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Abstract
Bi-functional meta-surfaces capable of simultaneously controlling polarization states and wave-fronts of electromagnetic fields are introduced into the design of Cassegrain system for the synthesis of multi-beams. More specifically, electromagnetic fields reflected by the secondary meta-surface with tailored diverged wave-fronts would be collimated by the primary meta-surface into multi-beams with transformed polarization states that can directly go through the secondary meta-surface without any blockage. Especially, we show that such a polarization-twisting meta-surface Cassegrain system can possess much more compact configuration by properly devising the phase distribution over the secondary meta-surface, and can also achieve high-purity polarized multiple radiations when we enlarge the secondary meta-surface as a radome. The present approach of integrating two bi-functional meta-surfaces into the design of Cassegrain system for the generation of multi-beams should pave the way for building up more advanced meta-surface based architectures with specific characteristics.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Generating high-purity polarized multi-beams for wireless connections has been widely applied in developing satellite communication and multi-target radar systems [1], where reflectors with multi-sources are normally employed for the multi-beam synthesis. Such systems allow the independent control of multi-beams, thus have offered great freedom in multi-channeling applications with specific connecting requirements. However, large-scale feed array in these designs would partially block the forward radiations from the reflector with the rise of sidelobes and also degrade the distinctions of the released co-polarized radiation from its cross-counterpart in specific radiating directions. Cassegrain dual reflecting system with the rear-feed setting-up can fundamentally remove such shadows from the excitations [2], but at the same time, brings in the blockage from the secondary reflector. Therefore, the feed-offset Cassegrain system is recommended in most scenarios to ensure the well-collimated multiple radiations from the primary reflector to radiate directly without accessing any blockage [3]. On the other hand, folded reflectarrays with polarizing grids and polarization twisting reflectors have also been proved as qualified candidates to build up the multi-beam antenna systems [4–7] with the merits of high-purity radiations. However, the total heights of such designs are usually fixed to be the half of focal length of the polarization twisting reflector due to the constant phases imposed over the polarizer surfaces.
Meta-surfaces have demonstrated a flexible way to manipulate the wave-fronts of electromagnetic (EM) waves [8–19]. Multiple radiations can be created using a single source through properly arranging the subwavelength meta-atoms based on the superposition of aperture fields [13–17]. Especially, when integrating the meta-surface lens into the design of the Cassegrain system as the primary component with the combination of a secondary meta-mirror, the blockage effects from the secondary meta-mirror could also be eliminated when generating multi-beams [17]. In the meanwhile, meta-surfaces optimized through alternating projection method have also demonstrated the great capacity of synthesizing multi-beams for efficiently and flexibly controlling the emission beams [18,19]. In addition, meta-surfaces have been shown to be capable of perfectly tuning the polarization states of EM fields with simultaneously controlling the wave directions as bi-functional interfaces [20–36]. Instead of solely regulating the phase information, these studies have demonstrated the complete manipulation of the light propagation by simultaneously controlling the phases and amplitudes of EM fields. If the Cassegrain system can fully utilize such bi-functional meta-surfaces to manipulate both the wave-fronts and the polarization states of EM fields, we would also have the opportunities to eliminate blockage effects and generate high-purity multi-beams. To be more specifics, the secondary meta-surface (SM) can reflect the linearly polarized EM fields from the feed at the first place with tailored diverged wave-fronts, while the primary meta-surface (PM) would then generate the well collimated multi-beams and simultaneously twist the polarization states of EM fields into the cross-linearly polarized counterparts, so that the final synthesized multi-beams would penetrate through the SM directly. With these considerations, we demonstrate the high-purity polarized multi-beam generations by proposing a polarization-twisting meta-surface Cassegrain system (PTMCS) with dual bi-functional meta-surfaces capable of controlling polarization states and wave-fronts of EM fields simultaneously. As opposed to the multi-source configuration, this approach using single feed integrated with bi-functional meta-surfaces would provide advantages in terms of blockage reduction and polarization purity, although does not allow for the independent control of radiating beams. In addition, our proposed design can obtain more compact configuration as long as we employ appropriate phase distributions over the SM instead of only imposing a constant phase as the conventional folded reflectarrays and the Cassegrain antennas with the same simplified phase setting over the SM. Especially, we will show that such a PTMCS in our design can also achieve high-purity polarized multiple radiations when we enlarge the SM as a radome.
