# High-Efficiency Electromagnetic Wave Controlling with All-Dielectric Huygens’ Metasurfaces

Authors: Zheng-bin Wang; Jin Shi; Jin-chang Chen
Journal: International Journal of Antennas and Propagation
 (2015)

---

## Abstract

Subwavelength dielectric blocks with varying thicknesses are introduced to realize 0∼2π phase change. A Huygens’ metasurface composed of such nonuniform building blocks is shown to efficiently refract normally incident waves in a broadband. According to the same physical mechanism, we fabricate an electrically thin lens with concentric subwavelength dielectric blocks and integrate it with a patch antenna to form a three-dimensional (3D) ultra-low-profile lens antenna system. Full-wave simulation demonstrates the lens antenna’s excellent performances in high directivity, broadband, low loss, and low side-lobe levels.


---

## Body

## 1. Introduction

In recent years, the development of metamaterials has opened up the researcher’s minds on how to control electromagnetic (EM) waves from microwave to optical frequencies [1, 2], or even acoustic waves [3, 4]. Most EM metamaterials are fabricated by arranging a set of subwavelength scatters throughout a region of space, which can generate the required EM properties as bulk materials [5]. More recently, the concept was further extended by wisely placing electrically small structures into a planar pattern [6–12]. These microscopic scatterers can modulate the phase and amplitude of each Huygens’ secondary source on the interface and in turn manipulate the transmitted EM waves. Such electrically thin interfaces are called metafilms, or more generally, metasurfaces. In the past few years, most of the reported metasurface designs relied on resonant anisotropic elements, such as V-shaped antennas [6, 7], H-shaped antennas [8, 9], and dipoles [10]. Such approaches are narrowbanded, sensitive to electric polarization, and the transmission efficiency is also very low (on the order of 5%), which restrict them from further applications. Last year, Pfeiffer et al. presented a novel metasurface that can bend light efficiently by cascading three patterned, metallic sheets [11]. The transmission efficiency can be up to 30% at a specific frequency.In this work, we present another high-efficiency approach to Huygens’ metasurfaces, which are composed of all-dielectric electrically thin blocks. Such metasurfaces are broadbanded, easy to fabricate, high efficient, and insensitive to electric polarization. In addition, compared with metallic approaches, all-dielectric metasurfaces are immune to some negative effects brought by high-power incident EM waves, such as heating due to ohmic losses, arcing at field concentration points. A refractive metasurface is first proposed to demonstrate the feasibility of the all-dielectric approach. Then, an all-dielectric metasurface lens is designed to focus incident plane waves. Finally, the lens is further integrated with a patch antenna to form a three-dimensional (3D) ultra-low-profile lens antenna system, which exhibits high directivity, broadband, low side-lobe levels, and steerable capabilities.


