High-efficiency transparent vortex beam generator based on ultrathin Pancharatnam&#x2013;Berry metasurfaces

Shiwei Tang; Tong Cai; Jian-Gang Liang; Yu Xiao; Cheng-Wu Zhang; Qing Zhang; Ziyang Hu; Tao Jiang

doi:10.1364/OE.27.001816

*tangshiwei@nbu.edu.cn

1. Introduction

Recently, enlarging the communication capacity and improving the transmission data-rate is believed to be necessary for future communication systems [1,2]. Vortex beam generator is extraordinarily promising and considered as an excellent resolution to solve these issues due to its unique electromagnetic (EM) properties of carrying the orbital angular momentum (OAM) [3–6]. To date, various approaches have been proposed to generate vertex beams, such as spiral phase plate [3,4,7], computer generated holograms [8,9], spiral reflectors [10], antenna arrays [11] and meta-surfaces [12–24], leading to wide applications in optical devices, radio communication as well as metrology. These metasurfaces-based vortex beam generators have achieved versified functionalities based on polarization/helicity control [6], multichannel supervisions of OAM states in only one planar slab [19], and even OAM integration devices with polarization-dependent transmission and reflection properties [20].

Despite these fruitful achievements obtained so far, the reported vortex beam generators working in transmission geometries, intrinsically exhibit multilayer structures to realize a 2π phase shift range [20], and operate in very low efficiencies [25–29], usually coming from non-ideal transmission amplitudes and large fluctuations, which seriously limit their further applications. Pancharatnam–Berry (PB) metasurfaces, also called geometry metasurfaces, can manipulate the EM wavefronts by rotating the planar resonant meta-atoms [21–23,30]. The dispersionless property of PB metasurfaces has successfully enhanced the working bandwidth of the designed meta-devices [30]. Very recently, Zhou et al. established a certain criterion to achieve nearly 100% efficiencies for the transmissive PB metasurfaces [21]. However, this multilayer structure exhibits complex fabrication and high profile. Meanwhile some ultrathin transmissive metasurfaces with only electric resonators are theoretically restricted to have an efficiency of below 25% [25,31,32]. Therefore, it is a huge challenge to realize an ultrathin and compact transmissive vortex beam generator with very high efficiency.

In this article, we propose a new strategy for realizing high-performance vortex beam generator with a deep-subwavelength thickness. Our meta-device consists of a totally transparent ultrathin PB metasurface which is excited by a self-made Archimedes spiral antenna. By carefully integrating the cross-bar structure with positive permittivity ( $+ ε$ ) and holey metallic ring resonator with negative permittivity ( $- ε$ ) on both sides of a dielectric substrate, we achieve nearly unit transmittance with π phase difference at the target frequency of 10.6 GHz with an ultrathin thickness ( $0.07 λ_{0}$ ), which is a wonderful candidate to act as a PB meta-atom. To illustrate the concept, we design and fabricate a realistic vortex beam generator, which can be seen in Fig. 1 Both near-field and far-field experiments are performed to demonstrate that our meta-device has an absolute efficiency of 87%, which is much higher than those achieved by any other approaches [20–23]. Our novel strategy can motivate the realization of ultrathin and high-efficiency transmissive vortex beam generators and other related high-performance microwave meta-devices.

Fig. 1 Schematics and working principles of the high-performance vortex beam generator. The meta-device can convert the quasi-spherical beam to vortex beam with the topological charge m = + 1. Inset shows the top-view of the Archimedes spiral antenna.

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2. Concept and meta-atom design

We now describe our strategy to design an ultrathin and high-efficiency vortex beam generator. The key step is to design a collection of meta-atoms with transmission amplitudes of near 1 and tuned transmission phase that covers 2π range. PB metasurface can control the phase profile exactly by rotating the structure and the amplitude can keep consistent under excitation of circular polarization waves [21–23,30], which is a simple but efficient way to design functional devices. For a transmissive PB metasurface with mirror symmetry, the scattering parameters of a meta-atom with a rotation angle under excitation of circular polarization wave can be calculated as

\begin{array}{l} t_{R L} = \frac{1}{2} (t_{x x} - t_{y y}) e^{- j 2 ϕ} \\ r_{L L} = \frac{1}{2} (r_{x x} - r_{y y}) e^{- j 2 ϕ} \\ t_{L L} = \frac{1}{2} (t_{x x} + t_{y y}) \\ r_{R L} = \frac{1}{2} (r_{x x} + r_{y y}) \end{array}

