2. Wideband multifunctional metasurface for polarization conversion and gain enhancement

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 the radiation performance of the system.

#### 2.1. Linear-to-circular metasurface design

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

Figure 16. Topology of the proposed LTC-PCMS unit cell with g = t = 0.4 mm, p = 10 mm, and d = 3 mm. (a) Front view and (b) perspective view. The metallic is shown in green, while the slot is shown in white.

make the reflecting phase change with the polarization of the incident wave. The reflection matrix (R matrix), which connects the incident fields and reflected fields, can be described as:

$$\mathcal{R} = \begin{pmatrix} \mathcal{R}\_{\text{xx}} & \mathcal{R}\_{\text{yx}} \\ \mathcal{R}\_{\text{xy}} & \mathcal{R}\_{\text{yy}} \end{pmatrix} \tag{5}$$

ð7Þ

43

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

ð8Þ

ð9Þ

ð10Þ

ð11Þ

ð12Þ

where k is the wave number. In the following, we will discuss that our LTC-PCMS supports

As described in Eq. (11), it can be concluded that the polarization of the reflected wave is LHCP. In the second case of , we can obtain following results by taking similar

In this situation, a RHCP reflected wave has been obtained. Figure 18 depicts a practical realized scheme of our system, where the LTC-PCMS fed by a Vivaldi antenna is built by 13 � 13 single-layered CCR unit cells. The voltage standing wave ratio (VSWR) with its geometrical parameters has been shown in Figure 19. We can conclude that the Vivaldi antenna has a VSWR less than 2 dB within the frequency band of 9–15 GHz. Three-dimensional radiation patterns and AR results of the LTC-PCMS are shown in Figure 20. As shown, the far-field patterns achieve CP radiation but the directivity of the Vivaldi antenna has been broken by the MS. To conquer this problem, an additional focusing profile needed to be

linear wave to LHCP or RHCP wave conversion in two special cases.

For the case of , the incident E fields can be described as:

Then, the reflected E fields can be calculated as:

brought in to correct the wave-front of the outing wave.

calculations.

where Rij represents the reflection coefficient of j polarization incident wave and i polarization reflected wave. And we use Am(Rij) and Arg(Rij) to describe the amplitude and phase of Rij, respectively. At the case of r<sup>x</sup> = 4.06 mm and r<sup>y</sup> = 3.6 mm, we can obtain that Am(Rxx) = Am (Ryy) = 1, Am(Ryx) = Am(Rxy) = 0 and Arg(Rxx)-Arg(Ryy) ≈ �90� around 10 GHz from Figure 17. In this situation, the R matrix is,

$$R = \begin{pmatrix} \cdot j & 0\\ 0 & 1 \end{pmatrix} e^{\cdot j \cdot \mathbf{r}} \tag{6}$$

We suppose that the LTC-PCMS is illuminated by a plane wave propagating along �z direction, then the formulation of the incident wave can be described as Eqs. (7) and (8).

Figure 17. The (a) amplitudes and (b) angles of the R matrix.

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 43

$$
\stackrel{\rm V}{E}\_t = (\hat{\mathfrak{x}}E\_\mathbf{x} + \hat{\mathfrak{y}}E\_\mathbf{y})e^{\cdot \beta \mathbf{z}}\tag{7}
$$

$$
\begin{pmatrix} E\_\times \\ E\_\times \end{pmatrix} = \begin{pmatrix} \cos\theta \\ \sin\theta \end{pmatrix} e^{\ast \cdot \theta \mathbf{z}} \tag{8}
$$

where k is the wave number. In the following, we will discuss that our LTC-PCMS supports linear wave to LHCP or RHCP wave conversion in two special cases.

