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Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome

Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome applied sciences Article Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome 1 , † 2 , † 2 3 4 Jihyung Kim , Sangsu Lee , Hokeun Shin , Kyung-Young Jung , Hosung Choo 2 , and Yong Bae Park * Hanwha Systems, Yongin 17121, Korea; jihyung.kim@hanwha.com Department of Electrical and Computer Engineering, Ajou University, Suwon 16499, Korea; lss1507@ajou.ac.kr (S.L.); hokeun0305@ajou.ac.kr (H.S.) Department of Electronic Engineering, Hanyang University, Seoul 04763, Korea; kyjung3@hanyang.ac.kr School of Electronic and Electrical Engineering, Hongik University, Seoul 04066, Korea; hschoo@hongik.ac.kr * Correspondence: yong@ajou.ac.kr; Tel.: +82-31-219-2358 † Equally contributed first authors. Received: 29 October 2018; Accepted: 19 November 2018; Published: 22 November 2018 Abstract: Radiation from a cavity-backed circular aperture array antenna enclosed by a frequency selective surface (FSS) radome is studied using the hybrid analysis method, by combining the mode matching method, the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface currents on the apertures are derived from the aperture electromagnetic fields, which are calculated based on the mode matching method. The rays are generated from the equivalent magnetic surface currents and used to analyze the FSS radome based on the ray tracing technique. After being obtained from both the mode matching method and the ray tracing technique, electromagnetic fields on an outermost radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s principle. The radiated fields are computed from the equivalent surface currents and compared with the measured data. Keywords: frequency selective surface radome; cavity-backed circular aperture array antenna; mode matching method; ray tracing technique 1. Introduction A radome, a portmanteau of radar and dome, is a structural and weatherproof enclosure, and thus it is used to protect microwave antennas. The radome usually comprises dielectric layers that minimally affect electromagnetic signals to be transmitted or received by the antenna. Due to the effects of the radome on the electromagnetic signals, a thorough analysis of the radome is needed. To understand electromagnetic properties of the radomes, there have been extensive studies on various radome configurations [1–10]. The radiation from a circular aperture surrounded by a hemisphere radome was predicted based on the dyadic Green’s function technique and physical optics (PO) method [2]. The Von Karman radome, one of the renowned radome structures, has been analyzed using the method of moments (MoM) [3], the coupled surface integral equation [4], and the aperture integration-surface integration (AI-SI) [5]. Furthermore, the radiation characteristic of hemisphere, tangent-ogive, and cone-shaped radomes with multiple sources has been investigated based on the multilevel fast multipole algorithm (MLFMA) [6]. The iterative physical optics-boundary integral-finite element method (IPO-BI-FEM) was used to analyze the sandwich tangent-ogive radome [7]. These studies focused on the radome consisting of dielectrics; however, the dielectric radome is generally responsible for the increase in radar cross section (RCS) of aircraft due to its broadband transmission characteristic. Instead, a frequency selective surface (FSS) radome, which Appl. Sci. 2018, 8, 2346; doi:10.3390/app8122346 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 2346 2 of 9 is a curved FSS within a multi-layer radome, is employed to reduce RCS over a wide frequency range because it exhibits bandpass or bandstop characteristics. Previous studies have investigated electromagnetic characteristics of single- and multi-layer FSS radomes based on the pole residue matching (PRM) [8] and the ray tracing technique [9,10]. The FSS are one kind of the metasurfaces showing a bandpass or a bandstop characteristic. These characteristics are not found in natural materials. Metasurfaces, metamaterials, graphene, and plasmonics are gaining increasing popularity among researchers due to their ability to adjust permittivity or permeability purposely and manipulate electromagnetic waves passing through the materials. Due to numerous potential applications, a variety of studies have been conducted for sensing technology, plasmonics, graphene, and photonics [11–16]. There have also been studies on analyzing the properties of metamaterials and metasurfaces [17,18]. However, the investigation of electromagnetic properties for the complex structures which consist of a radome with the metasurfaces such as FSS and an aperture array antenna has not been presented. This is because it is hard to use the full-wave methods to analyze them, for a given memory usage and time, when an object is electrically large in size and complicated. Therefore, hybrid techniques combining the full-wave methods (such as MoM, FEM, finite-difference time-domain (FDTD), and the mode matching method) and the asymptotic methods (such as the ray tracing technique and geometric optics (GO)) are required, but related studies on radiation properties from array antennas enclosed by an FSS radome seem to be lacking. Therefore, it is of great significance to investigate electromagnetic properties of the aperture array antennas with the FSS radome using a hybrid technique combining the mode matching method for modeling aperture fields and the ray tracing technique for analyzing the radome. In this paper, we analyze the radiation from a cavity-backed circular aperture array antenna enclosed by an FSS radome using the hybrid analysis method combining the mode matching method, the ray tracing technique, and Huygens’s principle. Towards this purpose, in particular, three different ways are carried out step by step. Firstly, electromagnetic characteristics of the cavity-backed circular aperture array antenna is predicted based on the mode matching method [19]. The obtained tangential electric fields are transformed into the equivalent magnetic current sources which in turn become rays to be used in the subsequent step. While using the rays, the ray tracing technique is employed to analyze the multi-layer FSS radome [10], and reflection and transmission properties of the FSS layer come from FEM simulations on HFSS. After obtained from the mode matching method and the ray tracing technique, electromagnetic fields on the outermost radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s principle, and radiation fields in the far-field region are computed from the equivalent surface currents. In brief, we take an advantage of the hybrid analysis method combining the mode matching method, the ray tracing technique, and HFSS, a commercial EM simulator, based on FEM for an analysis of the aperture array antenna enclosed by the FSS radome. To verify our formulation, the FSS radome enclosing the cavity-backed circular aperture array antenna is fabricated and our computation results are compared with the measured data. 2. Field Analysis Figure 1 shows the problem geometry. Assume that the z-oriented electric point source is located in a circular cavity with multiple circular apertures in a conducting plane. e and d are dielectric n n constant and loss tangent of each layer (n = 1, 2, 3, 4, 5). Electromagnetic properties and size of each layer are shown in Table 1. Appl. Sci. 2018, 8, 2346 3 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 9 Figure 1. Problem geometry. Figure 1. Problem geometry. Table 1. Design parameters of the frequency selective surface (FSS) radome. Table 1. Design parameters of the frequency selective surface (FSS) radome. Parameters Value Parameters Value Parameters Value Parameters Value D 284.8 mm L 290.5 mm 1 D1 284.8 mm L11 290.5 mm D 286.4 mm L 291.5 mm 2 2 D2 286.4 mm L2 291.5 mm D 292.3 mm L 295.2 mm 3 3 D3 292.3 mm L3 295.2 mm D 292.4 mm L 295.3 mm 4 4 D4 292.4 mm L4 295.3 mm D 298.4 mm L 299.1 mm 5 5 D 300 mm L 300 mm D5 298.4 mm L5 299.1 mm 6 6 e 4.35 d 0.0032 r1 1 D6 300 mm L6 300 mm e 1 d 0.0038 r2 2 ϵr1 4.35 δ1 0.0032 e 4.4 d 0.02 r3 3 ϵr2 1 δ2 0.0038 e 1 d 0.0038 r4 4 e ϵr3 4. 4.354 δd 3 0.02 0.0032 r5 5 ϵr4 1 δ4 0.0038 ϵr5 4.35 δ5 0.0032 Figure 2 shows an entire analysis procedure for the radiation from a cavity-backed circular aperture array antenna with the FSS radome based on the hybrid analysis method combining the Figure 2 shows an entire analysis procedure for the radiation from a cavity-backed circular mode matching method, the ray tracing technique, and HFSS, a commercial EM simulator, based aperture array antenna with the FSS radome based on the hybrid analysis method combining the on FEM. Firstly, for analysis of the antenna, we solved the electromagnetic boundary-value problem mode matching method, the ray tracing technique, and HFSS, a commercial EM simulator, based on of the circular cavity with the circular aperture array antenna based on the mode matching method FEM. Firstly, for analysis of the antenna, we solved the electromagnetic boundary-value problem of in our previous study [19]. The mode matching method provides an advantage in the fact that the circular cavity with the circular aperture array antenna based on the mode matching method in its solution is rigorous and theoretically robust. Moreover, it is time-efficient in an analysis of our previous study [19]. The mode matching method provides an advantage in the fact that its open-boundary problems compared to other numerical techniques such as FEM, FDTD, and MoM, solution is rigorous and theoretically robust. Moreover, it is time-efficient in an analysis of to name a few. An analysis using the mode matching method takes the following steps. Above all, open-boundary problems compared to other numerical techniques such as FEM, FDTD, and MoM, the whole region to be solved is divided into sub-regions on a basis of boundary. Electromagnetic to name a few. An analysis using the mode matching method takes the following steps. Above all, fields are defined in each region. Afterwards, boundary conditions are enforced to obtain a set the whole region to be solved is divided into sub-regions on a basis of boundary. Electromagnetic of simultaneous equations for modal coefficients. Matrix calculation enables an evaluation of the fields are defined in each region. Afterwards, boundary conditions are enforced to obtain a set of modal coefficients and electromagnetic fields in all regions can be calculated based on the obtained simultaneous equations for modal coefficients. Matrix calculation enables an evaluation of the modal coefficients. Note that the mode matching method should be used in the separable coordinate modal coefficients and electromagnetic fields in all regions can be calculated based on the obtained systems where eigen-modes can be defined in all regions. By using the tangential electromagnetic modal coefficients. Note that the mode matching method should be used in the separable coordinate field established from the mode matching method and the surface equivalence theorem [20], we