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 An artificial surface demonstrating angular and polarization dependency to the polarization of the applied field is introduced. This artificial surface consists of a periodic strip grating on a grounded dielectric slab. A method based on Floquet's modal expansion is presented to solve the scattering problem of such surfaces. A code based on method of moments (MoM) is also developed to analyze and design these artificial surfaces. The obtained results using these methods are compared against each other. The extracted reflection parameters are then employed to characterize the surface impedance of the artificial surface for different incident angles and both TE and TM polarizations. This artificial surface is used as the ground plane of cavity resonance antennas. Next, a highly reflective frequency selective surface (FSS) is designed to show high reflectivity at two different frequencies. This FSS is to be used as the superstrate layer of the cavity resonance antenna. The impedance surface of the artificial ground plane and the equivalent admittance of the designed FSS are employed in the transverse equivalent network (TEN) model to obtain radiation properties of such antennas. Finally, compact high-gain dual-band dual-orthogonally polarized antennas are designed based on the aforementioned analyses.
 Periodic conducting strip gratings over a grounded dielectric slab has been subjected to extensive research for past several decades [Chen et al., 1995; Lee and Son, 1999; Kalhor, 1988; Aas, 1991]. Owing to the electromagnetic properties which they possess, such structures are potentially useful in several antenna applications [Kildal et al., 2005]. A schematic of a periodic conducting strip grating on grounded dielectric slab is shown in Figure 1. One example of the application is in low-profile high-gain cavity resonance antennas, which comprise a ground plane and a superstrate layer that produce resonances within the cavity for attaining enhanced antenna gain. Conventionally, the ground plane is perfectly electric conducting (PEC), and the superstrate is composed of a dielectric layer [Jackson and Alexopoulos, 1985; Wu et al., 2006] or frequency selective surfaces (FSSs) [Von Trentini, 1956; Zhao et al., 2005]. More recently, the use of artificial surfaces as the ground plane of these antennas has been investigated [Feresidis et al., 2005]. In spite of this, as existing literature suggests, most of such prior studies simply adopted archetypical artificial surfaces as the ground planes of cavity resonance antennas, and not much effort has been devoted into the study of their effects on the antenna performance, nor into an exploration of alternative forms of such surfaces.
 On the other hand, recently, there has been intensive research devoted to artificial surfaces that cause EM fields to portray unusual behaviors within a finite frequency band [Kildal et al., 2005]. These surfaces typically entail a lattice or periodic arrangement of elemental scatterers, each of which is ordinary by itself (micro-sense), but collectively, the periodic structure possesses extraordinary EM properties as a whole (macro-sense). Periodic strip-loaded dielectric slabs constitute one such group of artificial surfaces. Structures of this kind, being different from the conventional doubly periodic type of FSS, can also be potentially used as the ground planes of cavity resonance antennas. This configuration is one example of alternative ground structure that has not received much attention. Like their FSS counterparts, such strip-type periodic structures are able to exhibit artificial magnetic conductor (AMC) characteristics. However, another significant property which distinguishes them from doubly periodic FSSs is their asymmetry about the two principal planes. When designed for the frequency at which a high impedance (or AMC) surface is attained, the antenna profile can be lowered as compared to the use of a conventional PEC ground. For the same structure, due to its asymmetry about the principal planes (unlike the usual double-periodic FSSs which often comprise symmetric elements), this periodic strip configuration can also display artificial electric conductor (AEC) behavior in a wider frequency band for the other field polarization and principal plane of incidence. Therefore, such strip-type periodic structures are able to exhibit both AMC and a wideband AEC characteristics, depending on the polarization and plane of incidence of the applied electromagnetic field. Subsequently, strip-type artificial surfaces may be operated in two modes: AMC mode, and AEC mode, each pertaining to a certain frequency, polarization, and plane of incidence. This motivates our studies for the possibility of using such strip-type grounded cavity resonance antennas for achieving dual-band dual orthogonally polarized capabilities. By designing the FSS superstrate to possess high reflectivity at both the AMC and AEC frequencies, the gain of the cavity resonance antenna can be enhanced for both modes of operation [Von Trentini, 1956]. Hence, with all these attributes collected together, a high-gain compact dual-band dual orthogonally polarized antenna can be achieved.
