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Abstract
We propose a dual-band achromatic focusing metasurface based on polarization multiplexing and dispersion engineering. An anisotropic resonant phase meta-atom is designed to realize independent nonlinear phase manipulation along the orthogonal directions. Achromatic focusing metasurface and broadband reflectarray antenna are further constructed in the microwave region with a computer-assisted particle swarm optimization algorithm. The standard deviation of focus offset at 11-16 GHz (for x-polarization) and 18-24 GHz (for y-polarization) are compressed to 19.83% and 16.60% of the dispersive metasurface, respectively. The radiation gains of the reflectarray antenna increase by an average of 19.49 dB and 15.08 dB in the broadband region compared with the bare standard rectangle waveguides. Furthermore, such an achromatic metasurface can be utilized to realize different functions with polarization selectivity and applied to other frequency ranges, which holds great promise in integrated optics.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, metasurfaces, a planar counterpart of metamaterials, have attracted enormous interest owing to unprecedented flexibility in electromagnetic (EM) wave manipulation and ultrathin subwavelength profiles [1,2]. Comprehensive modulation of EM waves was achieved through properly tailoring and arranging the unit cells of the metasurfaces [3–6]. Generally, the thickness of the metasurfaces can be dramatically reduced by employing abrupt phase changes at interfaces, which makes the metasurface a promising alternative for the integrated optical elements. Many planar meta-devices, including polarization converter [7], flat lens [8,9], meta-hologram [10–12], vortex beam generators [13,14], RCS reduction metasurface [15,16], and so on, have been created from optical to microwave regions. More recently, some multiplexing approaches have been employed to achieve higher integration and versatility [17,18], such as polarization multiplexing, frequency multiplexing, and illumination angles multiplexing. For instance, In Ref. [19], the method of frequency and wavevector degree of freedom multiplexing was demonstrated to design a spin-decoupled high-capacity multifunctional metasurface. In addition, based on the orbital angular momentum (OAM) beam multiplexing, different holograms were obtained by using the OAM as an independent information carrier [20].
Although great progresses have been achieved, it should be noted that chromatic aberrations were seriously neglected in most of the multiplexed metasurface. The electromagnetic response often operates in a narrow band owing to the resonant nature of the unit cells constituting the metasurface, which will result in significant limitations in practical applications. Achromatic methods were extensively exploited to broaden the operation bandwidth and have been another hot spot in the field of the metasurface [21,22]. Aieta et al. realized the three-wavelength achromatism by introducing an additional phase for fitting [23]. Some works achieved continuous achromatism by combining geometric phase and transmission phase with circular polarization incidence [24,25]. The polarization insensitive achromatic metasurface lens antenna designed by Huang et al. achieved broadband modulation in full polarization states in 11-16GHz [26]. The dispersion engineering metasurface proposed by Lu et al. realized beam deflection control in X - band in full polarization [27]. Above all, recent researches have shown that achromatic deflection and focusing can be achieved, however, the above achromatic metasurface can only work in one polarization direction or the same operating band for different polarization directions. In fact, the multiplexing scheme and achromatic method for metasurface are often considered as isolated investigation branches. A syncretic framework has not been established until now and few researches are reported that can simultaneously integrate multiplexing and achromatic capabilities.
Here, we propose a polarization multiplexing achromatic metasurface based on anisotropic dispersion engineering. Dual-band focusing is realized under x-polarization and y-polarization illumination. The scheme can achieve large operation bandwidth with ultrathin profiles. As a proof of concept, a polarization multiplexing achromatic focusing metasurface is demonstrated in the microwave region. Independent nonlinear phase manipulation covering 0∼2π is introduced both in the x-direction and y-direction with an anisotropic double-layer meta-atom. Achromatic focusing metasurface and broadband reflectarray antenna are further designed with computer-assisted particle swarm optimization (PSO) algorithm. The simulation results show that broadband focusing is realized at 11-16 GHz for x-polarization and 18-24 GHz for y-polarization, respectively. The standard deviation of focus offset is compressed to 19.83% and 16.60% of the dispersive metasurface. The average gains increase 19.49 dB and 15.08 dB compared with the bare standard rectangle waveguides. The operation bandwidth of the reflectarray antenna was broadened with the achromatic design. In general, the scheme can realize bandwidth expanding and is suitable for cross-band anisotropic design, which has great potential in multi-function integration and integrated optics.