2. Design and numerical results
Figure 1 schematically demonstrates the proposed PTMCS based on dual bi-functional meta-surfaces for the synthesis of four-beams at 15 GHz with $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 4}$ = $\begin {bmatrix} 15^\circ & 15^\circ & 15^\circ & 15^\circ \\45^\circ & 135^\circ & 225^\circ & 315^\circ \end {bmatrix}$. The SM consists of the top-side periodic metallic stripe polarizer, intermediate F4B dielectrics, and the bottom-side metallic sheet of gradient split ring resonators (SRRs) offering the required phase distributions, where each of the SM unit cell contains five metallic stripes. Such a structural construction would reflect the $y$-polarized EM waves with customized phases to mimic the hyperbolic reflector generating diverged wave-fronts for the more uniform illumination over the PM. In the meanwhile, the SM would also allow $x$-polarized EM waves from the PM to penetrate through the SM with few degradation of the overall radiation performances. On the other hand, the PM with gradient skew double-headed arrow resonators (DHARs) on the grounded F4B substrate would generate multi-beams. Such skew units with −45$^\circ$ and +45$^\circ$ are able to convert the original co-linearly polarized EM waves into its cross counterpart, while offering the sufficient phase gradients to tune the wave-fronts and radiating directions. The aperture size of the PM is chosen as 180 $\times$ 180 mm$^{2}$ with 9$\lambda _{0}$ $\times$ 9$\lambda _{0}$ at 15 GHz in the free space for the synthesis of multiple directive beams. It consists of 30 $\times$ 30 PM meta-atoms with 6 $\times$ 6 mm$^{2}$ for each unit cell. We have the focal length of $f_{PM}$ = 0.9$D_{PM}$ = 162 mm for the PM and set the separating distance $l$ between the PM and the SM equal to 1/3 of the focal length $f_{PM}$ through imposing proper phase distribution over the SM. The aperture size of SM is chosen as 120 $\times$ 120 mm$^{2}$ also with 30 $\times$ 30 SM meta-atoms having the size of 4 $\times$ 4 mm$^{2}$ for every unit cell. The SM can be further enlarged as there is no blockage in such a design. The focal length of the SM here is simply devised as the same value with $l$ having $f_{SM}$ = 54 mm. As a result, the maximum incident angles $\theta _{1}$ and $\theta _{2}$ of the SM and PM are 56$^\circ$ and 40$^\circ$ respectively. The corresponding incident angles for the meta-atoms over the SM and PM should be carefully determined due to the fact that the phase responses are sensitive to the incident angles. The phase distributions provided by the SM and PM can be calculated as
where $k$ refers to the wave number in the free space, $\varDelta l$ refers to the difference value between the physical length of $F_{1}A$ and the physical length of $F_{2}A$, $\varPhi _{p1}$ over the PM would reform the wave-fronts of the EM fields into the plane waves and $\varPhi _{p2}$ with additional phase gradients can split the plane waves into different directions, $\varPhi _{0}$ refers to an arbitrary phase constant that can adjust the phase distributions freely. More specifically, the phase compensations would followFigure 2 thus demonstrates the corresponding phase distributions of the four-beam PTMCS at 15 GHz and their synthesis using bifunctional meta-surfaces. The halo shaped phase pattern over the SM in Fig. 2(a) offers the required phase distribution to diverge the reflected $y$-polarized EM waves for the more uniform illumination over the PM. At the same time, the SM should give the passport to the $x$-polarized EM waves while maintaining a constant transmitting phase change, so