For the case of , the incident E fields can be described as:

$$
\begin{pmatrix} E\_\mathbf{x} \\ E\_\mathbf{y} \end{pmatrix} = \frac{\sqrt{2}}{2} \begin{pmatrix} 1 \\ 1 \end{pmatrix} e^{\mathbf{x}^{\prime \mathbf{A} \mathbf{z}}} \tag{9}
$$

Then, the reflected E fields can be calculated as:

make the reflecting phase change with the polarization of the incident wave. The reflection matrix (R matrix), which connects the incident fields and reflected fields, can be described as:

Figure 16. Topology of the proposed LTC-PCMS unit cell with g = t = 0.4 mm, p = 10 mm, and d = 3 mm. (a) Front view

and (b) perspective view. The metallic is shown in green, while the slot is shown in white.

where Rij represents the reflection coefficient of j polarization incident wave and i polarization reflected wave. And we use Am(Rij) and Arg(Rij) to describe the amplitude and phase of Rij, respectively. At the case of r<sup>x</sup> = 4.06 mm and r<sup>y</sup> = 3.6 mm, we can obtain that Am(Rxx) = Am (Ryy) = 1, Am(Ryx) = Am(Rxy) = 0 and Arg(Rxx)-Arg(Ryy) ≈ �90� around 10 GHz from Figure 17.

We suppose that the LTC-PCMS is illuminated by a plane wave propagating along �z direc-

tion, then the formulation of the incident wave can be described as Eqs. (7) and (8).

In this situation, the R matrix is,

42 Metamaterials and Metasurfaces

Figure 17. The (a) amplitudes and (b) angles of the R matrix.

ð5Þ

ð6Þ

$$\begin{aligned} \begin{pmatrix} E\_{\pi\pi} \\ E\_{\pi\eta} \end{pmatrix} &= R \frac{\sqrt{2}}{2} \begin{pmatrix} 1 \\ 1 \end{pmatrix} \mathbf{e}^{\prime\prime\pi} \mathbf{e}^{\cdot\prime\prime} \\ &= \frac{\sqrt{2}}{2} \begin{pmatrix} -j \\ 1 \end{pmatrix} \mathbf{e}^{\prime\prime kz} \mathbf{e}^{\cdot\prime\prime q} \\ \times \quad \dots \quad \dots \quad \dots \quad \dots \end{aligned} \tag{10}$$

$$\begin{aligned} E\_r &= E\_{rr}\hat{\mathbf{x}} + E\_{r\rho}\hat{\mathbf{y}} \\ &= \frac{\sqrt{2}}{2}(-j\hat{\mathbf{x}} + \hat{\mathbf{y}}) \cdot e^{\mu\mathbf{x}} e^{-j\varphi} \end{aligned} \tag{11}$$

As described in Eq. (11), it can be concluded that the polarization of the reflected wave is LHCP. In the second case of , we can obtain following results by taking similar calculations.

$$\begin{split} \stackrel{\bullet}{E}\_r &= E\_{rx}\hat{\mathbf{x}} + E\_{ry}\hat{\mathbf{y}} \\ &= \frac{\sqrt{2}}{2}(j\hat{\mathbf{x}} + \hat{y}) \quad e^{jkr}e^{-j\phi} \end{split} \tag{12}$$

In this situation, a RHCP reflected wave has been obtained. Figure 18 depicts a practical realized scheme of our system, where the LTC-PCMS fed by a Vivaldi antenna is built by 13 � 13 single-layered CCR unit cells. The voltage standing wave ratio (VSWR) with its geometrical parameters has been shown in Figure 19. We can conclude that the Vivaldi antenna has a VSWR less than 2 dB within the frequency band of 9–15 GHz. Three-dimensional radiation patterns and AR results of the LTC-PCMS are shown in Figure 20. As shown, the far-field patterns achieve CP radiation but the directivity of the Vivaldi antenna has been broken by the MS. To conquer this problem, an additional focusing profile needed to be brought in to correct the wave-front of the outing wave.

