Compact Antenna with Enhanced Performances Using Artificial Meta-Surfaces Compact Antenna with Enhanced Performances Using Artificial Meta -Surfaces

In recent years, artificial meta‐surfaces, with the advantages of smaller physical space and less losses compared with three‐dimensional (3D) metamaterials (MTM), have intrigued a great impetus and been applied widely to cloaks, subwavelength planar lenses, holograms, etc. Typically, one most important part for meta‐surfaces’ applica‐ tions is to improve the performance of antennas. In this chapter, we discuss our effort in exploring novel mechanisms of enhancing the antenna bandwidth using the magneto‐ electro‐dielectric waveguided meta‐surface (MED‐WG‐MS), achieving circular polariza‐ tion radiation through fractal meta‐surface, and also realizing beam manipulation using cascaded resonator layers, which is demonstrated from aspects of theoretical analysis, numerical calculation, and experimental measurement. The numerical and measured results coincide well with each other. Note that all designed antenna and microwave devices based on compact meta‐surfaces show advantages compared with the conven‐ tional cases.


Introduction
Microstrip antennas have been used widely in recent wireless communication systems due to their coplanar structures, easy fabrication, and stable performances. However, conventional microstrip antennas face huge challenges, such as large size, narrow bandwidth, and inconvenient tuning of the working frequency. abilities in improving the performances of conventional devices, MS antenna has become a research hotspot with remarkable achievements. However, using the MSs to increase the impedance BW of an electrically smaller microstrip patch antenna is still rarely reported.
Artificial magneto-dielectric substrate has been verified to be a promising avenue to reduce the antenna size and extend the working band width [1][2][3][4]. A reported patch antenna, using a magneto-dielectric substrate, achieves a relative 3.2% BW ordered by 6 dB return loss. However, the antenna suffers from a high profile, which is difficult for integration in compact devices. A magneto-dielectric substrate using an embedded meander line (EML) is proposed in reference [5]. A patch antenna based on this substrate realizes an antenna miniaturization and a BW improvement. Unfortunately, it needs an additional shield metal plate that complexes the fabrication. Therefore, it is an essential issue to design an MS antenna realizing simultaneously size reduction, BW extension, and also flexible frequency turning. In this section, we explored an improved strategy to simultaneously address aforementioned issues. An electrically smaller MS element is proposed by combining the electro-dielectric and magnetodielectric waveguided substrates, defined as the magneto-electro-dielectric waveguided MS (MED-WG-MS) [6]. The MED-WG-MS provides a freedom to control the wave impedance and refractive index simultaneously, achieving antenna miniaturization, bandwidth enhancement, and also flexible frequency modulation.

The concept and working mechanism of MED-WG-MS
As discussed in reference [5], planar WG-MS is a special kind of artificial material residing in the planar waveguide environment, which is made up of an upper metallic layer and a lower ground plane. By introducing electric and magnetic resonators in the upper and lower metallic layers, MED-WG-MS is composed, which would bring about a series of interesting characteristics, including EM manipulation, further miniaturization, and also bandwidth enhancement. In addition, the MED-WG-MS is able to tune the working frequency easily, since more freedom is provided by the element. In other words, the antenna can work at any frequency just by manipulating the electric or magnetic resonators.
Then, we will discuss about the working mechanisms of the MED-WG-MS. There is a link between the patch size and the refractive index of the used substrate for a conventional patch antenna, which can be calculated as Eq. (1a) [7], where ε ref is the effective permittivity of the substrate. The quality factor Q is inversely proportion to the working bandwidth. The Q of a microstrip antenna is written as Eq. (1c), here G r denotes the radiation conductance. For an MS antenna, with a tunable effective permeability μ eff and the effective permittivity ε eff , the basic principle is almost the same as the conventional counterpart. The length and quality factor of this MS antenna can be calculated in Eqs. (1b) and (2b) [6].
Therefore, normalized with the conventional patch antenna, the compact factor (CF), defined as the ratio between the patch size for the conventional antenna and the MS antenna, can be derived from Eq. (1a) and (1b) as The BW improving factor (BIF), evaluated by the BW ratio between the conventional antenna and the MS antenna, can be calculated as Based on Eqs. (1)-(4) [6], CF and BIF can be controlled by manipulating the material parameters ε eff or μ eff . Our goal in this section is to achieve a smaller CF and a larger BIF to improve the patch antenna performance. The reported magneto-dielectric substrate [1,4] is just a special case for manipulating the parameter μ eff , however, the proposed MED-WG-MS in this chapter can control both ε eff and μ eff , simultaneously.

