1. Wideband reflected high-gain antenna based on single-layered focusing metasurface

In last several years, metasurface (MS) has become a research hotspot since it relieves the drawbacks of bulk metamaterials. An MS usually consists of a set of periodic or locally nonperiodic unit cells with subwavelength thickness. The phase gradient metasurface (PGMS) is a special kind of MS which has been proposed by Yu et al. to demonstrate the general Snell's law [1]. Since the PGMS is able to provide predefined in-plane wave vectors to manipulate the directions of the refracting/reflecting waves, it consequently attracts a lot attention in beam steering. In Ref. [1], the authors designed a PGMS by using nano-V-antennas with different shapes to verify anomalous reflection/refraction effects, which opens the door to the rapid

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

development of MS for beam steering. Over the last 5 years, the MS has ushered in the golden age of theoretical and practical researches. Many applications of MS have emerged in the areas of focusing [2–8], anomalous refraction/reflection [6, 7], surface-plasmon-polariton coupling [8, 9], radar cross section (RCS) reduction [10–12], and polarization manipulation [13]. Generally, a wide phase-steering range covering 2π is an essential characteristic for the MS element. The phase is manipulated by changing the structure size or rotating the angle of the particle on the substrate. Then, by fixing proper phase distributions on the MS, we can flexibly manipulate the wavefronts and the polarizations of the EM waves. These characteristics as well as compact size and low loss mean the MS can be a good candidate to improve antenna performance by enhancing the antenna gain [4], reducing the RCS of the antenna [12], converting the antenna polarization [13]. We call this kind of high-performance antenna based on MS as MS antenna. Thereinto, the focusing MSs usually have been used to enhance the gain of the antenna. They can also transform spherical wave emitted by a point source placed at the focal point to plane wave theoretically. In such case, the directivity and gain of the point source can be improved greatly.

#### 1.1. Theory

Figure 1 depicts the schematic used to derive the generalized law of reflection. The introduction of an abrupt phase shift, denoted as phase discontinuity, at the interface between two media allows us to revisit the law of reflection by applying Fermat's principle. The incident angle of the electromagnetic wave is θi. Assuming that the blue and red paths are infinitesimally close to the actual light path, then the phase difference between them is zero.

$$k n\_i \sin(\theta\_\circ) d\mathbf{x} \wedge \Phi + d\Phi \cdot \left| k n\_i \sin(\theta\_\circ) d\mathbf{x} + \Phi \right| - 0 \tag{1}$$

where Φ is the phase discontinuity at a local position on the MS, n<sup>i</sup> is the index of the incident medium, and θ<sup>r</sup> (θi) is the reflected (incident) angle of the electromagnetic wave. By insertion of k = 2π/λ, we can obtain the following generalized reflection Snell's law [1]:

$$
\sin(\theta\_r) \text{-} \sin(\theta\_i) = \frac{\lambda}{2\pi n\_i} \frac{d\Phi}{d\mathbf{x}} \tag{2}
$$

As shown in Figure 2(a), if the designed dΦ/dx is a constant, anomalous reflection will be achieved, and the reflected angle can be controlled. The phase distribution of the focusing MS

where L is the focal distance, φ<sup>1</sup> is the phase shift through the first unit cell, which is placed at the point x = 0, y = 0. The MS can focus the incident plane wave to its focal point as shown in Figure 2(b). Likewise, the sphere wave emitted by the source placed at its focal point can be converted to plane wave as shown in Figure 2(c), which can be used for designing high-gain

Figure 3 shows the structure of the MS element, which is utilized to build the reflected MS. The top metallic layer is composed of a cross and a cross-ring (CCR), and the bottom layer is totally metal. The dielectric layer has a substrate with the permittivity of 2.65 and

Figure 2. Schematics used to describe (a) anomalous reflection (b) focusing effect, and (c) operating mechanism of the MS

ð3Þ

33

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351

has to satisfy the following Eq. (3).

antennas.

antenna.

1.2. Unit cell design

Figure 1. Schematic used to derive the generalized law of reflection.

