A dual layer wideband angular stable frequency selective surface for linear to circular and circular to linear polarization conversion for 5G applications (2025)

In electromagnetics, the polarization of electromagnetic (EM) radiation plays a crucial role in many applications such as wireless signal transfer¹, radar imaging², and communication. While the use of linearly polarized (LP) radiation is used to double its channel capacity, they are susceptible to degradation due to Faraday rotation, multipath fading³, and antenna orientations. In this regard, circularly polarized (CP) electromagnetic (EM) radiation can solve these issues and provide an efficient transmission. For point-to-point and satellite communications, CP radiation results in higher directivity, low losses, and dual polarization capability. With the advancement of technology, the use of high-frequency bands (> 20GHz) for faster wireless data transfer has become necessary. Therefore, there is a significant interest in the investigation of producing circularly polarized EM radiation at high frequencies.

The production of CP EM radiation is possible using a microstrip patch⁴, dual feed⁵, helical^6,7, and spiral antennas⁸. However, at high frequencies (> 20GHz), these sources work for a narrow band and are not efficient. An alternative way to achieve CP is by using polarization converters that convert LP to CP. Natural sources of polarization converters of EMR are bi-refrigerants, like calcite quarter-wave plates, that have different refractive indices in different directions helping to achieve the required path and phase differences. However, for microwave and millimeter waves, the conventional polarization converters become bulky and have high insertion losses.

The use of frequency-selective surfaces (FSS) and meta-surfaces (MS) is another option for producing LP to CP conversion at microwave and millimeter wave frequencies which helps in the miniaturization of the converter. It is well known that the FSS⁹ and MS¹⁰ can control the transmission, reflection, and absorption¹¹ of electromagnetic waves. They can also manipulate the phase of the radiation as well as their polarization states. Therefore, MS and FSS have emerged as alternatives to natural polarization converters that can convert linear to linear^12,13, linear to circular^14,15,16, circular to linear^17,18,19, and circular to circular¹⁷ polarization states. Carefully changing the shape, size, and orientation of the structure efficient LP to CP polarization conversion can be achieved.

Polarization converters using FSS can work either in reflection^20,21,22 or transmission modes^23,24,25. The transmission mode polarization converters are preferable for point-to-point communication and other equivalent applications. Multilayer Structures^{26,27,28,29,30,31} for polarization converters exhibit a low insertion loss and work for broadband frequencies. Cross-layer capacitance between layers and better impedance matching enables lower loss and broadband characteristics. However, this performance enhancement increases fabrication difficulties, and repeatability is harder to achieve. Due to high structural complexity, the fabrication of multiple layers for polarization converters consists of alignment and assembly errors and is unsuitable for practical application. Also, due to multiple resonating elements, it is observed that higher-profile polarization converters are less stable for oblique incidences. A polarization converter with low insertion loss and lower structural¹¹ complexity is relevant for practical application. Yong et al. proposed an FSS circular polarizer consisting of three cascaded metal screens³². The Jerusalem slot was used as an element for the FSS circular polarizer to produce an entirely metallic screen. The proposed polarizer operated from 27.5 to 30.1GHz, while stable up to angle of incidence θ = 20°. Lin et al.³³ proposed a transmission mode meta-surface that consisted of dual-substrate layer FSS for LP to CP conversion in the frequency range from 12.21 to 18.39GHz. However, no angular stability was reported in the literature. Naseri et al. also proposed a dual-substrate layer LP-to-CP converter that worked in two bands of 19.7–20.2GHz and 29.5–30GHz with an angular stability of 45° but with a narrow bandwidth of 0.5GHz³⁴. Bin Wang et al. suggested a dual-band linear-to-circular polarization converter based on two metal layers on a dielectric substrate³⁵. The element of the converter consists of two identical metallic layers with a combination of a connected Jerusalem cross and an I-type dipole for each layer. The 3-dB bandwidth of the proposed structure is 18.46 to 21.27GHz and 26.94 to 30.13GHz with 20° angular stability.

