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Abstract
Metasurfaces have exhibited versatile capacities of controlling electromagnetic (EM) waves due to the high degree of freedom of designing artificially engineered meta-atoms. For circular polarization (CP), broadband phase gradient metasurfaces (PGMs) can be realized based on P-B geometric phase by rotating meta-atoms; while for linear polarization (LP), realization of broadband phase gradients has to resort to P-B geometric phase during polarization conversion and polarization purity has to be sacrificed for broadband properties. It is still challenging to obtain broadband PGMs for LP waves without polarization conversion. In this paper, we propose the design of 2D PGMs by combining the inherently wideband geometric phases and non-resonant phases of meta-atom, under the philosophy of suppressing Lorentz resonances that usually bring about abrupt phase changes. To this end, an anisotropic meta-atom is devised which can suppress abrupt Lorentz resonances in 2D for both x- and y-polarized waves. For y-polarized waves, the central straight wire is in perpendicular to electric vector Ein of incident waves, Lorentz resonance cannot be excited although the electrical length approaches or even exceeds half a wavelength. For x-polarized waves, the central straight wire is in parallel with Ein, a split gap is opened on the center of the straight wire so as to avoid Lorentz resonance. In this way, the abrupt Lorentz resonances are suppressed in 2D and the wideband geometric phase and the gradual non-resonant phase are left for broadband PGM design. As a proof of concept, a 2D PGM prototype for LP waves was designed, fabricated and measured in microwave regime. Both simulated and measured results show that the PGM can achieve broadband beam deflection for reflected waves for both x- and y-polarized waves in broadband, without changing the LP state. This work provides a broadband route to 2D PGMs for LP waves and can be readily extended to higher frequencies such as terahertz and infrared regimes.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials, as a kind of artificial composite structures consist of a series of subwavelength units arranged in a specific way, can exhibit fascinating properties that are not exist or difficult to obtain in nature material [1–4]. It is not only a material form, but also a material design paradigm, which opens a gate towards scientific research, engineering design. Metasurfaces, as the 2D version of metamaterials, exhibit versatile capacities for the delicate manipulations of electromagnetic (EM) waves due to their flexible design freedom, including the topology and array sequence of the meta-atom [5–9]. The polarization state, phase, and amplitude of the EM waves can be controlled by adjusting the structure of meta-atoms upon interfaces [10–14].
With the development of equipment and communication technology, electromagnetic integration and miniaturization technology of electromagnetic devices becomes an important development trend in the future. Therefore, it is indeed significant to explore the multifunction-integration in a single metasurface aperture. To this end, the research of new and multifunctional electromagnetic integrated devices around metasurfaces has gradually become a hot topic, especially the polarization- and frequency- dependent multifunctional metasurfaces [15–17].
For circular polarization (CP), the polarization multifunction metausrface has been investigated via hybrid phase scheme combining P-B geometric phase and other phase schemes, which is also known as spin-decoupled metasurface [18–20]. For example, in the Ref. [18], a new phase modulation pathway based on chiral V-shaped holes was proposed, which enable fully decoupled one-handed phase modulation of the two eigen spin-states. And based on this, two enantiomers are proposed to realize decoupled functions for the two eigen-states. However, the conventional geometric phase (P-B phase) is usually associated with circular polarization (CP) wave or linear polarization (LP) wave with cross-polarization conversion. And few works are focused to explore geometric phases for polarization-keeping LP waves. For LP, in order to achieve independent regulation of different polarization states with broadband characteristics, it is inevitable to sacrifice polarization purity or utilize the multi-layer resonant structure [21,22]. As described in Ref. [21], by synergizing dual-layer indium tin oxide (ITO) films and a sandwiched dual-mode metallic layer on a back metallic ground, near-zero and near-unity reflections for dual-orthogonal linear polarizations can be regulated, and by using the proposed architecture, two metasurfaces with integrated radiation-absorption and integrated diffusion-absorption function are implemented. Therefore, right now, it is challenging to realize independent regulation of linear polarization waves with both high polarization purity and broadband characteristics simultaneously using only one single layer.