As shown in Figure 2(a), if the designed dΦ/dx is a constant, anomalous reflection will be achieved, and the reflected angle can be controlled. The phase distribution of the focusing MS has to satisfy the following Eq. (3).

$$\varphi(\mathbf{x}, \boldsymbol{\nu}) = \frac{2\pi}{\lambda} (\sqrt{\mathbf{x}^2 + \mathbf{y}^2 + L^2} \cdot L) + \boldsymbol{\varphi}\_{\parallel} \tag{3}$$

where L is the focal distance, φ<sup>1</sup> is the phase shift through the first unit cell, which is placed at the point x = 0, y = 0. The MS can focus the incident plane wave to its focal point as shown in Figure 2(b). Likewise, the sphere wave emitted by the source placed at its focal point can be converted to plane wave as shown in Figure 2(c), which can be used for designing high-gain antennas.

#### 1.2. Unit cell design

ð1Þ

ð2Þ

development of MS for beam steering. Over the last 5 years, the MS has ushered in the golden age of theoretical and practical researches. Many applications of MS have emerged in the areas of focusing [2–8], anomalous refraction/reflection [6, 7], surface-plasmon-polariton coupling [8, 9], radar cross section (RCS) reduction [10–12], and polarization manipulation [13]. Generally, a wide phase-steering range covering 2π is an essential characteristic for the MS element. The phase is manipulated by changing the structure size or rotating the angle of the particle on the substrate. Then, by fixing proper phase distributions on the MS, we can flexibly manipulate the wavefronts and the polarizations of the EM waves. These characteristics as well as compact size and low loss mean the MS can be a good candidate to improve antenna performance by enhancing the antenna gain [4], reducing the RCS of the antenna [12], converting the antenna polarization [13]. We call this kind of high-performance antenna based on MS as MS antenna. Thereinto, the focusing MSs usually have been used to enhance the gain of the antenna. They can also transform spherical wave emitted by a point source placed at the focal point to plane wave theoretically. In such case, the directivity and gain of the point source can be improved greatly.

Figure 1 depicts the schematic used to derive the generalized law of reflection. The introduction of an abrupt phase shift, denoted as phase discontinuity, at the interface between two media allows us to revisit the law of reflection by applying Fermat's principle. The incident angle of the electromagnetic wave is θi. Assuming that the blue and red paths are infinitesimally close to the

where Φ is the phase discontinuity at a local position on the MS, n<sup>i</sup> is the index of the incident medium, and θ<sup>r</sup> (θi) is the reflected (incident) angle of the electromagnetic wave. By insertion

of k = 2π/λ, we can obtain the following generalized reflection Snell's law [1]:

actual light path, then the phase difference between them is zero.

Figure 1. Schematic used to derive the generalized law of reflection.

1.1. Theory

32 Metamaterials and Metasurfaces

Figure 3 shows the structure of the MS element, which is utilized to build the reflected MS. The top metallic layer is composed of a cross and a cross-ring (CCR), and the bottom layer is totally metal. The dielectric layer has a substrate with the permittivity of 2.65 and

Figure 2. Schematics used to describe (a) anomalous reflection (b) focusing effect, and (c) operating mechanism of the MS antenna.

thickness of 3 mm. For characterization, the unit cell is simulated in CST Microwave Studio by using periodic boundary. To illustrate the operating mechanism of the CCR unit cell clearly, Figure 4 shows the current distribution on the upper surface of the unit cell and Figure 5 shows the phase of S11 in a broad frequency band. As shown in Figure 5, the phase of S11 changes fast around 4.5 and 9.5 GHz, which is the two resonances of the CCR unit cell. From Figure 4, it can be find that the lower resonant frequency (4.5 GHz) is brought by the cross-ring structure and the higher one is brought by the cross-structure. Due to the dual-resonance structure, the phase difference of the CCR unit cell has successfully reached about 620 just by changing the parameter of rn as

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 35

In addition, the curves in Figure 7 have good linearity especially during 10–12 GHz, which makes the CCR unit cell very suitable for broadband design. To completely evaluate the reflected phase character of the unit cell, a parameter scan has been made with the step of 0.01 mm for r<sup>n</sup> in CST, and curves of the reflected phase change with r<sup>n</sup> (2 mm–4.9 mm) at 10, 11, and 12 GHz are shown in Figure 10. The three curves are almost parallel with each other, which guarantee that the phase distribution changes little with frequency during the range of

After successfully designing the required broadband unit cell, we use it to design the focusing MS. The reflected phase difference distribution in the plane which is perpendicular to the direction of the incident plane-wave should satisfy the profile mentioned in Eq. (3). The period of the CCR unit cell is p, so the location of the unit cell can be discretized as x = n p,

shown in Figure 6.

