An ultra-wideband thin metamaterial linear cross-polarization conversion

Abstract

This article presents the design of a novel ultra-wideband, thin metamaterial linear cross-polarization converter (CPC) operating at microwave frequencies. The CPC consists of two concentric deformed rings on a dielectric substrate backed by a metallic surface. It demonstrates co-polarization and cross-polarization reflection coefficients below − 11 and above − 1.1 dB, respectively, over a wide frequency range of 8.75–17.75 GHz, achieving a 68% bandwidth. Within this range, the polarization conversion ratio exceeds 90%, with three prominent peaks at 9.3 GHz, 13 GHz, and 17.4 GHz, reaching 99.5%, 99.8%, and 99.3% respectively. The unit cell dimensions are compact at 6.3 × 6.3 × 2 mm³. The CPC’s performance was analyzed under varying polarization and oblique incidence angles, and the surface current distributions were studied to elucidate the polarization conversion mechanism. Simulations using CST and FEKO demonstrated substantial agreement, also equivalent circuit is determined and compared to CST software. The compact, thin, and ultra-wideband design makes this CPC a promising candidate for applications in advanced communication systems such as radar cross-section reduction and electromagnetic interference suppression. The results are validated further by experimental measurements of the fabricated CPC.

Introduction

In today’s world, with the growing popularity of wireless telecommunications and the widespread use of various frequency bands, polarization has become a key concept in electromagnetic theory¹. Polarization refers to the direction in which the electric field oscillates, perpendicular to the direction of wave propagation.

Polarization converters, essential electromagnetic devices, modify the polarization state of electromagnetic waves, leading to significant enhancements². Given the wide range of polarization applications, controlling polarization has attracted significant attention from researchers^3,4. Polarization converters have been explored for various applications, such as enhancing antenna gain⁵, reducing radar cross-section (RCS)⁶, and in measurement rooms and antenna laboratories. Researchers aim to develop cross-polarization converters (CPCs) that are not only thin, lightweight, and cost-effective but also offer maximum bandwidth. Researchers design CPCs to transform linear polarization into an orthogonal state, enabling advanced functionality in numerous electromagnetic applications.

Historically, the design of polarization converters involved large, cumbersome devices⁷. The narrow bandwidth of these early designs, along with the challenges of miniaturization, limited their practical applications. Due to their lightweight and compact nature, researchers have developed metamaterial polarization converters to address these issues¹.

It is possible to change the polarization of metamaterials and metasurfaces across a wide range of frequency ranges^8,9, such as microwave^10–12, terahertz^13,14, infrared¹⁵, and visible¹⁶. These materials find applications in optical lenses¹⁷, antennas¹⁸, energy harvesting¹⁹, sensors²⁰, cloaking devices, absorbers^21–23, and polarization converters^24–27. They are employed in single-layer^28–30 and multi-layer^12,31,32configurations, including cross-polarization converters (CPCs)^{12,29,33–36}.

This study introduces a novel ultra-wideband, single-negative metamaterial cross-polarization converter (CPC) that overcomes the limitations of existing designs, such as narrow bandwidth, large size, and low efficiency. Unlike traditional polarization converters, the proposed CPC achieves a compact design with dimensions smaller than λ/4, making it lightweight and ideal for integration into modern electromagnetic systems. Existing CPC designs often struggle to achieve high polarization conversion ratios (PCR) over broad frequency ranges while maintaining compactness and simplicity. Our proposed structure addresses this gap by offering a wide operating bandwidth from 8.75 GHz to 17.75 GHz (68%), with a PCR exceeding 90% across the entire band, and peak PCR values above 99% at specific frequencies (9.3 GHz, 13 GHz, and 17.4 GHz).

The significance of this work lies in its ability to combine ultra-wide bandwidth, high efficiency, and compactness, making it suitable for practical applications such as radar cross-section reduction, electromagnetic compatibility (EMC), antenna performance enhancement, and energy harvesting. By employing a novel concentric deformed ring configuration, we achieved these performance characteristics while maintaining fabrication simplicity. Additionally, we modeled the structure using an equivalent circuit, which provides valuable insights into the electromagnetic behavior of the CPC and serves as an additional tool for optimizing and analyzing its performance.