The circuit model and EM property of MED-WG-MS
Based on the analysis in Section 1.1, we proposed a basic element as shown in Figure 1(a) [6]. The element is a well-known sandwich structure, consisting of an upper metallic two-turn complementary spiral ring resonator (CSR) and a lower embedded Hilbert-line (EHL) resonator, separated by a 1.5-mm-thick F4B spacer (dielectric constant ε r = 2.65 and the loss tangent tan δ = 0.001).
The meta-surface, composing of a periodic element, is shined with a plane wave as the Efield polarized along the z-direction and propagation along the x-direction, as the simulation set-up shown in Figure 1(a). For a systematical analysis of the basic element, we proposed the effective circuit model shown in Figure 2. Under a waveguide circumstance, the conventional sandwich structure (composing of metallic layers and a dielectric spacer) can be represented by a parallel resonant tank (consisting of an inductor L and a capacitor C) and a parallel shorted capacitor C 0 . The MD-WG-MS is designed by introducing the magnetic EHL in the ground plane of the basic element. A fractal EHL can be used effectively to control the ε eff of the material. As a result, an additional inductor L EHL is added in the parallel branch to represent the effect of the EHL as shown in Figure 2(a) [6]. An ED-WG-MS is composed of etching a two-turn complementary spiral ring resonator (CSR) in the upper metallic layer, as shown in Figure 2(b). CSR has been demonstrated with compact size and electric resonant property in references [8,9], which is suitable to tune the permeability μ eff . And an additional capacitor C CSRs is added in the series branch of the circuit model. By integrating the effect of the CSR and EHL, a new MED-WG-MS is designed with the structure shown in Figure 2(c).
Consequently, the circuit model can be obviously obtained as shown in Figure 2(c). Further analysis shows that the permeability μ eff is decided by the series branch, whereas the permittivity ε eff is decided by the shunt branch. In other words, both material parameters μ eff and ε eff can be individually manipulated by adjusting the geometrical parameters of the EHL and CSR. For characterization, we obtain the EM performance of the element by using the finite element method (FEM)-based commercial software Ansoft HFSS, and the circuit parameter by using the Ansoft Serenade. Figure 1(b) illustrates the calculated S-parameters by EM simulation and circuit simulation as a function of frequency. There is a reasonable agreement between them, indicating a rationality of the circuit model. As can be seen, band gaps at about 3 GHz are clearly observed. Next, we extracted the effective constitutive material parameters of four types of WG-MSs using the standard retrieval process [10,11] based on the calculated S-parameters; the results are shown in Figure 3. With introduced CSR structures, electric resonances (about 2.86 GHz)  are observed clearly for the MED-WG-MS, 90°-rotated MED-WG-MS and ED-WG-MS cases. However, by inserting EHL, magnetic resonances (about 2.95 GHz) can be seen for the MED-WG-MS, 90°-rotated MED-WG-MS, and MD-WG-MS structures. Routinely, the corresponding antiresonances in vicinity of these resonant frequencies are also appeared in the curves of material parameters, resulting from the magneto-electric coupling among cells and the finite size of the periodic structure [12]. The losses of these elements, represented by the imaginary part of the material parameters, can be ignored in all cases. Due to the anisotropic property of the proposed MED-WG-MS element, there is a slight resonant frequency shift and a small difference between the material parameters for the element and its 90°-rotated counterpart. A comparison of the material parameters indicates that the CSR can realize a manipulation of ε eff and EHL accounts for the control of μ eff . As is expected, according to Eqs. (3) and (4), a desirable combination of a smaller ε eff with flat slope and a larger μ eff is obtained for the proposed MED-WG-MS element. The good performances of the designed element indicate that it is capable of improving the antenna bandwidth and reducing the antenna size. However, undesirable small μ eff and large ε eff are obtained for the MD-WG-MS. While small μ eff and ε eff with a sharp slope are obtained for the ED-WG-MS structure. Both of the ED-WG-MS and MD-WG-MS elements are not able to improve the performance of the bandwidth and reduce the structure dimension.

Design of compact microstrip antenna with enhanced bandwidth
With a desirable MED-WG-MS element in hand, we can obtain effective parameters μ eff = 4.5 + j0.025 and ε eff = 1.05 + j0.033 at 3.5 GHz, according to the aforementioned analysis. Upon introducing these effective parameters into Eqs. Frequency tuning is essential in determining the antenna performances. In the following part, we will derive a three-step frequency tuning method to achieve a flexible frequency tuning property. First, a coarse control over the operating frequency is considered by changing the outer radius r 1 of the CSR structure. As r 1 varies from 1.8 to 2.2 mm in steps of 0.1 mm, Figure 5(a) depicts the frequency-dependent reflection coefficients [6]. To ensure a fair comparison, the residual geometrical parameters of the CSR are kept as p x = p y = 5mm, d = 0.3 mm,  changes. In all cases, good impedance-matching performances are obtained for all cases with the reflection better than 19 dB. Second, a fine control over the operating frequency is studied as the parameter d increases from 0.2 to 0.5 mm. Here, the value d determines the inner circle size of CSR. Referring to Figure 5(b), the reflection valleys undergo a continuous blue shift, changing from 3.4 to 3.6 GHz. Third, Figure 5(c) plots the reflection coefficients with a tunable parameter g. It can be seen clearly that only a small resonant frequency shift (3.47 to 3.53 GHz) appear as g varies from 0.2 to 0.7 mm. Therefore, the parameter g affords an exact control over the operating frequency. It is worth noting that the proposed three-step frequency tuning method provides a comprehensive guideline in designing antenna with an exact working frequency. Compared with the conventional patch antenna, the working frequency can be controlled easier by using the derived method.
The bianisotropic response of the CSR has a large effect on the antenna behavior. By rotating the gap orientation θ from 0 to 180°, Figure 6(a) plots the reflection coefficients against frequency. As θ is 90°, best performances of the antenna with wider bandwidth and lower return loss are obtained. A slightly changing resonant frequency results from the different interactions between the EHL and the CSR with different gap orientations. Here, the dependence of antenna performances on different kinds of WG-MSs is also investigated, as the results shown in Figure 6(b). Desirable antenna performances of size reduction and BW enhancement are  obtained for the CSR-EHL-loaded (MED-WG-MS) antenna. While for the EHL-CSR-loaded case, by etching the EHL cells in the upper patch structure and CSR elements in the ground plane, a poor impedance matching property at the resonant frequency 3.67 GHz is seen, which can be explained as the asymmetrical property of the MED-WG-MS cell along the z-direction. Therefore, we demonstrate that MED-WG-MS elements are the best choice to enhance the antenna performances.

