4. Single-layer metasurface for ultrathin planar lens antenna application

As we all known, it is hard to cover 360� phase shift range with satisfying efficiencies by singlelayered (bi-layered metal) structures, though they are easier of fabrication. Multilayer stack adopted in above section is a valid technique to expand the phase shift range of MS. However, it is not the only method to achieve this goal. In Ref [20], three kinds of single-layer unit cells are used together to provide adequate phase range by skillfully connecting each phase shift section of them. In this section, an element group consist of two similar single-layered transmitting unit cells was designed. The phase steering ranges of the two elements have been well connected to achieve a phase shift range of 415�. And we use this element group to successfully design an ultrathin planar lens antenna.

#### 4.1. Single-layer element design

The structures of the element 1 and the element 2 are shown in Figure 39, in which the metal layer of the element 1 is a cross and a double cross-ring structure (cross and double cross-ring, CDCR), and the metal layer of the element 2 is a cross and cross-ring structure (cross and crossring, CCR). The dielectric layers of the two elements are all 3 mm thick with a relative dielectric constant of 4.3. The dimensions shown in Figure 39 are, p = 8 mm, w = 0.9 mm, g = t = 0.15 mm, r<sup>1</sup> = 3.9 mm, and r<sup>2</sup> = 3.7 mm. Element 1 and element 2 regulate their phases by changing the values of r1n and r2n, respectively. For the CDCR element structure, the transmission coefficient amplitude curve of r1n = 3.38 mm and r1n = 1.10 mm are shown in Figure 40. In this figure, when r1n = 3.38 mm, there are three frequency bands, in which the transmission rate is more than 0.7. The third band is in the X band, and the transmission rate in this band changes slowly. Indeed, this resonant frequency band is mainly controlled by the cross-structure, which means that different transmitted phases at 10 GHz can be obtained by changing the cross-length (r1n). Under the requirement of the transmission efficiency over 0.7 at 10 GHz, we adjust the length r1n of the cross to make the frequency point of 10 GHz fall on the rising and descending edge of the third frequency ranges. The phase changing range is shown in Figure 41. The difference

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 55

Figure 40. Transmitted amplitudes of the element 1 with minimum and maximum sizes of the inner cross.

In order to achieve the phase tuning range of 360�, we remove the outermost cross-frame structure on the basis of CDCR element and get the second element namely the CCR element.

between the minimum and the maximum transmitted phase at 10 GHz is 204�.

Figure 41. Transmitted phases of the element 1 with minimum and maximum sizes of the inner cross.

Figure 39. Structure and simulated setup of the element 1 (a, b) and element 2 (c, d).

Figure 40. Transmitted amplitudes of the element 1 with minimum and maximum sizes of the inner cross.

is 66�. The aperture efficiency of antenna at 10 GHz can be calculated to be about 30%

4. Single-layer metasurface for ultrathin planar lens antenna application

As we all known, it is hard to cover 360� phase shift range with satisfying efficiencies by singlelayered (bi-layered metal) structures, though they are easier of fabrication. Multilayer stack adopted in above section is a valid technique to expand the phase shift range of MS. However, it is not the only method to achieve this goal. In Ref [20], three kinds of single-layer unit cells are used together to provide adequate phase range by skillfully connecting each phase shift section of them. In this section, an element group consist of two similar single-layered transmitting unit cells was designed. The phase steering ranges of the two elements have been well connected to achieve a phase shift range of 415�. And we use this element group to successfully design an

The structures of the element 1 and the element 2 are shown in Figure 39, in which the metal layer of the element 1 is a cross and a double cross-ring structure (cross and double cross-ring, CDCR), and the metal layer of the element 2 is a cross and cross-ring structure (cross and crossring, CCR). The dielectric layers of the two elements are all 3 mm thick with a relative dielectric constant of 4.3. The dimensions shown in Figure 39 are, p = 8 mm, w = 0.9 mm, g = t = 0.15 mm, r<sup>1</sup> = 3.9 mm, and r<sup>2</sup> = 3.7 mm. Element 1 and element 2 regulate their phases by changing the values of r1n and r2n, respectively. For the CDCR element structure, the transmission coefficient amplitude curve of r1n = 3.38 mm and r1n = 1.10 mm are shown in Figure 40. In this figure,

Figure 39. Structure and simulated setup of the element 1 (a, b) and element 2 (c, d).

by Eq. (4) (Figure 38).