We validated the CPC’s performance through CST and FEKO simulations, as well as experimental measurements, demonstrating excellent agreement between the simulated and measured results. The remainder of this paper is organized as follows: Section "Structural design" outlines the structural design, Section "Analysis of metamaterial CPC in the proposed unit cell" presents the analysis of the metamaterial CPC in the proposed unit cell, and Section "Design and simulation results" provides numerical results, including an analysis of surface current distributions, parametric studies, and the equivalent circuit to explain the cross-polarization converter mechanism. Additionally, applications of the proposed structure, such as RCS reduction and EMC improvement, are discussed. Finally, Sect. 6 describes the fabrication process and compares the measured results with the simulations.

Structural design

This section outlines the design methodology for the proposed ultra-wideband metamaterial cross-polarization converter (CPC) in a systematic manner. First, the operational frequency range (8.75 GHz to 17.75 GHz) and target performance metrics, including a polarization conversion ratio (PCR) greater than 90% and compact dimensions (< λ/4), are defined.

The next step is to select an appropriate material to achieve the desired electromagnetic characteristics. Following this, the principles of metamaterials, specifically focusing on single-negative metamaterial behavior, are applied to design a compact and efficient unit cell.

Subsequently, a concentric deformed ring structure on a dielectric substrate is developed and optimized for high polarization conversion. The upper layer consists of a metallic patch, while the bottom layer serves as the ground plane. These two layers are separated by a 2 mm thick FR4 dielectric substrate. The top layer features two slits, and both the top and bottom layers are made of copper with a thickness of 0.035 mm. The unit cell dimensions are 6.3 × 6.3 × 2 mm³. Figure 1a illustrates the structure of the proposed ultra-wideband CPC.

Fig. 1.

(a) The dimensions of the CPC. (b) U–V coordinate in the proposed structure.

The dimensions of the proposed unit cell structure are illustrated in Table 1.

Table 1.

Dimensions of the proposed unit cell structure (unit: mm).

Ro	Rm	Ri	Wo	Wm	Wi	g1	g2	g3	P
2.65	1.625	1.325	0.5	0.8	0.7	0.5	0.8	0.7	6.3

Analysis of metamaterial CPC in the proposed unit cell

The study of metamaterial cross-polarization converters (CPCs) is divided into two parts; co-polarization and cross-polarization. For the cross-polarization converter, the magnitude of co-polarization reflection coefficient (|S_11xx|) is near zero, while the cross-polarization reflection coefficient (|S_11yx|) is close to unity. For |S₂₁|, both the co-polarization and cross-polarization transmission coefficients are near zero. These conditions result in a polarization conversion ratio (PCR) approaching one within the proposed bandwidth.

Analysis of co-polarization absorption

The relative permittivity and permeability of metamaterials are given by ε_r(ω) = ε₁ + iε₂ and μ_r(ω) = μ₁ + iμ₂, respectively. By designing a unit cell of the CPC and optimizing its parameters, it is possible for μ₁(ω) or ε₁(ω) to become negative. When β is imaginary (as shown in Eq. (1)), it leads to an increase in co-polarization loss. Consequently, the metamaterial surface attenuates the field (Eq. (2)), leading to the absorption of the incident wave in co-polarization.

1

2

Then refractive index is extracted from Eq. (3)³⁷. Also permeability and permittivity coefficients are extracted from Eq. (4) and Eq. (5)³⁸, respectively.

3

4

5

As shown in Fig. 2a, the real component of the relative permittivity of the designed structure is positive in certain frequency ranges and negative in others. In the frequency range where ε_r(ω) is negative, the real component of μ_r(ω) is positive, and vice versa. Prior to this bandwidth, a peak appears at 7.5 GHz. μ_r(ω) exhibits a sharp resonance, characterized by a peak followed by a dip. This behavior is typical in metamaterials designed for cross-polarization conversion, as it often corresponds to strong magnetic responses. ε_r remains relatively smooth and stable, which is engineered for magnetic resonance with minimal electric-field distortion.

Fig. 2.

