1. Introduction

Phase is a significant attribute of electromagnetic (EM) waves. Therefore, it is highly recommended to control the phase of EM waves in a desired manner for functional photonic devices. In particular, the manipulation of the wavefront of EM waves based on phase modulation is crucial for novel physical phenomena and practical applications. Recently, optically-thin metasurface with phase discontinuity was proposed as a new strategy for the modulation of EM waves. It is low cost, lightweight, and easy to manufacture, and has led to the generalization of the Snell's laws of reflection and refraction [1]. Metasurfaces, i.e., planar metamaterials with one or more layers, are a new category of artificially structured metamaterials, the use of which has been proposed in the control of wavefront propagation of EM waves using arrays of gradient elements. Many interesting applications have been already reported which utilize EM waves from the visible to the terahertz regime such as ultrathin flat lens [2,16], anomalous reflection [1,3], surface mode conversion [4,5], EM wave absorber [6–10], high impedance surface and artificial magnetic conductor [11], and near-field vortex beam [1,12]. In particular, the metasurface flat lens technology provides a new way for realizing lightweight, thin, compact, and highly efficient focusing designs in the field of metamaterials.

Metasurfaces using focusing lenses have been reported in the visible [13], mid infrared spectra [14], and microwave frequencies [15,16] in the transmission mode. Focusing lens designs for the reflection mode in visible [17], near infrared [18–20], and mid infrared [21] spectra have also been reported. In particular, near-diffraction-limited focusing of a flat lens with high efficiency of 80% has been demonstrated [22]. It is highly desirable to achieve high efficiency focusing by using metasurfaces to manipulate the wavefront. One typical metasurface is a mushroom-shaped structure with a metallic ground plane. To our knowledge, there have been no instances of demonstrations of near-diffraction-limited focusing with high efficiency using mushroom-shaped metasurfaces in the reflection mode in the microwave region. In this paper, we proposed and experimentally demonstrated a highly efficient flat focusing lens based on a gradient high-impedance metasurface composed of mushroom-shaped elements in the microwave region. The gradient high-impedance metasurface can be used for the realization of a full-range (2π) reflection phase shift modulation, following which a near-diffraction-limited focusing with high focusing efficiency of 80% can be easily achieved. When the fabrication error and scattering are ignored, the experimental result is in good accordance with the results observed in the numerical simulation.

2. Model design

Conventional photonic devices need to be designed in specific shapes and thicknesses to modify the wavefront of a light beam. A common approach for beam focusing is to use a hyperbolic reflector. A hyperbolic in-plane profile of the phase difference of the reflected beam is achieved by the phase accumulation of different spatial paths. An intuitive idea is to use an inhomogeneous metasurface for beam reflection, assuming that the reflected phase change on the metasurface has a hyperbolic profile. It is noted that at frequencies where magnetic resonance occurs, a mushroom-shaped metasurface reflects incident waves with a phase shift in the range of $2\pi$. The high-impedance metasurface with mushroom-shaped elements has a specific reflection phase of incident waves that causes the metasurface to behave like an artificial magnetic conductor (AMC), where the reflection phase depends on the size of the patch layer and the gap.

We designed a flat focusing lens model with a gradient high-impedance metasurface as shown in Fig. 1(a). The metasurface consisted of 15 × 15 mushroom-shaped elements in two dimensions. The structure of the element is schematically depicted in Figs. 1(b) and 1(c). The element of the metasurface is a three-layered structure, which comprises of one metallic ground layer, one dielectric layer, and one metallic patch layer. A metal plated via is used to connect the two metal layers. The element can be visualized as a mushroom-shaped structure from the top of the surface. This designed structure is easy to fabricate using printed circuit board (PCB) technology. The two metal layers lie in the x-y plane and each layer has a thickness of t = 0.035 mm. The dielectric layer has a thickness of h = 1.60 mm and a dielectric constant of 2.65. The dimensions of the structure are marked in Figs. 1(b) and 1(c). The lattice constant is p = 10 mm and the radius of the metal plated via is r = 0.5 mm. The side length of the metallic patch a is the only adjustable parameter which can significantly influence the reflection phase.