## 2. A Huygens’ Metasurface Composed of Electrically Thin Dielectric Building Blocks

Figure1 shows a typical subwavelength dielectric building block of the metasurface. The length and height of the square unit cell are l and h, respectively. The relative permittivity of the dielectric substrate is εr. Now consider an incident EM beam with transverse magnetic (TM) polarization transmitting through the element. The incident plane is xz⊥ plane of the local coordinate system, and the incident angle is θi. Assume each dielectric block as a homogeneous planar layer; a two-port network model (shown in Figure 1(b)) can be obtained according to the transmission line theory [12, 13]. The TM fields on the surfaces z=0 and z=h can be related to each other through the ABCD matrix as shown as follows:(1)ExzHyzz=0=cos⁡⁡βhjZcsin⁡βhjYcsin⁡βhcos⁡⁡βhExzHyzz=h,where β=ω(εr-sin2θi)ε0μ0, Zc=1/Yc=η0/εr-sin2θi. ω and η0 are the angular frequency and the characteristic impedance of free space, respectively. The tangential fields at the top (z=0) and bottom (z=h) surfaces are the same, which leads to the boundary conditions (2)Ex0=-η0cos⁡⁡θiHy0+2Eicos⁡⁡θi,ExhHyh=η0cos⁡⁡θi.Combine (1) and (2); we can obtain the transmission coefficient of the element(3)TTM=ExhEi=2η0cos⁡2⁡θi2η0cos⁡⁡βhcos⁡⁡θi+jsin⁡βhZc+η02Yccos⁡2⁡θi,which presents the exact transmission field on the bottom surface of the dielectric block. According to the duality theorem, the transmission coefficient of transverse electric (TE) polarization waves can also be obtained(4)TTE=EyhEi=2η0cos⁡2⁡θi2η0cos⁡⁡βhcos⁡⁡θi+jsin⁡βhη02Yc+Zccos⁡2⁡θi.Through modeling the electric field on the surface as an aperture field distribution, we can further obtain the far-field pattern.Figure 1
(a) 3D topology of a subwavelength dielectric building block for oblique incident TM waves and (b) the equivalent two-port transmission line circuit model.
(a)
(b)From (3) we can extract the phase shift of the transmitted field that has propagated through the dielectric layer(5)φTMT=tan-1⁡Zc+Ycη02cos⁡2⁡θi2η0cos⁡⁡θitan⁡βh.The phase shift of the transmitted TE waves can be extracted from (4) (6)φTET=tan-1⁡Ycη02+Zccos⁡2⁡θi2η0cos⁡⁡θitan⁡βh.From the above equations we can see that if the incident angle (θi) and the dielectric constant (εr) are given, the phase shift of the transmission field depends on the height of the building block, h. Here, we should notice that when the height of the dielectric block varies from 0~λ0/εr, the phase shift of the transmission field will change from 0 to 2π, which is essential for fully controlling the transmitted beam. When high-permittivity dielectrics are chosen, the total height of the metasurface will be far less than the free-space wavelength.Then, a proof-of-concept Huygens’ metasurface is designed to refract normally incident plane waves (θi = 0) in a wide band. Figure 2(a) shows the super unit cell of an all-dielectric nonuniform metasurface, which is composed of eight subwavelength square blocks with different heights (h1~h8) and a thin substrate with height, hs. The width of each building block is b, which depends on the requirement for the gradient of phase discontinuity along the x direction (dφ/dx) [6, 8]. The dashed lines in Figure 2(a) refer to