A dual-band dual-polarized low-side-lobe transmitarray using independent amplitude and phase controllable elements

In this paper, a novel transmitarray (TA) element with independent control capability of amplitude and phase under dual-band dual-polarized operation is proposed. By changing the physical size of the TA element, the phase variation of the element can cover 360° at two bands. Moreover, the phase change of the frequency band is less than 30° when the phase of the other band is changed. Meanwhile, a higher maximal transmission amplitude can be maintained when varying the phase. Amplitude modulation is achieved by rotating the TA element. Utilizing the proposed TA element, a dual-band dual-linear polarization (LP) TA with low side lobe level (SLL) operating at 12.5 GHz and 14.25 GHz is designed. The SLL can be decreased by amplitude modulation of the elements. The measured peak gains of the proposed TA are 25.96 dBi and 25.89 dBi at 12.5 GHz and 14.25 GHz. In addition, the measured SLLs of the yoz/xoz planes are −22.4 dB/−22.4 dB and −22.5dB/−22.3 dB at 12.5 GHz and 14.25 GHz, respectively. The proposed TA shows good SLL performances and great application potential in satellite communication systems.


Introduction
Antennas with high gain and beam steerable are required in many applications, such as deep space exploration, microwave remote sensing, radar technology, satellite communication, etc Owing to the advantages of high gain, low profile, and light weight, transmitarray (TA) antennas and reflectarray (RA) antennas have attracted more and more attention in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Moreover, compared with the RA, the feed source and radiation field of TA are respectively on both sides of the array. Therefore, there is no problem of feed blockage in TA design.
Generally, for TA antennas, there are two essential requirements for the design of the element: (1) it must be possible to vary the transmission phase over 360°; (2) the transmission amplitude must remain high throughout the varying range. There are three existing methods for designing TA. The receiver-transmitter (R-T) method is often used [6,7]. It can be seen as a simplified phased array where the receive and transmit parts are separated by phase shifters. The multilayer frequency-selective surface (MFSS) method is widely used in TA design due to its simple structure [8][9][10]. Recently, a new method based on metasurfaces (MS) has been reported to design TA [11][12][13][14]. Due to the use of non-resonant elements, the MS method offers better bandwidth characteristics compared to the MFSS method.
In most cases. the EM wavefront can be effectively tuned using TAs with only phase tunable ability. However, TAs which amplitude and phase can be independently tuned at the same time are required for some high-quality wave control, such as low-side lobe level (SLL) wave generation. Due to the convenient and straightforward modulation, polarization-converting surfaces [12][13][14][15] are often used to achieve independent amplitude and phase control. Amplitude modulation is achieved by changing the polarization conversion ratio. And the phase modulation is achieved by changing the geometry size.
For the design of dual-band TA, the phase change of the TA element should be able to cover 360°at two bands independently, and the transmission loss should be as small as possible at the same time. In satellite communication systems, different polarizations are usually required for the transmission and reception of antennas. For such TAs, independent phase control in each band becomes more challenging due to the polarization requirements. Some dual-band and dual-polarized TAs using two interlaced elements with good performance are proposed in [16][17][18][19]. However, elements of these TAs only have phase tunable ability. To the best of the authors' knowledge, there are no open papers in the literature devoted to the element of dual-band dual-LP TAs with independent amplitude and phase control capability.
To achieve high-quality dual-polarized wave control at two bands, we propose a novel TA element with independent control capability of amplitude and phase under dual-band dual-polarized operation. A dual-band (12.5/14.25 GHz) dual-LP TA with high antenna gain is designed using the TA element. Additionally, the SLLs of the far field patterns can be controlled by changing the amplitude distributions of the MS. To verify the design performance, the prototype of the proposed TA is finally fabricated and measured.

