through a linear polarizer. This polarizer is transparent to a linearly polarized wave with a given field vector while it completely reflects a wave whose field vector is directed orthogonal to that given direction. In this RH-CPSS case, the linear polarizer transmits the waves with field vectors directed towards $û$ while it reflects those with $v̂$-directed field vectors. The reflected linearly polarized wave passes through the first polarization converter again and is transformed to an RHCP wave propagating in the $−ẑ$ direction. The linearly polarized waves passing the linear polarizer, on the other hand, pass through the other polarization converter and are transformed to LHCP waves propagating in the $ẑ$ direction. To do so, the second polarization converter needs to be 90° rotated with respect to the first one. This way, the cascaded RH-CPSS structure transmits the LHCP waves while it reflects RHCP waves over the frequency band of operation. This frequency band is set by the operating bands of LP-to-CP polarization converters as well as the linear polarizer.

The CPSS shown in Fig. 2(a) is implemented using miniaturized element frequency selective surfaces of the type reported in Ref. 30. The structure includes two MEFSS-based polarization converters and a wire grid linear polarizer. MEFSS-based polarization converters⁴³ are multilayer anisotropic structures composed of arrays of subwavelength capacitive patches and inductive wire grids separated from one another by thin dielectric substrates. The difference in the frequency response for two orthogonal polarizations in these polarization converters is achieved by using patches and wire grids with asymmetric features. In Ref. 43, it was shown that this type of converter can provide the unique combination of wide bandwidth, thin profile, and stable response with respect to the angle of incidence. The linear polarizer, on the other hand, is a periodic arrangement of metallic strips that are tilted 45° relative to $x̂$ and $ŷ$ directions. If the polarization of the incident wave is aligned with the strips, the surface acts as an inductive impedance surface. On the other hand, if the incident electric field is perpendicular to the strips, the surface has a capacitive response. If the parameters are chosen such that the cut off frequency is much higher than the operating band, the surface can act as a short circuit for waves having polarizations aligned with the strips and as an open circuit for the waves with perpendicular polarizations. This way, for an RH-CPSS, the linear polarizer passes the incident waves polarized along the $û$ (see Fig. 2) while reflecting those waves polarized along the $v̂$⁠. The reflected wave then passes through the first converter and is transformed to an RHCP wave propagating along $−ẑ$ while the transmitted wave passes through the second converter and is transformed to an LHCP wave. To maintain the same polarization in the incident and transmitted waves, the second polarization converter needs to be rotated by 90° relative to the first one. Fig. 3 shows the three-dimensional (3D) topology of the proposed CPSS. The top view of one unit cell of the capacitive layer, inductive layer, and linear polarizer are shown in the inset of Fig. 3. The dimensions of the unit cell along the $x̂$ and $ŷ$ directions are D_x = D_y = D. The capacitive patches are in the form of rectangular patches with dimensions of P_x and P_y in $x̂$ and $ŷ$ directions, respectively. The inductive wire grids are the combination of two metallic strips with the widths of w_x and w_y oriented perpendicularly to each other. Finally, the width of the strips in the linear polarizer is w_LP, and the spacing between the strips is g_LP.

As discussed in Section II, the proposed CPSS is a combination of two LP-to-CP polarization converters that are separated by a linear polarizer. Therefore, the design procedure consists of few steps including designing the converters and the linear polarizer and the integration. We assume that the desired operational bandwidth of the device, BW, and the types of available dielectric materials are known and use them as design parameters in this process. The first step in the design procedure of the CPSS is to design the polarization converters. The polarization converters used in the CPSS architecture are the same with the exception that one of them is rotated by 90° in the x-y plane relative to the other one. Therefore, only one converter needs to be designed. The required parameters to design the converters are its operating bandwidth, Δf_pc, and the dielectric constant of the substrates. To assure satisfying the bandwidth condition of the CPSS, the bandwidth of the polarization converters must be chosen to be larger than or equal to the bandwidth of the CPSS (i.e., Δf_pc ≥ BW). The design procedure of the polarization converters are based on synthesizing the transmission characteristics of the required responses for vertical and horizontal polarizations. As discussed in Ref. 43, these response (e.g., order of the response and the frequency band) are determined based on the required bandwidth Δf_pc. After determining the required responses, the structure is first designed based on the equivalent circuit model (e.g., see Fig. 3 of Ref. 43) and then the geometrical parameters including the wire widths and gap spacings are calculated using (23) and (24) in Ref. 43. For brevity, the details of this design procedure will not be repeated here and the reader is referred to Section III of Ref. 43. The next step in the design of CPSS is to design the linear polarizer. As discussed in Section II, the linear polarizer is a capacitive impedance sheet that acts as a low pass filter for the passing waves. The cut off frequency for this filter is 1/Z₀C, where Z₀ = 377 Ω is the free-space impedance and C is the capacitance of the impedance sheet which can be calculated using Equation (23) of Ref. 30. The cut off frequency of the linear polarizer needs to be higher than the operating frequency band of the CPSS. Based on this, it can be shown that the widths of strips as well as the gap spacings between them should satisfy the following inequality:

where w_LP is the width of the strips, g_LP is the spacing between strips, ε₀ is the free-space permittivity, ε_r,eff represents the effective permittivity of the surrounding the strips, Z₀ = 377 Ω is the free-space impedance, and f_max is the upper frequency in the band of operation. Since the strips are assumed to be sandwiched between two dielectric substrates, the effective permittivity is the same as that of the substrates. The integration of the polarization converters and the linear polarizer is the final step. Depending on the design, some small modifications might be needed to compensate for the changes caused by the coupling between different components of the CPSS. In this design example, these modifications were done by slightly changing the dimensions of capacitive patches.