(a) Real part of εr(ω) and μr(ω). (b) Imaginary part of εr(ω) and μr(ω).

As shown in Fig. 2b, the imaginary component of the proposed structure’s relative permittivity is positive across the entire bandwidth. This figure utilizes Eqs. (4) and (5). Imaginary component of μ shows prominent peaks, which suggests energy absorption and dissipation in the magnetic domain. Imaginary components of ε_r remains close to zero, indicating negligible dielectric losses compared to magnetic losses. The values of relative permittivity and permeability are shown in Table 2.

Table 2.

The values of relative permitivity and permeability.

Frequency (GHz)	8.75	12.25	17.75
ε	125.3 + i123.8	52.1 + i130	− 6.7 + i54
μ	− 142 + i207	− 28.8 + i164	64 + i200

The parameters of the proposed structure are carefully designed to achieve an impedance ratio approximately equal to that of free space across the bandwidth ().

6

Equation (6) represents the normalized impedance of the CPC structure. To achieve the optimal value of S₁₁, there must be impedance matching between free space and the proposed structure. This results in Z(ω) to be close to one.

In Fig. 3a, the real part of the normalized impedance is plotted against the refractive index. The normalized impedance remains close to unity across the entire bandwidth, indicating excellent impedance matching within this frequency range. The refractive index varies, with some frequencies being negative and others being positive. Moreover, Fig. 3a displays a peak at 7.5 GHz.

Fig. 3.

(a) The real part of the normalized impedance and refraction index. (b) The imaginary part of the normalized impedance and refraction index.

As shown in Fig. 3b, the imaginary part of the refraction index remains above 99 across the bandwidth. The imaginary part of the normalized impedance is approximately zero. The exact values of the normalized impedance and refractive index are shown in Table 3.

Table 3.

The values of impedance and refrective index.

Frequency (GHz)	8.75	12.75	16.75
Impedance	0.916 + i0.6	1.014 + i0.036	1.149 + i0.205
Refractive index	19.96 + i209.33	12.24 + i1147.59	23.88 + i178.32

Analysis of cross-polarization conversion

The previous section demonstrated the absorption of the incident wave in the co-polarization direction. This section shows that, in the cross-polarization direction, absorption is eliminated, and the wave is instead reflected in the orthogonal direction.

The designed structure in relation to u-polarized and v-polarized incident fields is analyzed to understand the mechanism of polarization conversion. The structure features perpendicular axes aligned at + 45° and − 45°, as illustrated in Fig. 1b. It means incident field is and reflected electrical field is . Because of the chiral structure of the unit cell, cross-pol components are zero (). In addition, for cross polarization converting, we have . Therefore, it is concluded that . Now, that is phase difference of and is calculated, according to the reference³⁹:

7

For normal angle, |r_xx| must be equal zero for perfect cross-pol converting. Therefore must be 180° or − 180° for the above condition to be satisfied.

One condition for effective polarization conversion is that the amplitudes of r_uu and r_vv should be close to unity. As shown in Fig. 4a, the magnitudes of the u-polarized and v-polarized reflected fields are approximately equal to one. The losses within the structure are responsible for the observed decrease in amplitude.

Fig. 4.

(a) Amplitude of ruu and rvv. (b) Phase difference of ruu and rvv.

Another condition for effective polarization conversion is that the phase difference between r_uu and r_vv should be 180°. There are three instances of this 180° phase difference across the bandwidth, one at the beginning of the frequency range, another in the middle, and the third at the end. This is illustrated in Fig. 4b.

Reflected electromagnetic waves from the metasurface contain co-polarized and cross-polarized components. The matrix representing co-polarization and cross-polarization can be expressed as:

8

where R_xx and R_yy are the co-polarized reflected coefficients and R_xy and R_yx are the cross-polarized reflected coefficient.

Figure 5a illustrates that a zero incident angle results in a co-polarized reflection of less than − 11 dB from 8.75 to 17.75 GHz. In Fig. 5b, when the incident angle is zero, the cross-polarized reflection is above − 1.1 dB from 8.75 to 17.75 GHz, resulting in a bandwidth of 68%.