with r_LL, r_RL/t_LL, t_RL being the reflection/transmission coefficients in circular polarization base and r_xx, r_yy/t_xx, t_yy being reflection/transmission coefficients in linear polarization base. Thus, the theoretical 100% efficiency for a transmissive PB metasurface can be retrieved as [21]

r_{x x} = r_{y y} = 0, | t_{x x} | = | t_{y y} | = 1, φ_{x x} = φ_{y y} \pm π

Metamaterials provide an efficient way to manipulate the material parameters, and many kinds of divarication have been successfully demonstrated to exhibit specific behaviors that do not occur in nature [33–35]. Here, we find that an anisotropic structure with two resonators A and B on both sides of a spacer layer, shown in the inset of Fig. 2(a), can satisfy Eq. (2) when certain criterion is satisfied. Figure 2(a) depicts the transmission amplitude |t| varying against the permittivities of two resonators, denoted as

ε_{A}

and

ε_{B}

, with resonator A being isotropic while B being anisotropic. And the thicknesses of metamaterial layer

d_{M}

and dielectric layer

d_{D}

are fixed for a convenience of realistic meta-atom design. By tuning the ratio of

ε_{A}

and

ε_{B}

, not only the transmission amplitude |t| can be controlled, but also the transmission phase φ can be manipulated. Indeed, we find two parallel |t| = 1 lines with almost π phase difference for our system as shown in Figs. 2(a) and 2(b), which is very desirable to design a high efficiency transmissive PB meta-atom by appropriately chosen effective-medium parameters. Here, we set

ε_{A x} = ε_{A y} = - 276

,

ε_{B x} = 447

and

ε_{B y} = 246.23

, marked by blue stars in Figs. 2(a) and 2(b), which means our design is a highly anisotropic structure. We choose a holey metallic ring resonator for A structure and anisotropic cross bar for B profile, as shown in the inset of Fig. 2(c). The single layer A is opaque for both polarizations, while single layer B exhibit different transmission amplitudes under two linear polarizations, as depicted in Fig. 2(c). The combination of resonators A and B on both sides of the dielectric substrate can reach very high transmission amplitudes at both polarizations while presents a π phase difference. Moreover, we can also find from Fig. 2(d) that the finite-difference-time-domain (FDTD) simulated transmission spectra coincide very well with that calculated by effective medium theory (EMT). The inherent physics of prefect transparency at two polarizations are quite different. For the y-polarization, the transparency is governed by the Fabry-Perot resonance, generated by the coupling between two structure layers [27–30]. The mechanism for another polarization is the scattering cancellation, with the dielectric substrate providing an important positive permittivity [20,36].

Fig. 2 Effective medium theory for our designed system. (a) Transmission amplitudes and (b) transmission phases in the $ε_{A} - ε_{B}$ diagram for our system ( $d_{M} = 0.1 m m$ , $d_{D} = 1.8 m m$ and $ε_{D} = 4.3$ ) calculated by the transfer-matrix-method (TMM) at target frequency of $f_{0} = 10.6 GHz$ . Inset to (a) illustrates the structure of our system. (c) FDTD calculated transmission amplitudes for single holey metallic ring resonator A and cross bar resonator B. (d) FDTD and EMT calculated transmission spectra for a combination of A and B resonators placed at both sides of a dielectric substrate.