Numerical and experimental results
With the derived three-step frequency tuning method, we can design an antenna operating exactly at frequency 3.5 GHz as shown in Figure 4. For experimental demonstration, we fabricate the antenna with the photograph shown in Figure 7  Then, we evaluate the reflection coefficients of the proposed antenna and the reference antenna through the ME7808A vector network analyzer. Figure 6(c) illustrates the results of the reflection coefficients. There is a good agreement between the simulation and measurement for the designed antenna. Both the proposed antenna and the reference antenna operate exactly at 3.5 GHz, with the numerical (experimental) resonant dips as -25(-40) dB for the designed antenna and -21.5 dB for the reference one, respectively. The simulated (measured) 10 dB impedance bandwidth is about 115 (132) MHz for the designed antenna, corresponding to 3.29% (3.77%). However, it is 43 MHz for the reference antenna. A simply calculation indicates that the BW has been enhanced significantly by 207% for the designed antenna. Table 1 shows a detailed comparison between the two antennas, including the patch size, BW, and the values of CF and BIF. Note that the theoretical and simulated CF and BIF are in reasonable agreement with each other. The small CF = 0.57 and large BIF = 2.67 indicate that the designed antenna has the best performance compared with previous magneto-dielectric antennas [1][2][3][4][5]. The higher measured BIF is mainly ascribed to the random errors in measurement. To summarize, the proposed MED-WG-MS element, coupled with the derived three-step working frequency method provide a guideline to design the antenna with a bandwidth enhancement at any frequency. In addition, the fabrication of the designed antenna is more convenient without using parasitic elements or metallic via holes [13,14].
There is a link between the slope of the input admittance and the BW for an antenna. A flatter response of the input admittance means a wide impedance-matching property. Figure 8 shows comparison of the input admittance for the designed antenna and the reference antenna [6]. It is worth noting that both the real part and the imaginary part of the input admittance for the designed antenna show a flatter response than that of the reference antenna, indicating an enhanced BW for the designed antenna.
Next, we evaluate the field distributions for both the designed antenna and the reference one. Figure 9(a) and (b) shows the comparison of the H-field distributions for both antennas [6]. There is a nearly periodic distribution for the H-field of the proposed antenna, which is attributed to the loading of the MED-WG-MS cells. More importantly, based on the material  parameters, there is larger wave impedance √ _______ μ eff / ε eff for the designed antenna. The larger wave impedance induces a weaker H-field intensity and a smaller quality factor, which explained the enhancement of the BW from another aspect. The field intensity along the line y = 0 is also studied, as the results shown in Figure 9(c) and (d), both the E-field and the Hfield intensity are normalized to the maximum value. With the loading of the MED-WG-MS elements, the E-field, and the H-field intensity are periodic for the proposed antenna, while the distributions are almost consistent for the reference antenna. Therefore, we can conclude that the loading of MED-WG-MS elements induces a redistribution of the electromagnetic energy.
Finally, we examine the far-field radiation performances by HFSS simulation and measurement in an anechoic chamber. The three-dimensional (3D) radiation patterns at three representative frequencies (the lower frequency 3.440 GHz, the center frequency 3.5 GHz, and upper frequency 3.555 GHz) are depicted in Figure 10(a)-(c) [6]. Given the defects in the ground plane, seemingly bidirectional radiation patterns are observed for the three frequencies. But consistent with the conventional patch antenna, the designed one still works at TM 10 mode. The radiation patterns in both principal planes at 3.5 GHz are measured, as the results shown in Figure 10(d). The level of the cross-polarization is better than -22.8 dB. Referring to the antenna gain in Figure 10(e), good agreement is observed for the simulated and measured results. Within the 10 dB impedance bandwidth, the gain is higher than 4.6 dBi. Moreover, the radiation efficiency of the antenna is about 93.23%.
In summary, a new strategy of enhancing the BW and reducing the size of a patch antenna is proposed by simultaneously manipulating the material parameters μ eff and ε eff . For proof of