that the collimated beams from the PM can perfectly transmit through. The PM in Fig. 2(b) possesses a series of concentric phase zones with superimposing the additional phase gradients of 0$^\circ$ and 180$^\circ$ simultaneously for the four-beam synthesis, while transforming the $y$-polarized EM waves into $x$-polarized EM waves. We can observe in Figs. 2(c) and 2(d) that the reflected amplitudes from the periodic SM units are shown to be nearly perfect and the reflected phases would be capable of covering 330$^\circ$ when the structural parameter $b_{2}$ varies from 1.0 mm to 3.9 mm under the illuminations from 0$^\circ$ to 56$^\circ$ for the $y$-polarized EM waves. Such a phase variation is sufficient for the phase responses of the SM. For the $x$-polarized EM waves, we can also observe in Figs. 2(e) and 2(f) that the transmitting amplitudes of the SM unit would keep a high level transmission and the transmitting phases of the SM unit only experience very small difference when the structural parameter $b_{2}$ varies the same. For the PM, the cross-polarization conversion efficiency is defined as $\eta _{PC}= r_{xy}^{2}/(r_{yy}^{2}+r_{xy}^{2})$, where $r_{yy}$ and $r_{xy}$ are the reflected coefficients of the co- and cross-polarized components, respectively. We can observe in Figs. 2(g) and 2(h) that the reflected phases from the −45$^\circ$ PM unit array would cover [125$^\circ$, 180$^\circ$] and [−180$^\circ$, 24$^\circ$] when $d$ varies from 1.8 mm to 4.8 mm with high efficiency of polarization conversion. We can also observe that the +45$^\circ$ PM unit array offers the compensation of 180$^\circ$ phase coverage from −54$^\circ$ to 156$^\circ$ with the same quality polarization conversion efficiency, as shown in Figs. 2(i) and 2(j). Clearly, both −45$^\circ$ and +45$^\circ$ PM units can create more than 180$^\circ$ phase responses and such an integration of these two skew PM unit structures should be sufficient to generate multi-beams and twist the $y$-polarized EM waves into $x$-polarized EM waves simultaneously.
Fig. 1. Multi-beam synthesis from the PTMCS at 15 GHz. (a) The configuration of the four-beam PTMCS. The embedded pictures refer to the bottom side of the SM, and the demonstration of ray tracing. The apertures of the SM and the PM are chosen as 120 $\times$ 120 mm$^{2}$ and 180 $\times$ 180 mm$^{2}$ with the focal length $f_{PM}$ of 162 mm and the length $l$ of 54 mm. $F_{1}$ and $F_{2}$ refer to the focal points of SM and PM respectively. Unit structural information of the SM (b) and the PM (c). The physical parameters are $a$ = 4 mm, $b_{1}$ = 3.5 mm, $t_{1}$ = 1 mm, $w$ = 0.4 mm, $w_{1}$ = $d$ = 0.2 mm, $c$ = 6 mm, $r$ = 5.5$\sqrt {2}$ mm, $t_{2}$ = 3 mm, $w_{2}$ = 0.3 mm, $\beta$ = +45$^\circ$, $\alpha$ = −45$^\circ$.
Fig. 2. Phase distributions of the four-beam PTMCS and their synthesis at 15 GHz. The required phase distributions over the SM (a) and the PM (b). The relationships between the dimension $b_{2}$ of the periodic SM units and reflected amplitudes (c), and reflected phases (d) of the $y$-polarized EM fields. The relationships between the dimension $b_{2}$ of the periodic SM units and transmitting amplitudes (e) and transmitting phases (f) of the $x$-polarized EM fields. The relationships between the dimension $d$ of the periodic PM units and the polarization conversion efficiency (g) and the cross-polarized reflected phases (h) when $\alpha$ = −45$^\circ$. The relationships between the dimension $d$ of the periodic PM units and the polarization conversion efficiency (i) and the cross-polarized reflected phases (j) when $\beta$ = +45$^\circ$.