can systems where eigen-modes can be defined in all regions. By using the tangential electromagnetic derive the equivalent magnetic surface currents on the apertures from the aperture fields, which will field established from the mode matching method and the surface equivalence theorem [20], we can be used in a formation of rays. Meanwhile, the FSS layer is a cross-loop dipole FSS which has a derive the equivalent magnetic surface currents on the apertures from the aperture fields, which will passband resonant frequency at 10 GHz. A detailed configuration and size of the designed FSS can be used in a formation of rays. Meanwhile, the FSS layer is a cross-loop dipole FSS which has a be found in the reference [10]. Reflection and transmission coefficients of the designed FSS layer are passband resonant frequency at 10 GHz. A detailed configuration and size of the designed FSS can obtained via numerous simulations using HFSS, an electromagnetic full-wave simulator. Reflection and be found in the reference [10]. Reflection and transmission coefficients of the designed FSS layer are transmission coefficients between dielectric layers, not involved with FSS layer, can be determined on obtained via numerous simulations using HFSS, an electromagnetic full-wave simulator. Reflection a polarization basis, as described in the reference [10]. Afterwards, to apply the ray tracing technique and transmission coefficients between dielectric layers, not involved with FSS layer, can be for the analysis of the radiation from the cavity-backed circular aperture antenna enclosed by the FSS determined on a polarization basis, as described in the reference [10]. Afterwards, to apply the ray tracing technique for the analysis of the radiation from the cavity-backed circular aperture antenna Appl. Sci. 2018, 8, 2346 4 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 9 enclosed by the FSS radome, we determined intercept points of the rays and the surfaces of the FSS radome, we determined intercept points of the rays and the surfaces of the FSS radome using the radome using the iterative method [1]. Then, we can generate the rays from the equivalent magnetic iterative method [1]. Then, we can generate the rays from the equivalent magnetic surface currents surface currents on the apertures and trace the rays passing through the radome. When analyzing on the apertures and trace the rays passing through the radome. When analyzing the multi-layer FSS the multi-layer FSS radome, we used the ray tracing technique and the reflection and transmission radome, we used the ray tracing technique and the reflection and transmission coefficients at the FSS coefficients at the FSS layer from the simulation of HFSS based on FEM [21]. Therefore, our hybrid layer from the simulation of HFSS based on FEM [21]. Therefore, our hybrid method provides a more method provides a more time-efficient method for analyzing the aperture array antenna enclosed by time-efficient method for analyzing the aperture array antenna enclosed by the multi-layer FSS radome the multi-layer FSS radome than the method using the full-wave analysis only. On the other hand, it than the method using the full-wave analysis only. On the other hand, it is noted that locally flat is noted that locally flat condition should be satisfied for the accuracy of the ray tracing technique. condition should be satisfied for the accuracy of the ray tracing technique. Since our radome structure Since our radome structure has smooth surfaces, the ray tracing technique can be employed. Rough has smooth surfaces, the ray tracing technique can be employed. Rough surfaces, ripples, and defects surfaces, ripples, and defects on the surface may decrease the accuracy. Additionally, the ray tracing on the surface may decrease the accuracy. Additionally, the ray tracing technique is applicable to the technique is applicable to the region where the far-field condition is satisfied. In our analysis, each region where the far-field condition is satisfied. In our analysis, each aperture is divided into hundreds aperture is divided into hundreds of small cells to apply the ray tracing technique. Then, we of small cells to apply the ray tracing technique. Then, we calculated the radiation field from each calculated the radiation field from each small cell, respectively, and summed up all the computed small cell, respectively, and summed up all the computed fields based on the superposition principle. fields based on the superposition principle. In this case, the far-field condition of each aperture is In this case, the far-field condition of each aperture is given by 2D / = 0.0267 m. Our ray tracing given by 2D /λ = 0.0267 m. Our ray tracing technique satisfies the far-field condition because the technique satisfies the far-field condition because the distance from the aperture center to the radome distance from the aperture center to the radome inner surface is larger than 0.142 m (4.75 λ). Lastly, inner surface is larger than 0.142 m (4.75 ). Lastly, we calculated the electromagnetic fields and the we calculated the electromagnetic fields and the equivalent electric and magnetic surface currents equivalent electric and magnetic surface currents over the radome’s outer surface via using the results over the radome’s outer surface via using the results from the ray tracing technique. Then, the from the ray tracing technique. Then, the equivalent currents on the radome’s outer surface can be equivalent currents on the radome’s outer surface can be used to calculate the radiation fields in the used to calculate the radiation fields in the far-field region. far-field region. Figure 2. Analysis procedure. Figure 2. Analysis procedure. 3. Numerical Results and Measurement 3. Numerical Results and Measurement Before proceeding with the analysis of radiation pattern of the 3  3 circular aperture array Before proceeding with the analysis of radiation pattern of the 3 × 3 circular aperture array antenna enclosed by the multi-layer FSS radome as shown in Figure 3, it is important to check the antenna enclosed by the multi-layer FSS radome as shown in Figure 3, it is important to check the accuracy of our mode matching formulation and to analyze the antenna properties in detail. Firstly, accuracy of our mode matching formulation and to analyze the antenna properties in detail. Firstly, the number of modes used is m = 19 ( direction) and n = 10 (z direction). In order to ensure the number of modes used is m= 19 (ϕ direction) and n = 10 (z direction). In order to ensure that the convergence was made, we tabulated the modal coefficients in the circular cavity in Table 2. that the convergence was made, we tabulated the modal coefficients in the circular cavity in Table 2. From Table 2, we figured out that the contributing modes are TM , TM , TM , TM , TM , TM , From Table 2, we figured out that the contributing mod 02 03es are 04 TM 05 06, (4)5 -4 5 TM , TM , TM , TM , TM , TM , TM , and TE . Also, we plotted normalized magnetic fields 02 03 04 05 06 07 45 02 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 9 Appl. Sci. 2018, 8, 2346 5 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 9 in the circular cavity at 10 GHz in Figure 4. It is seen that z-oriented electric point source affects the in the circular cavity at 10 GHz in Figure 4. It is seen that z-oriented electric point source affects the TM , TM , and TE . Also, we plotted normalized magnetic fields in the circular cavity at 10 GHz in TM and TE modes simultaneously. Figure 5 depicts the magnitude of electric fields on each aperture. 07 45 02 in the circular cavity at 10 GHz in Figure 4. It is seen that z-oriented electric point source affects the TM and TE modes simultaneously. Figure 5 depicts the magnitude of electric fields on each aperture. Figure 4. It is seen that z-oriented electric point source affects the TM and TE modes simultaneously. Note that the peak value occurs at the center of the middle aperture and the radiation becomes peak TM and TE modes simultaneously. Figure 5 depicts the magnitude of electric fields on each aperture. Note that the peak value occurs at the center of the middle aperture and the radiation becomes peak Figure 5 depicts the magnitude of electric fields on each aperture. Note that the peak value occurs at in a direction normal to the aperture array antenna. If the location of the electric point source in the Note that the peak value occurs at the center of the middle aperture and the radiation becomes peak in a direction normal to the aperture array antenna. If the location of the electric point source in the the center of the middle aperture and the radiation becomes peak in a direction normal to the aperture cavity is changed, the electric fields on the apertures and radiation patterns are also changed. It in a direction normal to the aperture array antenna. If the location of the electric point source in the cavity is changed, the electric fields on the apertures and radiation patterns are also changed. It array antenna. If the location of the electric point source in the cavity is changed, the electric fields on means that the equivalent magnetic currents on the apertures can affect the radiation properties of cavity is changed, the electric fields on the apertures and radiation patterns are also changed. It means that the equivalent magnetic currents on the apertures can affect the radiation properties of the apertures and radiation patterns are also changed. It means that the equivalent magnetic currents the aperture array antenna enclosed by the multi-layer FSS radome and the electric and magnetic means that the equivalent magnetic currents on the apertures can affect the radiation properties of the aperture array antenna enclosed by the multi-layer FSS radome and the electric and magnetic on currents on the apertur the radome surfac es can affect thee. radiation properties of the aperture array antenna enclosed by the the aperture array antenna enclosed by the multi-layer FSS radome and the electric and magnetic currents on the radome surface. multi-layer FSS radome and the electric and magnetic currents on the radome surface. currents on the radome surface. Figure 3. The 3 × 3 cavity-backed circular aperture array antenna. Figure 3. The 3 × 3 cavity-backed circular aperture array antenna. Figure 3. The 3 × 3 cavity-backed circular aperture array antenna. Figure 3. The 3  3 cavity-backed circular aperture array antenna. (a) (b) (a) (b) (a) (b) Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H (xz-plane), y y (xz-plane), (b) H (yz-plane). Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H (b (xz ) H -plane), ( (yz-plane). b) H (yz-plane). (xz-plane), (b) H (yz-plane). Figure 5. The magnitude of electric fields on each aperture. Figure 5. The magnitude of electric fields on each apertur e. Figure 5. The magnitude of electric fields on each aperture. Figure 5. The magnitude of electric fields on each aperture. Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 9 Appl. Sci. 2018, 8, 2346 6 of 9 Table 2. Convergence behaviors of the modal coefficients of the cavity. | | A . m= 19 ⋯ m= 4 ⋯ m = 0 ⋯ m = 4 ⋯ m = 19 mn −14 −1 −1 −1 −14 n = 1 1.34 × T 1 able 0 2. Conver ⋯ −gence 3.89 ×behaviors 10 ⋯ of the 1.40 modal × 10 coef ⋯ ficients −3.59 of the × 10 cavity ⋯ . −1.36 × 10 −15 −2 −2 −15 n = 2 ⋯ ⋯ ⋯ ⋯ 2.25 × 10 −2.89 × 10 −2.05 −1.88 × 10 −2.29 × 10 jA j m = 19  m = 4  m = 0  m = 4  m = 19 mn −16 −2 −2 −16 n = 3 5.57 × 10 ⋯ 2.48 × 10 ⋯ 1.53 ⋯ 3.01 × 10 ⋯ −5.7 × 10 14 1 1 1 14 n = 1 1.34  10  3.89  10  1.40  10  3.59  10  1.36  10 −16 −1 −1 −1 −17 n = 4 ⋯ ⋯ ⋯ ⋯ 1.18 × 10 2.87 × 10 9.92 × 10 2.92 × 10 −1.75 × 10 15 2 2 15 n = 2   2.05 2.25  10 2.89  10 1.88  10 2.29  10 −17 −19 16 2 2 16 n = 5 1.64 × 10 ⋯ −2.41 ⋯ 1.82 ⋯ −2.44 ⋯ −1.59 × 10 n = 3 5.57  10  2.48  10  1.53  3.01  10  5.7  10 16 1 1 1 17 −20 −3 −3 −19 n = 4 1.18  10  2.87  10  9.92  10  2.92  10  1.75  10 n = 6 ⋯ ⋯ −1.82 ⋯ ⋯ −6.85 × 10 2.89 × 10 2.92 × 10 7.03 × 10 17 19 n = 5 1.64  10  2.41  1.82  2.44  1.59  10 −19 −6 −6 −19 n = 7 −7.44 × 10 ⋯ 6.69 × 10 ⋯ −3.42 ⋯ 7.02 × 10 ⋯ 1.99 × 10 20 3 3 19 n = 6 6.85  10  2.89  10  1.82  2.92  10  7.03  10 ⋮ ⋮ 19 ⋰ ⋮ 6 ⋰ ⋮ ⋱ ⋮ 6 ⋱ ⋮ 19 n = 7 7.44  10  6.69  10  3.42  7.02  10  1.99  10 −22 −8 −5 −8 −22 n = . 10 −7.33. × 10 ⋯ −9.2 × 10 . ⋯ −2 × 10 . ⋯ −9.3 × 10 . ⋯ 6.36 × . 10 . . . . . . . . . . . . . . . . . . |B | m= 19 ⋯ m= 4 ⋯ m = 0 ⋯ m = 4 ⋯ m = 19 22 8 5 8 22 mn n = 10 7.33  10  9.2  10  2  10  9.3  10  6.36  10 −15 −1 −2 −1 −15 n = 1 2.06 × 10 ⋯ −4.98 × 10 ⋯ −8.15 × 10 ⋯ −4.97 × 10 ⋯ −1.77 × 10 jB j m = 19  m = 4  m = 0  m = 4  m = 19 mn −16 −1 −1 −16 n = 2 3.56 × 10 ⋯ −1.7 × 10 ⋯ −1.52 ⋯ −1.66 × 10 ⋯ −2.91 × 10 15 1 2 1 15 n = 1 2.06  10  4.98  10  8.15  10  4.97  10  1.77  10 −17 −1 −1 −2 −17 n = 3 9.16 × 10 ⋯ −1 × 10 ⋯ 6.52 × 10 ⋯ −9.1 × 10 ⋯ −7.06 × 10 16 1 1 16 n = 2 3.56  10  1.7  10  1.52  1.66  10  2.91  10 17−17 1 −2 1−1 2−2 − 17 17 n = 3 n = 4 9.16 2.07 ×10 10 ⋯ − 4.31 1  × 10 10 ⋯ 6.52 3.33 ×10 10 ⋯ −5.44 9.1  ×10 10 ⋯ −7.06 1.44 ×10 10 17 2 1 2 17 n = 4 2.07  10  4.31  10  3.33  10  5.44  10  1.44  10 −18 −1 −1 −1 −18 n = 5 3.22 × 10 ⋯ 3.1 × 10 ⋯ 3.27 × 10 ⋯ 3.31 × 10 ⋯ −1.64 × 10 18 1 1 1 18 n = 5 3.22  10  3.1  10  3.27  10  3.31  10  1.64  10 −20 −4 −2 −4 −19 n = 6 9.88 × 1 020 ⋯ −2.1 × 104 ⋯ −4.46 × 102 ⋯ −2.1 × 104 ⋯ 2.15 × 1 019 n = 6 9.88  10  2.1  10  4.46  10  2.1  10  2.15  10 19 −19 6−6 − 22 −6 6 19−19 nn== 7 7 −1.22 × 10 ⋯ −7.1 × 10 ⋯  −9.29 × 10 ⋯  −6.5 × 10 ⋯  1.68 × 10 1.22  10 7.1  10 9.29  10 6.5  10 1.68  10 . . . . . . . . .⋮ .⋮ ⋰ .⋮ ⋰ .⋮ ⋱ . .⋮ ⋱ . .⋮ . . . . . . . . −22 −8 −6 −8 −22 22 8 6 8 22 n = 10 ⋯ ⋯ ⋯ ⋯ −3.42 × 10 −1.9 × 10 −8 × 10 −1.6 × 10 3.07 × 10 n = 10 3.42  10  1.9  10  8  10  1.6  10  3.07  10 In order to further validate our formulation, we conducted the experiment. Figure 6 shows the In order to further validate our formulation, we conducted the experiment. Figure 6 shows the normalized radiation pattern of the 3 × 3 cavity-backed circular aperture array antenna at 10 GHz. normalized radiation pattern of the 3  3 cavity-backed circular aperture array antenna at 10 GHz. The comparison between our computation result (blue solid line with circle) and measured data The comparison between our computation result (blue solid line with circle) and measured data (red dotted line with plus) generally shows a good agreement. Meanwhile, because of a difficulty in (red dotted line with plus) generally shows a good agreement. Meanwhile, because of a difficulty predicting reflection and transmission coefficients of a curved FSS layer, we exploited reflection and in predicting reflection and transmission coefficients of a curved FSS layer, we exploited reflection transmission coefficients under an assumption that the FSS layer is locally flat. The discrepancy and transmission coefficients under an assumption that the FSS layer is locally flat. The discrepancy between two results at higher degrees above about 75 comes from the fact that we assumed an between two results at higher degrees above about 75 comes from the fact that we assumed an infinite infinite conductor plane when modeling the antenna. conductor plane when modeling the antenna. Figure 6. Radiation pattern of the 3 × 3 cavity-backed circular aperture array antenna (φ = 0°). Figure 6. Radiation pattern of the 3  3 cavity-backed circular aperture array antenna (j = 0 ). W We f e fabricated abricated a t a tangent-ogive angent-ogive m multi-layer ulti-layer F FSS SS ra radome dome ( (see see F Figur iguree 7 7a) a) a and nd t the he u unit nit c cell ell o off the the cross-loop dipole FSS layer (see Figure 7b and reference [10]). The multi-layer FSS radome is a cross-loop dipole FSS layer (see Figure 7b and reference [10]). The multi-layer FSS radome is a foam-cor foam-core s e sandwich andwich t type ype FSS. FSS. To be sp To be speci ecif fic, ic, t the he inn innermost ermost and o and outermost utermost laye layer r are E are E-glass/epoxy -glass/epoxy and the third layer is the FSS layer. The remaining layers consist of a foam. The initially fabricated and the third layer is the FSS layer. The remaining layers consist of a foam. The initially fabricated planar planar F FSSSlayer S layer is cut is cut to shape to shape and size,an and d size then, the and cut then the c pieces are molded ut piece thr s ough are molded thermal-forming through between the foam layers. The tangent-ogive multi-layer radome is one of the typical radomes. In this thermal-forming between the foam layers. The tangent-ogive multi-layer radome is one of the paper typica , l ra wedomes. In this designed and pa fabricated per, we de the signe FSSd radome and fabricated to validate the our FSS r hybrid adome t method. o valida When te our hybrid the cut pieces of the FSS sheet were molded on the radome, boundary lines between the pieces can cause an method. When the cut pieces of the FSS sheet were molded on the radome, boundary lines between Appl. Appl. Sci. Sci. 2018 2018,, 8 8,, x FO 2346 R PEER REVIEW 7 7 of of 9 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 9 the pieces can cause an unavoidable defect of the FSS layer. In order to reduce effects of the defect, the pieces can cause an unavoidable defect of the FSS layer. In order to reduce effects of the defect, unavoidable defect of the FSS layer. In order to reduce effects of the defect, we chose a cross-loop dipole we chose we chose a c a crross- oss-loop d loop diipole F pole FSS bec SS beca ause use it it is is les less s vulner vulnerable to able to the broken unit cell e the broken unit cell effe ffect than ct than FSS because it is less vulnerable to the broken unit cell effect than others. In addition, the cross-loop others. In addition, the cross-loop dipole FSS has an excellent bandpass characteristic and is easy to others. In addition, the cross-loop dipole FSS has an excellent bandpass characteristic and is easy to dipole FSS has an excellent bandpass characteristic and is easy to fabricate while maintaining the unit fabr fabricat icate wh e whil ile maint e mainta ain ining ing t th he unit e unit ce cell ll of t of th he F e FSS SS du due t e to o t th he rect e recta an ngul gula ar con r conf fi ig gurat uration ion.. Thi This s is why is why cell of the FSS due to the rectangular configuration. This is why we chose the tangent-ogive multi-layer we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully radome with the cross-loop dipole FSS. We also carefully fabricated the tip of the FSS radome to reduce f fa abri bric ca atted the ti ed the tip of the FSS ra p of the FSS radome to reduce th dome to reduce the di e distorti stortion of the tra on of the tran nsmi smitted wa tted wave. Tha ve. Thatt is why is why the distortion of the transmitted wave. That is why we chose the tangent-ogive multi-layer radome we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully with the cross-loop dipole FSS. We also carefully fabricated the tip of the FSS radome to reduce the ffa abri bric ca atted the ti ed the tip of p of the the FSS ra FSS radome dome to reduce to reduce the di the distorti stortion of the tra on of the tran nsm smiittted wa ted wave. Figure 8 ve. Figure 8 distortion of the transmitted wave. Figure 8 illustrates measurement setup. We measured the radiation illustrates measurement setup. We measured the radiation pattern of the cavity-backed circular illustrates measurement setup. We measured the radiation pattern of the cavity-backed circular pattern of the cavity-backed circular aperture array antenna enclosed by the radome. ap apert ertu ure re ar arra ray ant y ante enn nna enc a encl losed osed b by y t th he r e ra adom dome e.. (a) (b) (a) (b) Figure 7. Figure 7. ( (a a) Th ) The FSS rad e FSS rado ome a me an nd ( d (b b) ) the u the un nit it cell cell of of the F the FSS SS l la ay ye er. r. Figure 7. (a) The FSS radome and (b) the unit cell of the FSS layer. Figure 8. Figure 8. Measurement setup. Measurement setup. Figure 8. Measurement setup. Figure 9 illustrates the radiation patterns of the 3  3 cavity-backed circular aperture array Fi Figure gure 9 9 il illustra lustrates the radi tes the radia attiio on p n pa atterns of tterns of the the 3 3 ×× 3 3 cav caviitty y-b -back acke ed circu d circullar ar ap apert ertu ure re arr arra ay y antenna with the designed FSS and dielectric radomes. These values are normalized to the maximum antenna with the designed FSS and dielectric radomes. These values are normalized to the antenna with the designed FSS and dielectric radomes. These values are normalized to the magnitude of the designed antenna without any radome. The dielectric radome is comprised of three ma maximum ximum ma magnit gnitude of ude of the designed a the designed an ntenna wi tenna witth hout any out any r raadome. The d dome. The diielectr electric r ic raado dome is me is layers; comprithe sed of three la innermost and yers; the i outermost nnermost a layer arend oute E-glass/epoxy rmost layer and ar the e E-g inserted lass/epo layer xy and between the inserted them is a comprised of three layers; the innermost and outermost layer are E-glass/epoxy and the inserted foam. In other words, the second, third, and fourth layers are combined into one foam layer in Figure 1. l la ayer between them i yer between them is s a a f fo oa am m. In other . In other words, the words, the se second, thi cond, thir rd, d, and f and fo ourth la urth layers yers a ar re combined i e combined in nto to As onecan foabe m lseen ayer i fr n om Fig Figu ure 1 re . A 9,sthe canamount be seen f of ro the m F radiation igure 9, th field e am fr oom untthe of t3 he ra 3d cavity-backed iation field frocir m t cular he 3 one foam layer in Figure 1. As can be seen from Figure 9, the amount of the radiation field from the 3 aperture array antenna with the FSS radome is smaller than that with the dielectric radome. At q = 0 , ×× 3 ca 3 cav vi ity- ty-b ba ac cked ci ked circul rcular ar aperture aperture a ar rra ray y a an ntenna wi tenna with th the FSS ra the FSS radome i dome is s sm sma al ll le er r tha than n tha that t wi with the th the we dielectric r found out ado that me. At thereθis=a0discr °, we f epancy ound out tha betweentour there i theor s etical a discrep results ancy between our theoreti and measured data. Thisca