2. Polarization multiplexing dual-band achromatic metasurface design
Figure 1 shows the schematic diagram of the proposed polarization multiplexing dual-band achromatic metasurface. The metasurface consists of a double-layer resonant meta-atom (the schematic diagram of the meta-atom can be seen in Fig. 2(a)). Through the subtle unit structure design, the EM response under different polarization states can be manipulated independently. When x-polarized EM waves incident on the metasurface, the metasurface works in the lower band (11-16 GHz, shown as Mode 1). The operation band will shift to the higher band (18-24 GHz, shown as Mode 2) under y-polarized illumination. Then, broadband achromatic focusing is implemented based on dispersion engineering. The dual-band achromatism realized with the design of anisotropic unit cell can broaden the operation band of the metasurface and achieve higher integration.
Fig. 2. (a) Schematic diagram and parameters of unit cell; (b) Reflection phase of unit 1-unit 5 at 11-24 GHz under x-polarization incidence; (c) Reflection phase of unit 1-unit 5 at 11-24 GHz under y-polarization incidence; (d) Reflection phase of unit 6-unit 10 at 11-24 GHz under y-polarization incidence; (e) Reflection phase of unit 6-unit 10 at 11-24 GHz under x-polarization incidence.
The broadband achromatism in the two modes is realized based on dispersion engineering. A reference phase P(f) associated with frequency is introduced into the wavefront phase profile of the metasurface. The designed phase distribution of the achromatic metasurface is expressed
where x and y are coordinates in the x-direction and y-direction respectively, f0 is the focus length, f is the frequency, c is the speed of light. In order to explain the dispersion relationship, formula (1) is transformed to formula (2)As depicted in Fig. 2(a), the anisotropic unit cell is composed of a double-layer metallic cross-like structure printed on a ground-backed F4B substrate (2.65 + 0.003i) with the thickness of h = 1.5 mm. Other geometrical parameters shown in Fig. 2(a) are px = 8 mm, py = 4 mm, w = 0.7 mm, and d = 0.1 mm. The structure parameters lx1(2), tx1(2), ly1(2) and ty1(2) varies between 0.5 mm - 2.5 mm, 2 mm - 7.2 mm, 2 mm - 3.8 mm and 0.1 mm - 1.1 mm to independently control the reflection phases for x- and y-polarized incident waves. Figure 2(b) to (e) show the reflected phase for the unit cells with structural parameters listed in Table 1. The unit 1-unit 5 and unit 6-unit 10 have different structure parameters in the x direction and y direction, respectively. While the parameters in the y direction and x direction are consistent for unit 1-unit 5 and unit 6-unit 10. It can be seen that the reflected phase of the unit 1-unit 5 changes nonlinearly under x-polarized illumination, while the phase of the unit 6-unit 10 is unchanged in 11-24 GHz. Similarly, a nonlinear phase can be introduced in the y direction with unit 6-unit 10. The reflected phase of unit 1-unit 5 is almost identical under y-polarized illumination. This is owing to the surface current resonant in the horizontal direction when it is illuminated by x-polarized wave, while only the structure in the vertical direction is resonant when the meta-atom is illuminated by y-polarized wave [28]. Moreover, Fig. 2(b) and (d) demonstrate that the generated nonlinear phase of x polarization is mainly concentrated at 11-16 GHz while that of y polarization is mainly concentrated at 18-24 GHz, which is caused by the anisotropic unit cell design, indicating that the EM response in x and y directions can be regulated independently in different bands by changing the cross-like structures.
Table 1. The corresponding relationship between selected unit cell number and parameters(mm)
The database of the phase response for both x and y polarization was established. Compared with other meta-atoms proposed in previous work [28], the double-layer design contains more variable parameters. Thus, a large number of parameter combinations can be realized. Moreover, the multilayer structure is conducive to realizing multiple resonances and obtaining nonlinear phase responses. In this work, one thousand sets of parameters of lx1(2), tx1(2) in the x-direction and one thousand sets of parameters of ly1(2), ty1(2) in the y-direction are simulated to construct the database, which presents the relationship between the structural parameters and EM response. Then, the PSO algorithm (The setting details are present in the Appendix A) is employed to optimize φ (x, y, f) according to formula (1). Note that the PSO algorithm needs to be run respectively for two vertical polarization states.
Figure 3 present the actual phase obtained through algorithm fitting and the one-dimensional (1D) target phase. The results show that the actual phase is almost consistent with the target phase. The phases in different directions can be obtained by approximation or averaging, which has been demonstrated in previous work [29]. For example, the length and number of unit cells in the x direction are 8 mm×40, which can be obtained by interpolation according to the existing optimization 1D results. The two-dimensional (2D) actual phase distribution and 2D target phase distribution at 11 GHz are shown in Fig. 4(a) and (b), respectively. It can be seen that the phase distributions are nearly identical.