54 Metamaterials and Metasurfaces

ultrathin planar lens antenna.

4.1. Single-layer element design

when r1n = 3.38 mm, there are three frequency bands, in which the transmission rate is more than 0.7. The third band is in the X band, and the transmission rate in this band changes slowly. Indeed, this resonant frequency band is mainly controlled by the cross-structure, which means that different transmitted phases at 10 GHz can be obtained by changing the cross-length (r1n). Under the requirement of the transmission efficiency over 0.7 at 10 GHz, we adjust the length r1n of the cross to make the frequency point of 10 GHz fall on the rising and descending edge of the third frequency ranges. The phase changing range is shown in Figure 41. The difference between the minimum and the maximum transmitted phase at 10 GHz is 204�.

In order to achieve the phase tuning range of 360�, we remove the outermost cross-frame structure on the basis of CDCR element and get the second element namely the CCR element.

Figure 41. Transmitted phases of the element 1 with minimum and maximum sizes of the inner cross.

Figure 42. Transmitted amplitudes of the element 2 with minimum and maximum sizes of the inner cross.

To ensure that the simulated conditions are exactly the same, the size of the CCR element is slightly adjusted. When r2n takes 3.46 mm and 1 mm, the curves of the transmitted amplitude are shown in Figure 42. The number of the frequency band, in which the transmittance is over 0.7, is reduced to two. The second resonant frequency band is mainly controlled by the cross-structure (r2n). When r2n takes 3.46 mm and 1 mm, the rising and falling edges of the band fall at 10 GHz, respectively. And the corresponding transmission phase curve is shown in Figure 43. In combination with Figures 41 and 43, we find that the difference between the minimum transmission phase (absolute value) of the element 1 (CDCR element) and the maximum transmission phase (absolute value) of element 2 is 15� at 10 GHz, which indicates that the two elements have

achieved good phase abutment. At the same time, the 360 full coverage is achieved after abutting the two elements. Figure 44 gives two curves of transmittance and transmission phase

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 57

Figure 44. Transmission (a) phases and (b) amplitudes versus the r<sup>1</sup> and r<sup>2</sup> for element 1 and element 2.

From the previous analysis, it can be seen that the combination of CDCR and CCR unit cells can completely control the phase of transmitted wave under the precondition of the transmittance higher than 0.7, which meet the requirements of the transmitted focusing MS. The same as the Section 2, we use 13 13 elements to build the transmitted MS and improve the gain of the patch antenna. According to Eq. (13), we fix L = 30 mm to calculate the absolute phase distribution on MS and show it in Figure 45(a), in which the transmission phase of the original point (0, 0) is 740, the element form is CDCR, the cross-parameter is r1n = 3.38 mm, and the value of k is reasonably selected to make the transmission phase of each unit fall within the range of [0, 360]. According to the phase distribution shown in Figure 45(a) and the phase distribution curve given in Figure 44, we can determine the unit

of the elements varying with their respective parameters (r1n and r2n).

4.2. Single-layer metasurface design

Figure 43. Transmitted phases of element 2 with minimum and maximum sizes of the inner cross.

Figure 44. Transmission (a) phases and (b) amplitudes versus the r<sup>1</sup> and r<sup>2</sup> for element 1 and element 2.

achieved good phase abutment. At the same time, the 360 full coverage is achieved after abutting the two elements. Figure 44 gives two curves of transmittance and transmission phase of the elements varying with their respective parameters (r1n and r2n).