isl dielectric radome. At θ = 0°, we found out that there is a discrepancy between our theoretical because the realistic FSS radome encompasses the curved FSS layer, but we consider this layer to be a results results and and measured d measured da ata. This is be ta. This is because the cause the re realist alistiic F c FSS r SS ra ad do ome encompasses the c me encompasses the cu ur rv ved FSS ed FSS planar layer, but structur we consid e in computation er this layefor r to convenience, be a planar which structure in may lead com topthe utat dif ion ferfor ence. convenience, In addition, which there layer, but we consider this layer to be a planar structure in computation for convenience, which may also be a fabrication error. Our analysis method can be used in the research of aperture antennas may may le lead to t ad to th he diffe e difference. In ad rence. In addition dition, , there may there may al also be a fa so be a fabri bric cati atio on error. Our n error. Our a an nal alysi ysis s m me ethod thod enclosed can be used by in the re the radome, searcterahertz h of aperture sensors antennas enc and any materials losed by the protected radome, ter by the ahdome ertz sensor structur s and e, and any can be used in the research of aperture antennas enclosed by the radome, terahertz sensors and any multi-physics problems [22–26]. ma materia terial ls protected by the s protected by the dome structur dome structure, e, and m and mu ult lti i- -physics physics probl proble ems [ ms [2 22– 2–2 26 6]. ]. Appl. Sci. 2018, 8, 2346 8 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 9 Figure 9. The dielectric and FSS radome enclosing the 3 × 3 cavity-backed circular aperture array Figure 9. The dielectric and FSS radome enclosing the 3  3 cavity-backed circular aperture array antenna (φ = 0°). antenna (j = 0 ). 4. Conclusions 4. Conclusions The radiation from a cavity-backed circular aperture array antenna enclosed by a multi-layer The radiation from a cavity-backed circular aperture array antenna enclosed by a multi-layer FSS radome has been investigated using the hybrid technique combining the mode matching method, FSS radome has been investigated using the hybrid technique combining the mode matching the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface currents on the method, the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface apertures are derived from the aperture fields, which are calculated based on the mode matching currents on the apertures are derived from the aperture fields, which are calculated based on the method. Then, rays are generated from the equivalent magnetic surface currents, which are used in an mode matching method. Then, rays are generated from the equivalent magnetic surface currents, analysis of the multi-layer FSS radome by using the ray tracing technique. After obtained from both which are used in an analysis of the multi-layer FSS radome by using the ray tracing technique. After the mode matching method and the ray tracing technique, electromagnetic fields on an outermost obtained from both the mode matching method and the ray tracing technique, electromagnetic fields radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s on an outermost radome are transformed into the equivalent electric and magnetic surface currents principle. The radiated fields are computed from the equivalent electric and magnetic surface currents using Huygens’s principle. The radiated fields are computed from the equivalent electric and and compared with the measured data to validate our computation. We analyze the aperture array magnetic surface currents and compared with the measured data to validate our computation. We antenna enclosed by the FSS radome having a practical size and conduct the experiment for validation analyze the aperture array antenna enclosed by the FSS radome having a practical size and conduct as a future work. Also, we plan to compare our results with other analytical models for more reliability the experiment for validation as a future work. Also, we plan to compare our results with other of our method and to optimize our structure to improve the performance of the FSS radome through analytical models for more reliability of our method and to optimize our structure to improve the parametric studies. performance of the FSS radome through parametric studies. Author Contributions: The present work was conducted in cooperation with all authors. J.K. and S.L. analyzed Author Contributions: The present work was conducted in cooperation with all authors. J.K. and S.L. analyzed the problem and performed numerous simulations; J.K., S.L., H.S., K.-Y.J., H.C., and Y.B.P. contributed to the the problem and performed numerous simulations; J.K., S.L., H.S., K.-Y.J., H.C., and Y.B.P. contributed to the conceptualization, fabrication, and measurement; J.K. and S.L. wrote a draft which was edited by all co-authors. conceptualization, fabrication, and measurement; J.K. and S.L. wrote a draft which was edited by all co-authors. Funding: This research received no external funding. Funding: This research received no external funding. Acknowledgments: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (No. 2017R1A2B4001903) and the Basic Acknowledgments: This work was supported by Basic Science Research Program through the National Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (No. 2017R1A2B4001903) and Education (No. 2015R1A6A1A0303 1833). the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Conflicts of Interest: The authors declare no conflict of interest. Ministry of Education (No. 2015R1A6A1A0303 1833). Conflicts of Interest: The authors declare no conflict of interest. References 1. Kozakoff, D.J. Analysis of Radome-Enclosed Antennas, 2nd ed.; Artech House: Boston, MA, USA, 1997; References pp. 103–183. ISBN 978-1-59693-441-2. 1. Kozakoff, D.J. Analysis of Radome-Enclosed Antennas, 2nd ed.; Artech House: Boston, MA, USA, 1997; pp. 2. Li, L.W.; Leong, M.S.; Ma, X.; Yeo, T.S. Analysis of a circular aperture antenna and its covered dielectric 103–183, ISBN 978-1-59693-441-2. hemispherical radome shell over ground plane: Near- and far-zone patterns. Microw. Opt. Technol. Lett. 1999, 2. Li, L.W.; Leong, M.S.; Ma, X.; Yeo, T.S. Analysis of a circular aperture antenna and its covered dielectric 21, 238–243. [CrossRef] hemispherical radome shell over ground plane: Near- and far-zone patterns. Microw. Opt. Technol. Lett. 3. Arvas, E.; Rahhalarabi, A.; Pekel, U.; Gundogan, E. Electromagnetic transmission through a small radome of 1999, 21, 238–243. arbitrary shape. IEE Proc. H (Microw. Antennas Propag.) 1990, 137, 401–405. [CrossRef] 3. Arvas, E.; Rahhalarabi, A.; Pekel, U.; Gundogan, E. Electromagnetic transmission through a small radome 4. He, M.; Xu, X.; Hu, B.; Zheng, Y. Accurate analysis of arbitrarily shaped wire antenna-dielectric radome of arbitrary shape. IEE Proc. H (Microw. Antennas Propag.) 1990, 137, 401–405. structures. IEEE Antennas Wirel. Propag. Lett. 2007, 6, 408–410. [CrossRef] 4. He, M.; Xu, X.; Hu, B.; Zheng, Y. Accurate analysis of arbitrarily shaped wire antenna-dielectric radome structures. IEEE Antennas Wirel. Propag. Lett. 2007, 6, 408–410. Appl. Sci. 2018, 8, 2346 9 of 9 5. Meng, H.; Dou, W.; Yin, K. Analysis of antenna-radome system at millimeter wave band. In Proceedings of the 2008 Global Symposium on Millimeter Waves, Nanjing, China, 20–24 April 2008. 6. Lu, C.-C. Dielectric radome analysis using multilevel fast multiple algorithm. In Proceedings of the IEEE Antennas and Propagation Society International Symposium, Boston, MA, USA, 8–13 July 2001. 7. Meng, H.; Dou, W. Hybrid IPO-BI-FEM for the analysis of 2D large radome with complex structure. Microw. Opt. Technol. Lett. 2009, 51, 1348–1353. [CrossRef] 8. Martini, E.; Caminita, F.; Nannetti, M.; Maci, S. Fast analysis of FSS radome for antenna RCS reduction. In Proceedings of the IEEE Antennas and Propagation Society International Symposium, Albuquerque, NM, USA, 9–14 July 2006. 9. D’Elia, U.; Pelosi, G.; Pichot, C.; Selleri, S.; Zoppi, M. A physical optics approach to the analysis of large frequency selective radomes. Prog. Electromagn. Res. 2013, 138, 537–553. [CrossRef] 10. Kim, J.H.; Chun, H.J.; Hong, I.P.; Kim, Y.J.; Park, Y.B. Analysis of FSS radomes based on physical optics method and ray tracing technique. IEEE Antennas Wirel. Propag. Lett. 2014, 13, 868–871. 11. Zheludev, N.I.; Kivshar, Y.S. From metamaterials to metadevices. Nat. Mater. 2012, 11, 917–924. [CrossRef] [PubMed] 12. Spada, L.L.; Vegni, L. Near-zero-index wires. Opt. Express 2017, 25, 23699–23708. [CrossRef] [PubMed] 13. Yohan, L.; Sun-Je, K.; Hyeonsoo, P.; Byoungho, L. Metamaterials and metasurfaces for sensor applications. Sensors 2017, 17, 1726. 14. Spada, L.L.; Vegni, L. Electromagnetic nanoparticles for sensing and medical diagnostic applications. Materials 2018, 11, 603. [CrossRef] [PubMed] 15. Iovine, R.; Spada, L.L.; Vegni, L. Optical properties of modified nanorod particles for biomedical sensing. IEEE Trans. Magn. 2014, 50, 169–172. [CrossRef] 16. Vakil, A.; Engheta, N. Transformation optics using graphene. Science 2011, 332, 1291–1294. [CrossRef] [PubMed] 17. Padooru, Y.R.; Yakovlev, A.B.; Kaipa, C.S.; Hanson, G.W.; Medina, F.; Mesa, F.; Glisson, A.W. New absorbing boundary conditions and analytical model for multilayered mushroom-type metamaterials: Applications to wideband absorbers. IEEE Trans. Antennas Propag. 2012, 60, 5727–5742. [CrossRef] 18. Monticone, F.; Alù, A. Metamaterials and plasmonics: From nanoparticles to nanoantenna arrays, metasurfaces, and metamaterials. Chin. Phys. B 2014, 23, 047809. [CrossRef] 19. Kim, J.H.; Park, Y.B. Electromagnetic radiation from a circular cavity with circular apertures in a conducting plane. IEEE Trans. Antennas Propag. 2014, 62, 4846–4851. [CrossRef] 20. Balanis, C.A. Advanced Engineering Electromagnetics, 2nd ed.; Wiley: New York, NY, USA, 2012; pp. 328–333. ISBN 978-0-470-58948-9. 21. Philips, B.; Parker, E.A.; Langley, R.J. Ray tracing analysis of FSS radome for antenna RCS reduction. IEEE Proc. Microw. Antennas Propag. 1995, 143, 193–200. [CrossRef] 22. Spada, L.L.; Iovine, R.; Tarparelli, R.; Vegni, L. Conical nanoparticles for blood disease detection. Adv. Nanopart. 2013, 2, 259–265. [CrossRef] 23. Liu, Y.; Hao, Y.; Li, K.; Gong, S. Radar cross section reduction of a microstrip antenna based on polarization conversion metamaterial. IEEE Antennas Wirel. Propag. Lett. 2016, 15, 80–83. [CrossRef] 24. Iovine, R.; Spada, L.L.; Vegni, L. Nanoplasmonic sensor for chemical measurements. Opt. Sens. 2013, 8774, 877411. 25. Engheta, N. Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials. Science 2007, 317, 1698–1702. [CrossRef] [PubMed] 26. Shaltout, A.M.; Kim, J.; Boltasseva, A.; Shalaev, V.M.; Kildishev, A.V. Ultrathin and multicolour optical cavities with embedded metasurfaces. Nat. Commun. 2018, 9, 2673. [CrossRef] [PubMed] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute

Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome

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applied sciences Article Radiation from a Cavity-Backed Circular Aperture Array Antenna Enclosed by an FSS Radome 1 , † 2 , † 2 3 4 Jihyung Kim , Sangsu Lee , Hokeun Shin , Kyung-Young Jung , Hosung Choo 2 , and Yong Bae Park * Hanwha Systems, Yongin 17121, Korea; jihyung.kim@hanwha.com Department of Electrical and Computer Engineering, Ajou University, Suwon 16499, Korea; lss1507@ajou.ac.kr (S.L.); hokeun0305@ajou.ac.kr (H.S.) Department of Electronic Engineering, Hanyang University, Seoul 04763, Korea; kyjung3@hanyang.ac.kr School of Electronic and Electrical Engineering, Hongik University, Seoul 04066, Korea; hschoo@hongik.ac.kr * Correspondence: yong@ajou.ac.kr; Tel.: +82-31-219-2358 † Equally contributed first authors. Received: 29 October 2018; Accepted: 19 November 2018; Published: 22 November 2018 Abstract: Radiation from a cavity-backed circular aperture array antenna enclosed by a frequency selective surface (FSS) radome is studied using the hybrid analysis method, by combining the mode matching method, the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface currents on the apertures are derived from the aperture electromagnetic fields, which are calculated based on the mode matching method. The rays are generated from the equivalent magnetic surface currents and used to analyze the FSS radome based on the ray tracing technique. After being obtained from both the mode matching method and the ray tracing technique, electromagnetic fields on an outermost radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s principle. The radiated fields are computed from the equivalent surface currents and compared with the measured data. Keywords: frequency selective surface radome; cavity-backed circular aperture array antenna; mode matching method; ray tracing technique 1. Introduction A radome, a portmanteau of radar and dome, is a structural and weatherproof enclosure, and thus it is used to protect microwave antennas. The radome usually comprises dielectric layers that minimally affect electromagnetic signals to be transmitted or received by the antenna. Due to the effects of the radome on the electromagnetic signals, a thorough analysis of the radome is needed. To understand electromagnetic properties of the radomes, there have been extensive studies on various radome configurations [1–10]. The radiation from a circular aperture surrounded by a hemisphere radome was predicted based on the dyadic Green’s function technique and physical optics (PO) method [2]. The Von Karman radome, one of the renowned radome structures, has been analyzed using the method of moments (MoM) [3], the coupled surface integral equation [4], and the aperture integration-surface integration (AI-SI) [5]. Furthermore, the radiation characteristic of hemisphere, tangent-ogive, and cone-shaped radomes with multiple sources has been investigated based on the multilevel fast multipole algorithm (MLFMA) [6]. The iterative physical optics-boundary integral-finite element method (IPO-BI-FEM) was used to analyze the sandwich tangent-ogive radome [7]. These studies focused on the radome consisting of dielectrics; however, the dielectric radome is generally responsible for the increase in radar cross section (RCS) of aircraft due to its broadband transmission characteristic. Instead, a frequency selective surface (FSS) radome, which Appl. Sci. 2018, 8, 2346; doi:10.3390/app8122346 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 2346 2 of 9 is a curved FSS within a multi-layer radome, is employed to reduce RCS over a wide frequency range because it exhibits bandpass or bandstop characteristics. Previous studies have investigated electromagnetic characteristics of single- and multi-layer FSS radomes based on the pole residue matching (PRM) [8] and the ray tracing technique [9,10]. The FSS are one kind of the metasurfaces showing a bandpass or a bandstop characteristic. These characteristics are not found in natural materials. Metasurfaces, metamaterials, graphene, and plasmonics are gaining increasing popularity among researchers due to their ability to adjust permittivity or permeability purposely and manipulate electromagnetic waves passing through the materials. Due to numerous potential applications, a variety of studies have been conducted for sensing technology, plasmonics, graphene, and photonics [11–16]. There have also been studies on analyzing the properties of metamaterials and metasurfaces [17,18]. However, the investigation of electromagnetic properties for the complex structures which consist of a radome with the metasurfaces such as FSS and an aperture array antenna has not been presented. This is because it is hard to use the full-wave methods to analyze them, for a given memory usage and time, when an object is electrically large in size and complicated. Therefore, hybrid techniques combining the full-wave methods (such as MoM, FEM, finite-difference time-domain (FDTD), and the mode matching method) and the asymptotic methods (such as the ray tracing technique and geometric optics (GO)) are required, but related studies on radiation properties from array antennas enclosed by an FSS radome seem to be lacking. Therefore, it is of great significance to investigate electromagnetic properties of the aperture array antennas with the FSS radome using a hybrid technique combining the mode matching method for modeling aperture fields and the ray tracing technique for analyzing the radome. In this paper, we analyze the radiation from a cavity-backed circular aperture array antenna enclosed by an FSS radome using the hybrid analysis method combining the mode matching method, the ray tracing technique, and Huygens’s principle. Towards this purpose, in particular, three different ways are carried out step by step. Firstly, electromagnetic characteristics of the cavity-backed circular aperture array antenna is predicted based on the mode matching method [19]. The obtained tangential electric fields are transformed into the equivalent magnetic current sources which in turn become rays to be used in the subsequent step. While using the rays, the ray tracing technique is employed to analyze the multi-layer FSS radome [10], and reflection and transmission properties of the FSS layer come from FEM simulations on HFSS. After obtained from the mode matching method and the ray tracing technique, electromagnetic fields on the outermost radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s principle, and radiation fields in the far-field region are computed from the equivalent surface currents. In brief, we take an advantage of the hybrid analysis method combining the mode matching method, the ray tracing technique, and HFSS, a commercial EM simulator, based on FEM for an analysis of the aperture array antenna enclosed by the FSS radome. To verify our formulation, the FSS radome enclosing the cavity-backed circular aperture array antenna is fabricated and our computation results are compared with the measured data. 2. Field Analysis Figure 1 shows the problem geometry. Assume that the z-oriented electric point source is located in a circular cavity with multiple circular apertures in a conducting plane. e and d are dielectric n n constant and loss tangent of each layer (n = 1, 2, 3, 4, 5). Electromagnetic properties and size of each layer are shown in Table 1. Appl. Sci. 2018, 8, 2346 3 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 9 Figure 1. Problem geometry. Figure 1. Problem geometry. Table 1. Design parameters of the frequency selective surface (FSS) radome. Table 1. Design parameters of the frequency selective surface (FSS) radome. Parameters Value Parameters Value Parameters Value Parameters Value D 284.8 mm L 290.5 mm 1 D1 284.8 mm L11 290.5 mm D 286.4 mm L 291.5 mm 2 2 D2 286.4 mm L2 291.5 mm D 292.3 mm L 295.2 mm 3 3 D3 292.3 mm L3 295.2 mm D 292.4 mm L 295.3 mm 4 4 D4 292.4 mm L4 295.3 mm D 298.4 mm L 299.1 mm 5 5 D 300 mm L 300 mm D5 298.4 mm L5 299.1 mm 6 6 e 4.35 d 0.0032 r1 1 D6 300 mm L6 300 mm e 1 d 0.0038 r2 2 ϵr1 4.35 δ1 0.0032 e 4.4 d 0.02 r3 3 ϵr2 1 δ2 0.0038 e 1 d 0.0038 r4 4 e ϵr3 4. 4.354 δd 3 0.02 0.0032 r5 5 ϵr4 1 δ4 0.0038 ϵr5 4.35 δ5 0.0032 Figure 2 shows an entire analysis procedure for the radiation from a cavity-backed circular aperture array antenna with the FSS radome based on the hybrid analysis method combining the Figure 2 shows an entire analysis procedure for the radiation from a cavity-backed circular mode matching method, the ray tracing technique, and HFSS, a commercial EM simulator, based aperture array antenna with the FSS radome based on the hybrid analysis method combining the on FEM. Firstly, for analysis of the antenna, we solved the electromagnetic boundary-value problem mode matching method, the ray tracing technique, and HFSS, a commercial EM simulator, based on of the circular cavity with the circular aperture array antenna based on the mode matching method FEM. Firstly, for analysis of the antenna, we solved the electromagnetic boundary-value problem of in our previous study [19]. The mode matching method provides an advantage in the fact that the circular cavity with the circular aperture array antenna based on the mode matching method in its solution is rigorous and theoretically robust. Moreover, it is time-efficient in an analysis of our previous study [19]. The mode matching method provides an advantage in the fact that its open-boundary problems compared to other numerical techniques such as FEM, FDTD, and MoM, solution is rigorous and theoretically robust. Moreover, it is time-efficient in an analysis of to name a few. An analysis using the mode matching method takes the following steps. Above all, open-boundary problems compared to other numerical techniques such as FEM, FDTD, and MoM, the whole region to be solved is divided into sub-regions on a basis of boundary. Electromagnetic to name a few. An analysis using the mode matching method takes the following steps. Above all, fields are defined in each region. Afterwards, boundary conditions are enforced to obtain a set the whole region to be solved is divided into sub-regions on a basis of boundary. Electromagnetic of simultaneous equations for modal coefficients. Matrix calculation enables an evaluation of the fields are defined in each region. Afterwards, boundary conditions are enforced to obtain a set of modal coefficients and electromagnetic fields in all regions can be calculated based on the obtained simultaneous equations for modal coefficients. Matrix calculation enables an evaluation of the modal coefficients. Note that the mode matching method should be used in the separable coordinate modal coefficients and electromagnetic fields in all regions can be calculated based on the obtained systems where eigen-modes can be defined in all regions. By using the tangential electromagnetic modal coefficients. Note that the mode matching method should be used in the separable coordinate field established from the mode matching method and the surface equivalence theorem [20], we can systems where eigen-modes can be defined in all regions. By using the tangential electromagnetic derive the equivalent magnetic surface currents on the apertures from the aperture