Fig. 5.

(a) Co-polarized reflection. (b) Cross-polarized reflection.

To determine the efficiency of cross-polarization the polarization conversion ratio (PCR) can be expressed as , |R_yx|² is the reflected power in y direction where the incident wave is in x direction and |R_xx|² is the reflected power in x direction where the incident wave is in x direction. Due to the metallic backside, the transmitted power is zero in both the x and y directions.

Figure 6 illustrates that the polarization conversion ratio of the vertically incident wave exceeds 90% across the entire bandwidth. Three polarization peaks are visible at 9.3, 13, and 17.4 GHz, with absorption of 99.5%, 99.8%, and 99.3%, respectively.

Fig. 6.

Polarization conversion ratio.

Design and simulation results

In this part the numerical results and an analysis of the surface current distributions, parametric studies, equivalent circuit are presented to explain the cross-polarization converter mechanism. Additionally, applications of the proposed structure such as RCS reduction and EMC are determined.

Various polarization and angles

The polarization behavior of the broadband CPC is analyzed under different incident angles, ranging from 0° to 90°, to understand the metamaterial structure’s response.

As shown in Fig. 7, both S_11,xx and S_11,yx exhibit two-fold symmetry. The reflectivity gradually increases as the polarization angle increases, reaching a maximum at 45°, and then decreases as the polarization angle approaches 90°. At normal incidence, for efficient polarization conversion, the amplitude of S_11,xx (co-polarized reflection) must approach zero. This minimizes the energy retained in the incident polarization state, ensuring that most of the energy is reflected in the cross-polarized state. Ideally, ∣S_yx∣≈1 and ∣S_xx∣≈0, leading to near-perfect polarization conversion.

Fig. 7.

S11 in different polarization angles. (a) S11xx. (b) S11yx.

At oblique incidence, the incident electric field has both parallel (TE-like) and perpendicular (TM-like) components with respect to the structure. The interaction between these components and the resonant modes of the structure becomes more complex. Specifically, at a 45° oblique incidence, the electric field components are maximally coupled to the resonant modes of the structure. This coupling results in significant amplitudes for both S_11,xx and S_11,yx, unlike at normal incidence. At this angle, the energy is efficiently distributed between the co-polarized and cross-polarized states due to the excitation of multiple resonant modes. This enhanced coupling improves the overall polarization conversion efficiency. Consequently, ∣S_11,xx∣ is near unity, while ∣S_11,yx∣ is near zero. However, the key metric remains the high polarization conversion efficiency, which arises from the resonant interaction between the fields. The formula analysis for this aspect was explained earlier, before Fig. 4.

It is observed in Fig. 8 that by rotating the inner part of the upper layer (inner deformed SRR loop) from 0° to 90° only the middle resonance increases up to 45°, then decreases up to 90°. The diagrams for other frequencies are nearly identical. The S₁₁ diagram remains under − 10 dB all over the bandwidth.

Fig. 8.

S11xx in different incident angles for TE polarization.

The designed CPC for different incident angles (up to 45°) are also investigated, as shown in Fig. 9. It is observed that for both S_11xx and S_11yx, as the oblique incident angle increases, the ultra-wideband S_11xx and S_11yx responses change rarely from wide-band to dual-band polarization. Up to 30degrees The S_11xx diagram remains under − 10 dB all over the bandwidth (Fig. 9a).

Fig. 9.

Amplitude of reflection in different incident angles (up to 45°). (a) S_11xx. (b) S_11yx.

Surface current distributions

The surface current distribution analysis reveals the resonant modes and their contribution to the polarization conversion mechanism. The interaction of the surface currents at different frequencies demonstrates how the structure supports multiple resonances, which result in ultra-wideband operation.

To understand all types of currents in the CPC structure, we plot the distribution of surface current at two frequencies. Through the FR4 dielectric, conduction current is present on the top and bottom conductors, while displacement current is present between the top and bottom layers. Figure 13 displays the surface current distribution. The outer split primarily distributes the surface current at 9.3 GHz. At 17.4 GHz, a small current flows through the inner ring. At 13.1 GHz surface current is distributed between the inner and outer ring with rotation of 90 degrees. This behavior ensuring ultra-wideband performance for cross polarization converter (Fig. 10).

