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Abstract
This work presents a strategy for independent control of the amplitude and phase of transmissive circular-polarization (CP) waves. The designed meta-atom consists of an elliptical-polarization receiver and a CP transmitter. By changing the axial ratio (AR) and polarization of the receiver, amplitude modulation can be realized based on polarization mismatching theory, with negligible cumbrous components. While by rotating the element, a full phase coverage enabled by the geometric phase is achieved. Subsequently, a CP transmitarray antenna (TA) with high gain and low side-lobe level (SLL) is implemented to experimentally validate our strategy, and the tested results match well with the simulated ones. During the operating band from 9.6 to 10.4 GHz, the proposed TA obtains an average SLL of −24.5 dB, a lowest SLL of −27.7 dB at 9.9 GHz, and a maximum gain of 19 dBi at 10.3 GHz, with the measured AR lower than 1 dB, which mainly benefits from high polarization purity (HPP) of the proposed elements. The proposed strategy for full amplitude-phase manipulation of CP waves together with HPP paves a way for complicated field manipulations and indicates a promising candidate in antenna applications, such as anti-jamming systems and wireless communications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces (MSs), which can be treated as the 2D equivalence of metamaterials, have attracted enormous interest in flexibly manipulating electromagnetic (EM) waves since their first introduction in 2011 [1]. By introducing abrupt phase gradients and arranging periodic or aperiodic subwavelength structures [2–5], MSs can be exploited to implement exceptional applications, such as optical computing [6,7], invisible cloaks [8–10], electromagnetic detectors [11,12], vortex beam generators [13–15], and high-performance antennas [16–18].
Despite the success in effectively modulating EM wavefront for most cases, when applied for some sophisticated or high-quality wavefront tailoring, phase-only MSs still face big challenges. For example, for multi-mode diffraction [19], beam shaping [20], and high-quality hologram [21], special amplitude and phase profiles are required. There have been some attempts to independently and simultaneously control the amplitude and phase responses of MSs by EM energy conversion or absorption. In [19], a C-shaped meta-atom is designed to simultaneously engineer the transmissive amplitude and phase of cross-polarization waves and is applied to realize a multi-mode meta-grating. In [22], a five-layer anisotropic metasurface is developed to control the co-polarization amplitude and phase of two orthogonal linear polarizations. Different from transforming EM energy into unwanted polarization mentioned above, in [23], an ohmic sheet is introduced to absorb the unwanted power and arbitrarily tailor the amplitude and phase of transmissive cross-polarization waves.
MSs with the capability of providing independent amplitude and phase control have also attracted much attention in the antenna community. One of the most promising potentials is to suppress the side lobe, since side-lobe level (SLL) is a pivotal parameter of antennas for practical applications, such as anti-jamming systems and wireless communications. According to the theory of array antenna pattern synthesis, a feasible approach to control SLL is to redistribute the amplitude profiles as Chebyshev-distribution or Taylor-distribution, which has been widely applied to design low side-lobe antennas. A polarization-converting MS is reported to simultaneously engineer the amplitude and phase of reflective waves and reduce SLLs of linearly polarized (LP) reflectarray antennas (RAs). Despite that a lowest SLL of −25.3 dB can be obtained, the energy of reduced side lobes is transferred to the cross-polarization due to the energy transformation mechanism, resulting in the polarization isolation level (PIL) deterioration from 17.9 dB to 13 dB [24]. Based on a similar concept, a circular-polarization (CP) dual-phase MS-based RA is well studied in [25], and the SLL can be reduced by 8 dB; yet the axial ratio (AR) performance deteriorates compared with the original phase-only RA. To overcome this limitation, a strategy to improve the polarization purity of transmitted waves is developed by reflecting the unwanted power to reflection space. The MS with classic orthogonal metallic grating layers proposed in [26] is applied to suppress SLL and improve the PIL performance, and a SLL of around −30 dB is achieved with PILs higher than 25 dB. This scheme is also conducted in a single-substrate MS [27]. Nevertheless, up to now, most proposed MSs with high polarization purity (HPP) are conducted on linear polarization owing to the readily available polarization grids [20,21,26], leaving that of circular polarization unexplored, which sorely restricts its applications in engineering designs.