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Figure 3(a) shows the final optimized transmissive PB meta-atom that can exhibit the mentioned high efficiency EM characteristics. The meta-atom consists of one 2 mm-thick FR4 dielectric spacer ( $0.07 λ_{0}$ ) and two layers of loaded composite structures. The advantages of this meta-atom are obvious. The anisotropic cross bar structure can generate positive permittivities for both polarizations, which can be tuned by the opaque background to realize material permittivities for different polarizations. To demonstrate our concept, we fabricate a metasurface composed by a periodic array of meta-atoms (60 × 60 cells with a total size of 420 × 420 mm²) with its picture shown in Fig. 3(b). We measured the transmission characteristics under linear polarizations and circular polarizations, respectively. In former case, when shining linearly-polarized EM waves normally onto the fabricated metasurface by a horn antenna, Figs. 3(c) and 3(e) illustrate that our meta-atom is totally transparent for both linear polarizations with the transmission-phase difference of about 180° within a frequency range of 10.3-10.8 GHz. Moreover, FDTD simulations show excellent agreements with the experimental results for both linear polarizations. In latter case, four transmission/reflection amplitude spectra ( $| t_{L L} |$ , $| t_{R L} |$ , $| r_{L L} |$ , $| r_{R L} |$ with L/R being the left/right circular polarization) are measured, with the results shown in Figs. 3(d) and 3(f). Under illumination of a left-handed circular polarization microwave, $| r_{R L} |$ can approach 95% at frequency of f₀ = 10.6 GHz, and other three channels are completely suppressed ( $| t_{L L} | = | r_{L L} | = | r_{R L} | \approx 0$ ). In fact, the transmission/reflection coefficients can also be retrieved by putting the measured transmission spectra into Eq. (1), which shows good consistency with the measurements. As predicted by Eq. (1), the transmission phase can be controlled exactly by rotating the structure due to the carried PB operation [19,20,26,37]. Thus, we can design a lot of functional meta-devices based on the proposed meta-atom by carefully arranging the geometric-phase-based particles.

Fig. 3 EM characteristics of our designed meta-atom. (a) Schematic of the designed meta-atom composed by sandwich structure with two identical composite resonators separated by a dielectric spacer with thickness h = 2 mm and $ε_{r} = 4.3$ . The detailed geometrical parameters are fixed: P = 8 mm, a₁ = 1.5 mm, b₁ = 6.5 mm, a₂ = 0.15 mm, b₂ = 6.3 mm. (b) The picture of the fabricated meta-atom array. Measured and FDTD simulated (c) transmission amplitudes and (e) phase spectra for the periodic metasurface under excitations with different linearly-polarized microwaves. Measured and FDTD simulated (d) transmission amplitude ( $| t_{L L} |$ , $| t_{R L} |$ ) and (f) reflection amplitude ( $| r_{L L} |$ , $| r_{R L} |$ ) for the periodic metasurface under illumination of the left-handed circularly-polarized EM wave.

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3. Experimental results and discussions

We now describe how to design a compact and high-performance vortex beam generator. For a convenient application and a compact structure, we excite the metasurface with a self-made Archimedes spiral antenna, shown in the inset of Fig. 5(a), which can radiate quasi-spherical left-handed circular polarization waves within a very wide bandwidth (6-13GHz) [30]. More importantly, its diameter is only about 30 mm, which is electrically smaller than that of the conventional horn antenna. Therefore, the metasurface should incorporate two distinct phase profiles of a lens and a vortex plate, which satisfies the following distributions:

φ = k_{0} (\sqrt{F_{0}^{2} + y^{_{2}} + x^{_{2}}} - F_{0}) + m \cdot \tan^{- 1} (y / x)

with

k_{0} =2 π / λ_{0}

being the propagation constant,

F_{0}

being the focal length of the lens and m being the topological change. Without loss of generality, we set

F_{0} = 70 m m

and

m = 1

. The phase distributions are plotted in Fig. 4(b). Then, the corresponding rotation angels on the metasurface can be obtained as

θ = φ / 2

. We fabricate a realistic metasurface with its picture shown in Fig. 4(a), which consists of 20 × 20 meta-atoms and exhibits a total size of 160 × 160 mm².

Fig. 4 Design of transmissive PB vortex beam generator. (a) Picture of our designed/fabricated meta-device. (b) Transmission phase ( $φ$ ) distribution at each meta-atom of the designed/fabricated meta-device.