Miniaturized circularly polarized antenna with fractal meta-surface and fractal resonator
We have discussed about the strategy of employing MED-WG-MS element to manipulate the effective material parameters μ eff and ε eff in the last subsection. In this section, we explore a new scheme to realize miniaturized circularly polarized (CP) antenna with fractal metasurface and fractal resonator. The fractal meta-surface is used to design reactive impedance surface (RIS) to improve the antenna performance in terms of reducing substrate thickness and achieving good front-to-back ratio, whereas fractal resonator with strong space-filling property achieves the CP property and further size reduction.
Unlike linearly polarized (LP) antennas, microstrip circularly polarized (CP) antennas have a stable date transmission rate regardless of the polarizations of the transmitter and the receiver, thus have found numerous applications in the recent wireless communication system [15,16]. However, traditional CP antennas are designed by involving various perturbations (such as truncated corners), which conflicts with the miniaturization requirement and wide bandwidth applications [17,18]. In recent years, meta-surfaces, such as reactive impedance surface (RIS), have been applied to enhance the performances of CP antennas [19][20][21][22][23][24][25][26][27][28], such as realizing miniaturization by loading RIS [20], achieving multi-frequency operation [21,25]. However, there are never open reported techniques to reduce the profile of the CP antenna. In this section, fractal concept has been introduced to design RIS, which realizes both miniaturization and low profile. Good performances of the designed CP antenna by using the fractal RIS are numerically and experimentally demonstrated.
First, we show the perspective view of the proposed Hilbert fractal RIS (HRIS)-inspired Wunderlich-shaped fractal complementary split ring resonator (WCSRR)-loaded CP antenna [29], as shown in Figure 11 [29]. The antenna consists of three layers, the upper metallic radiator, the HRIS spacer, and the lower metallic ground plane. WCSRR is etched in the metallic radiator to realize both antenna miniaturization and CP wave. 6 × 6 HRIS elements are loaded on the F4B substrate under the patch radiator. Two inexpensive F4B dielectric layers (ε r = 2.65, tanδ = 0.001) are adopted in the proposed antenna with h 1 = 1.5 mm and h 2 = 1 mm. The overall antenna occupies a volume of 40 mm × 45 mm × 2.5 mm, and the patch radiator has a dimension of 21.5 mm × 21.5 mm. The working frequency of the antenna is chosen as 3.5 GHz (Wimax band). For characterization, we perform numerical simulations using a finite element method (FEM)-based solver Ansoft HFSS.

The EM property of the fractal RIS
RIS, proposed by Kamal et al. [22], has been used widely in antennas to reduce the radiator size and enhance the working bandwidth. In Figure 12(a) [29], conventional RIS (CRIS) consists of a periodic system of metallic patches (l a × l b = 4.3 mm × 3.8 mm), 1-mm-thick F4B spacer, and a metallic ground plane. The upper substrate is introduced to support the patch radiator. In simulation, an infinite CRIS meta-surface is illuminated by transverse electric and magnetic (TEM) plane wave with the propagation vector along the z-direction and the electric field along the y-direction. Therefore, perfect electric conductor (PEC) conditions are assigned in front and back boundaries, and perfect magnetic conductor (PMC) conditions in left and right boundaries, respectively. Under this circumstance, the CRIS element can be represented by a parallel resonant tank which consists of an inductor L and a capacitor C. The  inductor L is mainly decided by the dielectric constant ε r and the thickness h 2 . While the shunt capacitor C is determined by the edge coupling between the adjacent cells. A variation of the geometrical parameters (l a , l b , p a , p b , and h 2 ) induces a change of the lumped circuit elements, and thus the resonant frequency. We can increase the lumped inductor L by introducing compact structures in the periodic patch, corresponding to reduce the substrate thickness h 2 . For example, mushroom-like RIS increases the inductor L by digging the metallic via holes which brings about considerable losses for the concentrating currents around the holes [22]. Here, we propose the concept fractal RIS to increase the inductor L. An additional inductor L 1 is introduced to represent the EM response of the fractal structure. In fact, the fractal structure can be chosen arbitrary, e.g., the Sierpinski curve and Koch curve. Here, we adopt the Hilbert RIS, as the topology shown in Figure 12(b). The value of L 1 is determined by the iteration orders (IO). Figure 13 shows three kinds of HRISs with IO = 0, 1, and 2, respectively. Different from the traditional Hilbert fractal curve, these curves are revised by extending the start and the end points with the length of a minimum fractal segment, and then connect the terminals.  To evaluate the EM response of the HRIS, Figure 14(a) depicts the reflection phases of HRIS with different IOs. Note that the fair comparison is made with the geometrical parameters consistent except the IOs of the HRISs. At the resonant frequency, the reflection phase is about zero [27]. As seen from Figure 14(a), the operating frequency changes from 9.1 to 7.41 GHz as IO increases from 0 to 2. The second HRIS cell occupies a dimension of λ 0 /8.1 × λ 0 /9 × λ 0 /16.2, which is much smaller than the working wavelength. With a larger IO of the HRIS, stronger space-filling property of the structure is obtained, which induces a smaller resonant frequency. Here, IO = 2 is selected from the tradeoff of an easy fabrication and an electrically smaller structures. Figure 14(b) illustrates the dependence of reflection phase for RISs on the substrate thickness h 2 . The resonant frequencies decrease as h 2 increases. It is worth noting that the HRIS with h 2 = 1 mm has an almost same resonant frequency with that of the CRIS with h 2 = 2 mm, which means a reduction of substrate thickness for the HRIS. Compared with the conventional RIS, fractal RIS has huge advantages in smaller size, lower thickness, and also easier working frequency control. Since more circuit parameters are inserted by the fractal structure, more freedom is provided to tune the working frequency.