In this work, we develop a new strategy for independent and simultaneous control of transmissive amplitude and phase for CP waves with negligible cumbrous components. Initially, we outline the basic theory of the proposed amplitude and phase control strategy. The transmitted amplitude of CP components is theoretically analyzed and evaluated through polarization mismatching theory, and Jones matrix is utilized to investigate the phase response. Subsequently, the designed receiver-transmitter meta-atom is numerically simulated to demonstrate the proposed concept. Finally, using the proposed well-designed MS, we design, fabricate and test a transmitarray antenna (TA) with low SLL for the first time, which experimentally validates the superior capability of the proposed MS.
2. Concept and meta-atom design
As presented in Fig. 1(a), an elliptically polarized (EP) receiver and a CP transmitter are cascaded by a metallic via to independently and simultaneously control the amplitude and phase of CP waves. When illuminated by CP plane waves, part of the incidence is reflected back to the reflection space, while the other energy is received by the EP receiver, and then, converted to guided waves, passing through the metallic via and radiating to transmission space with cross polarization, together with modulated amplitude and phase.
Fig. 1. (a) Schematic of the proposed strategy for simultaneous amplitude and phase control of CP waves. (b) The designed offset patch with a rectangular slot and probe-fed model for simulation. The rectangular slot is rotated with an angle of $\alpha$ in xoy plane along z axis, to control the polarization and AR of receiver/transmitter patch. (c) The AR and polarization of the designed patch with different $\alpha$ at 10 GHz when looking along -z direction.
2.1 Polarization mismatching theory
Here, we begin our strategy by discussing the classical polarization mismatching theory in the antenna community. According to the classical polarization mismatching theory [28], for a CP receiver antenna, when illuminated by free space waves, the received EM energy is closely related to the ARs and polarizations of both the receiver antenna and incident waves. In detail, without considering impedance mismatching and losses, the normalized intercepted energy can be quantitatively calculated as follows:
2.2 Meta-atom design
Offset circular patches loaded with rectangular slots are chosen as the receiver and transmitter patches. Here, the polarization and AR of receiver/transmitter patch can be controlled by the rotation angle $\alpha$ of the rectangular slot, and a probe-fed patch model under periodic boundary conditions is adopted for numerical simulation, as displayed in Fig. 1(b). The feed port and the Floquet port applied along $z$ axis are denoted as Port 1 and Port 2, respectively. To not lose generality, the working frequency is set at the microwave frequency. After parameter optimization, the dimensions are set to meet with a working frequency of 10 GHz. Also, the numerical simulation when $\alpha$ varies from −45$^{\circ }$ to 45$^{\circ }$ is conducted. As depicted in Fig. 1(c), at 10 GHz, when $\alpha$ varies from −45$^{\circ }$ to 0$^{\circ }$, the AR changes from 1.02 to infinity, for which the receivers/transmitters can be treated as right-handed EP (RHEP) patches. When $\alpha$ varies from 0$^{\circ }$ to 45$^{\circ }$, the AR changes from infinity to 1.02, for which the receivers/transmitters can be treated as left-handed EP (LHEP) patches. According to Formulas (2) and (3), when illuminated by incident waves with fixed ARs and polarizations, the amplitude of transmitted waves can be arbitrarily engineered by combining receivers and transmitters with different ARs and polarizations. To realize high-efficiency amplitude control and maintain HPP in transmission space simultaneously, a LHCP patch with an AR of 1.02 ($r_{3}$ = 1.02) is chosen as the transmitter. According to Formula (3), only LHCP waves exist in transmission space.
The topology of designed meta-atom is presented in Figs. 2(a)–2(d). The unit cell consists of four metallic layers, among them, the top receiver and the first metallic ground are printed on the first F4B substrate while the second metallic ground and the bottom transmitter are printed on the second F4B substrate, and the receiver is connected with the transmitter through a metallic via, as shown in Fig. 2(a). These two 2 mm-thick substrates ($\varepsilon _{r}$ = 2.65 + 0.001i) are bonded by a 0.1 mm-thick FR4 prepreg ($\varepsilon _{r}$ = 4.3 + 0.01i). The dimensions illustrated in Fig. 2(c) and 2(d) are set as $p$ = 12, l = 7.9, w = 1, s = 1.7, r = 5.8, $r_{v}$ = 0.6 and $r_{k}$ = 1.8, all in millimeters.
Fig. 2. The topology of designed meta-atom. (a) Overall geometry. The receiver, transmitter and metallic via (feed point) are all rotated with an angle of $\beta$ to realize a full phase coverage. (b) Top receiver. The rectangular slot of top receiver is rotated with an angle of $\alpha$ to realize amplitude control. (c) Bottom transmitter. (d) Middle ground.