CP waves play an important role in efficiently transmitting signals in satellite and point-to-point communication. However, receiving CP waves with LP antennas causes a 3 dB energy loss. Therefore, CP to LP conversion efficiently receives the CP signal even with conventional LP antennas. Though one can find a lot of research on LP-to-LP and LP-to-CP conversions, very little has been done for CP-to-LP conversion with a special interest in transmission mode. Nan Shao et al.¹⁸ proposed a design of a CP to LP converter operating for 5.35 to 6.3GHz based on an FSS consisting of two types of via-coupled patch modules. The structure has a low loss however the angular stability is not reported for the structure. Also the structure works in a narrow frequency band. Andrey Sayanskiy et al.³⁶ designed a self-complimentary meta-surface for CP to LP conversion for sub-terahertz frequencies. The metasurface consists of rectangular patches and apertures of an aluminum layer deposited on a thin polypropylene film. This MS works for a frequency range of 230–540GHz. Here the total insertion loss is not mentioned but from graphs it is observed that structure has high loss over the working frequency band. Also the angular stability is not mentioned. Zhen Qiao et al.³⁷ proposed a reconfigurable circular-to-linear polarization converter. The converter is a three metallic layers on two substrates type design, which also consists of metal via between the layers. The frequency-selective surface works for 8.11–9.95GHz with an insertion loss of −1.4 dB and an angular stability of 15°.

Though there exists literature on FSS-based LP to CP converters, there is a necessity to look for new designs that have an improvement in the angular stability, insertion loss, and structural complexity. Transmissive CP to LP converters have great scope for research due to their importance in receiving signals efficiently. This paper focuses on designing a simple, transmission-type FSS for the LP to CP and CP to LP converter suitable for operating in the 5G band (24 to 28GHz). The proposed design achieves a perfect linear to circular polarization conversion at 27.3GHz with nearly zero loss. The structure also exhibits a transmission greater than 98% with a wide 3 dB axial ratio bandwidth of 21.9–28.4GHz. The polarization conversion is stable at an angle of incidence upto 60°, which makes it the most angularly stable structure reported so far. At the same time, the proposed structure can convert CP to LP with a polarization conversion ratio (PCR) of 90% or more at this frequency range. Perfect circular to linear polarization conversion is observed at 27.3GHz with PCR of 99.99% and transmission of more than 98%. Though this structure has been intended for high-band 5G frequencies, it can be tuned for a wide range of frequencies just by scaling the lateral dimensions.

Design

The available FSS-based polarization converters with multiple layers and high structural complexity are hard to realize, so the idea is to make a simple FSS for polarization conversion. Dielectric substrates with metallic layers on both sides are easily available and selected for making this polarization converter. To make a non-lossy transmission-type polarization converter, a low dielectric constant of the substrate was chosen with a small loss tangent (tanδ). The unit cell of the FSS is made up of periodic unit cells of copper on each side of the dielectric substrate. Rogers RT5880 with a dielectric constant (ε) of 2.2 and loss tangent (tanδ) of 0.0009 is used as the substrate. The thickness of the substrate, h is 1.57mm. The unit cell has a periodicity of a = 5mm. The schematic of the structure is shown in Fig.1. and the dimensions in millimeters are given as: a = 5, w1 = 0.3, b = 2.40, w2 = 0.21, and g = 0.4. The thickness of the copper is 0.035mm, and its conductivity is 5.8 × 10⁷ S/m.

Conversion of LP to RCP & LCP

The unit cell structure is simulated using CST Microwave Studio with Floquet mode in the frequency domain. The unit cell boundary condition is used for x- and y- directions indicating that the structure is infinitely periodic. On the other hand, for the z direction which is the direction of propagation of EM wave, an open add space boundary condition is used. For LP to CP conversion simulations, TE₀₀ (Y-polarized: \(\:\:{E}_{yi}=\:{E}_{0}{e}^{-jkz\:}{\widehat{e}}_{y}\)) and TM₀₀ (X-polarized: \(\:{E}_{xi}\:=\:{E}_{0}{e}^{-jkz\:}{\widehat{e}}_{x}\)) modes of electric field were used as incident waves.

The transmission characteristics of the electromagnetic wave can be expressed by the matrix

The amplitude of the incident and transmitted fields can be expressed as

Here \(\:\left|{T}_{xx}\right|\), \(\:\left|{T}_{yx}\right|\), \(\:\left|{T}_{xy}\right|\), and \(\:{|T}_{yy}|\) are the transmission coefficients and \(\:{\theta\:}_{xx}\), \(\:{\theta\:}_{yx}\), \(\:{\theta\:}_{xy}\), and \(\:{\theta\:}_{yy}\) are their corresponding phases. The transmission coefficients are given by:.