fields, which will field established from the mode matching method and the surface equivalence theorem [20], we can be used in a formation of rays. Meanwhile, the FSS layer is a cross-loop dipole FSS which has a derive the equivalent magnetic surface currents on the apertures from the aperture fields, which will passband resonant frequency at 10 GHz. A detailed configuration and size of the designed FSS can be used in a formation of rays. Meanwhile, the FSS layer is a cross-loop dipole FSS which has a be found in the reference [10]. Reflection and transmission coefficients of the designed FSS layer are passband resonant frequency at 10 GHz. A detailed configuration and size of the designed FSS can obtained via numerous simulations using HFSS, an electromagnetic full-wave simulator. Reflection and be found in the reference [10]. Reflection and transmission coefficients of the designed FSS layer are transmission coefficients between dielectric layers, not involved with FSS layer, can be determined on obtained via numerous simulations using HFSS, an electromagnetic full-wave simulator. Reflection a polarization basis, as described in the reference [10]. Afterwards, to apply the ray tracing technique and transmission coefficients between dielectric layers, not involved with FSS layer, can be for the analysis of the radiation from the cavity-backed circular aperture antenna enclosed by the FSS determined on a polarization basis, as described in the reference [10]. Afterwards, to apply the ray tracing technique for the analysis of the radiation from the cavity-backed circular aperture antenna Appl. Sci. 2018, 8, 2346 4 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 9 enclosed by the FSS radome, we determined intercept points of the rays and the surfaces of the FSS radome, we determined intercept points of the rays and the surfaces of the FSS radome using the radome using the iterative method [1]. Then, we can generate the rays from the equivalent magnetic iterative method [1]. Then, we can generate the rays from the equivalent magnetic surface currents surface currents on the apertures and trace the rays passing through the radome. When analyzing on the apertures and trace the rays passing through the radome. When analyzing the multi-layer FSS the multi-layer FSS radome, we used the ray tracing technique and the reflection and transmission radome, we used the ray tracing technique and the reflection and transmission coefficients at the FSS coefficients at the FSS layer from the simulation of HFSS based on FEM [21]. Therefore, our hybrid layer from the simulation of HFSS based on FEM [21]. Therefore, our hybrid method provides a more method provides a more time-efficient method for analyzing the aperture array antenna enclosed by time-efficient method for analyzing the aperture array antenna enclosed by the multi-layer FSS radome the multi-layer FSS radome than the method using the full-wave analysis only. On the other hand, it than the method using the full-wave analysis only. On the other hand, it is noted that locally flat is noted that locally flat condition should be satisfied for the accuracy of the ray tracing technique. condition should be satisfied for the accuracy of the ray tracing technique. Since our radome structure Since our radome structure has smooth surfaces, the ray tracing technique can be employed. Rough has smooth surfaces, the ray tracing technique can be employed. Rough surfaces, ripples, and defects surfaces, ripples, and defects on the surface may decrease the accuracy. Additionally, the ray tracing on the surface may decrease the accuracy. Additionally, the ray tracing technique is applicable to the technique is applicable to the region where the far-field condition is satisfied. In our analysis, each region where the far-field condition is satisfied. In our analysis, each aperture is divided into hundreds aperture is divided into hundreds of small cells to apply the ray tracing technique. Then, we of small cells to apply the ray tracing technique. Then, we calculated the radiation field from each calculated the radiation field from each small cell, respectively, and summed up all the computed small cell, respectively, and summed up all the computed fields based on the superposition principle. fields based on the superposition principle. In this case, the far-field condition of each aperture is In this case, the far-field condition of each aperture is given by 2D / = 0.0267 m. Our ray tracing given by 2D /λ = 0.0267 m. Our ray tracing technique satisfies the far-field condition because the technique satisfies the far-field condition because the distance from the aperture center to the radome distance from the aperture center to the radome inner surface is larger than 0.142 m (4.75 λ). Lastly, inner surface is larger than 0.142 m (4.75 ). Lastly, we calculated the electromagnetic fields and the we calculated the electromagnetic fields and the equivalent electric and magnetic surface currents equivalent electric and magnetic surface currents over the radome’s outer surface via using the results over the radome’s outer surface via using the results from the ray tracing technique. Then, the from the ray tracing technique. Then, the equivalent currents on the radome’s outer surface can be equivalent currents on the radome’s outer surface can be used to calculate the radiation fields in the used to calculate the radiation fields in the far-field region. far-field region. Figure 2. Analysis procedure. Figure 2. Analysis procedure. 3. Numerical Results and Measurement 3. Numerical Results and Measurement Before proceeding with the analysis of radiation pattern of the 3  3 circular aperture array Before proceeding with the analysis of radiation pattern of the 3 × 3 circular aperture array antenna enclosed by the multi-layer FSS radome as shown in Figure 3, it is important to check the antenna enclosed by the multi-layer FSS radome as shown in Figure 3, it is important to check the accuracy of our mode matching formulation and to analyze the antenna properties in detail. Firstly, accuracy of our mode matching formulation and to analyze the antenna properties in detail. Firstly, the number of modes used is m = 19 ( direction) and n = 10 (z direction). In order to ensure the number of modes used is m= 19 (ϕ direction) and n = 10 (z direction). In order to ensure that the convergence was made, we tabulated the modal coefficients in the circular cavity in Table 2. that the convergence was made, we tabulated the modal coefficients in the circular cavity in Table 2. From Table 2, we figured out that the contributing modes are TM , TM , TM , TM , TM , TM , From Table 2, we figured out that the contributing mod 02 03es are 04 TM 05 06, (4)5 -4 5 TM , TM , TM , TM , TM , TM , TM , and TE . Also, we plotted normalized magnetic fields 02 03 04 05 06 07 45 02 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 9 Appl. Sci. 2018, 8, 2346 5 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 9 in the circular cavity at 10 GHz in Figure 4. It is seen that z-oriented electric point source affects the in the circular cavity at 10 GHz in Figure 4. It is seen that z-oriented electric point source affects the TM , TM , and TE . Also, we plotted normalized magnetic fields in the circular cavity at 10 GHz in TM and TE modes simultaneously. Figure 5 depicts the magnitude of electric fields on each aperture. 07 45 02 in the circular cavity at 10 GHz in Figure 4. It is seen that z-oriented electric point source affects the TM and TE modes simultaneously. Figure 5 depicts the magnitude of electric fields on each aperture. Figure 4. It is seen that z-oriented electric point source affects the TM and TE modes simultaneously. Note that the peak value occurs at the center of the middle aperture and the radiation becomes peak TM and TE modes simultaneously. Figure 5 depicts the magnitude of electric fields on each aperture. Note that the peak value occurs at the center of the middle aperture and the radiation becomes peak Figure 5 depicts the magnitude of electric fields on each aperture. Note that the peak value occurs at in a direction normal to the aperture array antenna. If the location of the electric point source in the Note that the peak value occurs at the center of the middle aperture and the radiation becomes peak in a direction normal to the aperture array antenna. If the location of the electric point source in the the center of the middle aperture and the radiation becomes peak in a direction normal to the aperture cavity is changed, the electric fields on the apertures and radiation patterns are also changed. It in a direction normal to the aperture array antenna. If the location of the electric point source in the cavity is changed, the electric fields on the apertures and radiation patterns are also changed. It array antenna. If the location of the electric point source in the cavity is changed, the electric fields on means that the equivalent magnetic currents on the apertures can affect the radiation properties of cavity is changed, the electric fields on the apertures and radiation patterns are also changed. It means that the equivalent magnetic currents on the apertures can affect the radiation properties of the apertures and radiation patterns are also changed. It means that the equivalent magnetic currents the aperture array antenna enclosed by the multi-layer FSS radome and the electric and magnetic means that the equivalent magnetic currents on the apertures can affect the radiation properties of the aperture array antenna enclosed by the multi-layer FSS radome and the electric and magnetic on currents on the apertur the radome surfac es can affect thee. radiation properties of the aperture array antenna enclosed by the the aperture array antenna enclosed by the multi-layer FSS radome and the electric and magnetic currents on the radome surface. multi-layer FSS radome and the electric and magnetic currents on the radome surface. currents on the radome surface. Figure 3. The 3 × 3 cavity-backed circular aperture array antenna. Figure 3. The 3 × 3 cavity-backed circular aperture array antenna. Figure 3. The 3 × 3 cavity-backed circular aperture array antenna. Figure 3. The 3  3 cavity-backed circular aperture array antenna. (a) (b) (a) (b) (a) (b) Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H (xz-plane), y y (xz-plane), (b) H (yz-plane). Figure 4. Normalized internal (within the cavity) magnetic field in dB scale at 10 GHz. (a) H (b (xz ) H -plane), ( (yz-plane). b) H (yz-plane). (xz-plane), (b) H (yz-plane). Figure 5. The magnitude of electric fields on each aperture. Figure 5. The magnitude of electric fields on each apertur e. Figure 5. The magnitude of electric fields on each aperture. Figure 5. The magnitude of electric fields on each aperture. Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 9 Appl. Sci. 2018, 8, 2346 6 of 9 Table 2. Convergence behaviors of the modal coefficients of the cavity. | | A . m= 19 ⋯ m= 4 ⋯ m = 0 ⋯ m = 4 ⋯ m = 19 mn −14 −1 −1 −1 −14 n = 1 1.34 × T 1 able 0 2. Conver ⋯ −gence 3.89 ×behaviors 10 ⋯ of the 1.40 modal × 10 coef ⋯ ficients −3.59 of the × 10 cavity ⋯ . −1.36 × 10 −15 −2 −2 −15 n = 2 ⋯ ⋯ ⋯ ⋯ 2.25 × 10 −2.89 × 10 −2.05 −1.88 × 10 −2.29 × 10 jA j m = 19  m = 4  m = 0  m = 4  m = 19 mn −16 −2 −2 −16 n = 3 5.57 × 10 ⋯ 2.48 × 10 ⋯ 1.53 ⋯ 3.01 × 10 ⋯ −5.7 × 10 14 1 1 1 14 n = 1 1.34  10  3.89  10  1.40  10  3.59  10  1.36  10 −16 −1 −1 −1 −17 n = 4 ⋯ ⋯ ⋯ ⋯ 1.18 × 10 2.87 × 10 9.92 × 10 2.92 × 10 −1.75 × 10 15 2 2 15 n = 2   2.05 2.25  10 2.89  10 1.88  10 2.29  10 −17 −19 16 2 2 16 n = 5 1.64 × 10 ⋯ −2.41 ⋯ 1.82 ⋯ −2.44 ⋯ −1.59 × 10 n = 3 5.57  10  2.48  10  1.53  3.01  10  5.7  10 16 1 1 1 17 −20 −3 −3 −19 n = 4 1.18  10  2.87  10  9.92  10  2.92  10  1.75  10 n = 6 ⋯ ⋯ −1.82 ⋯ ⋯ −6.85 × 10 2.89 × 10 2.92 × 10 7.03 × 10 17 19 n = 5 1.64  10  2.41  1.82  2.44  1.59  10 −19 −6 −6 −19 n = 7 −7.44 × 10 ⋯ 6.69 × 10 ⋯ −3.42 ⋯ 7.02 × 10 ⋯ 1.99 × 10 20 3 3 19 n = 6 6.85  10  2.89  10  1.82  2.92  10  7.03  10 ⋮ ⋮ 19 ⋰ ⋮ 6 ⋰ ⋮ ⋱ ⋮ 6 ⋱ ⋮ 19 n = 7 7.44  10  6.69  10  3.42  7.02  10  1.99  10 −22 −8 −5 −8 −22 n = . 10 −7.33. × 10 ⋯ −9.2 × 10 . ⋯ −2 × 10 . ⋯ −9.3 × 10 . ⋯ 6.36 × . 10 . . . . . . . . . . . . . . . . . . |B | m= 19 ⋯ m= 4 ⋯ m = 0 ⋯ m = 4 ⋯ m = 19 22 8 5 8 22 mn n = 10 7.33  10  9.2  10  2  10  9.3  10  6.36  10 −15 −1 −2 −1 −15 n = 1 2.06 × 10 ⋯ −4.98 × 10 ⋯ −8.15 × 10 ⋯ −4.97 × 10 ⋯ −1.77 × 10 jB j m = 19  m = 4  m = 0  m = 4  m = 19 mn −16 −1 −1 −16 n = 2 3.56 × 10 ⋯ −1.7 × 10 ⋯ −1.52 ⋯ −1.66 × 10 ⋯ −2.91 × 10 15 1 2 1 15 n = 1 2.06  10  4.98  10  8.15  10  4.97  10  1.77  10 −17 −1 −1 −2 −17 n = 3 9.16 × 10 ⋯ −1 × 10 ⋯ 6.52 × 10 ⋯ −9.1 × 10 ⋯ −7.06 × 10 16 1 1 16 n = 2 3.56  10  1.7  10  1.52  1.66  10  2.91  10 17−17 1 −2 1−1 2−2 − 17 17 n = 3 n = 4 9.16 2.07 ×10 10 ⋯ − 4.31 1  × 10 10 ⋯ 6.52 3.33 ×10 10 ⋯ −5.44 9.1  ×10 10 ⋯ −7.06 1.44 ×10 10 17 2 1 2 17 n = 4 2.07  10  4.31  10  3.33  10  5.44  10  1.44  10 −18 −1 −1 −1 −18 n = 5 3.22 × 10 ⋯ 3.1 × 10 ⋯ 3.27 × 10 ⋯ 3.31 × 10 ⋯ −1.64 × 10 18 1 1 1 18 n = 5 3.22  10  3.1  10  3.27  10  3.31  10  1.64  10 −20 −4 −2 −4 −19 n = 6 9.88 × 1 020 ⋯ −2.1 × 104 ⋯ −4.46 × 102 ⋯ −2.1 × 104 ⋯ 2.15 × 1 019 n = 6 9.88  10  2.1  10  4.46  10  2.1  10  2.15  10 19 −19 6−6 − 22 −6 6 19−19 nn== 7 7 −1.22 × 10 ⋯ −7.1 × 10 ⋯  −9.29 × 10 ⋯  −6.5 × 10 ⋯  1.68 × 10 1.22  10 7.1  10 9.29  10 6.5  10 1.68  10 . . . . . . . . .⋮ .⋮ ⋰ .⋮ ⋰ .⋮ ⋱ . .⋮ ⋱ . .⋮ . . . . . . . . −22 −8 −6 −8 −22 22 8 6 8 22 n = 10 ⋯ ⋯ ⋯ ⋯ −3.42 × 10 −1.9 × 10 −8 × 10 −1.6 × 10 3.07 × 10 n = 10 3.42  10  1.9  10  8  10  1.6  10  3.07  10 In order to further validate our formulation, we conducted the experiment. Figure 6 shows the In order to further validate our formulation, we conducted the experiment. Figure 6 shows the normalized radiation pattern of the 3 × 3 cavity-backed circular aperture array antenna at 10 GHz. normalized radiation pattern of the 3  3 cavity-backed circular aperture array antenna at 10 GHz. The comparison between our computation result (blue solid line with circle) and measured data The comparison between our computation result (blue solid line with circle) and measured data (red dotted line with plus) generally shows a good agreement. Meanwhile, because of a difficulty in (red dotted line with plus) generally shows a good agreement. Meanwhile, because of a difficulty predicting reflection and transmission coefficients of a curved FSS layer, we exploited reflection and in predicting reflection and transmission coefficients of a curved FSS layer, we exploited reflection transmission coefficients under an assumption that the FSS layer is locally flat. The discrepancy and transmission coefficients under an assumption that the FSS layer is locally flat. The discrepancy between two results at higher degrees above about 75 comes from the fact that we assumed an between two results at higher degrees above about 75 comes from the fact that we assumed an infinite infinite conductor plane when modeling the antenna. conductor plane when modeling the antenna. Figure 6. Radiation pattern of the 3 × 3 cavity-backed circular aperture array antenna (φ = 0°). Figure 6. Radiation pattern of the 3  3 cavity-backed circular aperture array antenna (j = 0 ). W We f e fabricated abricated a t a tangent-ogive angent-ogive m multi-layer ulti-layer F FSS SS ra radome dome ( (see see F Figur iguree 7 7a) a) a and nd t the he u unit nit c cell ell o off the the cross-loop dipole FSS layer (see Figure 7b and reference [10]). The multi-layer FSS radome is a cross-loop dipole FSS layer (see Figure 7b and reference [10]). The multi-layer FSS radome is a foam-cor foam-core s e sandwich andwich t type ype FSS. FSS. To be sp To be speci ecif fic, ic, t the he inn innermost ermost and o and outermost utermost laye layer r are E are E-glass/epoxy -glass/epoxy and the third layer is the FSS layer. The remaining layers consist of a foam. The initially fabricated and the third layer is the FSS layer. The remaining layers consist of a foam. The initially fabricated planar planar F FSSSlayer S layer is cut is cut to shape to shape and size,an and d size then, the and cut then the c pieces are molded ut piece thr s ough are molded thermal-forming through between the foam layers. The tangent-ogive multi-layer radome is one of the typical radomes. In this thermal-forming between the foam layers. The tangent-ogive multi-layer radome is one of the paper typica , l ra wedomes. In this designed and pa fabricated per, we de the signe FSSd radome and fabricated to validate the our FSS r hybrid adome t method. o valida When te our hybrid the cut pieces of the FSS sheet were molded on the radome, boundary lines between the pieces can cause an method. When the cut pieces of the FSS sheet were molded on the radome, boundary lines between Appl. Appl. Sci. Sci. 2018 2018,, 8 8,, x FO 2346 R PEER REVIEW 7 7 of of 9 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 9 the pieces can cause an unavoidable defect of the FSS layer. In order to reduce effects of the defect, the pieces can cause an unavoidable defect of the FSS layer. In order to reduce effects of the defect, unavoidable defect of the FSS layer. In order to reduce effects of the defect, we chose a cross-loop dipole we chose we chose a c a crross- oss-loop d loop diipole F pole FSS bec SS beca ause use it it is is les less s vulner vulnerable to able to the broken unit cell e the broken unit cell effe ffect than ct than FSS because it is less vulnerable to the broken unit cell effect than others. In addition, the cross-loop others. In addition, the cross-loop dipole FSS has an excellent bandpass characteristic and is easy to others. In addition, the cross-loop dipole FSS has an excellent bandpass characteristic and is easy to dipole FSS has an excellent bandpass characteristic and is easy to fabricate while maintaining the unit fabr fabricat icate wh e whil ile maint e mainta ain ining ing t th he unit e unit ce cell ll of t of th he F e FSS SS du due t e to o t th he rect e recta an ngul gula ar con r conf fi ig gurat uration ion.. Thi This s is why is why cell of the FSS due to the rectangular configuration. This is why we chose the tangent-ogive multi-layer we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully radome with the cross-loop dipole FSS. We also carefully fabricated the tip of the FSS radome to reduce f fa abri bric ca atted the ti ed the tip of the FSS ra p of the FSS radome to reduce th dome to reduce the di e distorti stortion of the tra on of the tran nsmi smitted wa tted wave. Tha ve. Thatt is why is why the distortion of the transmitted wave. That is why we chose the tangent-ogive multi-layer radome we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully we chose the tangent-ogive multi-layer radome with the cross-loop dipole FSS. We also carefully with the cross-loop dipole FSS. We also carefully fabricated the tip of the FSS radome to reduce the ffa abri bric ca atted the ti ed the tip of p of the the FSS ra FSS radome dome to reduce to reduce the di the distorti stortion of the tra on of the tran nsm smiittted wa ted wave. Figure 8 ve. Figure 8 distortion of the transmitted wave. Figure 8 illustrates measurement setup. We measured the radiation illustrates measurement setup. We measured the radiation pattern of the cavity-backed circular illustrates measurement setup. We measured the radiation pattern of the cavity-backed circular pattern of the cavity-backed circular aperture array antenna enclosed by the radome. ap apert ertu ure re ar arra ray ant y ante enn nna enc a encl losed osed b by y t th he r e ra adom dome e.. (a) (b) (a) (b) Figure 7. Figure 7. ( (a a) Th ) The FSS rad e FSS rado ome a me an nd ( d (b b) ) the u the un nit it cell cell of of the F the FSS SS l la ay ye er. r. Figure 7. (a) The FSS radome and (b) the unit cell of the FSS layer. Figure 8. Figure 8. Measurement setup. Measurement setup. Figure 8. Measurement setup. Figure 9 illustrates the radiation patterns of the 3  3 cavity-backed circular aperture array Fi Figure gure 9 9 il illustra lustrates the radi tes the radia attiio on p n pa atterns of tterns of the the 3 3 ×× 3 3 cav caviitty y-b -back acke ed circu d circullar ar ap apert ertu ure re arr arra ay y antenna with the designed FSS and dielectric radomes. These values are normalized to the maximum antenna with the designed FSS and dielectric radomes. These values are normalized to the antenna with the designed FSS and dielectric radomes. These values are normalized to the magnitude of the designed antenna without any radome. The dielectric radome is comprised of three ma maximum ximum ma magnit gnitude of ude of the designed a the designed an ntenna wi tenna witth hout any out any r raadome. The d dome. The diielectr electric r ic raado dome is me is layers; comprithe sed of three la innermost and yers; the i outermost nnermost a layer arend oute E-glass/epoxy rmost layer and ar the e E-g inserted lass/epo layer xy and between the inserted them is a comprised of three layers; the innermost and outermost layer are E-glass/epoxy and the inserted foam. In other words, the second, third, and fourth layers are combined into one foam layer in Figure 1. l la ayer between them i yer between them is s a a f fo oa am m. In other . In other words, the words, the se second, thi cond, thir rd, d, and f and fo ourth la urth layers yers a ar re combined i e combined in nto to As onecan foabe m lseen ayer i fr n om Fig Figu ure 1 re . A 9,sthe canamount be seen f of ro the m F radiation igure 9, th field e am fr oom untthe of t3 he ra 3d cavity-backed iation field frocir m t cular he 3 one foam layer in Figure 1. As can be seen from Figure 9, the amount of the radiation field from the 3 aperture array antenna with the FSS radome is smaller than that with the dielectric radome. At q = 0 , ×× 3 ca 3 cav vi ity- ty-b ba ac cked ci ked circul rcular ar aperture aperture a ar rra ray y a an ntenna wi tenna with th the FSS ra the FSS radome i dome is s sm sma al ll le er r tha than n tha that t wi with the th the we dielectric r found out ado that me. At thereθis=a0discr °, we f epancy ound out tha betweentour there i theor s etical a discrep results ancy between our theoreti and measured data. Thisca isl dielectric radome. At θ = 0°, we found out