#### 4.2. Single-layer metasurface design

To ensure that the simulated conditions are exactly the same, the size of the CCR element is slightly adjusted. When r2n takes 3.46 mm and 1 mm, the curves of the transmitted amplitude are shown in Figure 42. The number of the frequency band, in which the transmittance is over 0.7, is reduced to two. The second resonant frequency band is mainly controlled by the cross-structure (r2n). When r2n takes 3.46 mm and 1 mm, the rising and falling edges of the band fall at 10 GHz, respectively. And the corresponding transmission phase curve is shown in Figure 43. In combination with Figures 41 and 43, we find that the difference between the minimum transmission phase (absolute value) of the element 1 (CDCR element) and the maximum transmission phase (absolute value) of element 2 is 15� at 10 GHz, which indicates that the two elements have

Figure 42. Transmitted amplitudes of the element 2 with minimum and maximum sizes of the inner cross.

56 Metamaterials and Metasurfaces

Figure 43. Transmitted phases of element 2 with minimum and maximum sizes of the inner cross.

From the previous analysis, it can be seen that the combination of CDCR and CCR unit cells can completely control the phase of transmitted wave under the precondition of the transmittance higher than 0.7, which meet the requirements of the transmitted focusing MS. The same as the Section 2, we use 13 13 elements to build the transmitted MS and improve the gain of the patch antenna. According to Eq. (13), we fix L = 30 mm to calculate the absolute phase distribution on MS and show it in Figure 45(a), in which the transmission phase of the original point (0, 0) is 740, the element form is CDCR, the cross-parameter is r1n = 3.38 mm, and the value of k is reasonably selected to make the transmission phase of each unit fall within the range of [0, 360]. According to the phase distribution shown in Figure 45(a) and the phase distribution curve given in Figure 44, we can determine the unit

form at every position of the MS and get the corresponding cross-parameter values. The distribution of element form is shown in Figure 45(b), where red represents CDCR unit and yellow represents CCR unit. The corresponding r1n or r2n value distribution is shown in

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 59

Figure 48. Prototype of the proposed lens antenna (a) single-layer MS and (b) the farfield measured setup.

Figure 49. Simulated and measured 2D radiation patterns in (a) xoz-plane and (b) yoz-plane.

According to the distribution of Figure 45(b) and (c), a single-layer transmitted focusing MS is constructed, and the patch antenna shown in Figure 34 is used as the feed source. Figure 46

Figure 45(c).

Figure 45. The (a) absolute phases, (b) element types, and (c) values of r1n or r2n for all the unit cells on the MS.

Figure 46. Simulated electric field distribution (Ex) at 10 GHz in (a) xoz-plane and (b) yoz-plane.

Figure 47. The (a) 3D radiation pattern at 10 GHz.

Figure 48. Prototype of the proposed lens antenna (a) single-layer MS and (b) the farfield measured setup.

Figure 45. The (a) absolute phases, (b) element types, and (c) values of r1n or r2n for all the unit cells on the MS.

Figure 46. Simulated electric field distribution (Ex) at 10 GHz in (a) xoz-plane and (b) yoz-plane.

Figure 47. The (a) 3D radiation pattern at 10 GHz.

58 Metamaterials and Metasurfaces

form at every position of the MS and get the corresponding cross-parameter values. The distribution of element form is shown in Figure 45(b), where red represents CDCR unit and yellow represents CCR unit. The corresponding r1n or r2n value distribution is shown in Figure 45(c).

According to the distribution of Figure 45(b) and (c), a single-layer transmitted focusing MS is constructed, and the patch antenna shown in Figure 34 is used as the feed source. Figure 46

Figure 49. Simulated and measured 2D radiation patterns in (a) xoz-plane and (b) yoz-plane.

shows the electric-field distribution at 10 GHz on the xoz- and yoz-planes. It can be seen from the figure that the spherical wave is transformed into a near-plane wave by the MS, thus increasing the gain of the feed source, as verified by the pen-shaped farfield pattern shown in Figure 47.