 

Fig. 1 (a) Schematic diagram of a gradient high-impedance metasurface reflectarray with M × N elements consisting of square mushroom-shaped elements of different sizes. The center-to-center distance of the discs is 10 mm in all cases. (b) and (c) 3D schematic and side view of the mushroom-shaped element. The size of the element is 10 mm x 10 mm.

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Various reflectarray structures that operate in the microwave region have been frequently proposed [16,19,21,22]. Metals behave like perfect electric conductors (PEC) in the microwave band and a reflectarray built using elements of variable dimensions can reflect the incident waves with high efficiency. Compared to other metasurface structures such as the one in [23], the two metal layers of the high-impedance metasurface fabricated in this study are adjacent and connected by one metal plated via. This causes strong near-field coupling, which can produce a magnetic resonance at the operational frequency. The induced currents on the two layers are antiparallel with each other, thereby generating strong magnetic fields in the region sandwiched between them. The reflection phase of the mushroom-shaped metasurface causes it to behave like an AMC and suppress the surface waves on a high-impedance ground plane [11]. Therefore, it is highly desirable to achieve high efficiency focusing using a mushroom-shaped metasurface to manipulate the wavefront phase. Metallic ground layer and metallic patch layer can be treated as PECs. Our model had a total thickness of $1.67\text{mm}$, which is much smaller than the operational wavelength. Our metasurface model lay on the x-y plane. The reflection phase shift profile ${\varphi }_{mn}(x,y)$ in two dimensions must satisfy the following equation [13]:

A continuous curve of phase shift in the range of [145°, −180°] as shown in Fig. 2(a) can be achieved by changing the side length a of the metallic patch layer. The maximum range of the phase shift at 10 GHz can reach 325°, which is close to a full cycle and sufficient for the intended operation of a reflectarray while maintaining the amplitude of the reflected wave above 0.8. For our model, the operational frequency was chosen to be 10 GHz and the focal length was f = 100mm. The schematic of the graded structure with eight metallic patch layers of different side lengths is given in Fig. 2(b). We can see clearly from the figure that our metasurface contains eight concentric parts with different values of parameter a and the values change gradually along the radial direction. In the graded structure, we have changed the side length parameter a of the metallic patch alone to get the desired phase shift. The side lengths of patches in the eight different parts are 1.91 mm, 3.92 mm, 6.02 mm, 6.70 mm, 7.48 mm, 7.92 mm, 8.32 mm, and 10 mm respectively. The reflection phases of the eight concentric parts fulfill Eq. (1), which is determined by the side length of the metallic patch while all the other parameters are fixed for simplicity.

 

Fig. 2 (a) The amplitudes (blue square dots) and reflection phase shift (black circular dots) of a metasurface with different side lengths with mushroom-shaped elements at 10 GHz frequency. (b) The graded structure composed of eight concentric parts with metallic patches of different sizes. The colormap is expressed in mm.

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3. Simulation and experiment

We performed full-wave simulation using CST Microwave Studio Software to solve the reflection spectra of the metasurface structure. In the simulation, the plane waves were normally incident on the metallic patch layer at the top of the metasurface. These waves propagated along the negative z-direction and simultaneously were linearly polarized along the orientation of the metallic patch layer in the incident plane. The reflection spectrum was visualized by calculating the spatial field distributions at a frequency of 10 GHz. The focusing behavior of the gradient high-impedance metasurface reflectarray can also be viewed through the electric field energy density distribution in the x-z plane as shown in Fig. 3(a), where the focus length f is approximately equal to 100 mm. Figure 3(b) demonstrates the reflection intensity distribution in the x-z plane at z = 120 mm, z = 100 mm, and z = 80 mm, respectively. We can see that the energy is the strongest, the light spot is the smallest, and the focusing effect is the best at z = 100 mm. Figure 3(c) demonstrates the reflection intensity distribution in the x-y focal plane. The focusing conversion efficiency was approximately 80%, which was calculated as the ratio of energy of the focal spot to the total energy of the incident wave.