that there is a discrepancy between our theoretical because the realistic FSS radome encompasses the curved FSS layer, but we consider this layer to be a results results and and measured d measured da ata. This is be ta. This is because the cause the re realist alistiic F c FSS r SS ra ad do ome encompasses the c me encompasses the cu ur rv ved FSS ed FSS planar layer, but structur we consid e in computation er this layefor r to convenience, be a planar which structure in may lead com topthe utat dif ion ferfor ence. convenience, In addition, which there layer, but we consider this layer to be a planar structure in computation for convenience, which may also be a fabrication error. Our analysis method can be used in the research of aperture antennas may may le lead to t ad to th he diffe e difference. In ad rence. In addition dition, , there may there may al also be a fa so be a fabri bric cati atio on error. Our n error. Our a an nal alysi ysis s m me ethod thod enclosed can be used by in the re the radome, searcterahertz h of aperture sensors antennas enc and any materials losed by the protected radome, ter by the ahdome ertz sensor structur s and e, and any can be used in the research of aperture antennas enclosed by the radome, terahertz sensors and any multi-physics problems [22–26]. ma materia terial ls protected by the s protected by the dome structur dome structure, e, and m and mu ult lti i- -physics physics probl proble ems [ ms [2 22– 2–2 26 6]. ]. Appl. Sci. 2018, 8, 2346 8 of 9 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 9 Figure 9. The dielectric and FSS radome enclosing the 3 × 3 cavity-backed circular aperture array Figure 9. The dielectric and FSS radome enclosing the 3  3 cavity-backed circular aperture array antenna (φ = 0°). antenna (j = 0 ). 4. Conclusions 4. Conclusions The radiation from a cavity-backed circular aperture array antenna enclosed by a multi-layer The radiation from a cavity-backed circular aperture array antenna enclosed by a multi-layer FSS radome has been investigated using the hybrid technique combining the mode matching method, FSS radome has been investigated using the hybrid technique combining the mode matching the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface currents on the method, the ray tracing technique, and Huygens’s principle. The equivalent magnetic surface apertures are derived from the aperture fields, which are calculated based on the mode matching currents on the apertures are derived from the aperture fields, which are calculated based on the method. Then, rays are generated from the equivalent magnetic surface currents, which are used in an mode matching method. Then, rays are generated from the equivalent magnetic surface currents, analysis of the multi-layer FSS radome by using the ray tracing technique. After obtained from both which are used in an analysis of the multi-layer FSS radome by using the ray tracing technique. After the mode matching method and the ray tracing technique, electromagnetic fields on an outermost obtained from both the mode matching method and the ray tracing technique, electromagnetic fields radome are transformed into the equivalent electric and magnetic surface currents using Huygens’s on an outermost radome are transformed into the equivalent electric and magnetic surface currents principle. The radiated fields are computed from the equivalent electric and magnetic surface currents using Huygens’s principle. The radiated fields are computed from the equivalent electric and and compared with the measured data to validate our computation. We analyze the aperture array magnetic surface currents and compared with the measured data to validate our computation. We antenna enclosed by the FSS radome having a practical size and conduct the experiment for validation analyze the aperture array antenna enclosed by the FSS radome having a practical size and conduct as a future work. Also, we plan to compare our results with other analytical models for more reliability the experiment for validation as a future work. Also, we plan to compare our results with other of our method and to optimize our structure to improve the performance of the FSS radome through analytical models for more reliability of our method and to optimize our structure to improve the parametric studies. performance of the FSS radome through parametric studies. Author Contributions: The present work was conducted in cooperation with all authors. J.K. and S.L. analyzed Author Contributions: The present work was conducted in cooperation with all authors. J.K. and S.L. analyzed the problem and performed numerous simulations; J.K., S.L., H.S., K.-Y.J., H.C., and Y.B.P. contributed to the the problem and performed numerous simulations; J.K., S.L., H.S., K.-Y.J., H.C., and Y.B.P. contributed to the conceptualization, fabrication, and measurement; J.K. and S.L. wrote a draft which was edited by all co-authors. conceptualization, fabrication, and measurement; J.K. and S.L. wrote a draft which was edited by all co-authors. Funding: This research received no external funding. Funding: This research received no external funding. Acknowledgments: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (No. 2017R1A2B4001903) and the Basic Acknowledgments: This work was supported by Basic Science Research Program through the National Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (No. 2017R1A2B4001903) and Education (No. 2015R1A6A1A0303 1833). the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Conflicts of Interest: The authors declare no conflict of interest. Ministry of Education (No. 2015R1A6A1A0303 1833). Conflicts of Interest: The authors declare no conflict of interest. References 1. Kozakoff, D.J. Analysis of Radome-Enclosed Antennas, 2nd ed.; Artech House: Boston, MA, USA, 1997; References pp. 103–183. ISBN 978-1-59693-441-2. 1. Kozakoff, D.J. Analysis of Radome-Enclosed Antennas, 2nd ed.; Artech House: Boston, MA, USA, 1997; pp. 2. Li, L.W.; Leong, M.S.; Ma, X.; Yeo, T.S. Analysis of a circular aperture antenna and its covered dielectric 103–183, ISBN 978-1-59693-441-2. hemispherical radome shell over ground plane: Near- and far-zone patterns. Microw. Opt. Technol. Lett. 1999, 2. Li, L.W.; Leong, M.S.; Ma, X.; Yeo, T.S. Analysis of a circular aperture antenna and its covered dielectric 21, 238–243. [CrossRef] hemispherical radome shell over ground plane: Near- and far-zone patterns. Microw. Opt. Technol. Lett. 3. Arvas, E.; Rahhalarabi, A.; Pekel, U.; Gundogan, E. Electromagnetic transmission through a small radome of 1999, 21, 238–243. arbitrary shape. IEE Proc. H (Microw. Antennas Propag.) 1990, 137, 401–405. [CrossRef] 3. Arvas, E.; Rahhalarabi, A.; Pekel, U.; Gundogan, E. Electromagnetic transmission through a small radome 4. He, M.; Xu, X.; Hu, B.; Zheng, Y. Accurate analysis of arbitrarily shaped wire antenna-dielectric radome of arbitrary shape. IEE Proc. H (Microw. Antennas Propag.) 1990, 137, 401–405. structures. IEEE Antennas Wirel. Propag. Lett. 2007, 6, 408–410. [CrossRef] 4. He, M.; Xu, X.; Hu, B.; Zheng, Y. Accurate analysis of arbitrarily shaped wire antenna-dielectric radome structures. IEEE Antennas Wirel. Propag. Lett. 2007, 6, 408–410. Appl. Sci. 2018, 8, 2346 9 of 9 5. Meng, H.; Dou, W.; Yin, K. Analysis of antenna-radome system at millimeter wave band. In Proceedings of the 2008 Global Symposium on Millimeter Waves, Nanjing, China, 20–24 April 2008. 6. Lu, C.-C. Dielectric radome analysis using multilevel fast multiple algorithm. In Proceedings of the IEEE Antennas and Propagation Society International Symposium, Boston, MA, USA, 8–13 July 2001. 7. Meng, H.; Dou, W. Hybrid IPO-BI-FEM for the analysis of 2D large radome with complex structure. Microw. Opt. Technol. Lett. 2009, 51, 1348–1353. [CrossRef] 8. Martini, E.; Caminita, F.; Nannetti, M.; Maci, S. Fast analysis of FSS radome for antenna RCS reduction. In Proceedings of the IEEE Antennas and Propagation Society International Symposium, Albuquerque, NM, USA, 9–14 July 2006. 9. D’Elia, U.; Pelosi, G.; Pichot, C.; Selleri, S.; Zoppi, M. A physical optics approach to the analysis of large frequency selective radomes. Prog. Electromagn. Res. 2013, 138, 537–553. [CrossRef] 10. Kim, J.H.; Chun, H.J.; Hong, I.P.; Kim, Y.J.; Park, Y.B. Analysis of FSS radomes based on physical optics method and ray tracing technique. IEEE Antennas Wirel. Propag. Lett. 2014, 13, 868–871. 11. Zheludev, N.I.; Kivshar, Y.S. From metamaterials to metadevices. Nat. Mater. 2012, 11, 917–924. [CrossRef] [PubMed] 12. Spada, L.L.; Vegni, L. Near-zero-index wires. Opt. Express 2017, 25, 23699–23708. [CrossRef] [PubMed] 13. Yohan, L.; Sun-Je, K.; Hyeonsoo, P.; Byoungho, L. Metamaterials and metasurfaces for sensor applications. Sensors 2017, 17, 1726. 14. Spada, L.L.; Vegni, L. Electromagnetic nanoparticles for sensing and medical diagnostic applications. Materials 2018, 11, 603. [CrossRef] [PubMed] 15. Iovine, R.; Spada, L.L.; Vegni, L. Optical properties of modified nanorod particles for biomedical sensing. IEEE Trans. Magn. 2014, 50, 169–172. [CrossRef] 16. Vakil, A.; Engheta, N. Transformation optics using graphene. Science 2011, 332, 1291–1294. [CrossRef] [PubMed] 17. Padooru, Y.R.; Yakovlev, A.B.; Kaipa, C.S.; Hanson, G.W.; Medina, F.; Mesa, F.; Glisson, A.W. New absorbing boundary conditions and analytical model for multilayered mushroom-type metamaterials: Applications to wideband absorbers. IEEE Trans. Antennas Propag. 2012, 60, 5727–5742. [CrossRef] 18. Monticone, F.; Alù, A. Metamaterials and plasmonics: From nanoparticles to nanoantenna arrays, metasurfaces, and metamaterials. Chin. Phys. B 2014, 23, 047809. [CrossRef] 19. Kim, J.H.; Park, Y.B. Electromagnetic radiation from a circular cavity with circular apertures in a conducting plane. IEEE Trans. Antennas Propag. 2014, 62, 4846–4851. [CrossRef] 20. Balanis, C.A. Advanced Engineering Electromagnetics, 2nd ed.; Wiley: New York, NY, USA, 2012; pp. 328–333. ISBN 978-0-470-58948-9. 21. Philips, B.; Parker, E.A.; Langley, R.J. Ray tracing analysis of FSS radome for antenna RCS reduction. IEEE Proc. Microw. Antennas Propag. 1995, 143, 193–200. [CrossRef] 22. Spada, L.L.; Iovine, R.; Tarparelli, R.; Vegni, L. Conical nanoparticles for blood disease detection. Adv. Nanopart. 2013, 2, 259–265. [CrossRef] 23. Liu, Y.; Hao, Y.; Li, K.; Gong, S. Radar cross section reduction of a microstrip antenna based on polarization conversion metamaterial. IEEE Antennas Wirel. Propag. Lett. 2016, 15, 80–83. [CrossRef] 24. Iovine, R.; Spada, L.L.; Vegni, L. Nanoplasmonic sensor for chemical measurements. Opt. Sens. 2013, 8774, 877411. 25. Engheta, N. Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials. Science 2007, 317, 1698–1702. [CrossRef] [PubMed] 26. Shaltout, A.M.; Kim, J.; Boltasseva, A.; Shalaev, V.M.; Kildishev, A.V. Ultrathin and multicolour optical cavities with embedded metasurfaces. Nat. Commun. 2018, 9, 2673. [CrossRef] [PubMed] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Journal

Applied Sciences – Multidisciplinary Digital Publishing Institute

Published: Nov 22, 2018

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