To overcome this challenge, in this paper, we propose the design of 2D phase gradient metasurfaces (PGMs) by combining the inherently wideband geometric phases and non-resonant phases of meta-atom, under the philosophy of suppressing Lorentz resonances that usually bring about abrupt phase changes. In our previous work, the quadru-arc structure (QAS), which consists of four symmetrical arcs connected by central straight wire, has been demonstrated to realize the broadband linear-polarization preserving (LPP) geometric phase covering a range of 0-2π under y-polarized waves illumination. And in this state, the central straight wire is in perpendicular to electric vector Ein of incident waves, Lorentz resonance cannot be excited although the electrical length approaches or even exceeds half a wavelength. For x-polarized waves, the central straight wire is in parallel with Ein, a split gap is opened on the center of the straight wire so as to avoid Lorentz resonance. In this way, the abrupt Lorentz resonances are suppressed in 2D and the wideband geometric phase and the gradual non-resonant phase are left for broadband PGM design. As the proof-of-concept, a 2D PGM prototype is designed. The schematics and working principles are shown in Fig. 1. Clearly, the reflection of both x- and y- polarized waves can be modulated independently and two different functions can be achieved. According to Generalized Snell's law, for normally incident y-polarized waves of 8.0-12.0 GHz frequency range, and x-polarized waves of 9.0-11.0 GHz frequency range, high-efficiency abnormal reflection can be realized, respectively. Simulated and measured results demonstrate the working principle unambiguously. Our work provides a broadband route to 2D PGMs for LP waves and can be readily extended to higher frequencies such as terahertz and infrared regimes.
2. Design and analysis of the meta-atom
In our previous work [23], the QAS, just as shown in Fig. 2(a), which consists of four symmetrical arcs connected by central straight wire, was proved that the reflection phase can be regulated by changing the length of the arcs. The length of arcs is decided by parameter α. Figure 2(b) and (c) show the surface current distributions at 11.0 GHz under the y- and x-polarized waves illumination respectively when α=85°, which are monitored by CST Microwave Studio. Clearly, in Fig. 2(b), when y-polarized waves illuminate, the surface current is mainly distributed on the four arcs, whereas the central straight wire barely responded and the mechanism that the reflection phase of the y-polarized waves can be adjusted by changing the length of the arcs has been proved in our previous work. In the frequency band of 8.0-12.0 GHz, the variation of reflection amplitude and phase for y-polarized waves is shown in Fig. 2(d) as parameter α changing. In this frequency band, the phase changes evenly, and the phase difference covers 360°, while ensuring high reflection efficiency. Furthermore, in Fig. 2(c), for x-polarized waves, the surface current is not only distributed on the arc structure, strong current distribution also appears on central straight wire. From the flow direction of the entire current on the whole structure, a typical and strong Lorentz resonance emerges. Our previous work has proved that, due to the phase mutation characteristic of strong Lorentz resonance, the variation of the reflection phase for x-polarized waves cannot cover the range of 0-360°. Just as shown in Fig. 2(e), the Lorentz resonance emerges at around 11.0 GHz where phase mutation also appears. In the frequency band of 9.0-11.0 GHz, although the reflection efficiency remains high, the reflection phase difference cannot cover 360°, and the variation of reflection phase is not even. So, in order to achieve the evenly variational phase covering 360° of x-polarized waves, some improvements should be made to restrain the strong Lorentz resonance.
Fig. 2. (a) Schematic illustration of the structure proposed in our previous work. The surface current distributions at 11.0 GHz of the (b) y- and (c) x-polarized waves when α=85°. The variation of reflection amplitude and phase changing the value of α for (d) y-polarized waves and (e) x-polarized waves.
Based on the previous analysis, in order to restrain the strong Lorentz resonance when x-polarized waves illuminate, and increase the design degree of freedom of modulating the reflection phase of x-polarized waves, just as shown in the Fig. 3(a) and (b), the central straight wire is turned into H-shape structure with a slit in the middle. The Fig. 3(a) is the vertical view of the modified quadru-arc structure (MQAS), and Fig. 3(b) is the front view. All the metallic patterns are etched on the F4B (εr = 2.65) dielectric laminate with thickness d = 4.0 mm. And the other geometrical parameters are: Px = 20.0 mm, Py = 10.0 mm, r1 = 2.0 mm, r2 = 2.4 mm, w1 = 0.6 mm, w2 = 0.6 mm, l1 = 12.8 mm, l2 = 2.5 mm, the angle parameter α which decides the length of arcs, and the length of slit g. In order to verify the suppression of Lorentz resonance, and the influence of structural parameters on the phase of reflected waves, firstly, when the parameters hold α=85°, g = 0.3 mm, the surface current distributions at 11.0 GHz of y- and x-polarized waves are monitored, using CST Microwave Studio, shown as Fig. 3(c) and (d) respectively. Obviously, in Fig. 3(c), the surface current is mainly distributed on the four arcs, whereas the middle H-shaped structures barely responded when the y-polarized waves illuminate, which is almost same with the phenomenon shown in Fig. 2(b). That’s to say, the influence of MQAS on the reflection phase of y-polarized waves can be negligible. The variation of reflection amplitude and phase for y-polarized waves also verify this, which is shown in Fig. 3(e), when remaining g = 0.3 mm, and changing the value of α. It can be seen from Fig. 3(e) that for y-polarized waves, in the frequency band of 8.0-12.0 GHz, the total phase difference among them covers 360°, while ensuring efficient reflection, which is in accord with Fig. 2(d). Furthermore, for x-polarized waves, in Fig. 3(d), the surface current is not only distributed on the arc structure, but also appears on the intermediate H-shape structure. However, by comparison with Fig. 2(c), it can be found that because of the existence of the slit in the middle, the surface current is cut off and evenly distributed on both sides of the slit, that is, the original strong resonance is divided into two series-wound resonance. Therefore, the original strong Lorentz resonance emerging at around 11.0 GHz is suppressed effectively right now. To further verify this, the variation of reflection amplitude and phase is provided when remaining α=85° and changing the value of g for x-polarized waves, as schematically depicted in Fig. 3(f). Clearly, the Lorentz resonance is adjusted and appears at around 12.0 GHz. And in the frequency band of 9.0-11.0 GHz, the variation of the reflection phase varies evenly as parameter g changes and can cover 360°, while the reflection efficiency remains high.
