Design of polarizer's unit cell

The proposed reflective polarizer consists of an eight-obsessed square loop as top FSS and orthogonally linked arrow, as shown in Fig. 1(a). The FSS is printed on the top of a commercially available FR-4 substrate with relative permittivity ɛ_r = 4.4, and loss-tangent tan δ = 0.02, which is metal-backed on the other side. Copper film with conductivity σ = 5.8 × 10⁷ S/m is used as metallic layer. The unit cell dimensions are optimized in a finite element method (FEM) based EM solver ANSYS HFSS with appropriate periodic boundary conditions. The final parameters are: p = 7.3 mm, l ₀ = 3.52 mm, l ₁ = 1.584 mm, l ₂ = 3.96 mm, w = 0.176 mm, g ₀ = 0.176 mm, and g ₁ = 0.13 mm, h = 2.4 mm, and t = 0.035 mm, as depicted in Fig. 1.

Fig. 1. (a) Top view, and (b) side view of the proposed reflective polarizer.

For a y-polarized wave incidence on the reflective polarizer, the co-pol (r _yy = |E _yr|/|E _yi|), and cross-pol (r _xy = |E _xr|/|E _yi|) reflectances are defined due to the asymmetry that exists. Here, E _x and E _y represent electric field oscillations along the x- and y-axes, respectively, with indices i and r denoting incident and reflected components. The simulated magnitudes and relative phase of the reflectances are shown in Fig. 2, and it seems clear that r _yy approaches zero at three frequencies, 5.05, 8.85, and 15.95 GHz, while r _xy reaches near-unity (see Fig. 2(a)). The term PCR determines the efficiency of any reflective linear-cross polarizer, expressed as

(1)$$PCR = r_{xy}^2 /( {r_{xy}^2 + r_{yy}^2 } ) $$

Fig. 2. Simulated (a) magnitudes and (b) phases of the co-pol and cross-pol reflectances of the proposed polarizer.

The PCR is above 90% from 4.92 to 5.18 GHz (C-band), 8.32 to 9.41 GHz (X-band), and 15.56 to 16.25 GHz (Ku-band), as shown in Fig. 3(a). In addition, the amount of energy getting dissipated in the substrate during the multiple reflections between the FSS and ground is estimated by energy conversion ratio (ECR), $ECR = r_{xy}^2 + r_{yy}^2$. The remaining energy is wasted via substrate losses, with almost 90% of incident energy reflected (see Fig. 3(a)). Besides linear-cross conversion, it also demonstrates linear-circular conversion. The circular polarization efficiency is calculated from the axial ratio (AR), calculated as in [Reference Li, Liu, Cheng, Chen and Tian18],

(2)$$R = \displaystyle{{r_{xy}} \over {r_{yy}}} \;$$

(3)$$Schi, \;\,\chi = 0.5\sin ^{{-}1}\left({\displaystyle{{2R{\rm sin}( {\Delta \phi } ) } \over {1 + R^2}}} \right)\;$$

(4)$${\rm Axial\;ratio}, \;\,AR = \vert {1/{\rm tan}( \chi ) \;} \vert $$

Fig. 3. Simulated (a) PCR, ECR, and (b) AR (dB) of the proposed polarizer with and without arrow dipole.

Here, the term schi (χ) represents the shape of the polarization ellipse. The simulated AR is ≤3 dB over the ranges 4.61–4.71 GHz (C-band), 5.44–7.68 GHz (C-band), 10.13–14.98 GHz (X, Ku-band), and 16.68–17.19 GHz (Ku-band), as shown in Fig. 3(b).