Fig. 13.

S11 of CST, equivalent circuit and FEKO simulation.

Fig. 10.

Surface current. (a) 9.3 GHz (b)13.1 GHz. (c) 17.4 GHz.

Parametric studies

In this part parametric variations are studied to evaluate the effects of Ro, Ri, Wo and Wi on the proposed structure.

As the radius of outer SRR (R_o) increases, the resonance frequencies shift to lower values (leftward shift on the frequency axis). This happens because increasing the outer radius increases the effective inductance and capacitance of the SRR and a larger loop creates a longer path for current flow and increases the resonator’s overall effective dimensions, lowering the resonant frequency, but for radius of inner deformed SRR (R_i) it is vice versa spatially for the values above 1.5 mm. It means as the radius of R_i increases, the resonance frequencies shift to higher values. The depth of the S₁₁ peaks also change. For smaller Ro, the resonances are weaker (shallow peaks). As R_o increases, the resonance peaks become deeper due to improved coupling and stronger resonance effects. The larger loop allows more effective interaction with the incident electromagnetic wave (Fig. 11a,b).

Fig. 11.

Parametric studies (a) variation of Ri. (b) Variation of Ro. (c) Variation of Wi. (d) Variation of Wo.

If width of outer SRR (W_o)​ increases, the resonant frequencies shift left (toward lower frequencies) and If W_o​ decreases, the resonant frequencies shift right (toward higher frequencies,). This occurs because the effective capacitance of the ring structure is sensitive to the geometry. A wider W_o increases the overlap of electric field lines (and thus capacitance), decreasing the system’s resonant response. Conversely, a narrower W_o decreases capacitance, allowing the system to resonate at higher frequencies. As W_i increases, the resonant frequencies in the S₁₁ plot shift to the right (toward higher frequencies). This happens because increasing Wⁱ reduces the effective capacitance of the structure by increasing the gap between the inner and outer rings. Lower capacitance leads to higher resonant frequencies (Fig. 11c,d).

Validation with the equivalent circuit model and FEKO

The provided circuit is a multi-resonant network consisting of resistors, inductors, capacitors and a transmission line, designed to achieve impedance matching and minimize signal reflection at specific frequencies (Fig. 12). The corresponding S₁₁ parameter plot (return loss) indicates how well the input impedance matches the characteristic impedance Z₀, over the frequency band. Three RLC resonators are connected to a transmission line. This RLC combination creates multiple resonant frequencies where the input impedance achieves a good match with the characteristic impedance (377Ω).

Fig. 12.

Equivalent circuit.

The values of the proposed circuit are demonstrated in Table 4.

Table 4.

Values of the equivalent circuit.

R1	L1	C1	R2	L2	C2	R3	L3	C3	C5	C6	L4
2.5 Ω	65 pH	0.61 pF	15.9 Ω	0.5 nH	46.6 pF	0.25 Ω	2.4 nH	150 pF	316.2 fF	0.16 pF	13 nH

Each RLC combination in the circuit creates dip in the s₁₁ plot. At first RLC₁, RLC₂, RLC₃ are designed to achieve minimal reflection at 9.4 GHz, 13 GHz and 17GHz, respectively calculated by . Then the whole circuit is optimized to extract the proper S₁₁ plot. As it is shown in Fig. 13 There is a good agreement between the S₁₁ plots of the equivalent circuit model and CST.

The structure is simulated using a unit cell with periodic boundaries in CST and FEKO software. Figure 13 also compares the results of the FEKO and CST simulations. The differences between the simulations are attributed to factors such as mesh size and solver settings. Overall, there is good agreement between the CST and FEKO results.

Applications

RCS Reduction in CPCs are useful for Minimizing the reflected radar signal (RCS) while maintaining high polarization conversion efficiency. They are crucial for stealth applications, such as military Stealth Technology for Aircraft, Radar and Communication Systems for Reducing interference and enhancing signal clarity and polarization-based sensing. EMC Applications of Metamaterial CPCs are Polarization Control that CPCs can reorient electromagnetic waves to minimize interference between systems. Metamaterial-based CPCs can control which polarization states are transmitted or reflected, reducing crosstalk in densely packed systems.