Axial ratio (AR) is the parameter that characterizes the extent of circular polarization³⁴.

and,

where the phase difference Δθ = \(\:\:{\theta\:}_{yy}-{\theta\:}_{yx}\)determines the extent of circular polarization conversion. It is well known that for LP to CP conversion, the amplitudes of co and cross-polarized components should be equal and the phase difference between them should be ± 90°. Moreover, for an ideal circular polarization, the axial ratio will be 1 (0 dB). However, an axial ratio greater than 0.5 (−3 dB) is considered allowed as CP waves.

The efficiency of the LP to CP polarization conversion is defined by the term polarization conversion ratio (PCR), which is defined by.

The incident CP waves interact with the FSS and the transmission matrix represents the electric fields of the transmitted LCP and RCP waves. The superscript of T denotes the transmission mode and the subscripts of ‘+’ and ‘-’ denote the RCP and LCP waves respectively. \(\:{T}_{+-}\) and \(\:{T}_{-+}\:\)represent the cross-polarization complex transmission coefficients of RCP and LCP waves.

To convert an incident RCP (or LCP) wave into an LP wave, equal components of RCP and LCP should be present and the phase difference between them must be 0° or 180^o. The following matrix can mathematically explain the CP-to-CP polarization conversion.

The transmission matrix³⁸ of the CP wave is,

Here, \(\:{T}_{++},{T}_{-+},{T}_{+-},{T}_{--\:}\)are the transmission coefficients. And \(\:{{T}_{xx},{T}_{yx},T}_{yy},{T}_{xy}\) are transmission coefficients for linear components. For an RCP incidence,

The transmitted CP waves can be broken down into LP components.

When RCP and LCP waves have a phase difference of 0° and 180°.

The conversion of CP to LP can be expressed in terms of linear components,

For CP-polarized EM waves, both incident components \(\:{E}_{xi}\) and \(\:{E}_{yi}\) are \(\:\frac{{E}_{0}}{\sqrt{2}}\).

Due to the symmetrical structure of FSS, the magnitude of transmission coefficients for co-polarized (|T_xx|= |T_yy|) and cross-polarized components (|T_yx|=|T_xy|) are equal for both X- and Y-polarized waves. For \(\:{jT}_{xx}={T}_{yx}\:\)and \(\:{jT}_{yy}={T}_{xy}\:\), RCP to Y polarization conversion is observed. A similar analysis confirms LCP to X polarization conversion.

The extent of CP to LP polarization conversion can be analyzed from the polarization conversion efficiency (PCR) of the transmitted wave is defined as,

Experimental setup

To verify the results of the polarization converter from simulations, the structure is fabricated on Rogers RT5880 laminate. The schematic of the fabricated sample is in Fig.2a).

The measurements are taken with a pair of horn antennas and a vector network analyzer (VNA) (FieldFox Network Analyzer N9951A). Two horn antennas, connected to the VNA, are used as the transmitter and receiver, as shown in Fig.2b), c). Transmission coefficients and phase differences are recorded for co- and cross-polarized components. Normalization is performed with air to offset the losses. Values are recorded for normal incidences of perpendicular polarization and oblique incidence up to 60° to check the angular stability.

Simulation results

Conversion of LP to RCP & LCP

Analysis of the results from the simulations suggests that the structure transmits an equal co-polarized and cross-polarized at 27.3GHz with a phase difference of ± 90° between them. Nearly zero insertion loss is observed at this frequency with a peak transmission of 98.21%. The axial ratio, almost 0 dB, and PCR of 99.98% at this frequency suggest a perfect CP polarization conversion. The 3-dB bandwidth of CP is observed at the frequency band from 21.9 to 28.4GHz, and PCR is more than 90%. For this frequency range, the maximum transmission loss is − 1 dB.

For the Y-polarised input, the phase difference is + 90° or −270°, and for the X-polarized input, the phase difference is − 90° or + 270° at 27.3GHz. So, Y-LCP and X-RCP conversion is seen here. The structure is symmetric to the two diagonal axes, and by 90° rotation of the FSS, the handedness of the CP wave can be changed. The band 21.9 to 28.4GHz has been studied in this paper for making a CP converter in a high-frequency 5G band. Figure3. shows variation of transmission coefficients, phase differences, axial ratio, and polarization conversion ratio.