10–12 GHz.

1.3. Focusing metasurface antenna design

Figure 6. Phase of S11 for the CCR unit cell.

Figure 3. Structure of the MS element and the simulated setup. (a) Top view and (b) perspective view. w = 2.4 mm, g = t = 0.4 mm, p = 10 mm, d = 3 mm, and n = 1, 2, 3, ….

Figure 4. Current distribution on the upper surface of the CCR unit cell at (a) 4.5 GHz and (b) 9.5 GHz.

Figure 5. Phase of S11 for three different unit cells.

thickness of 3 mm. For characterization, the unit cell is simulated in CST Microwave Studio by using periodic boundary. To illustrate the operating mechanism of the CCR unit cell clearly, Figure 4 shows the current distribution on the upper surface of the unit cell and Figure 5 shows the phase of S11 in a broad frequency band. As shown in Figure 5, the phase of S11 changes fast around 4.5 and 9.5 GHz, which is the two resonances of the CCR unit cell. From Figure 4, it can be find that the lower resonant frequency (4.5 GHz) is brought by the cross-ring structure and the higher one is brought by the cross-structure. Due to the dual-resonance structure, the phase difference of the CCR unit cell has successfully reached about 620 just by changing the parameter of rn as shown in Figure 6.

In addition, the curves in Figure 7 have good linearity especially during 10–12 GHz, which makes the CCR unit cell very suitable for broadband design. To completely evaluate the reflected phase character of the unit cell, a parameter scan has been made with the step of 0.01 mm for r<sup>n</sup> in CST, and curves of the reflected phase change with r<sup>n</sup> (2 mm–4.9 mm) at 10, 11, and 12 GHz are shown in Figure 10. The three curves are almost parallel with each other, which guarantee that the phase distribution changes little with frequency during the range of 10–12 GHz.

#### 1.3. Focusing metasurface antenna design

Figure 3. Structure of the MS element and the simulated setup. (a) Top view and (b) perspective view. w = 2.4 mm,

Figure 4. Current distribution on the upper surface of the CCR unit cell at (a) 4.5 GHz and (b) 9.5 GHz.

g = t = 0.4 mm, p = 10 mm, d = 3 mm, and n = 1, 2, 3, ….

34 Metamaterials and Metasurfaces

Figure 5. Phase of S11 for three different unit cells.

After successfully designing the required broadband unit cell, we use it to design the focusing MS. The reflected phase difference distribution in the plane which is perpendicular to the direction of the incident plane-wave should satisfy the profile mentioned in Eq. (3). The period of the CCR unit cell is p, so the location of the unit cell can be discretized as x = n p,

Figure 6. Phase of S11 for the CCR unit cell.

in Figure 8. The reflected phase of CCR unit cell has a range of [684, 136] at 10 GHz, we choose the middle range of the reflected phase [510, 150] which has better broadband character to design the focusing MS. The parameter rn varies from 4.2 to 2.2 mm in this design, and when the phase difference between one unit cell and the first unit cell (reflected phase is 510) is over 360 the reflected phase of this location should be deducted by 360. In order to illuminate the MS, we choose a spiral antenna as the feed source, and a metal ground is added at the bottom to make the antenna radiate only to the MS. The electric field distributions of the spiral antenna without and with the MS at 10 GHz are shown in Figure 9. As shown, both in the two orthogonal planes, MS transforms the quasi-sphere wave emitted by the spiral antenna to plane wave as the theoretical prediction, and it is the mechanism of the proposed high-gain antenna. The simulated and measured voltage standing wave ratios (VSWR) are shown in Figure 10. It is shown that the impedance band of the antenna covers

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 37

Then, the 3D radiation patterns at 10, 11, and 12 GHz are shown in Figure 11, it can be concluded from the figures that the gain of the feed source is remarkably enhanced and pencil-shaped radiation patterns are achieved. To clearly depict the antenna gain-enhancement via reflected MS, the 2D radiation patterns of the antenna with/without the MS are shown in Figure 12. As shown, the antenna beam width has been decreased greatly and the peak gain has been enhanced greatly compared with the planar spiral antenna. It is also necessary to notice that the source is right circular polarization, while the MS antenna is left circular

Figure 9. Simulated electric field distribution in (a, b) xoz-plane and (c, d) yoz-plane for the spiral antenna (a, c) without

the operating band (10–12 GHz) of the MS well.

the MS and (b, d) with the MS.