 In a bid towards obtaining these above-mentioned antenna capabilities, it is the objective of the present work to explore the prospects of using periodic conducting strip-gratings over grounded substrates as the ground planes of cavity resonance antennas. Concentric square rings are adopted here as the free-standing superstrate FSS elements. The strip-loaded ground structure will be designed for the two aforementioned operation modes, one at the AMC frequency, and the other at the AEC frequency, with the lowering of the antenna profile being established for the former. In addition, the dual-band dual orthogonally polarized functionality shall be demonstrated. Gain enhancement via tailoring of the superstrate FSS parameters will also be performed.
 This work also serves to highlight a vital aspect that might have been often neglected. It is known that the EM properties of idealized perfect electric conducting (PEC) and perfect magnetic conducting (PMC) surfaces remain unchanged regardless of frequency, polarization, and angle of incidence. However, for periodic strip-grated substrates, as are for all artificial surfaces, the EM characteristics depend not only on the frequency, polarization, and plane of incidence as described above, but also on the angle of incidence of the applied plane wave. Most previous works have only characterized artificial surfaces by their behavior at broadside incidence [Feresidis et al., 2005], and a few that considered the angular dependence of these structures have not studied it in details. For example, the reflection coefficient phases versus incidence angles have not been reported in [Aas, 1991]. The present work, on the other hand, has rigorously studied how the properties of both the strip-loaded ground plane and the FSS superstrate vary with different incidence angles. As such polarization and angular dependencies on the applied field will certainly affect the overall antenna performance, it is thus imperative to take this factor into consideration when characterizing the cavity resonance antenna. This important issue, which was proposed in [Foroozesh and Shafai, 2007] is addressed here in-depth. In fact, it will be shown later that these angular and polarization dependencies of artificial grounds, absent in perfectly conducting surfaces actually turn out to be beneficial, providing gain enhancement over those corresponding antennas that utilize conventional PEC ground planes. This finding marks a key value of the work, and it is believed that such a complete approach of investigation has not been widely performed elsewhere.
 A brief overview of the entire study approach adopted here is given. First, the physical intuitive concept of how the strip gratings backed by a grounded dielectric slab can act as AMC and AEC depending on the polarization of the applied field is provided. Next, this concept is verified by a full-wave analysis. A method based on Floquet's modal expansion is presented to solve the scattering problem of the structure. A code based on the method of moment (MoM) is also developed to analyze and design these artificial surfaces. The obtained results using these methods are compared with each other for validation and control purposes. The extracted reflection parameters are then employed to characterize the surface impedance of the artificial surface for different incident angles and both TE and TM polarizations. This artificial surface shall then serve as the ground plane of the cavity resonance antenna. Next, highly reflective FSS is designed to show high reflectivity at two different frequencies. This FSS is to be used as the superstrate layer of the antenna. The impedance surface of the artificial ground plane and the equivalent admittance of the designed FSS are then used in the transverse equivalent network (TEN) model to obtain the far-field radiation properties of such antennas. It is shown that using such a ground plane, a cavity resonance antenna can be designed to be highly directive, low profile, and operative at two different frequencies, each with a polarization that is orthogonal to the other.
2. AMC and AEC Concept
Figure 2a shows a unit cell of such a periodic structure when the electric component of the applied field is perpendicular to the strips. Its transmission line analogy of the resonance condition is shown in Figure 2b. In this case, any pair of adjacent strips introduces a capacitance [Marcuvitz, 1951]. When kh ≪ 1, which is usually the case in practice due to the thin dielectric substrate, the grounded dielectric slab can be modeled as an inductance. At the resonant frequency, XC = XL and therefore ZL → ∞. Thus, the reflection coefficient due to the normal incident field is +1, and eventually, an AMC is realized. In the vicinity of the resonant frequency, a high impedance surface (HIS) is produced. Figure 3a shows a unit cell of a periodic conducting strip grating on grounded dielectric slab, when the electric field is parallel to the strips. Its transmission line analogy is shown in Figure 3b. In this case, the infinitely long strip is equivalent to an inductance [Munk, 2000]. As before, when kh ≪ 1, the grounded dielectric slab can be modeled as an inductance, too. Therefore, two inductances in parallel constitute another equivalent inductance with a value lower than any of the first two. Since, kh ≪ 1, the equivalent inductance produces a value less than X (Figure 3b) which eventually results in a very small XL. Therefore, a low impedance surface is realized. The reflection coefficient in this case is very close to −1. Thus, the periodic structure acts as an AEC. The above-mentioned concept is verified using two different analysis methods, namely modal expansions and method of moments in the next section.