Subsequently, the unit cell is analyzed under periodic boundary conditions, and the CP incidence impinges along -z direction to excite the structure, also depicted in Fig. 2(a). The simulated and theoretically calculated amplitudes of transmitted CP waves at 10 GHz when $\alpha$ varies from −45$^{\circ }$ to 45$^{\circ }$ are plotted in Fig. 3(a), which are consistent with each other. Here, the AR of incidence is set as 1 ($r_{1}$ = 1), and an amplitude modulation of transmitted LHCP waves from 0$\sim$1 can be realized and the amplitude of RHCP components keeps below 0.03, which exhibits the property of HPP. The slight difference between theoretical calculation and simulation may be attributed to the impedance mismatching of the receivers and transmitters. Moreover, the simulated phase of transmitted LHCP waves is displayed in Fig. 3(b), and the extra phase shift is introduced due to the resonances of patches.
Fig. 3. The performance of designed meta-atom.(a) The simulated and theoretically calculated amplitude of transmitted CP waves at 10 GHz. (b) The simulated phase of transmitted LHCP waves.
The scattering properties plotted in dB from 8.5 to 11.5 GHz and current distributions corresponding to RHCP incidence when $\alpha$ equals −45$^{\circ }$, 0$^{\circ }$, and 45$^{\circ }$ are also presented in Figs. 4(a) to 4(f) to intuitively investigate the wideband characteristics. It is clearly demonstrated that the amplitudes of transmitted RHCP keep below −30 dB around 10 GHz, which mainly benefits from the high selectivity of the utilized LHCP transmitter patch. From Figs. 4(d), 4(e) and 4(f), it can be clearly observed that the transmission energy decreases gradually when $\alpha$ varies from −45$^{\circ }$ to 45$^{\circ }$. Specially, the incidence is totally reflected back to free space when $\alpha$ equals 45$^{\circ }$, due to the complete polarization mismatching between incident RHCP waves and the LHCP receiver, which intuitively proves our strategy. Therefore, by changing the AR and polarization of the receiver patch, a high-efficiency amplitude modulation with negligible cumbrous modes can be achieved.
Fig. 4. The scattering properties when $\alpha$ equals (a) −45$^{\circ }$, (b) 0$^{\circ }$, and (c) 45$^{\circ }$. Current distributions when $\alpha$ equals (d) −45$^{\circ }$, (e) 0$^{\circ }$, and (f) 45$^{\circ }$.
Then, how to control the phase of transmitted CP waves with negligible impact on amplitude is illustrated. Generally, the transmission coefficient of unit cell can be described by the Jones matrix: $\boldsymbol {T_{C}}=\left [\begin {array}{ll} T_{R R} & T_{R L} \\ T_{L R} & T_{L L} \end {array}\right ]$, where $T_{ij}$ symbolizes the transmission coefficient, j and i represent the polarizations of the incident and transmitted waves, respectively. Due to the perfect AR performance of the utilized LHCP transmitter patch mentioned above, transmitted RHCP components are completely suppressed. Therefore, $T_{RL}$= 0 and $T_{RR}$ = 0, and the Jones matrix can be simplified as:
If the element is rotated with an angle of $\beta$ in xoy plane along z axis as shown in Fig. 2(a), the Jones matrix will be changed to:
Thus, under RHCP illumination, we can find that the transmitted phase $\varphi _{LR}$ can be controlled by a geometric phase of 2$\beta$, while the modulated amplitude $\left |T_{LR}\right |$ remains unchanged. To validate the above predictions, the amplitude and phase responses of $T_{LR}$ with different $\alpha$ and $\beta$ are simulated. For brevity, only the simulated results corresponding to $\beta$ = 0$^{\circ }$, 15$^{\circ }$, 30$^{\circ }$ and 45$^{\circ }$, when $\alpha$ equals −45$^{\circ }$ and 0$^{\circ }$, are plotted in Figs. 5(a) and 5(b). As presented in Fig. 5(a), $\left |T_{LR}\right |$ keeps stable, meanwhile, a 2$\beta$ phase shift can be clearly observed in Fig. 5(b). It should be noted that the additional phase shift in Fig. 3(b) can be counteracted by tuning $\beta$. In a word, based on the aforementioned analysis and verification, our strategy can realize independent and simultaneous control of $\left |T_{LR}\right |$ and $\varphi _{LR}$ by rotating the top receiver and the whole element, respectively, and the unwanted modes are completely suppressed. Moreover, the proposed amplitude-phase control strategy is also applicable for co-polarized transmission channel (see details in the Supporting Information).