Working principle of compact fractal resonator
With a unique EM property and a planar structure, split ring resonator (SRR), and its complementary part, CSRR have been utilized in designing microwave devices and enhancing their performances. However, it is still a great challenge to excite CP wave by integrating the fractal strategy with the CSRR structure. We combine the Wunderlich-shaped fractal structure and the CSRR (WCSRR) to achieve not only antenna miniaturization but also good CP radiation. To demonstrate the advantage of WCSRR over the traditional CSRR, the EM response of three kinds of CSRRs is compared. Figure 15 presents the basic topologies of different SRRs, such as conventional SRR, meander-line-loaded SRR (MSRR), and WSRR. Based on the Babinet principle, we etched the CSRR, MCSRR, and WCSRR structures in the patch radiator. The reflection coefficients and axial ratio (AR) for antennas with different slots are provided in Figure 16. Good impedance matching property for all cases can be observed clearly by the  resonant dips, as shown in Figure 16(a). The conventional antenna without CSRR loading operates at about 3.8 GHz, whereas the center frequency reduces significantly to 3.75, 3.65, and 3.5 GHz for the CSRR-, MCSRR-, and WCSRR-loaded antennas, respectively. The extending of the current path caused by the fractal curve induces the considerable reduction of operating frequency, which is equivalent to realize antenna miniaturization working at the same frequency. Figure 16(b) shows the effects of CSRRs on the AR performances. Note that the slots have a significant effect on the antenna AR. An obvious linearly polarized antenna is obtained without loading CSRRs. The values of AR reduce significantly by loading CSRRs. The best performance of the CP antenna is observed by loading WCSRR, which achieves a lower operating frequency and a smaller AR value. Therefore, we can use the Wunderlichshaped fractal slot to improve CP antenna performances.

Numerical results of a CP antenna
The feeding position as well as the slot position is very important in determining both input impedance and AR value. Antenna performances are simulated by HFSS via tuning the feeding position. The parameter d 6 increases from 0 to 3 mm in steps of 0.5 mm, the  corresponding reflection coefficients and AR values are shown in Figure 17. The operating frequencies keep almost consistent when d 6 increases from 0 to 2 mm, while the impedance matching property deteriorates slightly. A slight red shift of the working frequency appears as d 6 varies from 2.5 to 3 mm. The AR has been significantly improved as d 6 increases, while the AR valleys decrease continuously from 3.52 to 3.48 GHz. As d 6 = 2 mm, both the dip of the reflection coefficient and the AR valley appear at 3.5 GHz, which is interesting and should be highlighted. Figure 17(c) and (d) shows the comparison of the magnitude ratio E y /E x and phase difference δ x -δ y as d 6 varies. Note that E y /E x decreases as d 6 increases, so as the δ x -δ y . As d 6 = 2 mm, the best performance with a flattest curve of the E y /E x and an exact 90° δ x -δ y is obtained at frequency of 3.5 GHz. Therefore, d 6 = 2 mm is selected for the final CP antenna design.
Then, we study the electric field distribution of the CP wave at 3.5 GHz, as the results shown in Figure 18. The electric field is mainly concentrates on the radiation patch and the WCSRR slot. Left-handed CP wave is observed clearly with a clockwise-rotated electric field. The variation of the field on the WCSRR indicates that the slot plays an essential role in exciting the CP wave. Right-handed CP wave can be excited by changing the position of the slot. Figure 17. Simulated reflection coefficients, ARs, magnitude ratio as well as phase difference with different feeding positions [30]. The dependence of (a) reflection coefficients, (b) ARs, (c) magnitude ratio, and (d) phase difference on d 6 .

Fabrication and experimental results
For experimental demonstration, the finally double-layered CP antenna is fabricated based on a standard printed-circuit-board (PCB) technology, with the fabricated sample for the upper layer and the lower layer shown in Figure 19. The two layers with the same footprints are boned tightly together by an adhesive. Then we experimentally evaluate the performances of the CP antenna.  Then, we evaluate the AR ratio of the designed CP antenna. In the experiment, the AR is measured by the intensity ratio between Ey and Ex, which is obtained in an anechoic chamber through the far-field measurement system. As seen from Figure 20(b), the 3-dB AR bandwidth for the simulated and measured results is 55 and 65 MHz, corresponding to 1.58 and 1.86%, respectively. And the minimum values of the AR are 0.41 and 0.75 for the simulated and measured results. Note that 3-dB AR BW is completely within the 10-dB impedance BW.
Finally, we measure the far-field radiation patterns in xoz and yoz planes, as the results shown in Figure 21. There is a good agreement between the simulation and measured results. The   CP wave is detected as expected. We can see clearly that the direction of the peak radiation is around the boresight direction. A pure CP wave is demonstrated for that the crosspolarization is better than 18.5 dB in both simulated and measured results, which should be highlighted. The front-to-back ratio (F/B) is larger than 15 dB in the experimental result. The radiation gain is about 6.3 dBic for both numerical and experimental results. The designed CP antenna realizes 91.5% antenna efficiency. Good radiation performances, such as good AR property and comparable antenna gain, indicate that the antenna has a potential value in the recent wireless communication system.
In summary, we have proposed a new strategy to design CP antenna by combining a fractal RIS and a fractal slot. For proof of the strategy, a CP antenna by loading HRIS structure and the WCSRR slot is designed, assembled, and measured. The experimental result coincides well with the simulated case. The antenna advances in many aspects such as a compact size (40 mm × 45 mm × 2.5 mm), good AR property (0.75 dB), and comparable radiation gain (6.3 dBic). In addition, the antenna is fabricated based on the PCB technology, free of via holes and without using the complex feeding network.