3. Full-Wave Analysis
 In this section, two analysis methods are presented to analyze the scattering problem of the periodic structure shown in Figure 1. The first method is based on plane wave Floquet's modal expansion of the fields, both inside the dielectric and in the air region. Upon satisfying boundary conditions, a set of equations and unknowns is produced. Solving this set of equations gives the reflection coefficient of the structure, which is in our interest. The second method, however, deals with solving an integral equation and basically is a periodic moment method (PMM) [Mittra et al., 1988; Ng Mou Kehn et al., 2006]. In both methods, entire domain basis functions are used for the current expansions on the conducting strips. In order for the structure to be studied in a broader sense, two different decompositions with respect to y and z directions are intentionally considered. It is known that any two components of (Ax, Ay, Az, Fx, Fy, Fz) can completely define a field in any space [Das and Pozar, 1987], where A and F are magnetic and electric vector potentials, respectively. In the following part, for the modal analysis, the conventional TE and TM decomposition with respect to y are performed to present conventional TEy (H-polarized) and TMy (E-polarized) cases. On the other hand, field decompositions of the magnetic and electric vector potentials with respect to z, are employed to obtain pertinent spectral-domain Green's functions [Das and Pozar, 1987], to be used in the PMM analysis. The obtained results of both modal analysis method and PMM are then compared to confirm their correctness as well as the validation of the numerical techniques. The agreement of the results can also imply that the decomposition of the fields with respect to any arbitrary cartesian direction is only a choice of preference and generality will not be lost.
3.1. Modal Expansion
 Two canonical field decompositions of scattering analysis of the periodic structure shown in Figures 1b and 1c are TEy (H-polarized) and TMy (E-polarized) cases. This problem has been tackled in [Kalhor, 1988] using modal expansion analysis and satisfying boundary conditions on the periodic conducting strips using point matching method. The same numerical method has been used in [Aas, 1991] to study the reflection phase of these types of periodic structures, except that the field decomposition of TEz and TMz have been employed. An analytical method has been proposed in [Chen et al., 1995], which holds for the low frequency cases under the condition that the periodicity is much smaller than the operating wavelength. A more accurate and general method has been proposed in [Lee and Son, 1999] where the modal analysis has been used in a general case with entire domain basis function expansions on either periodic strips or slots. For the H-polarized case, the same technique as was presented in [Lee and Son, 1999] is used to obtain corresponding results in this paper. However, for the TMy (E-polarized) case, entire domain basis functions are used to expand electric surface currents on the periodic strips in the y direction in contrast to the magnetic surface current on the slots in the x direction used in [Lee and Son, 1999]. The same basis functions have been successfully used in [Uchida et al., 1987] to expand electric surface currents on the free-standing periodic grating strip structure. The E-polarized scattering analysis which is different from [Lee and Son, 1999] is explained in details as follows.
 Consider the periodic structure shown in Figure 1. Only the tangential field components that are necessary for the modal expansion of the E-polarized case are employed, as follows. In the air region (z ≥ 0), one can write:
In the dielectric region with relative permittivity of ɛr (0 > z ≥ − h), satisfying the appropriate boundary condition at z = −h, which is vanishing the tangential component of the electric fields on the PEC ground plane surface, results in:
where kxn = k0sin(θi)cos(ϕi) + , kzn = , k1zn = , k0 = ω, k1 = k0, and ɛ1 = ɛrɛ0. Here, Rn and Pn are unknown complex amplitudes to be determined and the remaining parameters are defined as before. In order to determine these unknowns, the appropriate boundary conditions are imposed at z = 0 as follows:
where Jy(x,y) is the unknown surface current on the conducting strips and can be expanded into a product of series of cosine functions and a function satisfying the edge condition [Butler, 1985]. For the zeroth strip, this surface current is:
where ωv = vπ/2w. After satisfying boundary conditions and Fourier transforming from the spatial domain into the spectral domain, a set of linear equations are obtained as,
δ(n) denotes Kronecker delta, and η0(=ωμ/k0) is the characteristics impedance of the free space. J0(.) denotes Bessel function of the zeroth order. Employing equations (9) and (10) gives a relationship between Rn values in terms of the incident wave and coefficients Av values as follows
where bn = kzn + k1znjcot(k1znh), and Tn = −kzn + k1znjcot(k1znh). Substituting (11) in (13) results in
In order to determine Av values, equation (14) has to be used for ζ = 0,1, …, M − 1 to produce a complete set of M equations and M unknowns. Once Av values are determined, the reflection coefficient of the specular incidence (R0) can be found.