Since polarizer designs work based on the multiple plasmonic resonances, and three plasmonic resonances are dominant for the proposed design. The first resonance depends on the outer periphery of the figure of eight loops in the v-axis direction. The second resonance mainly depends on the substrate parameters like relative permittivity and thickness concerning ground, and the third resonance depends on the dimensions of the figure-of-eight loop along the u-axis direction (see Fig. 6). The PCR, ECR, and AR (dB) performance with and without arrow dipole is given in Fig. 3. For the design optimization for better performance, it is necessary to shift the higher resonance to the lower side by coupling along the u-axis direction to achieve a good AR bandwidth ≤3 dB. The arrow-shaped dipole is included in the proposed polarizer with square loops. The term ellipticity (e) can be used to describe the switching of circular rotation in successive bands, expressed as

(5)$${\rm Ellipticity}, \;\,e = \displaystyle{{2\vert {r_{xy}} \vert \vert {r_{yy}} \vert \sin ( {\Delta \phi } ) } \over {{\vert {r_{xy}} \vert }^2 + {\vert {r_{yy}} \vert }^2}}$$

The ellipticity range is varied from −1 (right-hand circular polarized, RHCP) to +1 (left-hand circular polarized, LHCP), as shown in Fig. 4. The handedness of circular rotation is sensitive to the relative phase (Δϕ) between co- and cross-pol reflectances, as in Fig. 2(b). This design is dual-polarized; the circular polarization's handedness will change if the y-polarized incidence is replaced with the x-polarized.

Fig. 4. Simulated ellipticity (e) of the proposed reflective polarizer.

Since the incoming wave on the metasurface is not always normal in practical scenarios, it is necessary to investigate the performance variation with the angle of incidence for both the transverse electric (TE) and transverse magnetic (TM) modes. The PCR and AR variations for different angles (0° to 60° in steps of 15°) are depicted in Fig. 5. If the incident angle varies, it is trivial that the input surface impedance seen by the EM wave is different for different incident angles and modes. For the proposed design, it is observed that the response is almost stable up to 45° (see Fig. 5), and performance degrades due to grating lobes at higher oblique angles and weak field couplings. Although PCR solely considers reflectance magnitudes, the behavior of PCR at various oblique angles is well explained by reflectance phases. PCR bandwidth is reduced as the angle of incidence is moved away from the normal. The cross-pol component (r _xy) has nearly unchanged amplitude and phase, whereas the co-pol reflectance has a significant angle of incidence dependence. The additional path between the metasurface and the ground influences the phase of co-pol reflectance significantly, creating a phase difference compared to normal incidence calculated by Bragg's diffraction [Reference Shukoor, Dey, Koul, Poddar and Rohde12].

(6)$$\Delta \phi = \phi _{oblique}-\phi _{normal} = 2\sqrt {\varepsilon _r} kd\left({\displaystyle{1 \over {\sqrt {1-\displaystyle{{{\sin }^2\theta } \over {\varepsilon_r}}} }}-1} \right) $$

Fig. 5. Simulated PCR for the (a) TE, (b) TM, and AR (dB) for the (c) TE and (d) TM modes for different elevation angles (θ).

Here, θ is angle made by the incident ray with reference to polarizer normal, k is the wavevector in the dielectric medium. The reason behind the multiband multi-polarization conversion is analyzed in later sections.

Analysis and discussion

Analysis using transfer matrix method (TMM)

To acquire a true understanding of the physical mechanism involved in the polarization conversion, two orthogonal axes, u- and v-, are specified at 45° counterclockwise to the x–y axes (see Fig. 6). The incident electric field for a wave traveling along the negative z-axis is expressed as $\overrightarrow {E_i} = ( E_i^u \tilde{u} + E_i^v \tilde{v}) e^{jkz}$, where $E_i^u$ and $E_i^v$ are the components along u- and v-axes, respectively. From the TMM technique [Reference Shukoor, Dey, Koul, Poddar and Rohde12], the reflected field components can be written as

(7)$$\left[{\matrix{ {E_r^u } \cr {E_r^v } \cr } } \right] = \left[{\matrix{ {r_{uu}} & {r_{uv}} \cr {r_{vu}} & {r_{vv}} \cr } } \right]\left[{\matrix{ {E_i^u } \cr {E_i^v } \cr } } \right] $$

Fig. 6. Schematic view of the proposed reflective polarizer unit cell for uv-analysis.