2.2. Multifunctional metasurface design

calculated by,

To ease the design, we want the unit cell can manipulate the x- and y-polarized waves independently and completely. By simulations, we find that the single-layered CCR element features good polarization-independence but lacks sufficient phase-tuning range. Then, we propose a bilayered CCR element to enlarge the phase-tuning range. The phases of Rxx and Ryy of the bilayered unit cell are shown in Figure 21. As shown, the parameter r<sup>x</sup> (r<sup>y</sup> = 4.06 mm) just affects the value of Arg(Rxx), while Arg(Ryy) is almost constant when r<sup>x</sup> increases from 2.3 to 4.06 mm. Meanwhile, the phase range of Arg(Rxx) has reached 360�. Since the CCR unit cell exhibits rotational symmetry, similar conclusion can be obtained by just tuning ry. In a word, the phases of x and y polarization incident waves are controlled by r<sup>x</sup> and ry, respectively, and they do not influence each other. This character will greatly simplify the design of the multifunctional MS.

For focusing MS, the phase difference distribution on the MS has to satisfy Eq. (13).

While for y-polarization incidence, the phase distribution is:

Figure 21. Phases of S11 for x/y polarizations of the dual-layered CCR unit cell with its structure.

where L is the focal distance, m(n) is the number of the unit cell in x(y) direction, and is the phase difference according to the unit cell, which is placed at the origin point (m = 0, n = 0). For LTC-MS, the phase of Rxx must have a 90� difference with the phase of Ryy through each unit cell around 10 GHz. Arg(Rxx)mn is controlled by the parameter of rx, while Arg(Ryy)mn is controlled by the parameter of ry. For x-polarization incidence, the phase distribution can be

ð13Þ

45

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

ð14Þ

Figure 18. The scheme of proposed wo situations for different E field directions at (a) θ = 45and (b) θ = 135.

Figure 19. The VSWR of the Vivaldi antenna. The geometrical parameters are W = 25 mm, L = 30 mm, L<sup>1</sup> = 25 mm, W<sup>1</sup> = 15 mm, W<sup>2</sup> = 1 mm, W<sup>3</sup> = 0.5 mm, and g = 0.5 mm.

Figure 20. 3D radiation patterns and AR results of the LTC-PCMS for (a) θ = 45and (b) θ = 135.

#### 2.2. Multifunctional metasurface design

To ease the design, we want the unit cell can manipulate the x- and y-polarized waves independently and completely. By simulations, we find that the single-layered CCR element features good polarization-independence but lacks sufficient phase-tuning range. Then, we propose a bilayered CCR element to enlarge the phase-tuning range. The phases of Rxx and Ryy of the bilayered unit cell are shown in Figure 21. As shown, the parameter r<sup>x</sup> (r<sup>y</sup> = 4.06 mm) just affects the value of Arg(Rxx), while Arg(Ryy) is almost constant when r<sup>x</sup> increases from 2.3 to 4.06 mm. Meanwhile, the phase range of Arg(Rxx) has reached 360�. Since the CCR unit cell exhibits rotational symmetry, similar conclusion can be obtained by just tuning ry. In a word, the phases of x and y polarization incident waves are controlled by r<sup>x</sup> and ry, respectively, and they do not influence each other. This character will greatly simplify the design of the multifunctional MS.

For focusing MS, the phase difference distribution on the MS has to satisfy Eq. (13).

ð13Þ

where L is the focal distance, m(n) is the number of the unit cell in x(y) direction, and is the phase difference according to the unit cell, which is placed at the origin point (m = 0, n = 0). For LTC-MS, the phase of Rxx must have a 90� difference with the phase of Ryy through each unit cell around 10 GHz. Arg(Rxx)mn is controlled by the parameter of rx, while Arg(Ryy)mn is controlled by the parameter of ry. For x-polarization incidence, the phase distribution can be calculated by,

$$\begin{aligned} \text{Arg}(R\_{\text{xx}})\_{\text{nn}} \cdot \text{Arg}(R\_{\text{xx}})\_{00} &= \frac{2\pi}{\lambda} (\sqrt{(mp)^2 + (np)^2 + L^2} \cdot L) \neq 2k\pi\\ &= \Delta \rho\_{\text{xx}}(m, n) \quad (k = 0, 1, 2...) \end{aligned} \tag{14}$$

While for y-polarization incidence, the phase distribution is:

Figure 19. The VSWR of the Vivaldi antenna. The geometrical parameters are W = 25 mm, L = 30 mm, L<sup>1</sup> = 25 mm,

Figure 20. 3D radiation patterns and AR results of the LTC-PCMS for (a) θ = 45and (b) θ = 135.