3.2. Periodic Moment Method
 The method of moments (MoM) analysis of electromagnetic scattering by a periodic strip grating on a grounded dielectric slab is concisely presented here. The procedure is similar to the one addressed in [Ng Mou Kehn et al., 2006]. However, different entire domain basis functions are employed in this work and the constraints due to the periodicity in the y direction are lifted.
3.2.1. Current Expansion on the Conducting Strips
 In general, for an arbitrary incidence, the induced current on the periodic conducting strips, shown in Figure 1, can be expressed as
The y-directed electric surface current density is defined in equation (8). The x-directed electric surface current is expanded as
For the periodic structures, it is more convenient to work in the spectral domain [Mittra et al., 1988]. Fourier transform of the vth term in equation (8) for the mth component of the wavenumber kxm has been presented in equation (12). Fourier transform of the vth term in equation (16) for the mth component of the wavenumber kxm is
where J1(.) denotes Bessel function of the first order.
3.2.2. Scattered Field Calculation
 The total electric field in the spectral domain is expressed as the sum of the incident excitations and scattered fields from the induced surface current on the periodic conducting strips both in the presence of the grounded dielectric structure, as
The scattered field in the x and y direction are calculated as
where 2N + 1 is the number of the Floquet's modes and , , and are spectral domain Green's functions and are calculated numerically using G1DMULT procedure described in [Sipus et al., 1998; Ng Mou Kehn et al., 2006]. The incident field is expressed as
3.2.3. Boundary Conditions and Impedance Matrix Construction
 The total electric field on the conducting periodic structure is zero. Using this boundary condition along with the Galerkin weighting functions, an integral equation is constructed to be solved. The solution to that integral equation are the coefficients of the expanded electric surface currents on the periodic conducting strips. The resulting equation in matrix form is
where the constructive elements of [Z] are
 [I] is the column vector containing the unknown coefficients of the current distribution and basically is [[Bv]T, [Av]T]T, where B and A are the surface current coefficients corresponding to Jx and Jy, as shown in equations (16) and (8), respectively, and T denotes matrix transpose. [V] = [[Vx]T, [Vy]T]T is the known column vector due to the excitations and evaluated as
where fx,ζ (x) and fy,ζ (x) are the ζth term of the current expressions in equations (16) and (8), respectively, and * denotes the complex conjugate of the corresponding quantity. Once the current coefficient matrix is found, the reflection coefficient can be obtained using equations (19) and (20).
3.3. Comparison and Verification
 In order to verify the aforementioned numerical methods, an analysis on the convergence of these methods with respect to the numbers of Floquet's modes and basis functions is performed. Figures 4 and 5show the reflection coefficient phase of the periodic structure depicted in Figure 1, based on modal expansion and MoM techniques, respectively. The total number of basis functions and Floquet's modes are M and 2N + 1, respectively. Dimensions of the periodic structure are h = 1.59 mm, 2w = 5 mm and p = 10 mm. The relative permittivity of the dielectric substrate is 2.5. As can be seen in the H-polarized case, the resonant frequencies are obtained as 13.5 and 13.8 GHz, using modal expansions and MoM techniques, respectively. The frequency shift is less than 2.5%. In this configuration, the artificial surface acts as an AMC. In the E-polarized case, the reflection coefficient phase is obtained around 167° at 13.5 and 13.8 GHz using modal expansion and MoM techniques, respectively. This frequency shift can be attributed to the different analysis methods used here. This difference can also be seen when commercial software packages are used. As an example, one can see a comparison between the results of the reflection phase of a periodic structure when three different software packages are employed [Foroozesh and Shafai, 2005]. It can be clearly observed that for the E-polarized case, the agreement is even better. In this configuration the reflection coefficient is close to that of PEC surface (180°) and it thus acts as an AEC. One should note that at ϕ = 0°, the field decompositions of TEy and TMy are equivalent to TMz and TEz, respectively. Therefore, in this study, the results obtained by modal expansion method using decomposition with respect to y direction are compared to those obtained by the MoM decomposed with respect to the z direction. In addition, as can be observed, when this surface acts as an AEC, it demonstrates a larger bandwidth than when it acts as an AMC surface.