Figure 7. Reflected phase change with rn at (a) 10 GHz, (b) 11 GHz, and (c) 12 GHz.

y = n p (n = 0, 1, 2, 3 …). In order to control the phase of the reflected wave well, the maximum phase difference along the +x direction should be over 360. However, taking the fabrication cost into consideration, the area of the MS should be not very large. From the unit cell design, we find that the CCR unit cell has a broadband character during 10–12 GHz. At the frequency of 10 GHz, we set L = 40 mm and seven unit cells are used in +x direction to achieve about 385 phase difference comparing with the first unit cell. Considering that the phase distribution on the MS should be symmetry, we use 13 13 unit cells to satisfy the whole profile in xoy-plane, and the two-dimensional phase distribution of the MS is shown

Figure 8. Absolute phase distribution on the focusing MS.

in Figure 8. The reflected phase of CCR unit cell has a range of [684, 136] at 10 GHz, we choose the middle range of the reflected phase [510, 150] which has better broadband character to design the focusing MS. The parameter rn varies from 4.2 to 2.2 mm in this design, and when the phase difference between one unit cell and the first unit cell (reflected phase is 510) is over 360 the reflected phase of this location should be deducted by 360. In order to illuminate the MS, we choose a spiral antenna as the feed source, and a metal ground is added at the bottom to make the antenna radiate only to the MS. The electric field distributions of the spiral antenna without and with the MS at 10 GHz are shown in Figure 9. As shown, both in the two orthogonal planes, MS transforms the quasi-sphere wave emitted by the spiral antenna to plane wave as the theoretical prediction, and it is the mechanism of the proposed high-gain antenna. The simulated and measured voltage standing wave ratios (VSWR) are shown in Figure 10. It is shown that the impedance band of the antenna covers the operating band (10–12 GHz) of the MS well.

Then, the 3D radiation patterns at 10, 11, and 12 GHz are shown in Figure 11, it can be concluded from the figures that the gain of the feed source is remarkably enhanced and pencil-shaped radiation patterns are achieved. To clearly depict the antenna gain-enhancement via reflected MS, the 2D radiation patterns of the antenna with/without the MS are shown in Figure 12. As shown, the antenna beam width has been decreased greatly and the peak gain has been enhanced greatly compared with the planar spiral antenna. It is also necessary to notice that the source is right circular polarization, while the MS antenna is left circular

y = n p (n = 0, 1, 2, 3 …). In order to control the phase of the reflected wave well, the maximum phase difference along the +x direction should be over 360. However, taking the fabrication cost into consideration, the area of the MS should be not very large. From the unit cell design, we find that the CCR unit cell has a broadband character during 10–12 GHz. At the frequency of 10 GHz, we set L = 40 mm and seven unit cells are used in +x direction to achieve about 385 phase difference comparing with the first unit cell. Considering that the phase distribution on the MS should be symmetry, we use 13 13 unit cells to satisfy the whole profile in xoy-plane, and the two-dimensional phase distribution of the MS is shown

Figure 7. Reflected phase change with rn at (a) 10 GHz, (b) 11 GHz, and (c) 12 GHz.

36 Metamaterials and Metasurfaces

Figure 8. Absolute phase distribution on the focusing MS.

Figure 9. Simulated electric field distribution in (a, b) xoz-plane and (c, d) yoz-plane for the spiral antenna (a, c) without the MS and (b, d) with the MS.

35.8, and 25.6%, respectively. And Figure 15 shows that the 3 dB axial ratio bandwidth

Figure 12. Simulated farfield radiation patterns at (a, b) 10 GHz, (c, d) 11 GHz, and (e, f) 12 GHz of the spiral antenna

with and without the MS in (a, c, e) xoy-plane and (b, e, f) yoz-plane.

ð4Þ

39

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351

covers the band of 10–12 GHz approximately.

Figure 10. Simulated and measured VSWR of the spiral antenna.

Figure 11. 3D simulated farfield radiation pattern for (a) 10 GHz, (b) 11 GHz, and (c) 12 GHz.

polarization, and the cross-polarization component of the source antenna is also enhanced by the MS while it is still much lower than the copolarization at the main radiation direction.