Fig. 3. Schematic illustration of the proposed MQAS: (a) front view, and (b) side view. The surface current distributions at 11.0 GHz of the (c) y- and (d) x-polarized waves when the parameters hold α=85°, g = 0.3 mm. (e) The variation of reflection amplitude and phase remaining g = 0.3 mm, and changing the value of α for y-polarized waves. (f) The variation of reflection amplitude and phase is provided when remaining α=85° and changing the value of g for x-polarized waves.
3. Metasurface design
In order to design broadband PGM with LPP, which can regulate the reflection of both x- and y- polarized waves to realize different functions respectively, we need to select atoms that satisfy the amplitude and phase conditions. In the Part 2, we have verified that the influence of the added middle split gap on the reflection phase of y-polarized waves can be negligible. So, firstly, for the regulation of the reflection phase of y-polarized waves, we can fix the parameters α. Then, on this basis, we can select different parameters g which can satisfy the amplitude and phase conditions of x- polarized waves. Just as shown in Fig. 4(a), a 2D PGM including 18 × 36 atoms (360 mm × 360 mm) is proposed. Obviously, one meta-atom includes 12 atoms with the same parameters except for parameters α and g. The parameters α and g of the 12 atoms are shown in Table 1.
Fig. 4. (a) The proposed broadband PGM with LPP including 18 × 36 elements (360 mm × 360 mm), and the arrangement of the meta-atom for x- and y- polarized waves. The reflection amplitude and phase of these atoms for (b) y- polarized waves and (c) x- polarized waves.
Table 1. The parameters α and g of these atoms.
For y- polarized waves, the reflection amplitude and phase of these atoms are shown in Fig. 4(b). Clearly, in the 8.0-12.0 GHz frequency range, all these atoms have high reflection efficiency, and according to the reflection phase, they are divided into 6 groups: ①: atom 1, 7; ②: atom 2, 8; ③: atom 3, 9; and ④: atom 4, 10; ⑤ atom 5, 11; ⑥ atom 6, 12. The reflection phases of atoms within the same group are almost identical. There is a π/3 phase difference between the groups, and the total phase difference among all these groups covers 2π. Or from another point of view, these 12 atoms can be divided into 2 meta-atom-xs: ①: atom 1, 2, 3, 4, 5, 6; ②: atom 7, 8, 9, 10, 11, 12. And the phase difference of one meta-atom-x covers 0-2π.
In the same way, for x- polarized waves, the reflection amplitude and phase of these atoms are shown in Fig. 4(c). In the 9.0-11.0 GHz frequency range, while ensuring high reflection efficiency, these atoms have a phase difference covering 2π, and they are divided into 4 groups according to the reflection phase: ①: atom 1, 5, 9; ②: atom 2, 6, 10; and ③: atom 3, 7, 11, ④ atom 4, 8, 12, between which, there is π/2 phase difference. Similarly, these 12 atoms also can be divided into 3 meta-atom-ys: ①: atom 1, 2, 3, 4; ②: atom 5, 6, 7, 8 and ③: atom 9, 10, 11, 12. And the phase difference of one meta-atom-y covers 0-2π.