Figure 18. The scheme of proposed wo situations for different E field directions at (a) θ = 45and (b) θ = 135.

W<sup>1</sup> = 15 mm, W<sup>2</sup> = 1 mm, W<sup>3</sup> = 0.5 mm, and g = 0.5 mm.

44 Metamaterials and Metasurfaces

Figure 21. Phases of S11 for x/y polarizations of the dual-layered CCR unit cell with its structure.

Figure 22. Absolute phase distributions for (a) x polarization and (b) y polarization.

Figure 23. Distributions of (a) r<sup>x</sup> and (b) r<sup>y</sup> on the multifunctional MS.

$$\begin{aligned} \text{Arg}(R\_{\text{yy}})\_{\text{nm}} \cdot \text{Arg}(R\_{\text{yy}})\_{00} &= \frac{2\pi}{\lambda} (\sqrt{(mp)^2 + (np)^2 + L^2} \cdot L) \neq 2k\pi\\ &= \Delta \rho\_{\text{yy}}(m, n) \quad (k = 0, 1, 2...) \end{aligned} \tag{15}$$

realized gains with AR results are shown in Figure 26. Comparing with LTC-PCMS, the new multifunctional MS enhances the gain and decreases beam width of the antenna in 3 dB AR band of 9.12–10.2 GHz. Specially, the realized gain has been enhanced 12 dB and a half power

Figure 26. (a) 3D radiation pattern (b) simulated and measured results of axis ratios and realized gains.

beam width of 13� has been achieved at 10 GHz.

Figure 24. Electric field distributions in (a) xoz and (b) yoz plane at 10 GHz.

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 47

Figure 25. 2D radiation patterns at 10 GHz (a) xoy-plane (b) yoz-plane.

where, in the focusing LTC-PCMS design, following equations have to be satisfied: Arg(Rxx)00- Arg(Ryy)00 = �90�. We insert L = 2λ, p = 10 mm, λ = 30 mm, and Arg(Rxx)00 = �700� into Eqs. (13) and (14) to obtain the phase distributions shown in Figure 22. And then the values of r<sup>x</sup> and r<sup>y</sup> at each position (m, n) on the MS can be ascertained and shown in Figure 23.

#### 2.3. Circular-polarized antenna design

Then, the proposed MS model is built in CST based on the matrixes of r<sup>x</sup> and ry, and a Vivaldi antenna is placed 60 mm away from MS as a feed source. As shown in Figure 18(a), we first set θ = 45� and an LHCP-reflected wave will be obtained consequently. Figure 24 describes the near-field electric field distributions in xoz- and yoz-planes, which illustrates that the incident plane wave has been converted into near-plane wave. For farfield results, the 2D patterns of xoz- and yoz-planes are shown in Figure 25 and the pencil-shaped 3D radiation pattern and the

Figure 24. Electric field distributions in (a) xoz and (b) yoz plane at 10 GHz.

Figure 25. 2D radiation patterns at 10 GHz (a) xoy-plane (b) yoz-plane.

ð15Þ

where, in the focusing LTC-PCMS design, following equations have to be satisfied: Arg(Rxx)00- Arg(Ryy)00 = �90�. We insert L = 2λ, p = 10 mm, λ = 30 mm, and Arg(Rxx)00 = �700� into Eqs. (13) and (14) to obtain the phase distributions shown in Figure 22. And then the values of

Then, the proposed MS model is built in CST based on the matrixes of r<sup>x</sup> and ry, and a Vivaldi antenna is placed 60 mm away from MS as a feed source. As shown in Figure 18(a), we first set θ = 45� and an LHCP-reflected wave will be obtained consequently. Figure 24 describes the near-field electric field distributions in xoz- and yoz-planes, which illustrates that the incident plane wave has been converted into near-plane wave. For farfield results, the 2D patterns of xoz- and yoz-planes are shown in Figure 25 and the pencil-shaped 3D radiation pattern and the

r<sup>x</sup> and r<sup>y</sup> at each position (m, n) on the MS can be ascertained and shown in Figure 23.