Polarization conversion & equivalent circuit

The polarization conversion action of the proposed converter is better understood by the response from its symmetrical axes. The proposed FSS is symmetrical with respect to two orthogonal u and v axes as shown in Fig.4a). For X or Y-polarized incidence, it can be decomposed into component form,

The condition of perfect LP to CP conversion is orthogonal components \(\:\left|{E}_{u}\right|=\left|{E}_{v}\right|\), and the phase difference (\(\:\varDelta\:{\phi\:}_{uv}\)) between them is 90°. As the u and v-polarized waves experience different structures, the transmission and phase response are different along these axes. High co-polarized transmission is observed for both u and v polarized waves which confirms low loss characteristics of the FSS, as shown in Fig.4b). The 3 dB axial ratio is found to be in 21.9–28.4GHz with a perfect LP to CP conversion at 27.3GHz as shown in Fig.4c).

The response of FSS is further verified with equivalent circuit analysis of responses from symmetrical axes. The values of capacitances and inductances are primarily calculated using Eqs.(16) and (17)³⁹. Then parameters are optimized to get a better idea of the polarization conversion.

The results from the simulation are compared with an equivalent circuit model. The equivalent circuits for u and v polarized waves are shown in Fig.5. The circuit analysis shows a good match with the simulation result, but with reduced performance that can be incorporated with the simplification of the FSS into lumped elements. The values of optimized lumped elements for v-polarized incidences are L1 = 0.638 nH, L2 = 0.3763 nH, L3 = 1.235 nH, L4 = 0.206 nH, L5 = 0.7003 nH, L6 = 0.531 nH, L7 = 0.4028 nH, L8 = 0.338 nH, C1 = 0.022 pF, C2 = 0.003 pF, C3 = 0.0209 pF, C4 = 0.001 pF, C5 = 0.0412 pF, C6 = 0.002 pF, C7 = 2.1058 pF. The optimized values lumped elements for u-polarized are C10 = 0.0209 pF, C11 = 0.4 pF, C12 = 0.149 pF, C13 = 0.024 pF, C14 = 0.093 pF, L9 = 0.267 nH, L10 = 0.1466 nH, L11 = 0.307 nH, L12 = 0.348 nH, L13 = 0.5437 nH.

Surface current and electric field analysis

The surface current and electric field patterns are analyzed to understand the polarization conversion action at 27.3GHz. The polarization conversion action is the result of surface plasmon resonances of different resonant structures and the coupling of the EM field with them. When an EM wave incident on the FSS, electrical currents flow on the copper elements. Copper patches act as an inductor whereas gaps in the patches act like capacitors. The flow of current in the metal structure gives rise to a magnetic field and the accumulation of charges induces capacitive coupling in the arms producing an electric field in the FSS.

For a Y-polarized electromagnetic incident wave, a maximum current density is observed at opposite arms of the inner square ring. The surface current distribution on the top and bottom layer is shown in Fig.6. Parallel currents flows in the opposite arms of the top layer. In the bottom layer also parallel current flows in the corresponding arms however in the opposite direction. Antiparallel current flowing between top and bottom layers causes strong magnetic resonance. This can be interpreted as current flowing in a closed loop between the top and bottom layers and the generate magnetic field that has a direction perpendicular to the loop (along u-axis). The obliquely placed inner square ring with respect to incident Y-polarized EM waves acts as cross polarization converter. EM wave on incidence on the FSS generates surface current on the top layer first and then surface current is induced on the bottom surface. This leads to a phase delay for surface current on the bottom layer with respect to the top layer. A Strong electric field is observed in the gaps of the inner square ring and between the arms of the inner and outer rings. The strong electric field is generated due to the coupling between metal structures. Electric field distribution for a Y polarization incidence is shown in Fig.7 on the upper layer (a) ϕ = π/2 (b) ϕ = 3π/2, and on the lower layer (c) ϕ = π/4 (d) for ϕ = 5π/4. The electric field in the front and back structures is out of phase, and some additional phase delay is present. The resultant electric field is directed towards the diagonal v-axis. Thus, the induced electric and magnetic field makes perpendicular walls that bend the incident LP radiation, and phase delays due to electrical and magnetic coupling enable the conversion of LP into CP radiation.