Ultra-thin polarization beam splitter using TGMS
Meta-surfaces, as a 2D planar inhomogeneous metamaterials, are composed of carefully selected elements with specific EM responses, have attracted much attention recently due to their strong abilities to manipulate the wavefront of transmitted and reflected EM waves. Very recently, scientists and engineers have designed functional devices by using meta-surfaces. One of the most important applications is to realize the polarization beam splitter (PBS). PBS is a typical device to manipulate the differently polarized waves independently, which has been found essential in photonics. Conventional PBSs, achieving by natural crystal birefringence [30] and 2D photonic crystals [31,32], suffer from low efficiencies and limited splitter angle. The PBS performances have been enhanced by using the semiconductor meta-surface [33], photonic-integrated circuits [34], and 2D metamaterials [35][36][37]. However, these devices are electrically large and complex in fabrication. In this subsection, we propose a novel PBS based on the 2D transmissive phase gradient meta-surface (TPGM) [38]. The proposed PBS is designed based on the generalized Snell's laws, which has a low-profile about 0.1 λ 0 , high transmission efficiency, and also convenient wave control.

Polarization-controlled mechanism of local element
According to the geometrical optics, the EM wave would be reflected or refracted when passing through the interface of two media. When the EM wave propagates in a uniform medium, the wave vector can be written as where k xi represents the wave-vector along the x-direction and k 0 is the propagation constant. The generalized laws of reflection and refraction, derived from the Fermat's principle, indicate that the anomalous reflection or refraction phenomenon can be observed at the interface when the phase discontinuity exists [39]. At the same time, the EM response of the GMS is independent when excited with differently polarized waves. Illuminated by a normally incident EM wave along the z-direction with the electric field along the i-direction (x-or y-direction), the wave vector of the transmission can be calculated as where the superscript i denotes the incident polarization E → / / x → or E → / / y → (horizontal and vertical polarizations, E // or E^). ξ x (i) represents that the gradient along the x-direction while the incident polarization is along the i-direction.
For the practical GMS, the phase gradient can be calculated as According to Eq. (7), two points should be highlighted. First, the phase distribution ϕ at the position (x, y) can be controlled by both the geometrical structuring and the polarization of the incident EM wave. Second, the phase gradient ξ is determined by the phase distribution ϕ(x,y) at different directions. The phase distribution ϕ(x,y) and the phase gradient ξ provide a powerful freedom to manipulate the EM wave, simultaneously.
Based on Eq. (7), a transmissive PBS can be realized by controlling the parameters ξ x (x ) and ξ y (y ) independently. In other words, we can manipulate the transmission phase ϕ x (x, y) and ϕ y (x, y) to achieve desirable gradients (dϕ x /dx and dϕ y /dy) along the x-and y-directions, respectively. According to the generalized Snell's law, the refraction angles to horizontal and vertical polarizations can be calculated as To make the principle of the PBS clear, Figure 22 provides the schematics of anomalous refractive phenomena in four different conditions. 2D TPGMs, positioned at the xoy plane with different phase distributions, are shined by hybrid EM waves along the z-direction, respectively. As seen from Figure 22(a), TPGM1 has no phase gradient along the x-and y-directions (dϕ x /dx = dϕ y /dy = 0). Based on the Fermat's principle, the transmitted wave propagates along the z-direction, and the hybrid EM waves cannot be separated. For the TPGM2 with a phase gradient in the x-direction (dϕ x / dx≠0) and consistent phase distribution along the y-direction (dϕ y /dy = 0), the horizontally polarized wave deflected to an angle θ 1 , while the vertical polarization wave propagates along the z-direction. The vertical polarization wave can be deflected to angle θ 2 for the TPGM3 with phase gradient existing only along the y-direction (dϕ x / dx = 0, dϕ y /dy≠0), as shown in Figure 22(c). As expected, hybrid EM waves can be deflected to angles θ 1 and θ 2 when passing through the TPGM4 with phase gradients along the x-and y-directions (dϕ x / dx ≠ 0, dϕ y /dy ≠ 0). Here, θ 1 and θ 2 are determined by Eq. (8). Therefore, we can realize an arbitrary splitting angle by carefully optimizing the phase distributions on TPGM.