At last, the proposed MS antenna has been fabricated and assembled, and the photographs are shown in Figure 13. The farfield results of the novel MS antenna are measured in an anechoic chamber. Figure 14 shows the simulated and measured peak realized gain in the band of 8–13 GHz. As shown, the 1 dB gain bandwidth of the proposed antenna is 10–12.3 GHz (with the fractional bandwidth is 20.6%), and in this band, the peak gain has an enhancement of 13.5 dB comparing with the spiral antenna in average. The peak gains at the frequencies of 10, 11 and 12 GHz are 19.2, 20.1 and 19.4 dB, respectively. Then, the aperture efficiency (AE) can be calculated by Eq. (4), where λ<sup>0</sup> is the free space wavelength and D is the side length of the MS. The calculated efficiencies at 10, 11 and 12 GHz are 35.2,

ð4Þ

35.8, and 25.6%, respectively. And Figure 15 shows that the 3 dB axial ratio bandwidth covers the band of 10–12 GHz approximately.

Figure 12. Simulated farfield radiation patterns at (a, b) 10 GHz, (c, d) 11 GHz, and (e, f) 12 GHz of the spiral antenna with and without the MS in (a, c, e) xoy-plane and (b, e, f) yoz-plane.

polarization, and the cross-polarization component of the source antenna is also enhanced by the MS while it is still much lower than the copolarization at the main radiation direction.

Figure 11. 3D simulated farfield radiation pattern for (a) 10 GHz, (b) 11 GHz, and (c) 12 GHz.

Figure 10. Simulated and measured VSWR of the spiral antenna.

38 Metamaterials and Metasurfaces

At last, the proposed MS antenna has been fabricated and assembled, and the photographs are shown in Figure 13. The farfield results of the novel MS antenna are measured in an anechoic chamber. Figure 14 shows the simulated and measured peak realized gain in the band of 8–13 GHz. As shown, the 1 dB gain bandwidth of the proposed antenna is 10–12.3 GHz (with the fractional bandwidth is 20.6%), and in this band, the peak gain has an enhancement of 13.5 dB comparing with the spiral antenna in average. The peak gains at the frequencies of 10, 11 and 12 GHz are 19.2, 20.1 and 19.4 dB, respectively. Then, the aperture efficiency (AE) can be calculated by Eq. (4), where λ<sup>0</sup> is the free space wavelength and D is the side length of the MS. The calculated efficiencies at 10, 11 and 12 GHz are 35.2,

Figure 13. The photographs of the MS antenna. (a) Top view, (b) bottom view of the reflected MS, (c) components of the spiral antenna, and (d) free view of the MS antenna.

2. Wideband multifunctional metasurface for polarization conversion and

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 41

The polarization state is one of the most important characteristics of the EM waves. We can classify the polarization conversion MS (PCMS) [14–19] into two categories according to the format of the MS—transmitting type [14–17] and reflecting type [18, 19]. Also, the PCMS also can be classified into cross-polarization conversion one [14–16, 18] or linear-to-circular/circular-to-linear (LTC/CTL) one [17, 19] according to specific functionalities. However, the mentioned PCMSs are all illuminated by plane waves and the radiation performances will be more or less deteriorated when they are directly feed by a spherical feed source like Vivaldi antenna. Taking the overall performances into consideration, a technique should be adopted for a PCMS design to control the direction of the scattering wave for spherical wave excitation. The focusing MS mentioned above can transfer the incident plane wave to its focal point, and vice versa. So, it can be predicted that the combination of the PCMS with focusing MS will improve

Anisotropic MSs have the character of manipulating electromagnetic waves with different polarizations, respectively. We still adopt the CCR unit cell shown in Figure 16 to design an anisotropic MS. Compared with the unit cell shown Figure 1, we set r<sup>x</sup> and r<sup>y</sup> with different values to

gain enhancement

the radiation performance of the system.

Figure 15. Measured and simulated axial ratio of the MS antenna.

2.1. Linear-to-circular metasurface design

Figure 14. Measured and simulated peak gain of the spiral antenna with/without the focusing MS.

Figure 15. Measured and simulated axial ratio of the MS antenna.

Figure 13. The photographs of the MS antenna. (a) Top view, (b) bottom view of the reflected MS, (c) components of the

Figure 14. Measured and simulated peak gain of the spiral antenna with/without the focusing MS.

spiral antenna, and (d) free view of the MS antenna.

40 Metamaterials and Metasurfaces