The full wave simulations (CST Microwave Studio) are then performed to verify the multi-beam radiation performances of the PTMCS as shown in Fig. 3. We can observe that the PTMCS can achieve perfect four beams of well collimated cross-polarized radiations with greatly suppressed co-polarized fields. The maximum gains of the cross-polarized radiations are 19.0 dBi, 19.3 dBi, 18.7 dBi, and 19.7 dBi in the directions of $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 4}$ = $\begin {bmatrix} 15^\circ & 15^\circ & 15^\circ & 15^\circ \\45^\circ & 135^\circ & 225^\circ & 315^\circ \end {bmatrix}$. While for the co-polarized radiation, we can hardly observe the main beams of the radiation as they are fully suppressed and the maximum gain of the co-polarized radiation is only 6.1 dBi. Clearly, all these demonstrations verify our design of high-purity polarized multi-beam generations from PTMCS.
Fig. 3. The radiation performances of the four-beam PTMCS at 15 GHz. Cross-polarized (a), and co-polarized (b) far-field radiation patterns. Cross-polarized (c), and co-polarized (d) far-field intensity maps. Far-field patterns in (e) $\varphi$ = 45$^\circ$ and (f) $\varphi$= 315$^\circ$
We continue to demonstrate the generation of three beams and five beams from the proposed PTMCS, as shown in Fig. 4, where the synthesized triple- and quintuple-beams are directed in $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 3}$ = $\begin {bmatrix} 15^\circ & 15^\circ & 15^\circ \\0^\circ & 120^\circ & 240^\circ \end {bmatrix}$ and $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 5}$ = $\begin {bmatrix} 15^\circ & 15^\circ & 15^\circ & 15^\circ & 15^\circ \\0^\circ & 72^\circ & 144^\circ & 216^\circ & 288^\circ \end {bmatrix}$. The SM still maintains the same phase distribution as the one for the four-beam generation, while the PM has to be redesigned. The corresponding phase distributions appear to have three and five parts, redirecting the radiations into specific angles as we expected with well collimated wave-fronts. The maximum gains of the cross-polarized radiations are found to be 19.6 dBi, 20.4 dBi and 20.4 dBi respectively for three beams and 18.0 dBi, 16.9 dBi, 19.3 dBi, 19.4 dBi and 17.5 dBi respectively for five beams. In the meanwhile, the co-polarized gains are also very low with only 5.5 dBi and 5.6 dBi respectively for three beams and five beams. These results further demonstrate the high-purity polarized multi-beam generations from our proposed PTMCS.
Fig. 4. Multi-beam radiations from the PTMCS. The phase distributions of the PM for three beams (a) and five beams (b). Cross-polarized (c), and co-polarized (d) far-field patterns for three beams. Cross-polarized (e), and co-polarized (f) far-field patterns for five beams.
Figure 5 demonstrates the bandwidth properties of the multi-beam radiations from the PTMCS. We can observe that the reflection coefficients of all these cases can maintain less than −10 dB from 14.5 GHz to 16.0 GHz. The preferred operating bandwidths with −1.5 dB gain degradations from the peak radiations are thus 14.7 GHz - 15.7 GHz for three-beam PTMCS, 14.5 GHz - 15.4 GHz for four-beam PTMCS and 14.5 GHz - 15.9 GHz for five-beam PTMCS, respectively. The proposed PTMCS obtains the peak radiations of 20.4 dBi at 15.1 GHz, 19.3 dBi at 15.1 GHz and 18.3 dBi at 15.1 GHz respectively for the three cases. The aperture efficiencies can be calculated by $\eta = \lambda ^{2}G_{S}/4\pi D^{2}$ [18,19], where $G_{S}$ refers to the overall gains of multi-beams following the definition of $G_{S} = 10lg(i\times 10^{G_{ave}/10})$ with $i$ standing for the number of the multi-beams and $G_{ave}$ as the average gain of the multi-beams. As a result, we can have the aperture efficiencies of the three cases as 32.5 $\%$, 33.3$\%$ and 33.3 $\%$ respectively.