Fig. 5. The (a) amplitude and (b) phase responses of $T_{LR}$ corresponding to $\beta$ = 0$^{\circ }$, 15$^{\circ }$, 30$^{\circ }$, and 45$^{\circ }$, when $\alpha$ equals −45$^{\circ }$ and 0$^{\circ }$.
3. Low Side-lobe transmitarray antenna design
To explore the rich potentials in the antenna community and experimentally verify our strategy, a high-gain CP TA with low SLL is designed using the proposed MS. Meanwhile, CP TA with phase-only modulation is also simulated as a comparison.
3.1 Primary feed design
Here, a classical CP patch antenna is chosen as the feed source to emit RHCP waves due to its simple architecture. As shown in Fig. 6(a), a probe-fed square patch with two oppositely truncated corners is printed on a 2 mm-thick F4B substrate ($\varepsilon _{r}$ = 2.65 + 0.001i). Open boundary conditions are adopted to numerically simulate the performance of the feed and the dimensions are optimized as pp = 14, ll = 8.12, and ss = 2.46, all in millimeters. The measured reflection coefficient in Fig. 6(b) is below −10 dB from 9 to 11.9 GHz, which shows a broader bandwidth than the simulated one (lower than −10 dB from 9.4 to 11.6 GHz). Additionally, the simulated 3 dB AR bandwidth covers from 9.75 to 10.25 GHz, showing the capacity of effectively radiating RHCP waves around the working frequency of 10 GHz.
Fig. 6. (a) The topology, (b) reflection coefficient and AR performance of the designed feed antenna.
3.2 Transmitarray antenna design
With the well-designed meta-atoms and feed antenna, a CP TA (denoted as AP TA: amplitude-phase transmitarray antenna) with low SLL can be implemented. Here, the focal length F is set as 140 mm, and the transmitarray is designed with a circular aperture that consists of 349 elements, covering a total area of around 7.5 $\times$ 7.5 $\lambda ^2$ at 10 GHz.
To obtain high-gain beams in the far-field region, the spherical waves emitted by the feed antenna must be converted to plane waves. The phase profiles (Fig. 7(b)) of emitted RHCP waves on the antenna aperture can be calculated as: $\varphi _{1}=-\frac {2 \pi }{\lambda }\left (\sqrt {(m p)^{2}+(n p)^{2}+F^{2}}-F\right )$, where (mp, np) is the position of the meta-atom, $\lambda$ is the free space wavelength.
Fig. 7. The (a) amplitude and (b) phase profiles of RHCP incidence on transmitarray aperture. (c) Taylor amplitude distribution with a side-lobe level of −30 dB. (d) Amplitude distribution of MS. The distribution of (e) $\alpha$ and (f) $\beta$.
The SLL of a TA is generally related to the amplitude distribution of the transmitarray aperture and the normalized amplitude profiles of RHCP illuminating on transmitarray are obtained (denoted as ${I}$) and presented in Fig. 7(a). Herein, the target SLL is set as −30 dB and the redistributed amplitude profiles (denoted as ${{A}_{T}}$) are obtained by utilizing Taylor distribution [15], and the result is distributed in Fig. 7(c). Then, the amplitude distribution of MS is given by ${{A}_{M}}={{A}_{T}}/I$, as depicted in Fig. 7(d). Based on this, according to Fig. 3(a), the rotation angle $\alpha$ can be determined, and its distribution is presented in Fig. 7(e). It is noteworthy that the additional phase shifts (denoted as $\varphi _{2}$) shown in Fig. 3(b) brought by amplitude modulation should also be counteracted. Thus, the compensation phase of MS is obtained as $\varphi = -{{\varphi }_{1}}-{{\varphi }_{2}}$, and the rotation angle $\beta$ is determined as $\beta =-\varphi /2$, as shown in Fig. 7(f). Finally, the CP TA is fabricated using the standard printed circuit board (PCB) technique and tested in a microwave anechoic chamber, and the prototype and experimental setup are shown in Fig. 8. A broadband CP antenna working from 8-18 GHz is employed as the receiver antenna, and the proposed CP TA is placed on a rotating platform to measure its far-field patterns.
