1. Introduction

According to Fermat’s principle, wavefront of a light beam can be modified by controlling the phase of light wave [1]. Conventional optical components rely on sophisticated design of permittivity distribution to gradually modulate the phase of light waves for the control of propagation path in bulk material. A propagation length comparable to operational wavelength is required for a specific phase shift. In contrast, metamaterial (MM) [2, 3] manipulates light waves in subwavelength scale, and exhibits exotic optical properties such as negative refraction [4–6], invisibility cloak [7–9], polarization manipulation [10–13], as well as extraordinary optical transmission (EOT) [14–19], etc. Such extreme optical responses arise from local resonances of subwavelength-sized units. An ultra-thin planar MM, i. e., a metasurface, enables abrupt phase discontinuity for scattering waves [20], opening a new era of light manipulation. An elegant example is the “V-shaped” antenna array, which ensures identical amplitudes of scattering waves at each unit, and provides a constant phase shift between two neighbor units. Beaming shaping, beam steering and phase modulation within an optically thin depth are favorable for various applications [20–32].

A metasurface relies on a certain type of resonant unit to modulate phase of transmitted or reflected waves. To achieve full control on beam steering or beam shaping, the phase variation of local fields at different points on a finite sized metasurface shall span a range of $[0,2\pi ]$. Meanwhile, high transmittivity or reflectivity is the other crucial merit to measure whether the functionality is efficient or not. A single-layered metasurface, adopted in most of the previous studies for beam manipulation, cannot fulfill the requirement of high efficiency. For the purpose of modulating phase of transmitted/reflected waves in a wide range, the operational frequency has to be far away from the resonant frequency of single-layered metasurface. As a result, the amplitude of scattering waves is very small, and the total efficiency is usually less than 10%. How to improve the efficiency is still under consideration [20, 22, 25].

It has been reported that a thin metal film perforated with an array of subwavelength holes exhibits extraordinary optical transmission (EOT) property due to the excitation of surface plasmon polaritons or localized resonances [14, 19]. And it has been found recently that the EOT passband can be very broad for a metal/dielectric multi-layers system that is perforated with an array of coaxial annular apertures (CAAs). In addition, within the EOT passband, the phase of transmitted waves varies smoothly from 0 to $-2\pi$ due to interlayer coupling [33]. Both features are advantageous for highly efficient beam steering. As the broadband EOT stems from the evanescent resonant coupling among adjacent perforated metallic layers through local resonance channels provided by CAAs, it is local resonance that primarily determines the EOT property [19], while the disorder of CAA arrays or the alignment of CAAs among different layers has little influence on it. More control calculations (not shown) indicate that the broadband EOT is robust against the structural disorder and imperfect alignment, which is very advantageous for practical application.

In this paper, we show that, by varying the geometric parameters of CAAs, a multi-layered metasurface can function as a beam steering transmitter. We also perform proof-of-principle experiments in microwave regime to verify the beam steering effect and high efficiency. Measured spatial distributions of electromagnetic local fields, in excellent agreement with finite-difference-time-domain (FDTD) simulations, clearly indicate that varied phase discontinuities on the metasurface dramatically modify the wavefront of transmitted beam. An efficiency of 65% and a deflection angle of 18° are verified by measuring the far-field radiation pattern. Thanks to high transmission and flexible phase modulation in the broad EOT band, the proposed metasurface is capable of refracting the incident beam in any polarization at a predetermined deflection angle.

2. Model description

Figure 1(a) presents the schematic of the gradient metasurface for beam steering. The metasurface is comprised of three metallic layers and two intermediate dielectric spacer layers. Each metallic layer, with a thickness of 0.035mm, is perforated with an array of CAAs. And metals in our model system are assumed to be perfect electric conductors (PECs) at the microwave frequencies. Each dielectric layer has a thickness of 1.575mm and a permittivity of 2.65. The gradient configuration is realized by varying the inner radius of CAAs along one direction of the array. As illustrated in the top view of the sample [see Fig. 1(b)], the CAAs, perforated through each metal film, are arranged in a square lattice with 9 columns (along $x$ direction) and 12 rows (along $y$ direction). The lattice period is $p=12\text{mm}$, such that the sample has a width of $L_x=108\text{mm}$ and a length of $L_y=144\text{mm}$. The outer radius of each CAA is fixed at $R=5.8mm$. The inner radius $r{}_n$ ($n=1,2,\mathrm{...9}$) of CAAs of the nine columns varies gradually from left to right. The incident plane waves are propagating along $+z$ direction with electric field along $x$ axis and magnetic field along $y$ axis. By tuning the inner radius of CAAs, phase gradient is assigned to the scattering waves along $x$ axis on the metasurface, so that the transmitted waves are refracted toward a prescribed direction.

 

Fig. 1 (a) Schematic of the metasurface, and the incident and transitted waves. (b) Photograph of a part of the sample.