Fig. 3. relationship between optimized actual phase (red dot) and target phase (blue line) at (a) 11-16 GHz for x polarization (b) 18-24 GHz for y polarization.
Fig. 4. (a) Actual 2D phase distribution optimized by the PSO algorithm and (b) target 2D phase distribution calculated by the formula (1) at 11 GHz; (c) top view of the part corresponding layout of the designed metasurface.
For the purpose of further confirming that the metasurface is achromatic in broadband, the focusing effect of the 2D metasurface corresponding to the optimization results is simulated. The metasurface model of 8 mm×40 in the x direction and 4 mm×80 in the y direction is established in CST. The part schematic diagram of the 2D metasurface array according to the actual phase is shown in Fig. 4(c).
The diffraction patterns of proposed anisotropic achromatic metasurface and dispersive metasurface (The focus position is set to 160mm at 13 GHz and 21 GHz respectively) in the xoz plane under the x-polarized EM of 11-16 GHz and y-polarized EM of 18-24 GHz illumination are shown in Fig. 5(a) and (b). The white dotted line represents the focus plane of the designed metasurface, z = 160mm. For the achromatic metasurface, the EM waves under different incident frequencies are focused on the same point in the z direction. Moreover, there is no obvious diffraction sidelobe in the whole simulated range. While for the dispersive metasurface, the focal length at other frequencies will deviate. The exact relationship between the position of focus length (determined by the position of maximum energy in the z-direction) in the xoz plane and frequency is shown in Fig. 5(c) and (d). The standard deviations of the focus lengths at different frequencies calculated in the two bands are 3.775 mm and 2.307 mm for achromatic metasurface, 19.032 mm and 13.894 mm for dispersive metasurface respectively, which are compressed to 19.83% and 16.60%. It is worth noting that the focus slightly deviates from the preset focus length of 160 mm, which may be related to the depth of focus, the error caused by the derived electric field, and imperfect phase fitting.
Fig. 5. Normalized vector diffraction patterns of anisotropic achromatic metasurface and dispersive metasurface in xoz plane in (a) 11-16 GHz and (b) 18-24 GHz, the focal position of the dispersive metasurface is calculated from the metasurface with central frequencies of 13 GHz and 21 GHz. (c) and (d) The focal length position of the achromatic metasurface and dispersive metasurface in each frequency.
To demonstrate the far-field performance of the proposed metasurface, a dual-band common-caliber flat plate antenna consisting of the same metasurface and a feed source antenna was designed and simulated. The standard waveguide at the focal position is used as a feed source antenna to emit spherical EM waves to the metasurface. The far-field simulation results (shown in Fig. 6(a) and (b)) depict that the metasurface can achieve a gain of no less than 25 dB and low sidelobe at each frequency, showing reliable broadband performance. In order to illustrate the effect of achromatic aberration on antenna performance, a dispersive metasurface with the same unit cell is designed and simulated at 13 GHz (for x-polarization) and 21 GHz (for y-polarization). The gains of the achromatic metasurface and the dispersive metasurface are depicted in Fig. 6(c)and (d). It is obvious that the metasurface with elaborately designed phase in each frequency shows higher and more stable gains in other frequency points compared with the dispersive metasurface.
Fig. 6. The simulated radiation patterns in (a) x-polarization and (b) y-polarization; (c) and (d) Comparison of achromatic metasurface gain and dispersive metasurface gain in different modulation frequency.
Overall, from the simulation results, this design achieved the achromatic band switch by changing the polarization state of the plane wave. On the other hand, when we place a feed at the focus position, we can also regard it as a broadband reflect antenna which can realize bandwidth expansion by rotating the feed.
3. Fabrication and measurement
The entire metasurface is fabricated using printed circuit board technology to experimentally validate the theoretic and simulated analysis above. Three 0.037 mm-thick metallic patterns are printed on two layers of F4B substrate, which is shown in Fig. 7(a) and (b). Subsequent experiments are carried out with a far-field test system in the anechoic chamber and the test details are given in the in the Appendix B:
Fig. 7. (a) The front and (b) back view of metasurface sample; (c) The measuring setup for performance; (d) The measured radiation patterns of the metasurface for the x polarization and (e) for the y polarization obtained from the test. The results are normalized to the maximum at different frequencies. The illustrations show the relative gain compared with the bare waveguide in each frequency, where the relative gain is defined as the difference between the measured gain of the metasurface and the gain of the bare waveguide directly measured by the same system.