The abovementioned procedure was followed to design an RH-CPSS operating over the frequency range of 12–18 GHz. The bandwidth is defined as the frequency range over which the desired co-polarized transmission coefficient is higher than −3 dB. In this design, the dielectric substrates used for polarization converters were assumed to be nonmagnetic and having a dielectric constant of ε_r = 10.2 (Rogers RT/duroid 6010). Based on the given parameters and the procedure described in Section III of Ref. 43, a third-order bandpass MEFSS with anisotropic unit cells and a Chebyshev response was used to design the polarization converters. After determining the parameters of the equivalent circuit model, the physical parameters were calculated. Fig. 4 shows one unit cell of the proposed CPSS, which uses this MEFSS-based polarization converter. The fabrication of the proposed structure requires multi-layer printed-circuit-board (PCB) fabrication technology. In such a case, the different metallic layers of the CPSS are fabricated on one or two sides of multiple dielectric substrates. The different dielectric substrates are then bonded together using bonding films. The presence of these bonding films does impact the response of the structure. Therefore, the effects of the bonding layers placed in between the adjacent substrates are also considered. The bonding material used in this design is Rogers 4450F prepreg with the dielectric constant of 3.52 and the thickness of h_b = 0.1 mm. Introduction of these bonding layers also creates an asymmetry in the topology of the structure, which can slightly change the frequency response of the structure. This asymmetry can be eliminated by using two closely spaced patches in two sides of the middle layer as shown in Fig. 4 instead of using just one patch placed on one side of this layer. The same method is also used for the linear polarizer to eliminate the asymmetry. The unit cell dimension of the structure is selected to be 3 mm, which is equivalent to approximately 0.15λ₀, where λ₀ is the free-space wavelength at the center frequency of operation. Using these unit cell dimensions, the widths of the wire grids and capacitive gap spacings of the polarization converters are calculated and listed in Table I. The polarization converter was simulated in CST Studio and its frequency response for both vertical and horizontal polarizations was calculated. Fig. 5(a) shows the full-wave simulated transmission coefficient of the polarization converter for both polarizations with the geometrical parameters reported in Table I. The phase difference between the transmission phases of both polarizations is also shown in Fig. 5(a). As can be seen, over the band of interest, the polarization converter is transparent for both polarizations and it creates a 90° difference between their transmission phases. Fig. 5(b) shows the axial ratio of the transmitted wave based on the full-wave simulated results shown in Fig. 5(a). Also, the total transmission coefficient of the polarization converter is shown in Fig. 5(b). Observe that the axial ratio remain below 3 dB and the insertion loss remains below 2 dB over the entire band of interest. The width of the strips in the linear polarizer is also reported in Table I. This width is calculated using (4) considering that the linear polarizer is sandwiched between two 0.508-mm Rogers RT/duroid substrates (ε_r = 2.2). These substrate are chosen primarily based on the practical design considerations. Fig. 6 shows the transmission response of the linear polarizer. As can be seen, this polarizer is transparent to the waves with the electric field vector perpendicular to the direction of strips over the band of interest.

In the final step, the polarization converters and the linear polarizer are cascaded to form the CPSS. As discussed previously, some small modifications were needed to account for the effects of the coupling between different components. The finalized values of the geometrical parameters are listed in Table II. Figs. 7(a) and 7(b) show the simulated transmission and reflection responses of the CPSS with the values reported in Table II. As can be observed, the transmission window in 12–18 GHz is achieved. Also, the level of co-polarized transmission discrimination, $S21LL/S21RR$⁠, is more than 15 dB over the band of interest. The co-polarized reflection coefficient discrimination, $S11RR/S11LL$⁠, is also more than 10 dB over most of the operating band. The frequency response of the structure was also simulated for oblique incidence angles and the results are presented in Figs. 8(a) and 8(b). Observe that for incidence angles in the range of ±60°, the CPSS provides a stable frequency response as a function of incidence angle with a polarization isolation better than 15 dB over this entire frequency band of operation. Such stable response in a wide field of view is mainly attributed to the small dimensions of the unit cells.

A new technique for designing circular-polarization selective surfaces with wide fields of views and extremely wide bandwidths was presented. The proposed structure is composed of two MEFSS-based linear-to-circular polarization converters that are separated by a linear polarizer. Each polarization converter is designed by exploiting an anisotropic miniaturized-element frequency selective surface. The linear polarizer is an array of sub-wavelength strips. The multilayer combination of these two structures were used to design a circular-polarization selective surface that is transparent to left handed circularly polarized waves while being opaque to right handed CP waves. A design procedure was presented and used to design a prototype capable of operating over the entire Ku-band in the 12–18 GHz frequency band. The full-wave simulated results confirmed that the RH-CPSS prototype operates over a 40% fractional bandwidth. Also, it was shown that the structure provides a stable frequency response for oblique incidence angles in the ±60°. The comparison between the performance of the proposed structure and a number of the other CPSSs reported in the literature is provided in Table III. Despite having many metal and dielectric layers, the overall thickness of this structure remains below a quarter of wavelength. However, it provides one of the widest bandwidths reported to date and has the widest field of view among all similar structures that are reported to date.

This material was based upon work supported by the Office of Naval Research under ONR Award No. N00014-16-1-2308 and by the National Science Foundation under NSF Award No. ECCS-1101146.