Figure 22. Absolute phase distributions for (a) x polarization and (b) y polarization.

46 Metamaterials and Metasurfaces

Figure 23. Distributions of (a) r<sup>x</sup> and (b) r<sup>y</sup> on the multifunctional MS.

2.3. Circular-polarized antenna design

Figure 26. (a) 3D radiation pattern (b) simulated and measured results of axis ratios and realized gains.

realized gains with AR results are shown in Figure 26. Comparing with LTC-PCMS, the new multifunctional MS enhances the gain and decreases beam width of the antenna in 3 dB AR band of 9.12–10.2 GHz. Specially, the realized gain has been enhanced 12 dB and a half power beam width of 13� has been achieved at 10 GHz.

In this section, we proposed a four-layered transmitting MS with a parabolic phase profile at 10 GHz. The MS elements are cautiously designed and optimized, aiming at affording high transmitting efficiencies for all the building elements. In that case, the MS can focus the incident plane wave with high efficiency. In current design, a patch antenna operating at 10 GHz is placed at the focal point of the MS to feed the PGMS and the F/D is designed as 0.19. The quasi-spherical wave emitted by the source will be transformed to near-plane wave by the MS, and thus a high

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 49

The structure of the unit cell, as shown in Figure 29, consists of a four metal layers and a three dielectric layers. The metal layer consists of a circular patch and a square outer frame. The transmission phase changes with the radius of r<sup>n</sup> of the circular patch. The dielectric substrate has a relative dielectric constant of 2.65 and a thickness of d = 1.5 mm, of which t = 0.1 mm, p = 10 mm. We simulate the elements with one, two, and three layers, respectively, in CST Microwave Studio, and their simulation results, the curves of phase, and amplitude varying with the frequency, are shown in Figure 30. It can be seen from the figure that when the patch size of the three units is changed, the transmission coefficients at 10 GHz are all above 0.8, and the phase control range increases with the increase of the number of layer. The phase coverage of the unit cell contains three dielectric layers already exceeding 360�. The curves of transmit-

For designing the transmitted focusing MS, the phase distribution should also obey Eq. (3). To not lose generality, we arbitrarily select f = λ = 30 mm in this particular design. The phase distribution is shown in Figure 32. And we can obtain the parameter distribution shown in Figure 33 and build the MS model. Owing to the narrow band characteristic of the MS, we adopt a microstrip patch antenna as the feed source, and its structure and reflection coefficient are shown in Figure 34. The feed source and the MS were simulated in CST, respectively. The electric-field distributions at xoz- and yoz-planes at 10 GHz are shown in Figure 35. It can be seen from the figure that the spherical wave emitted by the feed passes through the MS and the transmitted

Figure 29. Structure of the metasurface unit and the simulated setup. (a) Top view and (b) perspective view.

ted phase and amplitude varying with the patch size are shown in Figure 31.

3.2. High-efficiency transmitted focusing metasurface design

gain lens antenna with pencil-shaped beam will be achieved.

3.1. Multilayer metasurface unit cell design

Figure 27. 3D radiation patterns for (a) θ = 0� and (b) θ = 90�.

Figure 28. Photographs of the fabricated sample. (a) Vivaldi antenna, (b) multifunctional MS, and (c) whole system.

In addition, we simulate the models of θ = 0�, 90�, and 135�. It is similar as the LTC-PCMS, the results for θ = 135� and 45� are the same expect that the copolarization is LHCP for θ = 45�, while it is RHCP for θ = 135�. For θ = 0�, x-polarization reflecting wave is obtained as shown in Figure 27(a). While for θ = 90�, and y-polarization reflecting wave is obtained as shown in Figure 27(b). To some extent, the whole system is polarization-reconfigurable to some extent. Finally, the photographs of the fabricated sample are shown Figure 28.