Angular stability

There is always a finite probability that electromagnetic waves can incident obliquely onto the FSS. So, the angular stability of FSS is very important for the polarization conversion application. We find that the structure is stable up to 60° incidence. The angular stability is due to the consistent current path provided by the square ring structure under oblique incidences. This consistency minimizes variation in effective inductance and capacitances of the structure and gives a stable variation of phase and transmission. The surface currents for different oblique incidences on the top and bottom surfaces are similar, with dense currents in the opposite arms of the inner rings for normal and oblique incidences. The choices of simple structure and the elements used in the unit cell design were important for angular stability. An angularly stable LP to CP conversion at 27.3GHz is observed. For oblique incidences upto 60° only a small variation of axial ratio and PCR is observed. For a normal incidence, the 3-dB bandwidth of CP is observed at the frequency band from 21.9 to 28.4GHz. The axial ratio plot for angular stability is shown in Fig.8.

The introduction of a gap within the inner square ring is crucial for achieving LP to CP conversion, as it introduces structural anisotropy. Without a gap, no cross-polarization conversion is achieved and the axial ratio is always very high. The variation of axial ratio bandwidth with the gap (g) is plotted in Fig.9a). From the simulations, it is found that with an increase in the gap, the polarization conversion occurs in higher frequencies and also 3 dB fractional bandwidth increases. A fractional bandwidth of 23.8% achieved with g = 0.4mm is selected because it entirely covers the high band 5G frequencies and is centered in this frequency range.

Though we have used the commercial substrate, Rogers RT5880, which has a thickness of 1.57mm, we studied the effect of thickness variation on the performance. Figure9b) shows that the axial ratio is close to 0 dB at 27.3GHz for any thickness variation between 0.8 and 2.4mm.

It is also possible to shift the center frequency at which the conversion from LP to CP can be achieved by scaling the structure. The variation of the pattern of the center band with lateral scaling is shown in Fig.9c), where x is the scaling factor. With the increase in unit cell dimension, the center frequency shifts to a lower frequency. The structure can work for 11GHz (x = 2.4) to 35GHz (x = 0.7) frequency bands with high efficiency and low transmission loss. Therefore, the proposed unit cell can be tuned over a wide range of frequencies for polarization conversion.

Comparison with literature

Table1. provides a comparison between the proposed structure and the FSS reported in the literature. Structures with multiple layers mostly exhibit a low insertion loss and are effective for broadband frequencies. Multilayer structures^{26,27,29,30,31,40} demonstrate very high bandwidth with a transmission loss of less than 1 dB. These high bandwidths are superior to the proposed structure. However, due to high structural complexity, fabrication is error-prone and unsuitable for practical application. Our structure shows the same transmission loss of 1 dB and uses only one substrate layer. Additionally, these structures have limited angular stability, with a maximum of 30°. Our structure exhibits superior oblique incidence stability upto 60°.

In ref^41,42,43. present less complex structures, comprising three metallic layers on two substrates. These designs achieve low transmission loss (approximately 1 dB) and better angular stability at oblique incidences of 45° and 50°. However, their cascading layers have challenges for integration complexity and error associated with it, as well as limited bandwidth. The proposed structure, with its simpler two-layer design, offers improved angular stability (60°) while also achieving enhanced percentage bandwidth compared to these designs.

For similar dual metallic layer-based FSS designs^35,44,45,46, the 3 dB bandwidths achieved are comparable to the proposed FSS. However, a major improvement is observed in insertion loss compared to these reported structures. A low insertion loss of less than 1 dB is observed compared to previously reported 1.79 dB. Also, the proposed FSS is higher angular stable than the reported structures in the literature. The proposed FSS, with structural simplicity, high angular stability (60°), wide 3-dB bandwidth, and low insertion loss, makes it a compelling alternative for practical applications.