Fig. 8. (a) Measurement setup in microwave anechoic chamber. Photograph of the fabricated (b) receivers and (c) transmitters of TA.
3.3 Results and discussion
Figures 9(a) and 9(b) display the simulated and measured normalized radiation patterns at 9.9 GHz, where a lowest SLL of −27.7 dB is realized. As shown, the simulated SLLs are −29.2 dB and −27.6 dB in xoz and yoz planes, respectively, and the difference may be contributed to the asymmetric amplitude and phase distributions of the feed antenna. Additionally, the simulated SLLs are higher than the target SLL of −30 dB since the mutual coupling among the meta-atoms is not considered. The measured patterns show a great agreement with the simulated ones, and the SLLs of −27.7 dB and −27.4 dB are achieved in xoz and yoz planes, respectively. The slight deterioration is closely related to the fabrication tolerance, assembly error, and experimental imperfections. It is worth noting that the cross-polarization level is lower than −27 dB in the 3 dB beam bandwidth (about 10$^{\circ }$), which mainly benefits from the HPP of the proposed element.
Fig. 9. The normalized radiation patterns of AP TA at 9.9 GHz on (a) xoz plane and (b) yoz plane. The normalized radiation patterns of PO TA at 9.9 GHz on (c) xoz plane and (d) yoz plane.
A CP TA with phase-only modulation (denoted as PO TA: phase-only transmitarray antenna) is also employed and simulated for comparison. The PO TA is also designed with a circular aperture, which owns the same aperture area as the AP TA, and the rotation angles $\alpha$ and $\beta$ are determined as $\alpha =-45^{\circ }$ and $\beta ={{\varphi }_{1}}/2$, respectively. The normalized radiation patterns are plotted in Figs. 9(c) and 9(d). It is apparent that without amplitude modulation, the simulated SLLs are higher than −24.5 dB and −23.1 dB in xoz and yoz planes, respectively, validating the feasibility of our strategy at suppressing SLLs.
To further assess the performance of PA TA, the AR, gain, and highest SLLs from 9.6 to 10.4 GHz are displayed in Figs. 10(a) and 10(b). The simulated and measured gains of PA TA keep flat in the presented frequency range, showing reasonable agreements with each other. Additionally, the peak gain is achieved at 10.3 GHz with a value of 19.0 dBi. The measured AR keeps below 1 dB which matches well with the simulation, validating the capability of the designed MS to suppress cumbrous modes. The highest SLL is displayed in Figs. 10(b). The measured results are generally higher than the simulation, which mainly suffers from fabrication tolerance and assembly errors. Compared with those of PO TA, the SLLs are evidently reduced.
To gain further insight into the advantages of our strategy, comparisons between the proposed antenna and other representative works are presented, as listed in Table 1. By controlling the polarization conversion ratio and propagation phase of MSs, LP RA and TAs with low SLLs are proposed in [15,18]. In [16], propagation phase and geometry phase are used to tailor the amplitude and phase of CP waves, and a low SLL of about −25 dB is obtained. Specially, different from the above representative works, the amplitude modulation and HPP of MS are implemented by polarization mismatching in this work. Compared with the CP RA proposed in [16], a lower SLL of −27.4 dB is achieved and PIL performance is enormously improved to 27 dB, which is close to that of TA in [18]. Overall, enabled by the proposed strategy and well-designed MS, we achieve simultaneous amplitude and phase control of CP transmissive waves and greatly improve the polarization purity in transmission space.
Table 1. Comparisons with other reported MS-based low side-lobe antennasa
4. Conclusion
In conclusion, a strategy to independently and simultaneously engineer the amplitude and phase of transmissive CP waves is proposed. Polarization mismatching theory is applied for amplitude control with negligible cumbrous components while exploiting the geometry phase for phase modulation. To show its potential in the antenna community, a high-gain CP TA with low SLL and high PIL is designed and measured for the first time. The simulation and measurement are in good accordance with each other, validating the superior capability of the proposed MS. Our approach enriches the diversity of full amplitude-phase control and can be scaled to millimeter waves, or even terahertz bands, which may pave a way for complicated filed manipulation and advanced meta-device design for real-world applications.
Funding
National Natural Science Foundation of China (61871394, 61901512, 62101599).
Acknowledgments
The authors would like to thank the anonymous reviewers for their constructive suggestions.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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