The influence of cross-pol reflectance is very low and ignored since the unit cell design is symmetric along uv-axes. Then the reflected field component can be expressed as

(8)$$\overrightarrow {E_r} = ( r_{uu}E_i^u \tilde{u} + r_{vv}E_i^v \tilde{v}) e^{{-}jkz} $$

The simulated magnitudes and phases are depicted in Figs 7(a) and 7(b), respectively. The magnitudes of r _uu and r _vv are almost unity over the band, with a tiny dip at frequencies 4.95, 9.05, and 16.15 GHz (see Fig. 7(a)). The eigenmodes at 4.95 and 16.15 GHz are stronger (have a higher Q-factor) than the mode at 9.05 GHz. If the substrate loss is ignored, $r_{uu} = e^{j\varphi _u}$, $r_{vv} = e^{j\varphi _v}$, and Δφ = φ_u − φ_v are obtained [Reference Lin, Guo, Lv, Wu, Ma, Liu and Wang19]. Different combinations of magnitudes and phases with the conditions for possible polarization conversions are summarized in Table 1.

Fig. 7. Simulated (a) magnitudes of r_uu, r_vv, and (b) relative phase (Δϕ_uv).

Table 1. Summary of polarization conversion for different relative phases (Δφ) and magnitudes (r _uu and r _vv)

Surface current distribution analysis

Surface current patterns of the polarizer's metallic portion are investigated to better understand the physical phenomena behind polarization conversion. At resonant frequencies, 5.05, 8.85, and 15.95 GHz, the current profiles for the top FSS and ground are depicted in Fig. 8. The symmetric and asymmetric linkage of incident EM fields induces plasmonic resonances, which may be electric or magnetic. From Fig. 8, the induced surface currents are antiparallel for the top FSS and ground plane at 5.05 and 8.85 GHz resembling the magnetic or dielectric resonance. In contrast, the currents are parallel for the 15.95 GHz case, resulting in electric resonances [Reference Shukoor and Dey9].

Fig. 8. Surface current distributions of top FSS at (a) 5.05 GHz, (b) 8.85 GHz, (c) 15.95 GHz, and for the ground at (d) 5.05 GHz, (e) 8.85 GHz, (f) 15.95 GHz.

Fabrication and measurement setup

For the experimental verification, a 20 × 20 array (146 mm × 146 mm) of the proposed prototype is fabricated using traditional printed circuit board (PCB) technology, as shown in Fig. 9(a). The top FSS was printed on a thin 2.4 mm grounded FR-4 substrate. The free-space measurement technique is adopted for the reflection properties extraction of the sample [Reference Shukoor, Dey, Koul, Poddar and Rohde12], as depicted in Fig. 9(b). Two horn antennas (800 MHz–18 GHz) for the transmission and reception were connected to Keysight Power Network Analyzer (PNA) N5224B. The calibration of the PNA is done with the perfect electric conductor (PEC) sheet having the same dimension as the prototype. The measured reflectance (co-pol and cross-pol) is compared with the simulated one, and good matching is observed (see Fig. 10). The measured PCR and AR (dB) are depicted in Fig. 10.

Fig. 9. (a) A 20 × 20 array of the fabricated prototype. (b) Free-space measurement setup.

Fig. 10. Comparison of measured reflectances with the simulated results.

For the oblique TE incidence, the transmitting and receiving antennas were moved away from the normal of the designed metasurface. The incident angle is varied from 0° to 60° in steps of 15°, and the reflectance measurement was done for both co-and cross-pol components. Both the antennas were rotated by 90° for the TM case. The measured PCR and AR (dB) for TE and TM incidences are depicted in Fig. 11. The proposed polarizer's performance is compared to Table 2's other recently reported state-of-the-art designs. The authors strongly believe that this design has the potential which can be suitable for real-time applications due to its compact size and multi-conversion performance with circular rotation switching in consecutive bands.

Fig. 11. Measured PCR for the (a) TE, (b) TM, and AR (dB) for the (c) TE and (d) TM modes for different elevation angles (θ).

Table 2. Performance comparison of the proposed design with other recently reported state-of-the-art polarizers

*λ_L is the free-space wavelength corresponding to the band's lowest frequency.