Element design and analysis
The requirements of the MS element design are to achieve independent amplitude and phase control of two orthogonally linear polarizations with minimum insertion loss at dual-band. Polarization-converting surfaces are often used to achieve independent amplitude and phase control due to their convenient and straightforward modulation. Amplitude modulation is achieved by rotating the MS element to change the polarization conversion ratio, while phase modulation is achieved by varying the physical size of the MS element. We introduce here a novel polarization-converting surface to further reduce the impact of dual frequency bands. Inspired by the interleaving technique, a dual-band dual-LP operation is realized by staggering the higher frequency (HF) and lower frequency (LF) patches.
The proposed TA element, as shown in figure 1, includes two metallic layers and one substrate layer. The substrate is F4B with a relative permittivity of 2.2 and a loss tangent of 0.001. The smaller size patch and larger size patch, which are named as higher frequency (HF) patch and lower frequency (LF) patch, are interlaced to achieve dual-band dual-LP operation. One frequency patch consists of one dual split ring and three metal lines on the upper layer, while the lower layer was by rotating the upper patch 90°and mirroring it. Since the structure used in the element is a polarization conversion element, the three metal lines can act as a polarization grid and reduce the mutual influence of the two frequency bands. Compared with [14], the three metal lines are used to reduce the interaction between the two frequency bands. The value of the element's parameters is shown in table 1. We can only get a 180°phase change range just by changing the geometry parameters. Therefore, we need to mirror the patch structure to get another 180°phase change range. From [20] we can know that the gain loss of the array is less than 1dB when the phase error is less than 30°. Therefore, when we design a dual passband TA, we need to ensure that the phase change of one passband is less than 30°when the phase of another passband is adjusted. Then we select six cases in each group of patches to illustrate the effect of geometry parameters on the phase change. The geometry parameters of different cases are shown in table 2. The simulated results are shown in figures 3 and 4. The t y-x (t x-y ) represents the transmission coefficient of the unit cell. Figure 3(a) shows the simulated transmission amplitude when varying the parameters r and a of the LF patch. The x-polarized waves are converted into y-polarized waves at 12.5 GHz with a higher maximal transmission amplitude (> −2.5 dB). While polarization-converting component t x-y is less than −19 dB around the lower frequency band. The  Table 1. Geometry parameters of ta element.
y-polarized waves are converted into x-polarized waves at 14.25 GHz and the amplitude of t x-y is unchanged. The simulated transmission phase when varying the parameters r and a is shown in figure 3(b). It can be found that the phase of the proposed MS element can fully cover 360°at 12.5 GHz. While the phase change range is less than 26°at 14.25 GHz.
The simulated results when varying the parameters r1 and a1 of the HF patch are shown in figure 4. The y-polarized waves are converted into x-polarized waves at 14.25 GHz with a higher maximal transmission amplitude (> −3 dB) at different cases. The phase of the proposed MS element can fully cover 360°at 14.25 GHz. Furthermore, the phase change range is less than 28°at 12.5 GHz. The above results verify the independent phase control ability with orthogonal linear polarization at each band. The full 360°coverage of phase can be realized by changing the geometry parameters of LF and HF patches.
The amplitude and phase response of the TA elements as a function of the incident angles are simulated. Figure 5 shows the simulated transmission results versus the incident angles of case 3 in the LF group of patches. As can be seen from the results in the figure, the transmission amplitude of the unit changes slightly, and the transmission phase changes by 21°as the incidence angle increases from 0°to 40°. In addition, table 3 presents the magnitude and phase responses of the elements for various cases and the response for an incidence angle of 40°. From the above results, the performance of TA elements is acceptable when the incidence angle is 40°. By rotating the two patches of the TA element independently, amplitude modulation can be achieved. Figure 6 shows the simulated transmission results under different rotation angles of two band patches. As shown in figure 6(a), the transmission amplitude will decrease to −15 dB with the rotation angle increasing from 0°to 50°(decreasing from 0°to −50°) at both bands. From figure 6(b), we can see that the phase change range is less than 30°with the rotation angle changing at the dual band. Also, the phase of t y-y and t x-x are opposite at positive and negative rotation angles. This feature can be used to improve the cross-polarization level of the TA. The above results show the independent control capability of amplitude and phase under dual-band dual-polarized operation.
3. The dual-band dual-polarized TA design 3.1. TA with phase-only modulation A dual-polarized horn antenna is used for feeding due to its advantages of simple architecture. The radiation patterns of the feed antenna are shown in figures 7(a) and (b). It can be seen that the half-power beam widths of the feed are the same in the two planes. To achieve optimal efficiency, the 10 dB beam width is usually chosen to obtain a maximum aperture efficiency. Then the focal diameter ratio (F/D) is set as 0.67. The proposed TA is set as 302.4 mm × 302.4 mm, which consists of 21 × 21 HF elements and 20 × 20 LF elements. The discretized normalized amplitude distributions of the primary field illuminating the TA at dual band are shown in figures 7(c) and (d). These results can be used later in the amplitude modulation of TA.
A TA only with phase modulation is first designed in this section. To achieve a high gain antenna, the spherical phase profile should be compensated to a planar phase profile. To obtain the required compensation phase for each element, the needed phase distributions can be calculated using the method in [15]. Then