#### 3. High-gain lens antenna based on multilayer metasurface

Compared with the reflected MS, the feed of the transmitted MS does not block the radiated wave, making it more suitable for a high-gain antenna design. However, the design of the transmitting MS is more difficult since the transmitting efficiency must be taken into consideration. In this section, we proposed a four-layered transmitting MS with a parabolic phase profile at 10 GHz. The MS elements are cautiously designed and optimized, aiming at affording high transmitting efficiencies for all the building elements. In that case, the MS can focus the incident plane wave with high efficiency. In current design, a patch antenna operating at 10 GHz is placed at the focal point of the MS to feed the PGMS and the F/D is designed as 0.19. The quasi-spherical wave emitted by the source will be transformed to near-plane wave by the MS, and thus a high gain lens antenna with pencil-shaped beam will be achieved.

#### 3.1. Multilayer metasurface unit cell design

In addition, we simulate the models of θ = 0�, 90�, and 135�. It is similar as the LTC-PCMS, the results for θ = 135� and 45� are the same expect that the copolarization is LHCP for θ = 45�, while it is RHCP for θ = 135�. For θ = 0�, x-polarization reflecting wave is obtained as shown in Figure 27(a). While for θ = 90�, and y-polarization reflecting wave is obtained as shown in Figure 27(b). To some extent, the whole system is polarization-reconfigurable to some extent.

Figure 28. Photographs of the fabricated sample. (a) Vivaldi antenna, (b) multifunctional MS, and (c) whole system.

Compared with the reflected MS, the feed of the transmitted MS does not block the radiated wave, making it more suitable for a high-gain antenna design. However, the design of the transmitting MS is more difficult since the transmitting efficiency must be taken into consideration.

Finally, the photographs of the fabricated sample are shown Figure 28.

Figure 27. 3D radiation patterns for (a) θ = 0� and (b) θ = 90�.

48 Metamaterials and Metasurfaces

3. High-gain lens antenna based on multilayer metasurface

The structure of the unit cell, as shown in Figure 29, consists of a four metal layers and a three dielectric layers. The metal layer consists of a circular patch and a square outer frame. The transmission phase changes with the radius of r<sup>n</sup> of the circular patch. The dielectric substrate has a relative dielectric constant of 2.65 and a thickness of d = 1.5 mm, of which t = 0.1 mm, p = 10 mm. We simulate the elements with one, two, and three layers, respectively, in CST Microwave Studio, and their simulation results, the curves of phase, and amplitude varying with the frequency, are shown in Figure 30. It can be seen from the figure that when the patch size of the three units is changed, the transmission coefficients at 10 GHz are all above 0.8, and the phase control range increases with the increase of the number of layer. The phase coverage of the unit cell contains three dielectric layers already exceeding 360�. The curves of transmitted phase and amplitude varying with the patch size are shown in Figure 31.

#### 3.2. High-efficiency transmitted focusing metasurface design

For designing the transmitted focusing MS, the phase distribution should also obey Eq. (3). To not lose generality, we arbitrarily select f = λ = 30 mm in this particular design. The phase distribution is shown in Figure 32. And we can obtain the parameter distribution shown in Figure 33 and build the MS model. Owing to the narrow band characteristic of the MS, we adopt a microstrip patch antenna as the feed source, and its structure and reflection coefficient are shown in Figure 34. The feed source and the MS were simulated in CST, respectively. The electric-field distributions at xoz- and yoz-planes at 10 GHz are shown in Figure 35. It can be seen from the figure that the spherical wave emitted by the feed passes through the MS and the transmitted

Figure 29. Structure of the metasurface unit and the simulated setup. (a) Top view and (b) perspective view.

Figure 31. Simulated transmission phase difference (black square dots) and amplitude (blue circle dots) of the unit with

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 51

different radius r<sup>n</sup> of the solid circle (n = 1, 2…8) at 10 GHz.