References

2011;334:333-337

Nano Letters. 2012;12:4932-4936

and Propagation. 2017;65(3):1452-1457

[1] Yu NF, Genevet P, Kats MA, Aieta F, Tetienne J-P, Capasso F, Gaburro Z. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science.

Focusing MSs for High-Gain Antenna Applications http://dx.doi.org/10.5772/intechopen.79351 61

[2] Pors A, Nielsen MG, Eriksen RL, Bozhevolnyi SI. Broadband focusing flat mirrors based

[3] Li X, Xiao SY, Cai BG, He Q, Cui TJ, Zhou L. Flat metasurfaces to focus electromagnetic

[4] Aieta F, Genevet P, Kats MA, Yu NF, Blanchard R, Gaburro Z, Capasso F. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces.

[5] Li H-P, Wang GM, Liang JG, Gao XJ, Hou HS, Jia XY. Single-layer focusing gradient metasurface for ultrathin planar lens antenna application. IEEE Transactions on Antennas

[6] Sun SL, Yang K, Wang C, Cui JT, et al. High-efficiency broadband anomalous reflection by

[7] Ni X, Emani NK, Kildishev AV, Boltasseva A, Shalaev VM. Broadband light bending with

[8] Sun SL, He Q, Xiao SY, et al. Gradient-index meta-surfaces as a bridge linking propagating

[9] Wu CJ, Cheng YZ, Wang WY, He B, Gong RZ. Ultra-thin and polarization-independent phase gradient metasurface for high-efficiency spoof surface-plasmon-polariton coupling.

[10] Zhao JM, Sima BY, Jia N, et al. Achieving flexible low-scattering metasurface based on

[11] Song Y-C, Ding J, Guo C-J, Ren Y-H, Zhang J-K. Ultra-broadband backscatter radar cross section reduction based on polarization-insensitive metasurface. IEEE Antennas and

[12] Liu Y, Li K, Jia YT, Hao YW, Gong SX, Guo YJ. Wideband RCS reduction of a slot array antenna using polarization conversion metasurfaces. IEEE Transactions on Antennas and

[13] Li HP, Wang GM, Wang JG, Gao XJ. Wideband multifunctional metasurface for polarization conversion and gain enhancement. Progress in Electromagnetics Research. 2016;155:115-125

[14] Song K, Liu YH, Luo CR, Zhao XP. High-efficiency broadband and multiband crosspolarization conversion using chiral metamaterial. Journal of Physics D: Applied Physics.

randomly distribution of metaelements. Optics Express. 2016;24(2):27850

on plasmonic gradient metasurfaces. Nano Letters. 2013;13:829-834

waves in reflection geometry. Optics Letters. 2012;37:4940-4942

gradient meta-surfaces. Nano Letters. 2012;12:6223-6229

waves and surface waves. Nature Materials. 2012;11:426-431

plasmonic nanoantennas. Science. 2012;335:427

Applied Physics Express. 2015;8(12):122001

Wireless Propagation Letters. 2016;15:329-331

Propagation. 2016;64(1):326-331

2014;47:505104

#### 4.3. Lens antenna assembling and measurement

As is shown in Figure 48, the single-layer transmitted MS is fabricated and then assembled with a patch antenna. The lens antenna is measured in the microwave anechoic chamber. In Figure 49, the simulation and test patterns of the xoz- and yoz-planes at 10 GHz are given. It can be seen from the figure that the antenna gain at 10 GHz reaches 16.5 dB, which is 10 dB higher than the patch antenna, and the sidelobe level of the system is 15 dB. In addition, the area of the MS is 104 104 mm<sup>2</sup> . It can be calculated that the focal-to-diameter ratio at 10 GHz is 0.29, and the aperture efficiency is about 30%.