Fig. 5. Bandwidth properties of the multi-beam radiations from the PTMCS. The reflection coefficients (a) and the average gains (b) over the frequency band from 14.0 GHz to 16.0 GHz.
In order to further improve the high-purity polarized multi-beam radiation, we enlarge the SM in Fig. 6 as a semi-closed radome with the same aperture size as the PM. The SM consists of two parts with the central part being the original SM employed the phase distribution to reflect the co-linearly polarized EM waves with diverged wave-fronts while offering the transmitting passport for the cross-linearly polarized EM waves. The newly added surrounding polarizers composed of metallic strips in the SM would perfectly suppress the co-linearly polarized EM waves and simultaneously transmit the cross-linearly polarized EM waves. To be more specifics, such parallel metallic strips actually function as a polarization selective meta-surface and can completely reflect the linearly polarized EM waves with electric fields parallel to the grids, while offering the passport for the linearly polarized EM waves with the electric fields perpendicular to the grids. As a result, semi-closed SM should reduce the radiation level of the co-linearly polarized EM waves and improve the polarization purity of the cross-polarized radiations. The PM also remains the same to generate four-beam radiation. We can observe that the maximum gains of the cross-polarized radiations are 19.3 dBi, 19.8 dBi, 19.1 dBi, and 19.3 dBi in the directions of $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 4}$ = $\begin {bmatrix} 15^\circ & 15^\circ & 15^\circ & 15^\circ \\45^\circ & 135^\circ & 225^\circ & 315^\circ \end {bmatrix}$ and the maximum gain of the co-polarized radiation is greatly suppressed with only 2.9 dBi. In addition, we continue to construct four trapezoid polarizers to seamlessly connect the PM and the original SM and form the fully closed SM radome, as shown in Fig. 7, with the expectation to further improve the polarization purity. We can observe that the PTMCS with fully closed SM radome can realize much lower co-polarized radiation with high gains of cross-polarized radiations, where the maximum gains of the cross-polarized radiations are 19.6 dBi, 19.3 dBi, 18.8 dBi, and 19.9 dBi and the maximum gain of the co-polarized radiation is only 0.9 dBi. However, we can observe that the multiple secondary lobes appear in the cross-polarized far-fields due to the parasitic reflections from the fully closed radome. To be more specifics, the polarization conversion efficiency of the PM cannot be perfect and the remaining co-linearly polarized EM waves in the PTMCS with fully closed SM radome will thus be reflected back again to the PM and transformed again into cross-linearly polarized EM waves so as to finally radiate, leading to the increased multiple secondary lobes when compared with the original PTMCS. The co-polarized radiations are greatly suppressed with 3.2 dB and 5.2 dB when employing the semi-closed and fully closed SM radome structures, while both of the proposed constructions can still maintain the same high quality cross-polarized radiations of four beams.
Fig. 6. The radiation performances of the four-beam PTMCS with semi-closed SM radome at 15 GHz. (a) The configuration of the PTMCS with semi-closed SM radome. Cross-polarized (b), and co-polarized (c) far-field radiation patterns. Cross-polarized (d), and co-polarized (e) far-field intensity maps. Far-field patterns in (f) $\varphi$ = 45$^\circ$ and (g) $\varphi$= 315$^\circ$.
Fig. 7. The radiation performances of the four-beam PTMCS with fully closed SM radome at 15 GHz. (a) The configuration of the PTMCS with fully closed SM radome. Cross-polarized (b), and co-polarized (c) far-field radiation patterns. Cross-polarized (d), and co-polarized (e) far-field intensity maps. Far-field patterns in (f) $\varphi$ = 45$^\circ$ and (g) $\varphi$= 315$^\circ$.