Figure 32. Absolute phase distribution of the focusing MS.

Figure 33. The distribution of r<sup>n</sup> on the MS.

Figure 30. Phase (a, c, e) and amplitude (b, d, f) of S21 for single (a, b), two (c, d), and three (e, f) dielectric layers.

wave becomes a near-plane wave. The result is in agreement with the theoretical prediction, and it also means that the transmitted MS can be used to enhance the gain of the feed antenna. The penshaped farfield pattern given in Figure 36 is a more powerful proof of this characteristic.

Figure 31. Simulated transmission phase difference (black square dots) and amplitude (blue circle dots) of the unit with different radius r<sup>n</sup> of the solid circle (n = 1, 2…8) at 10 GHz.

Figure 32. Absolute phase distribution of the focusing MS.

Figure 33. The distribution of r<sup>n</sup> on the MS.

wave becomes a near-plane wave. The result is in agreement with the theoretical prediction, and it also means that the transmitted MS can be used to enhance the gain of the feed antenna. The pen-

shaped farfield pattern given in Figure 36 is a more powerful proof of this characteristic.

Figure 30. Phase (a, c, e) and amplitude (b, d, f) of S21 for single (a, b), two (c, d), and three (e, f) dielectric layers.

50 Metamaterials and Metasurfaces

Figure 34. The structure of the patch antenna and its measured reflection coefficients with/without the PGMS. lp = 12 mm and r<sup>p</sup> = 5.1 mm.

Figure 35. Simulated electric field distribution (Ex) 10 GHz in (a, b) xoz-plane and (c, d) yoz-plane, respectively, for the patch antenna without (a, c) and (b, d) with the metasurface.

#### 3.3. Lens antenna assembling and measurement

The multilayer MS is fabricated and then assembled with a patch antenna. The sample photographs are shown in Figure 37. We test the MS antenna in the microwave anechoic chamber. Figure 38 shows the simulated and measured patterns of the xoz- and yoz-planes at the 10 GHz of the MS and the contrasted patterns of the bare patch antenna. It can be seen from the figure that the MS increases the gain of the patch antenna and narrows the width of the beam, in which the gain enhancement is 11.6 dB and the half-power beam width decrease

Figure 38. Simulated and measured farfield radiation patterns at 10 GHz of the patch antenna with and without the

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 53

Figure 36. Three-dimensional pen shape pattern at 10 GHz of antenna.

Figure 37. Photographs of high-gain lens antenna.

metasurface. (a) xoy-plane and (b) yoz-plane.

Figure 36. Three-dimensional pen shape pattern at 10 GHz of antenna.

Figure 37. Photographs of high-gain lens antenna.

3.3. Lens antenna assembling and measurement

patch antenna without (a, c) and (b, d) with the metasurface.

and r<sup>p</sup> = 5.1 mm.

52 Metamaterials and Metasurfaces

The multilayer MS is fabricated and then assembled with a patch antenna. The sample photographs are shown in Figure 37. We test the MS antenna in the microwave anechoic chamber. Figure 38 shows the simulated and measured patterns of the xoz- and yoz-planes at

Figure 35. Simulated electric field distribution (Ex) 10 GHz in (a, b) xoz-plane and (c, d) yoz-plane, respectively, for the

Figure 34. The structure of the patch antenna and its measured reflection coefficients with/without the PGMS. lp = 12 mm

Figure 38. Simulated and measured farfield radiation patterns at 10 GHz of the patch antenna with and without the metasurface. (a) xoy-plane and (b) yoz-plane.

the 10 GHz of the MS and the contrasted patterns of the bare patch antenna. It can be seen from the figure that the MS increases the gain of the patch antenna and narrows the width of the beam, in which the gain enhancement is 11.6 dB and the half-power beam width decrease is 66�. The aperture efficiency of antenna at 10 GHz can be calculated to be about 30% by Eq. (4) (Figure 38).