the incident phase distribution (φin(x) on the bottom plane) and the desired outgoing phase distribution (φout(x) on the top plane), respectively. If the distance between the two planes is far less than the operating wavelength in the free space, that is, electrically thin, the nonuniform dielectric structure still can be looked on as a surface. Here, Rogers board with high permittivity (RO3210, εr = 10.2, tan⁡δ=0.0027) is chosen to fabricate the square blocks. As for the substrate, low-permittivity Rogers board is adopted (RT5880LZ, εr = 1.96, tan⁡δ=0.0019). According to (5) and (6), the heights of the eight building blocks are optimized to make the interval of phase shift to be π/4 around in a wide band, as shown in Figure 2(b). The frequency dependence of the transmittance of the eight blocks is shown in Figure 2(c). Obviously, the transmission efficiency of each block is above 55%, which, to the best of our knowledge, is much higher than the reported metasurface designs [6–11]. Here, it should be noted that the transmittances of each block are not identical, which will bring a little aberration in the transmitted field. In addition, the nonuniformity of the refract-array’s surface will also introduce some aberration.Figure 2
(a) Top and side view of the super unit cell of an electrically thin metasurface, which is composed of eight RO3210 dielectric building blocks and a RT5880LZ substrate. The detailed geometry of the super unit cell, in whicha=6.25 mm, b=5.5 mm, hs=0.76 mm, h1=7.43 mm, h2=6.50 mm, h3=4.92 mm, h4=4.12 mm, h5=3.58 mm, h6=2.53 mm, h7=1.06 mm, and h8=0.24 mm; (b) the calculated frequency dependence of the transmitted phase shift, and (c) transmittance of each building block.
(a)
(b)
(c)By extending the super unit cell in bothx and y direction we can fabricate a refractive metasurface. Its gradient of phase discontinuity along x direction is dφ/dx=2π/L (L is the length of the super unit cell). Then, the corresponding refractive angle can be obtained from the general Snell’s law [6](7)θt=sin-1⁡λ0L,where λ0 is the free-space wavelength of the incident wave. Figure 3 shows the time snapshots of the steady-state electric field simulated in the Computer Simulation Technology (CST) Microwave Studio, which is based on the finite integration method [14]. Plane waves with TE (Figures 3(a)–3(c)) and TM (Figures 3(d)–3(f)) polarization electric fields are normally incident at the metasurface. From these figures we can see that the nonuniform metasurface refracts the incident waves effectively in a wide band (16~20 GHz). And the refractive angle decreases with the operating frequency, which is consistent with the theoretical model in (6). Therefore, Huygens’ metasurfaces based on electrically thin dielectric blocks can be used to fully control transmitted electromagnetic waves and in turn to fabricate high-efficiency electromagnetic lenses.Figure 3
Time snapshots of the simulated steady-state electric field when plane waves are normally impinging on the nonuniform dielectric metasurface from the bottom. TE polarization incident waves (a) at 16 GHz, (b) at 18 GHz, and (c) at 20 GHz. TM polarization incident waves (d) at 16 GHz, (e) at 18 GHz, and (f) at 20 GHz.
(a)
(b)
(c)
(d)
(e)
(f)