4. Application in Cavity Resonance Antenna
 Cavity resonant antennas consisting of highly reflective FSS superstrates are known to be high-gain [Von Trentini, 1956]. When the excitation source is an electric Hertzian dipole, the far-field properties of these antennas can be computed using the transverse equivalent network (TEN) model [Zhao et al., 2005]. The profile of such an antenna when its ground plane is an artificial surface is shown in Figure 6a. A horizontal electric Hertzian dipole is embedded in an air-gap layer, over a ground plane at a distance d, and covered by an FSS superstrate layer. It is assumed that the ground plane structure, air gap layer and FSS cover are infinite in the transverse direction. Using the TEN model, this antenna is simplified to the source and its free space impedance characteristics accounting for the far-field incident wave, a susceptance representing the FSS superstrate, a transmission line section modeling the air-gap spacer and a reactance load termination accounting for the artificial ground plane as shown in Figure 6b. In this model, the electric Hertzian dipole is considered as a probe, which receives the electric field signal caused by the plane wave incident from the far field. Having this approach, the applied electric field on this probe is proportional to the voltage Vd, which is the voltage at the distance d from the load impedance. This Vd can be found using two sets of linear equations as follows [Wu et al., 2006],
where A, B, C and D are the elements of the ABCD matrix of the entire cascaded transmission line circuit and A′, B′, C′ and D′ are the elements of the ABCD matrix of the portion below the Hertzian dipole shown in Figure 6b. I(s) and I0 are the currents flowing through the source and the load, respectively. Other quantities, shown in Figure 6b, are defined as
ɛr and μr are the relative permeability and permittivity of the air-gap spacer, respectively, and assumed to be unity in this work. Assuming that the horizontal electric Hertzian dipole is placed at the origin and in the direction as
the corresponding far-field electric components are calculated as
This formula gives a good approximation of the directivity as long as the reflection phases of the surfaces do not show abrupt variation at close-to-normal incident angles for different azimuth angles (ϕ). Also, the coupling between two periodic layers in the substrate and the superstrate must be negligible. In other words, they are placed with enough distance from each other.
 The salient feature of the TEN model is its ability to deal with aperiodic sources (in this work an electric Hertzian dipole) in the presence of an infinite periodic structure. This can be done by looking at the periodic structure as an integrated surface represented by its impedance surface. This impedance surface can be in general dyadic, as it was assumed angular- and polarization-dependent in this work. By employing the TEN model, better light is shed onto the phenomenology of the cavity resonance antenna with artificial surface ground planes and FSS superstrate, where both admittance YB and impedance ZL, accounting for the FSS superstrate and artificial ground plane, respectively, are angular and polarization dependent. This physical insight is missing and not as rigorous when commercial software packages based on numerical methods are used. Moreover, in full-wave analysis both periodic structures employed in the superstrate and the ground plane have to be truncated resulting in large but finite arrays. Computer time and memory is a burden to solve such structures. Yet, TEN model is an excellent reliable CAD-tool to estimate the antenna far-field properties [Zhao et al., 2005; Wu et al., 2006].
4.1. Artificial Ground Plane Design
 The dual-mode artificial surface introduced earlier in this paper, consisting of periodic conducting strips on a grounded dielectric slab, is employed as the ground plane of the antenna shown in Figure 6. A periodic structure with dimensions of h = 1.59 mm, 2w = 5.54 mm and p = 6 mm, is considered. The relative permittivity of the dielectric substrate is 2.5. The top view of the configuration of excitations is shown in Figure 6c. In fact, two orthogonal electric Hertzian dipoles are employed at two different frequencies to excite the cavity resonance antenna. Corresponding reflection coefficient phases versus incident angle are plotted in Figures 7a and 7b for the frequencies 9.50 and 19.0 GHz, respectively. As can be seen, this artificial surface can act as an AMC at 9.5 GHz and as an AEC at 19.0 GHz.
4.2. Dual-Band Highly Reflective FSS Design
 As mentioned earlier, in order to achieve high directivity in cavity resonance antennas, the superstrate has to be highly reflective [Von Trentini, 1956]. The unit cell of two dual-band FSSs consisting of two concentric free-standing conducting rings is shown in Figure 8a. As can be observed from the reflection amplitude variation with frequency in Figure 8b, FSS1 is designed to demonstrate the highest reflectivity at 9.5 and 19.0 GHz. However, FSS2 is slightly detuned so that the highest reflectivities are no longer at 9.5 and 19.0 GHz. Yet, the reflectivity is still quite high at these frequencies (≃0.95). The purpose of considering this latter FSS design is to compare it with the former well-tuned design and then seek insights into the significance of attaining the condition of maximum reflectivity. One should note that 9.5 GHz and 19.0 GHz frequencies are the ones introduced in the previous sections at which the artificial ground plane acts as an AMC and AEC, respectively. The graphs of reflection coefficient amplitude versus incident angle for these FSS1 and FSS2 are shown in Figures 8c and 8d. As can be seen, reflection coefficients are highly angular-dependent and tend to approach zero at grazing angles for TM polarization. The theory and numerical procedure of solving such FSSs are based on periodic moment methods and has been presented in [Mittra et al., 1988].