3. Fabrication and experimental results
Finally, we fabricate the proposed two PTMCSs and experientially test the radiation performances as shown in Fig. 8. Both of the PTMCSs are excited by the WR62 rectangular waveguide with a coax feed, where the corresponding elements of the PM and the original SM are manufactured according to the original four-beam PTMCS and the one with fully-closed SM radome. In order to measure four beams of both PTMCSs, we rotate the PTMCSs 45$^\circ$ and the receiving horn −45$^\circ$ respectively along the $\varphi$-direction to test the cross-polarized radiation beams in $\varphi$ = 45$^\circ$ and $\varphi$ = 225$^\circ$. Similarly, we can also obtain two beams in $\varphi$ = 135$^\circ$ and $\varphi$ = 315$^\circ$ in the section of $\varphi$ = 315$^\circ$. In this way, it is readily to obtain the co-polarized radiation beam when the PTMCSs and the receiving horn are rotated in the same angle. We can observe that the maximum cross-polarized radiation gains of the original PTMCS are 17.7 dBi, 17.9 dBi, 18.7 dBi, 18.7 dBi in the directions of $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 4}$ = $\begin {bmatrix} 13^\circ & 14^\circ & 14^\circ & 13^\circ \\45^\circ & 135^\circ & 225^\circ & 315^\circ \end {bmatrix}$ respectively and the maximum gain of the co-polarized radiation is 4.7 dBi. While the maximum cross-polarized radiation gains of the PTMCS with fully closed SM radome are 17.4 dBi, 18.7 dBi, 18.3 dBi, 17.7 dBi in the directions of $\begin {bmatrix} \theta _{i}\\\varphi _{i} \end {bmatrix}_{i = 1\sim 4}$ = $\begin {bmatrix} 14^\circ & 14^\circ & 13^\circ & 14^\circ \\45^\circ & 135^\circ & 225^\circ & 315^\circ \end {bmatrix}$ and the maximum gain of the co-polarized radiation is −0.1 dBi. The perfectly suppressed co-polarized radiation can be observed from the measurements, while the cross-polarized four beams are well collimated as we expected although with a little bit shifts in the radiation directions and about 1 dB gain degradation compared with the simulations. These are mainly attributed to the fabrication tolerance and material losses of the meta-surfaces. However, the overall radiation performances are still satisfactory with high-purity polarized multi-beams as we devised.
Fig. 8. The comparisons between the measurement results and the simulation results of the PTMCSs. (a-c) Experimental setup and manufactured photos of the PTMCSs. Radiation patterns of the original PTMCS in (d) $\varphi$ = 45$^\circ$ and (e) $\varphi$ = 315$^\circ$. Radiation pattern of the PTMCS with fully closed SM radome in (f) $\varphi$ = 45$^\circ$ and (g) $\varphi$ = 315$^\circ$.
4. Conclusions
In conclusion, we have demonstrated the PTMCS for the synthesis of high-purity polarized multi-beams in this investigation through integrating dual bi-functional meta-surfaces as the PM and the SM to simultaneously control the polarization states and wave-fronts of EM fields and avoid the SM blockage. Especially, we show that such a PTMCS can possess much more compact configuration by properly devising the phase distribution over the SM, and can also achieve high-purity polarized multiple radiations when we employ the semi-closed SM radome and the fully closed SM radome to suppressing the co-polarized EM waves. We expect our design could offer an efficient way for building up more advanced meta-surface based architectures with specific characteristics, especially for applications fundamentally dependent on the simultaneous manipulations of polarization and ray-tracing of EM fields.
Funding
National Natural Science Foundation of China (61671344, 61301072).
Disclosures
The authors declare no conflicts of interest.
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