 

Fig. 3 Pictorial representation of the process for achieving near-diffraction-limited focusing using gradient high-impedance metasurface structure. (a) The electric field energy density distribution in the x-z plane at y = 0 mm. (b) The electric field energy density distribution in the x-y plane at z = 120 mm, z = 100 mm, and z = 80 mm, respectively. (c) The reflected electric field intensity distribution in the x-y plane and at the focus (z = 100 mm).

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For verification of the simulation results, we fabricated a 150 mm × 150 mm sample of a gradient high-impedance metasurface reflectarray with mushroom-shaped elements using PCB technology. The sample had the same structural parameters as the simulation model. As shown in Fig. 4(a), we fabricated eight elements whose sizes ranged from 1.91 mm to 10 mm with the same parameters as shown in Fig. 2. The experimental setup consisted of an Agilent Network Analyzer 8722ES, a probe (9 GHz–18 GHz), an X-band standard horn antenna, and a 2D electronic scanning station controlled by a computer. The measurements are performed in an anechoic chamber. The horn antenna, the probe, and the sample are placed in parallel in the x-y plane in order. The feeding source (10 GHz, gauss wave) from the horn antenna was normally incident on the bottom patch antenna layer of the sample plate and propagated along the negative z-direction. A program was developed to control the probe scanning in the x-y plane within a 75 mm span around the focal point (at z = 100 mm) in steps of 1 mm. The probe was connected with the network analyzer (Agilent 8722ES). The intensity and phase can be obtained from the measured reflection scattering parameters at each sampled point within a 75 mm span around the focal point and the reference signal was used to calculate the actual reflection electric field intensity and phase of the sample. Next, the actual intensity distributions and phase patterns in the x-y plane within a 75 mm span around the focal point were plotted using a Matlab code. Figure 4(b) demonstrates the measured intensity distributions in the x-y plane and at the focus z = 100 mm. The focusing behavior of the mushroom-shaped metasurface reflectarray can be obtained using the field distribution on the focal plane. The focusing spot is slightly asymmetric in the intensity profile because the scanning of the probe was asymmetric during the measurement. As shown in Fig. 4(c), the full width of the half-maximum energy density is w = 26 mm (0.87 λ) for the linearly polarized incident wave and the diffraction-limited full beam waist (2w₀ = 1.22λf/D) is 25 mm. Therefore, our experiment and simulation show that the focusing was near-diffraction-limited. In addition, we calculated the focusing efficiency of the flat lens. This lens had a very high focusing efficiency of approximately 78% at its designed frequency of 10 GHz, which is close to the simulated value. Note that the flat lens was fabricated using PCB technology and the discrepancy was due to the fabrication errors and scattering at the metasurface. The experimental results agree well with the numerical simulation when these errors are ignored.

 

Fig. 4 (a) Experimental sample of a gradient high-impedance metasurface reflectarray with mushroom-shaped elements. (b) Distribution of intensity measured in the x-y plane and at z = 100 mm. (c) Comparison of the profiles of measured intensity and simulated intensity of focusing on the focal plane and at y = 0 mm. The red and black solid lines correspond to the experimental measurement and the numerical simulation, respectively.

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4. Conclusion

A gradient high-impedance metasurface comprising of mushroom-shaped elements was proposed and experimentally demonstrated in the microwave band. The phase discontinuity on the metasurface depends only on the precise control of the mushroom shaped elements in a sub-wavelength dimension, in which the size of the mushroom-shaped metasurface has a linear relationship with the phase discontinuity. The results observed in the simulation and in the experiment demonstrate that the focusing is near-diffraction-limited with a high efficiency. The gradient high-impedance metasurface reflectarray with mushroom-shaped elements was simulated using CST Microwave studio software. The device was manufactured using PCB technology and measurements were taken in an anechoic chamber. Our proposal would inspire new ways of designing metamaterials. The generation of the near-diffraction-limited focusing will enhance the preciseness and efficiency of the manipulation of light beams.