4.3. Results on Far-Field Properties
 The cavity resonance antenna shown in Figure 6 is considered when either FSS1 or FSS2 (Figure 8) is employed as the superstrate and the previously characterized artificial surface is used as the ground plane. The directivities of the antennas versus the air-gap height of each configuration are shown in Figure 9, and compared against the cases where the ground plane is ideal PEC or PMC surfaces. The TEN model is employed to analyze their far-field properties.
 The graphs of antenna directivity versus the air-gap length of the cavity resonator are shown in Figures 9a and 9b, when FSS1 and FSS2 are used as the superstrate, respectively.
 As seen from Figure 9a, the FSS1 superstrate which was designed to achieve the highest reflectivity at 9.5 GHz and 19.0 GHz (as shown in Figure 8b) demonstrates maximum directivities at these two frequencies. This is what we have designed for, and the theory of [Von Trentini, 1956] is thus reasserted. However, for the FSS2, which is slightly detuned so that it becomes slightly less reflective than the previous case at the two resonant frequencies (Figure 8b), although maximum directivities at both frequencies are also obtained, as seen in Figure 9b, these maxima are lower than those of FSS1. The resonance directivities and their corresponding air-gap heights as well as the half-power beam widths in both E- and H-planes are listed in Tables 1 and 2, for the antennas using FSS1 and FSS2 superstrate, respectively. A comparison between these results reveals that the one using FSS1 superstrate gives more directivity. This is consistent with the theory presented in [Von Trentini, 1956] and [Zhao et al., 2005], which states that the higher reflective superstrate provides higher directivity. On the other hand, the resonance directivity is less sensitive to the air-gap height when the reflectivity of the FSS superstrate is less. In another interpretation, the directivity bandwidth of the cavity resonance antenna with lower-reflective FSS is wider, although its peak directivity is lower. Normalized radiation patterns of the aforementioned antennas are shown in Figure 10.
Table 1. Resonance Air-Gap Lengths and Their Corresponding Maximum Directivities of the Cavity Resonance Antennas With Different Ground Plane Types and FSS1 Superstrate Shown in Figure 8a
 Another interesting feature of using AMC surfaces instead of conventional PEC ones as the ground plane in cavity resonance antenna is reducing the air-gap height by half (almost λ/4 instead of λ/2) which results in a compact antenna design. This phenomenon has been proposed and studied in [Feresidis et al., 2005]. However, in this work, one can see that the angular dependence of the AMC has a beneficial impact on directivity enhancement (Figure 10b and Table 2), over ideal PMC ground plane. The reflection coefficient of an AMC is 0° at the normal incidence and may be different for other incident angles, whereas that of the PMC is 0° for all incident angles. In fact, according to the physical description of the phenomenon based on ray tracing by [Von Trentini, 1956; Feresidis et al., 2005], the directivity is highly dependent on the reflection phase of the FSS superstrate as well as the ground plane. However, the angular and polarization dependence has not been considered in their analyses. The key point in this work is that the angular and polarization dependencies of the reflection phases are very important in achieving and controlling the high directivity. Whereas, the resonant length is mainly determined by the reflection phases of the FSS superstrate and the ground plane at normal incidence (Figure 9b and Table 2).
 The concept of an artificial surface that acts as an AMC for one polarization and as an AEC for the other orthogonal polarization has been presented. This artificial surface plane consists of periodic conducting strip grating on a grounded dielectric slab. The phenomena were verified through rigorous full-wave analyses based on modal expansions and MoM, which have been developed. As a practical application, this artificial surface was then used as the ground plane of cavity resonance antennas. It was shown that highly directive compact antennas can be designed for dual orthogonally polarized dual-band excitations. The importance and beneficial features of the angular and polarization dependence of the artificial surface were described and highlighted through studying the practical application.