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Next, we experimentally characterize the performance of the designed vortex beam generator. The feed antenna and the metasurface are supported by a 70 mm-thick foam as shown in Fig. 5(a), and the foam has little influence on the meta-device. First, we measure the near field distribution. In our experiments, we employed a monopole antenna (~20 mm long) to detect the electric-field distributions at the transmission part and 30 cm in front of the meta-device with the aid of an automatically controlled scanning mapper system [20,21,28–30]. The monopole antenna and the vortex beam generator are both connected to a vector-field network analyzer (Agilent E8362C PNA), so that the electronic filed information can be recorded. The pure $Re (E_{y})$ distribution in Fig. 5(c) and spiral-shape of phase distribution verify that our meta-device can generate excellent vortex beam with $m = 1$ . The inherent physics is that the interferences among the high-efficiency transmitted waves passing through meta-atoms at different positions form the pure vortex beam. Secondly, we consider characterizing the far field performance of our meta-device. Figure 5(e) portrays the numerically calculated three-dimensional (3D) far-field radiation patterns at frequency of 10.6 GHz. The high-directive narrow beam, clear central null field at the origin and very low back lobe level reinforced the desirable vortex effect for a second time. We measured the two-dimensional (2D) radiation patterns through the far field measurement system in the anechoic chamber. From the radiation patterns on xoz plane shown in Fig. 5(f), we can see that the measured result agrees very well with that of the numerical calculation, and the slight difference can be attributed to inevitable fabrication errors. The radiation gain is lower than −25 dB (−23 dB) at the specular direction for measurement (simulation).

Fig. 5 The performance of our designed vortex beam generator. (a) Experimental setup of the vortex beam generator. Inset to (a) shows the picture of the fabricated Archimedes spiral antenna. (b) Measured efficiency against frequency for our vortex beam generator. Measured (c) $Re (E_{y})$ and (d) phase distributions on an xy plane 30 cm in front of the metasurface at 10.6 GHz. (e) FDTD simulated 3D radiation pattern of the metadevice at 10.6 GHz. (f) Measured and simulated 2D radiation patterns at xoz plane at 10.6 GHz.

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Finally, we quantitatively evaluate the working efficiency of our vortex beam generator by far field measurements. In our system, five channels are available to transfer the incident power: two transmissive channels ( $P_{t, L L}$ and $P_{t, R L}$ denoting the transmission power taken by left or right circular polarization, respectively), two reflective channels ( $P_{r, L L}$ and $P_{r, R L}$ denoting the reflection power taken by left or right circular polarization, respectively) and an absorption channel (A). Thus, the total power can be calculated as $P_{t o t} = P_{t, L L} + P_{t, R L} + P_{r, L L} + P_{r, R L} + A$ . Only the power carried by the cross-polarized transmission part $P_{t, R L}$ can be converted to carry vortex beams. Therefore, the absolute efficiency can be quantitatively estimated using the formula,

η = \frac{P_{t, R L}}{P_{t o t}} \times 100 % .

The transmission/reflection power can be retrieved by integrating the radiation patterns within the appropriate angle region occupied by the corresponding modes. The absorption A is very difficult to directly measure, and we adopt an FDTD simulation for an approximate estimation of ~ $2 % P_{t o t}$ . The same approach is applied to the whole frequency band, and the working efficiency against frequency is plotted in Fig. 5(b). Within the frequency interval of 10.4-10.9 GHz, our meta-device exhibits a very high efficiency of more than 70%, and other scattering power is seriously suppressed. As is expected, the best performance appears at 10.6 GHz with an efficiency of 87%, leaving the other three channels carrying $5 % P_{t o t}$ for $P_{t, L L}$ , $2 % P_{t o t}$ for $P_{r, L L}$ , and $4 % P_{t o t}$ for the $P_{r, R L}$ .

4. Conclusions

To sum up, we show that transmissive PB metasurface with nearly unit transmittance can be realized through an ultrathin slab ( $0.07 λ_{0}$ ) exhibiting two resonators with negative permittivity and positive permittivity satisfying certain criterions. We design and fabricate a microwave vortex beam generator, working at 10.6 GHz, to experimentally demonstrate that the maximum achievable efficiency reaches 87%. Both near field and far field measurements verify the very pure vortex beam performance of the proposed meta-device. Our findings not only pave a new way to design high-performance transmissive PB meta-devices at different frequency regions but also advance a step further in deeply low-profile transmissive PB metasurfaces.

Funding

National Natural Science Foundation of China (11604167, 61871394, 61501499); Navigation Foundation (20151896014); K. C. Wong Magna Fund in Ningbo University.

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High-efficiency transparent vortex beam generator based on ultrathin Pancharatnam–Berry metasurfaces

Abstract

1. Introduction

2. Concept and meta-atom design

3. Experimental results and discussions

4. Conclusions

Funding

References

Cited By

Figures (5)

Equations (4)

Optics Express