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We start by investigating the transmission of prototype of a tri-layered metasurface with respect to different inner radius of CAAs. Modal expansion method (MEM) [34, 35] is employed to calculate the intensity and phase difference of transmitted waves. Figure 2 shows the results for $R=5.8\text{mm}$, $r{}_n=4.57\text{mm}$ under normally incident plane wave. We see that there exists a broadband transparent window at 7-11GHz, and phase difference varies smoothly from 0 to $-2\pi$ through the whole passband. The CAA functions as an efficient resonant unit which provides full control on the phase of transmitted waves without sacrificing the transmittivity. The feature is very advantageous for a transmitter with beam steering functionality.

 

Fig. 2 Analytically calculated spectrum of transmission intensity (black square dots) and phase difference (red circular dots) from a tri-layered metasurface perforated with a periodic array of CAAs with $p=12\text{mm},R=5.8\text{mm},r{}_n=4.57\text{mm}$.

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The spectra of transmission intensity and phase difference present enough information for design the transmitter by selecting appropriate values of radii $r{}_n$. Table 1 presents the radii of CAAs in our model. The rule is to ensure a $\pi /4$ phase increment at two adjacent CAAs along $x$ axis to cover 0 to $-2\pi$ for phase variation over the metasurface, while maintaining the amplitude of the transmitted wave above 0.8 [see Fig. 3]. Following the generalized Snell’s law for reflection and refraction [20]

Table 1. Inner radii $r{}_n$ of our designed model

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Fig. 3 Analytically calculated transmission amplitude (black square dots) and phase difference (red circular dots) at 10GHz by assuming that inner radius of the periodic CAA arrays has the value of $r{}_n$ (see Table 1).

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3. Simulations and measurements of highly efficient beam steering

The theoretical predictions stated above are verified by FDTD simulations. In the calculations, only one period is modeled along $y$ axis for the sake of periodic boundary condition. The metasurface is finite along $x$ axis with the length of $L_x=108\text{mm}$. Perfectly matched layers (PMLs) are adopted along $x$ and $z$ directions to absorb scattering waves at boundaries. A one-way Gaussian beam at 10GHz is positioned 15mm away from the metasurface in $xy$ plane. The beam waist is 50mm. Figures 4(a) and 4(b) present the calculated magnetic field distributions $H_y(x,z)$ of transmitted waves without and with the metasurface. It is shown that the Gaussian beam is propagating through the metasurface with high efficiency at an angle of about ${18}^{\text{o}}$ with respect to $z$ axis. Measurements are taken in a microwave chamber. The sample, with a lateral size of $108\text{mm}\times \text{144mm}$, is fabricated by printed-circuit-board (PCB) fabrication technology. A standard horn antenna operating at 8.2GHz-12.4GHz with gain coefficient of 24.8dB serves as the Gaussian beam source. A small ring antenna as a probe, lying in $xz$ plane for measuring magnetic field $H_y$, is fixed on a two-dimensional movable platform. The platform is electrically driven by a computer with a maximum scanning range of $1\text{m}\times 1\text{m}$ and a finest resolution of 0.1mm along both $x$ and $z$ directions. The horn antenna and the ring antenna are connected to a vector network analyzer Agilent8722ES for the measurements. We see that experimental results illustrated in Figs. 4(c) and 4(d), are in excellent agreement with numerical simulations shown in Figs. 4(a) and 4(b), verifying the deflection angle of 17.5° in theoretical prediction.

 

Fig. 4 Simulated magnetic field distributions ($H_y$) for a Gaussian beam propagated (a) in free space and (b) through the metasurface. Measured magnetic field distributions ($H_y$) for a horn antenna (c) without and (d) with the sample.

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To quantitatively determine the deflection angle and the transmission efficiency, we also measure the radiation patterns in far field with a horn receiver. The sample is bound to the horn emitter which is placed on a rotary table with a finest angular resolution of 0.1°. We see from Fig. 5(a) that the deflection angle is 18° and the transmittivity is above 65% by comparing with the reference radiation pattern of the horn antenna in free space. It is in excellent agreement with FDTD simulations shown in Fig. 5(b). Both the near-field and far-field measurements confirm that wavefront and high directivity of incident Gaussian beam is preserved. The highly efficient beam steering achieved with an ultra-thin planar scheme shall have great potentials in wavefront engineering and light manipulation for future integrated metaphotonic devices.

 

Fig. 5 (a) Measured and (b) simulated far-field radiation patterns for a horn antenna with (blue line) and without (red line) the sample.

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4. Conclusion

In conclusion, we have demonstrated that a gradient metasurface is capable of highly efficient beam steering. Owing to the evanescent resonant coupling among the adjacent perforated metallic layers, the tri-layered structure provides a broadband transparent window where the phase discontinuities can be tuned flexibly in a whole range of 0 to $2\pi$. The high transmission property has a great tolerance for the geometric parameter and operating frequency, leading to a 65% efficiency of beam steering which is much higher than the previous reports. In the present scheme, the transmission dips within the EOT passband provide the lower limit of efficiency, and it is feasible to improve the efficiency by deliberately selecting the geometric parameters and locations of CAAs at different layers. Our findings present a route for beam manipulation on a subwavelength scale with an ultra-thin planar metasurface, and it is also possible to be utilized for beam bending, focusing and other functionalities.