High-efficiency transparent principle of the transmissive element
For the first step, we should find a transparent element not only with a high transmission coefficient but also a changeable transmission phase. In general, a complete phase shift range Figure 22. Anomalous refractive effects when 2D TPGMs with different phase distributions are illuminated by the hybrid EM waves [38]. Schematics of the hybrid EM waves passing through (a) the TPGM1 with dϕ x /dx = dϕ y /dy = 0, (b) the TPGM2 with dϕ x /dx ≠ 0 and dϕ y /dy = 0, (c) the TPGM3 with dϕ x /dx = 0 and dϕ y /dy ≠ 0, and (d) the PGM4 with dϕ x /dx ≠ 0 and dϕ y /dy ≠ 0. over 360° is required to guarantee a free wavefront control. Note that EM coupling among the cascaded layers can enlarge the transmission variation range and improve the transmission coefficient [40][41][42][43][44]. Here, three-layer cascaded element is chosen as the basic element, as the topology shown in Figure 23(a). The basic element consists of three identical metallic layers and two intermediate dielectric layers. The commonly F4B substrate is used with a thickness h = 1.5mm, dielectric constant ε r = 2.65, and the loss tangent tanδ = 0.001. We note that although the metallic mesh is not an absolutely necessary element in designing our basic element, its presence can significantly reduce the mutual couplings between adjacent subunit cells, which make our design robust and reliable. The cell has a lattice of Px × Py = 11 mm × 11 mm. We can tune the length d x and d y of the inner patch to manipulate the transmission spectra along the xand y-directions, respectively. We adopt the commercial FDTD solver CST Microwave Studio to obtain the EM property of our element. In simulation, the perfect electric conductor (PEC) boundary conditions are assigned along the x-or y-directions for the horizontally polarized wave or vertically polarized wave, respectively. The absorbing boundary condition is applied along the z-direction, as the simulation setup shown in Figure 23(b).
To obtain the transmission spectra of the basic element, we chose a typical element with d x = d y = 8.28 mm. Illuminated by a horizontally polarized plane wave, the transmission magnitude and phase of the element are presented in Figure 24(a). There exists a relatively wide transparency window between 5.4 and 10.35 GHz, and the transmission phase changes smoothly from -131 to -623° within the transparency window. To realize beam deflection for differently polarized waves, different phase gradients along the x-and y-directions should be satisfied. Here, the phase gradients along the x-and y-directions are arranged as ξ = 0.45 k 0 and ξ = − 0.45 k 0 , respectively, corresponding to 60° phase increment at the x-axis and a 60° phase reduction at the y-axis. By carefully tuning d x and d y , the spectra of the chosen elements are shown in Figure 24(b). The transmission coefficients for each chosen element are higher than 0.8, which guarantees a high efficiency of the elements. The polarization-independent property of the element is essential in determining the working efficiency of the device. We verify the polarization-independent property by scanning the parameter d x from 3 to 8 mm in steps of 1 mm under excitation of different polarizations. As seen from Figure 25(a), the range of about 330° phase variation is obtained as d x changes for the horizontal polarization, while it is about 20° for the vertically polarized transmitted wave. In addition, the transmission amplitude remains better than 0.8 for all cases. We can conclude that the designed element is polarization-independent based on the phase responses to different polarizations with changeable d x . The good performance of the element provides us possibilities to design PBS with high efficiency. More importantly, with an independent control of different polarizations, bifunctional meta-surface can be designed with very high performances, which shown great advantages over the conventional meta-surfaces.

Design and analysis of 2D TGMS
With a well-designed element in hand, we can design the TPGM by carefully chosen the elements satisfying the phases both for horizontal and vertical polarizations. A systematical study on the TPGM can provide a guideline for the upcoming PBS design. We derive a four-   [38]. (a) Transmission amplitude and phase for the element with P x = P y = 11 mm, d x = d y = 8.28 mm; (b) transmission spectra for the elements with 60° phase increment along the x-direction and 60° phase reduction along the y-direction.
step design procedure for the general TPGM. For the first step, a transmissive element with a high transmission coefficient and changeable transmission phase should be obtained. Second, the phase distributions at the position (x, y) should be calculated based on the achieving functionalities. Then, the proper subunit cells should be chosen according to the phase distributions. Finally, the EM response of the TPGM should be evaluated by the EM simulator.
Based on derived design procedure, four kinds of TPGM are designed based on the phase distributions, as shown in Figure 22. Figure 26 provides the electric fields distributions of E // and E^ at the working frequency of 10 GHz under excitation of a hybrid EM waves. As shown in Figure 26(a),a conventional meta-surface (TPGM1) without phase gradient is launched by a horn antenna. The transmitted wave of both E // and E^ propagate along the z-axis, as shown in Figure 26(b) and (c). We can conclude that the TPGM1 is impossible to separate the hybrid polarized waves. As dϕ x /dx = -60° and dϕ y /dy = 0 for the TPGM2, horizontally polarized wave is deflected to the angle with θ 1 = -27°, which coincides well with the theoretical value obtained by Eq. (8). However, vertically polarized wave is not deflected. Similarly, horizontally polarized wave propagates along the z-direction while vertical polarization is deflected to the y-direction with θ 2 = 27.1° for the TPGM3 with the phase distributions dϕ y /dy = 60° and dϕ x /dx = 0. For the TPGM4 shown in Figure 26(j) with phase gradients along the xand y-directions (dϕ y /dy = 60° and dϕ x /dx = -60°), both deflections of θ 1 = -27° and θ 2 = 27° are observed by illuminating with differently polarized waves.