TA with phase and amplitude modulation
Since antennas with low SLL can reduce EM interference, the SLL performance of the antenna is very important in practical applications. From the theory of array antenna pattern synthesis, we know that SLL can be controlled by the excitation amplitude distribution of arrays. The amplitude distribution shown in figure 7 is not the optimized distribution to obtain low SLLs, so the TA with phase-only modulation cannot meet the low SLL requirement. We have to introduce amplitude modulation into the TA design to control the SLL. According to the analysis of the MS element, we can change the amplitude of the MS element without changing the phase by rotating the patch at dual band. Then the TA with phase and amplitude modulation is designed.
In this paper, we planned to build a Taylor-distribution, widely used in antenna array design, to generate the required SLL values. Taylor distributions can be classified as one-dimensional (1D) or two-dimensional (2D) Taylor distributions, which produce specific SLLs in a plane or in the whole space, respectively. Furthermore, the 2D Taylor distribution can be composed of two 1D Taylor distributions. where T 1 is a column vector representing the 1D Taylor distribution, n is the specific sequence number of elements in T 1 , N is the total number of elements in T 1 . Then 2D Taylor-distribution T can be obtained by combining the 1D Taylor-distribution T 1 in the x-axis and the 1D Taylor-distribution T 2 in y-axis:

( )
Finally, the required amplitude distribution R can be obtained by the following equation: where T represents the required Taylor-distribution. I represent the obtained amplitude distribution shown in figure 7. A is the simulated amplitude of the MS element analyzed in section II. Then the rotation angle of each MS element can be obtained by combining R and the results shown in figure 6. The designed objective is set as −27 dB SLL Taylor distribution along y-direction and −27 dB SLL along x-direction. The rotation angle distributions of the TA are shown in figure 10. As shown in figure 6, the phase of t y-y and t x-x are contrary at positive and negative rotation angles. So the rotation angle distribution is divided into half positive angles and the other half negative angles according to the symmetry axis to improve the cross-polarization level. Figure 9 shows the simulated radiation patterns of the TA with phase and amplitude modulation at 12.5 GHz and 14.25 GHz. The simulated SLLs of the yoz/xoz planes are −22.6 dB/−22.7 dB and −22.9 dB/−22.7 dB at 12.5 GHz and 14.25 GHz, respectively. The simulated SLL is 0.3 dB lower than TA with phase only modulation in the yoz plane and 6.8 dB in the xoz plane at 12.5 GHz. Furthermore, the simulated SLLs are 0.2 dB and 6.5 dB lower than TA with phase only modulation in the yoz and xoz plane at 14.25 GHz, respectively. Because the transmission amplitude of the TA element is different when changing the element's phase, the practical realized SLLs are greater than the targeted SLLs.  To verify the proposed design, the TA is fabricated and measured. The photograph of the whole TA is shown in figure 11. Figure 12 shows the simulated and measured radiation patterns of the proposed TA at the center frequency. As in the figure, we use a layer of foam to support the feed antenna and TA. A good agreement can be seen between simulation and measurement. The     [17,19] presents TAs operating at dual-band, but the elements cannot achieve independent phase and amplitude control. Moreover, compared with the TAs proposed in [14,15] with independent phase  and amplitude control, the proposed TA shows the independent control capability of phase and amplitude at dual band. Overall, our proposed TA with dual-band dual-polarized operation exhibits the unique advantage of low SLL.

Conclusion
A dual-band TA element with independent amplitude and phase control capability is presented in this paper. The proposed TA element is used for the TA with low SLL under dual-band dual-polarized operation. After using amplitude modulation, the SLL of TA can be significantly reduced. Then the TA has been simulated, fabricated and measured. In addition, our proposed dual-band dual-LP TA has the advantages of simple structure and low SLL, so it has good application potential in satellite communication systems.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).