When there is a constant phase gradient at the interface of metasurface, for only reflection, Generalized Snell's law can be described as:
where ${\theta _i}$ and ${\theta _r}$ represent the incident angle and reflected angle, ${k_0} = (\omega /c) = 2\pi /{\lambda _0}$ is the wave vector in air, $\xi = d\phi /dx = 2\pi /{P_{1(2)}}$ is the gradient of the phase shift along the interface. When ${\theta _i} = 0$, that is, the electromagnetic wave irradiates on the surface vertically, the Eq. (1) can be simplified: where λ0 is the wavelength of the corresponding frequency in vacuum, P1(2) =s(m)*Py is the length of meta-atom for y- polarized waves or x- polarized waves, s or m is the number of atoms in one corresponding meta-atom, Py is the length of one atom along the y- axis.For y- polarized waves, according to Fig. 4(b), the phase difference of one meta-atom covers 2π. So, based on Eq. (2), the anomalous reflection angle can be calculated, just as Table 2 shown. In the same way, for x- polarized waves, the anomalous reflection angle can also be calculated, which is shown in Table 2 too.
Table 2. The comparison of calculated and simulated anomalous reflection angle.
To demonstrate this, by utilizing the CST Microwave Studio, we can get simulated normalized abnormal reflection intensity spectrums for y- polarized waves and x-polarized waves with normal incidence from + z direction, as schematically depicted in Fig. 5(a) and (g), respectively. The x-coordinate labels the frequency and the y-coordinate denote the refraction angle ${\theta _r}$. Also, the simulated anomalous reflection angles can be achieved and they are plotted in Fig. 5(a) and (g) using the red circles, and the comparison with calculated results are shown in Table 2.
Fig. 5. The normalized abnormal reflection intensity spectrums for (a) y- polarized waves and (g) x- polarized waves. The y-component of electric fields distribution in the yoz plane (the right) and the far fields results (the left) of proposed PGM for (b) 8.0 GHz, (c) 9.0 GHz, (d) 10.0 GHz, (e) 11.0 GHz and (f) 12.0 GHz. The x-component of electric fields distribution in the yoz plane (the right) and the far fields results (the left) of proposed metasurface for (h) 9.0 GHz, (i) 10.0 GHz and (j) 11.0 GHz.
In addition, under y-polarized waves incident, the y-component of electric fields distribution in the yoz plane (the right) and the far fields results (the left) of proposed metasurface for 8.0 GHz, 9.0 GHz, 10.0 GHz, 11.0 GHz and 12.0 GHz are summarized in the Fig. 5(b), (c), (d), (e) and (f). It can be found from these figures that under incident angles ${\theta _i} = 0$, high-efficiency anomalous reflection can be achieved, and the simulated anomalous reflection angles are agreeing well with the theoretically calculated results except for little deviation. In the same way, under x- polarized waves incident, the x-component of electric fields distribution in the yoz plane (the right) and the far fields results (the left) of proposed metasurface for 9.0 GHz, 10.0 GHz, and 11.0 GHz are summarized in the Fig. 5(h), (i) and (j). Also, the simulated anomalous reflection angles are agreeing well with the theoretically calculated results except for little deviation.
4. Experimental results
To further verify the design strategy, by utilizing the printed circuit board (PCB) technology, the prototype of our proposed PGM was fabricated, which includes 18 × 36 atoms (360 mm × 360 mm) and is shown in Fig. 6(a). Figure 6(a) also shows the experiment process, which was accomplished in the microwave anechoic chamber. In detail, a rotatable platform was used to fix the prototype and the transmitting horn antenna, while the receiving antenna was fixed on a stationary platform to receive the signal. The transmitting antenna is fixed perpendicular to the prototype to secure incident angle ${\theta _i} = 0$, and the receiving antenna can receive the reflected waves at different directions by rotating the rotatable platform. The measured normalized abnormal reflection intensity spectrums for y- polarized waves and x- polarized waves are given in the Fig. 6 (b) and (c). Overall, considering the tolerance in the fabrication and experiment, the measured results agree well with the calculated and simulated results.
Fig. 6. (a) The prototype and the experiment process. The measured normalized abnormal reflection intensity spectrums for (b) y- polarized waves and (c) x- polarized waves.
5. Conclusion
In conclusion, we have proposed and successfully demonstrated a strategy for broadband PGM design with LPP under the philosophy of suppressing Lorentz resonances. The proposed MQAS was proved that it cannot only realize 2π phase difference of y-polarized waves by changing the length of the arcs, but also can realize 2π phase difference of x-polarized waves by opening a split gap on the center of the straight wire to avoid Lorentz resonance. In order to verify the concept, a 2D PGM prototype for LP waves was designed in microwave regime which consists of 18 × 36 atoms. According to Generalized Snell's law, both simulated and measured results show that the PGM can achieve broadband beam deflection for reflected waves for both x- and y-polarized waves in broadband, without changing the LP state. This work provides a broadband route to 2D PGMs for LP waves and can be readily extended to higher frequencies such as terahertz and infrared regimes.
Funding
National Key Research and Development Program of China (SQ2017YFA0700201); National Natural Science Foundation of China (61901508, 61971435, 61971437, 62101588).
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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