Fabrication and evaluation of PBS
With a well-designed TPGM4, we can further optimize its performance and build a novel PBS by launching the meta-surface by a horn antenna working at the X band. Figure 27 shows the photograph of the fabricated sample. We can see that 24 × 24 unit cells are adopted for the final PBS, which occupies a total volume of 256 × 256 × 3 mm 3 , corresponding to 6.6 λ 0 × 6.6 λ 0 × 0.1 λ 0 . It is worth noting that the thickness of the PBS is much smaller than the reported cases. Moreover, the PBS has no complex structures and is fabricated based on the simple print circuit board (PCB) technology. The PBS consists of 4 × 4 super unit cells, as the top and side views of the super unit cell are shown in Figure 27(a) and (b). Compared with the working mechanism of the previous PBSs, the designed one is intuitionistic and simple. We can control the differently polarized waves independently due to the different phase gradients at x-and y-axis, respectively. More importantly, the polarization-independent property of the designed element guarantees the low coupling of different polarizations, which induces a high polarization splitting ratio.
The impedance matching property of the PBS plays an essential role in determining the working efficiency. We evaluate the reflection coefficients of the PBS by launching with different polarizations. First, we assemble the fabricated sample. We used a 20-mm-thick foam plate to support the TPGM and ensure the length l 1 = 20 mm between the TPGM and the horn antenna. The foam has a permittivity near 1 which will not affect the performances of the PBS system. The reflection coefficients are measured by an ME7808A vector network analyzer, and the polarizations of the horn antenna are controlled by the angle θ. The measurement process is shown in Figure 28(a). To obtain a systematical performance of the PBS system, three cases with horizontal, vertical, and hybrid polarizations are considered and measured. Under illuminating of a horizontal polarization with θ = 0°, Figure 28(b) provides the simulated and measured reflection coefficients as a function of frequency. There is a good agree-  Figure 28(d). The 10-dB impedance bandwidth can be observed clearly as 18.81 and 18.66% for the simulated and measured results, respectively. We can conclude that the designed PBS is insensitive to the polarization of the incident waves, and the PBS has a relatively wide bandwidth.
Then, we examine the 3D far-field patterns of the novel PBS at its working frequency of 10 GHz under excitation of differently polarized waves. Without the TGMS, the horn antenna radiates a narrow beam along the z-direction, which can be demonstrated in Figure 29(a).
Shining the TGMS with an x-polarized incident wave, the transmitted beam is deflected to an angle with θ 1 = -26.7°, which is consistent with the theoretical prediction, as shown in Figure 29(b). One point should be highlighted that the side lobe level has not been deteriorated due to the precise design of the PBS. Shining the TGMS with a y-polarized incident wave, the radiation beam propagates along θ 2 = 27°, which shows good agreement with the theoretical value based on Eq. (8) for a second time. Finally, the hybrid polarizations are used  to excite the PBS. Figure 29(d) shows two separated beams along the x-and y-directions.
Here, two points should be highlighted. First, the two deflected beams have consistent radiation angles with the theoretical values, which demonstrate the reasonable of the PBS design. Second, the radiation dip between the two main lobes is 30 dB lower than that of the radiation peaks, which indicates an excellent polarization splitting performance. To summarize, the well-designed PBC is able to split the orthogonally polarized wave successfully.
Next, we evaluate the 2D radiation patterns of the novel PBS through the far-field measurement system in an anechoic chamber. Here, three excitation polarizations are considered to investigate the far field performances of the designed PBS, as the simulated and measured results shown in Figure 30. The measured results coincide well with the simulation except the radiation pattern in the xoy plane as shown in Figure 30(c). The measured beam radiates along θ 1 = -30°, which is slightly departed from the simulated result with θ 1 = -27°. The difference comes from the inherent errors in measurement. In all simulated cases, the levels of the sidelobe are at least 12 dB lower than that of the mainlobe, while it is better than 10 dB for the measured case. Moreover, the front-to-back ratio is about 16 (13) dB for the simulation (measurement). The cross-polarization levels for all cases remain less than 15 dB. The good performances of the designed PBS provide potential applications in wireless communication systems.
The polarization splitting ratio, defined as the radiation gain between two separated radiation beams, is a very important factor for the PBS. We simulate and measure the radiation patterns at the conical surface θ = -27° to evaluate the polarization splitting ratio. As shown in Figure 31, the dip between two radiation peaks is about 30 (18) dB for the numerical (experimental) result, which can evaluate the beam separation degree clearly. Finally, we measure the working bandwidth of the designed PBS by examining the radiation patterns under different polarizations, as the results shown in Figure 32. We can see obviously that similar   In summary, we propose a new strategy to design the PBS aiming at reducing the structure thickness, realizing good polarization splitting ratio, and also high efficiency. A TPGM is proposed based on a carefully designed element, which realizes a high transmission coefficient of more than 0.8, a wide phase variation range over 330° and also a polarization-independent property. The TPGM achieves good beam separation performances as excited by different polarizations. Launched by a wideband horn antenna with a suitable length, an ultra-thin PBS is designed, fabricated, assembled, and measured. Numerical and experimental results show that the PBS can deflect incident waves with different polarizations to different directions with high polarization splitting ratio.

Conclusions
In this chapter, we have reviewed our recent efforts in utilizing electrically small meta-surface elements to improve antenna performances and design functional devices, among which three most important aspects have been investigated in depth. First, the constitutive material parameters are controlled by the proposed MED-WG-MS elements, achieving a compact microstrip antenna with enhanced bandwidth. Second, fractal meta-surface and fractal resonator are combined to achieve a CP antenna with a low profile. Third, a high-performance PBS has been proposed based on the TGMS, which shows advances in many aspects such as separating and controlling the orthogonally polarized waves with a polarized splitting ratio better than 18 dB, obtaining a comparable bandwidth of more than 600 MHz, and also gaining high transmission efficiency. Our results pave a new avenue for both engineers and scientists to realize their devices or demonstrate their findings.