The RCS of the proposed checkerboard surface can be written as⁴⁰:

9

The RCS reduction of the checkerboard surface, compared to that of PEC with the same dimension, can be approximated by

10

RCS Reduction behavior that is equal to S_11xx(dB), is shown in Fig. 13.

Fabrication

To test the proposed CPC in a real-world setting, a 37 cm × 37 cm sheet composed of unit cells was fabricated on a dielectric substrate. The 2 mm-thick dielectric FR4 substrate is placed on top of the metal surface. Figure 14 illustrates the fabricated structure.

Fig. 14.

Fabricated metamaterial CPC on FR4 substrate backed by a metallic surface.

For the measurements, a horn antenna is used. The reflected pattern is first measured from a linearly polarized antenna radiating toward the front of the CPC. Next, the radiation is measured from the back of the CPC, and the difference between these two measurements is referred to as the F/B ratio (front-to-back ratio). While reflection coefficients and PCR were directly evaluated in simulations, practical limitations in the measurement setup (e.g., alignment and calibration under varying incidence angles) prompted us to prioritize F/B ratio measurements as a robust and reliable experimental metric (Fig. 15).

Fig. 15.

Experimental setup for measuring the cross-polarization performance of the metamaterial in an anechoic chamber.

Figure 16 shows the F/B ratio measured at three frequencies. At 8.5 GHz, 12.5 GHz and 17.4 GHz the F/B ratio for fabrication are − 8 dB, − 18.04 dB and − 15.36 dB, respectively. And the value of F/B for simulation are − 8.1 dB, − 18.9 dB and − 16.4 dB, respectively.

Fig. 16.

F/B RATIO of the fabrication and simulation.

Figure 17 compares the results of the fabrication and simulation. The differences are attributed to factors such as errors in the fabrication process, testing equipment, and the antenna room. Nevertheless, the measured outcomes are consistent with the simulation results. As noted in Table 5, the new metamaterial structure offers a broader bandwidth compared to the other structures.

Fig. 17.

Measured return loss from CPC in (a) 8.5 GHz. (b) 12.5 GHz. (c) 17.5 GHz.

Table 5.

Polarization converter comparison.

Reference	Operating bandwidth (GHz)	Bandwidth (PCR > 0.9) (%)	Thickness (h/λ0)	Fabrication complexity	Incidence angle (°)	No of layers	Periodicity of unit cell (λ1) (in mm)
24	2.73–4.63	52	0.2	Complex	15	4	0.55 (22)
26	7.1–8 and 13.3–25.8	31	0.22	Simple	–	1	0.94 (7)
33	12–18	40	0.17	Complex	45	1	0.62 (6)
41	8–12	40	0.11	Simple	45	1	0.48 (6.92)
42	7.40–12.20	48	0.14	Complex	–	2	1.15 (17)
43	10.3–15.26	38	0.21	Simple	35	1	0.358 (12)
44	2.87–7.12	85	0.101	Simple	40	1	0.134 (14)
35	5.69–14.8	89	0.076	Simple	30	1	0.7 (13)
New structure	6.75–17.75	68	0.15	Simple	30	1	0.31 (6.3)

Conclusion

The study presents a highly efficient and compact ultra-wideband thin metamaterial cross-polarization converter (CPC) operating at microwave frequencies. The design demonstrates exceptional polarization conversion performance across a broad frequency range. Simulations and experimental validations confirm its reliability and effectiveness under varying conditions. The thin and compact structure makes it suitable for advanced communication systems, with promising applications in radar cross-section reduction and electromagnetic interference suppression. This work highlights the potential of the proposed CPC for practical use in modern technologies requiring wideband and efficient polarization conversion.

Author contributions

Pegah nochian has written the main manuscript and prepared figures. Dr. zahra atlasbaf has reviewed the manuscript.

Data availability

The calculated results during the current study are available from the corresponding authors on reasonable request.

Competing interests

The authors declare no competing interests.