The far-field pattern in the range of 11-16 GHz when x-polarization incident is measured at first, then the feed is replaced and the polarization direction is adjusted to measure the far-field pattern in the range of 18-24 GHz at the y-polarization incident. Figure 7(d) and (e) show the measurement of the far-field pattern when the feed is located at about 160 mm. It can be seen that excellent directionality was obtained in the modulation frequency of the metasurface, and the sidelobe is almost all less than −10 dB at 11-16 GHz (x-polarization incident) and 18-24 GHz (y-polarization incident). The error compared with the simulation results mainly comes from the shielding of the feed, manufacturing error, and test environment noise. In addition, the non-standard plane wave received by the horn antenna also affect the far-field patterns. The illustrations of Fig. 7(d) and (e) are the relative gains compared with the bare feed at each frequency. It can be seen that the gains are almost consistent at all frequencies. The average values are increased by 19.49 dB and 15.08 dB, respectively. Note that the gains at higher frequencies under y polarization are less than those at lower frequencies under x polarization, which may be due to the imperfect phase fitting between the unit cell phase and the target phase at higher frequencies. On the other hand, the influence of manufacturing error on high frequency is more evident. The gains can be further improved by designing an optimized feed or using an off-axis feed [30]. Therefore, we can place the feed source at the focus of the metasurface as a broadband switchable transmitting antenna, or receive electromagnetic waves to focus on one point to realize the reception of broadband cross-band signals.
4. Summary
In summary, we proposed a polarization multiplexing metasurface for dual-band achromatic focusing based on dispersion engineering, which is composed of the anisotropic double-layer unit cell. Electromagnetic waves in different polarization states can be independently manipulated in two bands (11-16 GHz for x-polarization, 18-24 GHz for y-polarization). The calculated vector diffraction field distribution indicates that the metasurface can realize the achromatic function, and the standard deviation of its focus offset is 19.83% and 16.60% of the dispersive metasurface. The far-field simulation results show that it has more obvious broadband performance than the dispersive metasurface. The experimental average gains improve 19.49 dB and 15.08 dB on average at 11-16 GHz (for x-polarization) and 18-24 GHz (for y-polarization) relative to the bare feed source, respectively, which can realize broadband modulation in two band ranges. Moreover, the unit cell proposed in this work can also realize polarization multiplexing with different functions in dual-band, so as to integrate diverse dual-band functions, such as deflection, hologram, or OAM beam. We believe that the simple but powerful methodology with excellent performance is promising for integrated optics and broadband wireless communication.
Appendix A: The settings of the PSO algorithm
The length of the target metasurface is set to 320 mm. The period and the number of unit cells are 4 mm and 80, which are determined by the minimum period of the unit cell and the total size of the whole metasurface. The focal length f0 is set to 160 mm for both x and y polarization. Integer points within 11-16 GHz and 18-24 GHz are selected as the optimization target frequency of x-polarization and y-polarization, respectively. The number of particles and iterations is set to 100 and 300.
Appendix B: Experimental section
Simulation setup: All simulation results are obtained by CST Microwave Studio. Frequency domain solver is employed to calculate the S-parameters of the unit cell in the range of 11-24 GHz. The unit cell boundary conditions are adopted in the x and y directions, while the boundary conditions in z-direction are set to open. The vector diffraction pattern and far-field pattern are simulated by the time domain solver with open (add space) boundary conditions in all directions. The result of diffraction pattern is derived from the electric field at z = 3.1 mm by the built-in electric field monitor, and then calculated by the vector diffraction algorithm with MATLAB. The simulated far-field pattern is obtained directly from the far-field monitor.
Experiment setup: The experimental setup is shown in the Fig. 7(c). A waveguide connected with the vector network analyzer (R&S ZVA40) is placed at the focus of the metasurface to transmit electromagnetic waves, the horn antenna working as receiving end is placed at the same side of the metasurface with a distance over 20λ. The metasurface is placed on a turntable controlled by computer. The vector network is employed to collect far-field radiation EM with the rotation angle from −90° to 90°. Waveguides and horns working in 8-12 GHz and 12-18 GHz are used to measure x-polarized EM while the results of y-polarized EM are measured with waveguide and horn with operation frequency of 18-26.5 GHz.
Funding
National Natural Science Foundation of China (61875253, 61975209, U20A20217); National Key Research and Development Program of China (SQ2021YFA1400121); Chinese Academy of Sciences Youth Innovation Promotion Association (2019371); Sichuan Science and Technology Program (2020JDJQ0006, 2020YFJ0001).
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.
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