Conversion of CP to LP

The simulations are performed in CST Microwave studio using the Floquet boundary conditions. Both RCP and LCP waves are used as excitation signals, and output is analyzed in CP and LP components. In the CP-to-CP module, transmission coefficients for Co- and cross-polarized (RCP and LCP) components are equal at 27.3 with a phase difference of 180° or −180° and 0° for RCP and LCP incidence, respectively. Using Eq.(12), RCP to Y-polarization conversion and LCP to X-polarization conversion are calculated at 27.3GHz. Similarly, by 90° rotation of the structure, LCP-to-Y polarization conversion and RCP-to-X polarization conversion are calculated at 27.3GHz. The PCR for CP to LP conversion is over 90%, and the maximum transmission loss is −1 dB for 21.9–28.3GHz. A peak PCR value of 99.99% is found at 27.3 with a transmission over 98%. In Table2, the performance of the proposed FSS is compared with that of already reported transmissive type CP to LP converters. It can be noted that the proposed FSS has a wide bandwidth and low transmission loss. Variations of transmission coefficients of CP and LP components, phase difference, and PCR for CP to LP conversion are shown in Fig.10.

Comparison with literature

The proposed structure has a lower loss than the reported^18,36,37 literature. A 3 dB percentage bandwidth of 80.5% is reorted³⁶ using a layer structure. However, this structure is subjected to higher loss, and no angular stability is reported. Our two-layer structure achieves a 3 dB percentage bandwidth of 23.8%. Also, it shows angular stability upto 60° for a reduced bandwidth of 25.6–27.6GHz with a PCR value of more than 90%.

Experimental results

Experiments are performed to verify polarization conversion. From the measured transmission coefficients and phase differences, the axial ratio, PCR, and CP components are calculated. Perfect linear to circular polarization conversion is observed at 28.4GHz. Equal Y- and X-polarized components are recorded at 28.4GHz and also phase difference between them is nearly 90°. The recorded transmission coefficients are shown in Fig.11a). The 3 dB bandwidth for normal incidence lies in the 22.4–29.6GHz range (Fig.11b)). As supplementary Fig. S1 presents, a peak RCP transmission is observed at 28.4GHz with a PCR of 99.9%. The PCR for the whole 3-dB range 22.4–29.6GHz is more than 90% (Fig.11c)). To verify the angular stability, measurements are taken with oblique incidence. The axial ratio plots for oblique incidence upto 60° are shown in Fig.12. Efficient CP conversion observed upto 60° however, the 3 dB bandwidth decreases at higher frequencies.

Circular to linear polarization conversion is verified using the fabricated sample. Co- and cross-polarized transmission coefficients and phase differences between them are measured for Y and X-polarized incident waves as shown in Fig.13a) and supplementary Fig. S2. The transmitted RCP and LCP components are calculated using Eq.(9). The variation of CP components is shown in Fig.13b). Equal RCP and LCP components are transmitted at 28.4GHz. The transmission of LP components under the incidence of RCP wave is calculated using Eq.(14), and transmission coefficients for Y- and X-polarized waves are plotted in supplementary Fig. S3. Perfect Y-polarization conversion is observed at 28.4GHz and for the entire range of 22GHz to 29.6GHz, the transmission coefficients of Y-polarized waves are much higher than X-components. The same can be concluded from Fig.13c) shows PCR for CP to LP conversion, which is more than 90% for the 22–29.6GHz range with a peak conversion of 99.9% at 28.4GHz.

Results from simulations and experiments closely match. It is found that the results of transmission coefficients and phase difference are nearly the same. However, results from experimental measurements are 1.1GHz offset compared to simulation results. The shift is due to practical limitations and errors. The major reason is fabrication errors. The smaller dimensions of the unit cells, especially for inner rings, were not perfect. The error in the fabrication of corners of the inner ring and the gap dimension leads to this shifting of frequency.

Authors and Affiliations

1. Microwave Laboratory, Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, Tamilnadu, India

   Akash Paramanik,Krishnamurthy Chitti Venkata&Venkatachalam Subramanian

Contributions

Akash Paramanik designed the frequency-selective surface, performed simulation and experiment, and wrote the main manuscript text. Krishnamurthy Chitti Venkata supervised the entire work and revised the manuscript. Venkatachalam Subramanian supervised the entire work, validated the findings, and edited the manuscript. All the authors have reviewed the manuscript.

Corresponding author

Correspondence to Venkatachalam Subramanian.

Competing interests

The authors declare no competing interests.

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