## 3. Ultra-Low-Profile Lens Antenna Design and Analysis

In this section, the ability of the high-efficiency metasurface’s fully controlling transmitted waves is utilized to fabricate a 3D ultra-low-profile lens antenna system. As we all know, lens antenna systems have been intensively studied throughout the microwave, millimeter-wave, and optical bands for their special property of radiating point-source EM waves at the focal point with high directivities, such as parabolic lens antennas [15], Fresnel lens antennas [16], and elliptic lens antennas [17]. Traditional dielectric lenses modulate applied waves by gradual phase changing, which is realized by engineering the curve surface topography or the refractive index of the spatial profile [18–21]. However, the lens with curve surface is bulky and heavy at low frequencies, and with the closing of the focal point to the lens surface, the total volume of the antenna system will be too large to be acceptable. As for the planar lens with varying refractive index, it is still very hard and complicated to fabricate it now.Here, we propose an ultra-low-profile lens antenna operated at Ku band, which is composed of an electrically thin dielectric metasurface lens and a planar patch antenna. Figure4 shows the detailed schematic of the antenna system. The metasurface lens is composed of many sector dielectric blocks, which can be clapped with Rogers’ RO3210 boards. The height of each building block can be obtained from (5) or (6), where the phase distribution at the radial direction depends on the equal optical path principle of convex lens [22](8)φr=2Nπ+k0r2+F2-F,where N is an arbitrary integer and r and F are the radial distance and the focal length, respectively. Here, the focal point should be designed as close as possible to the lens surface. Because of the mutual coupling between the lens and the patch antenna, as well as the need to make full use of the lens aperture, the focal length is optimized to be F = 15 mm (≈3λ0/4 of the centre frequency, f0 = 15.5 GHz). The width of each concentric sector block is d = 4 mm (≈λ0/5), and the gap between them is g=0.2 mm. The total aperture size is D = 102 mm (≈5.2λ0). The ratio of the lens’s focal length to its aperture diameter is F/D = 0.15 and can be further decreased by increasing the lens’s diameter. A planar back-feed patch antenna acts as the primary feed and is located at the focal point. The radiating metal plate, measuring W×W = 4.6 mm × 4.6 mm, is etched on a square Rogers’ RO4003 board (εr = 3.55, tan⁡δ=0.0027, Lant×Lant = 17 mm × 17 mm). The height of the substrate is hant = 0.813 mm.Figure 4
The detailed geometry of the ultra-low-profile lens antenna system, which is composed of a clapped dielectric metasurface and a patch antenna. The geometry of the lens:d = 4 mm, h1 = 3.05 mm, h2 = 2.78 mm, h3 = 2.00 mm, h4 = 6.84 mm, h5 = 6.20 mm, h6 = 5.04 mm, h7 = 3.56 mm, h8 = 2.76 mm, h9 = 1.11 mm, h10 = 6.45 mm, h11 = 5.50 mm, h12 = 3.84 mm, h13 = 3.00 mm, and g = 0.2 mm. The focal length and the diameter of the lens are F = 15 mm and D = 102 mm, respectively. The geometry of the antenna: w = 4.6 mm, Lant = 17 mm, and hant = 0.813 mm.
(a)
(b)
(c)As for the dielectric lens itself, it can converge the incident plane waves into the focal point very well. In Figure5(a), an x-polarized plane wave (operated at 16 GHz) impinges on the metasurface lens from the z-direction with the amplitude of 1 v/m. The simulated steady-state electric field Ex shows a clear focal point in the x-z plane. The measured focal length is F=16.8 mm. Figure 5(b) shows the power distribution along the x-direction in the focal plane (at z = 16.8 mm). Obviously, the transmitted power concentrates inside the main lobe, and the full width at half maximum (FWHM) is 12 mm (~0.63λ). Plane waves operated at other frequencies, such as 14.5 GHz and 16.5 GHz, are also simulated (not shown here). These simulation results demonstrate that with the increasing of the operating frequency, both the focal length and the FWHM are slightly decreasing.Figure 5
(a) The time snapshot of the steady-state electric field in thex-z plane; (b) intensity distribution of the steady-state electric field along the x-axis in the focal plane. The operating frequency of the incident plane waves is 16 GHz.
(a)
(b)Consider that the radiating metal plate of the patch antenna is smaller than the focal spot; it can be looked on as the point source and the phase center. Figure6(a) shows the simulated steady-state electric field of the lens antenna system at 16 GHz. Obviously, the metasurface lens transforms the spherical wavefront of the source antenna into a radiated plane wavefront. Figures 6(b)–6(d) show the simulated far-field gain of the patch antenna itself (the dashed line) and the integrated low-profile lens antenna (the solid line) at 14.5 GHz, 15.5 GHz, and 16.5 GHz, respectively. From these figures we can see that the existence of the electrically thin metasurface lens makes the far-field gain of the patch antenna increase more than 10 dB and the 3-dB angular width reduce to 15°, which means the directivity of the antenna is highly improved. These figures also demonstrate that the lens antenna system has more stable far-field gain (16.3–17.5 dB) in a wide band (14.5–16.5 GHz), and the side-lobe level is below −13 dB.Figure 6
The simulated results of the dielectric metasurface-based lens antenna system. (a) Comparison ofE-plane far-field radiation pattern of the lens antenna (solid line) and the patch antenna itself (dashed line) at 14.5 GHz, (b) at 15.5 GHz, and (c) at 16.5 GHz.
(a)
(b)
(c)
(d)It should be noted that, since the spacing between the patch antenna and the lens is less than one wavelength, the mutual coupling effects have to be taken into consideration. This interesting issue will be discussed in detail in the future work.


## 4. Conclusion

In this paper, we first propose a high-efficiency refractive metasurface composed of electrically thin dielectric blocks, which realize 0~2π phase shift through varying the heights of the building blocks. The full-wave analysis demonstrates that such Huygens’ metasurfaces can effectively refract normally incident waves in a wide band. Then, based on the same physical mechanism, a metasurface-based dielectric lens is designed and integrated with a patch antenna to form an ultra-low-profile lens antenna system, which exhibits high directivity, broadband, low loss, and low side-lobe levels. With the fast progress of material technology and 3D printing technology, dielectric Huygens’ metasurfaces will find broad applications in microwave, Terahertz, and even optical systems.



---

*Source: 432095-2015-05-19.xml*