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Abstract
High-order bandpass filtering responses are highly desirable for frequency-selective surfaces (FSSs) in narrowband antenna/radar systems. In this paper, the design process of a reconfigurable dual-band FSS with second-order response is presented. Initially, the basic dumbbell-shaped resonator used in this design is theoretically investigated using the characteristic mode analysis (CMA) method to study the relation between geometric design parameters and the excited orthogonal resonance modes in different frequency bands. Then, an additional CMA process was performed on a unit cell with four such patch resonators arranged with 90-degree rotation between adjacent ones. This detailed analysis leads to a polarization-independent FSS design with a high-order dual-band response. Two of these composite resonators are combined back-to-back through coupling apertures on the middle layer. Finally, PIN diodes are loaded on separate layers to realize independent pass-band switching. The loading place of the PIN diodes is carefully chosen based on electromagnetic field analysis. A prototype was also fabricated and experimentally tested. Experimental results show that this FSS has two independently switchable passbands centered at 3 GHz and 4.8 GHz.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent decades, frequency-selective surfaces (FSSs) have gained attention for a variety of applications spanning from microwave to optical frequency ranges [1–3]. FSSs act as spatial filters that use periodically arranged unit cells to achieve the desired transmission or reflection response within a specified frequency range. Recently, various unit cell structures have been developed for manipulating the amplitude, phase, and polarization of incident electromagnetic (EM) waves [4–7]. By integrating traditional pass-band FSSs with absorbers, polarizers, and reconfigurable circuits, more powerful devices such as frequency-selective radars (FSRs) and reconfigurable FSSs have been developed [8–15]. These new concept FSSs have profound applications in advanced radar and communication systems. [16–19].
One particular requirement for FSS is to achieve high frequency selectivity for antenna radomes. High-order bandpass filtering responses are highly desirable for this kind of FSS to suppress jamming outside the passband. Previous studies in the literature have provided several solutions to achieve sharpened rejection skirts [20–24]. One straightforward approach is to cascade multiple first-order bandpass FSSs, which leads to a bulky volume and huge insertion loss. In [20,21], substrate-integrated waveguide structures have been employed to achieve quasi-elliptic filtering response, albeit at the cost of increased fabrication complexity and cost. Narrowband FSS can also be implemented using 3D cavity elements [23,24], which have been recently proposed. However, this approach results in thick profiles and complicated assembly procedures. To meet the shielding and filtering needs of dual-frequency antennas in wireless radar/communication systems, a dual-band multilayer FSS with high selectivity and miniaturization characteristics was proposed [25]. Zhang et al. also proposed a dual-band FSS using a SIW, and this FSS only achieved the roll-off performance of the higher band [26]. However, few studies have achieved second-order responses in both bands with independent controllability.
Lei Zhu et al. introduced a remarkable breakthrough in their paper [27–30], where they presented the groundbreaking concept of aperture-coupled patch resonators (AC-PR). This concept serves as an exceptional solution for achieving highly efficient single-band or multiband high-order filtering. To achieve dual-band or even multiband response based on AC-PR, it is crucial that the patch resonator can support orthogonal modes. Although the multiport equivalent circuit method [27,28] has been used to interpret its operating principle in several papers, an efficient method with physical insight is still lacking to guide the design of meta-atoms with multimode resonance properties. In this paper, we will apply characteristic mode analysis theory (CMT) to design a dual-bandpass FSS with high selectivity. The CMT provides profound physical insights for analyzing both the fundamental mode and higher-order modes. Since its initial proposal by Garbacz, Harrington, and Mautz [31,32], this methodology has proven to be highly effective in guiding antenna design. The source-free CMA has the ability to predict possible orthogonal modal currents on a given metallic structure. The modal parameters defined in CMT, such as eigenvalue and characteristic angle, provide a quantitative analysis tool for antennas and scatterers. The potential of CMT has recently been recognized by researchers in the field of metamaterials. The value of CMA-based design for metasurface antennas and metamaterial absorbers has been demonstrated in [6,33–36]. But to the author’s knowledge, CMT has not been investigated for the design of dual-band AC-PR FSS.
On the other hand, reconfigurability is becoming a common requirement for FSS to achieve multi-functionality. Generally, the FSS incorporates active components such as PIN diodes, varactors, MEMS, etc. to change the transmission/reflection/absorption window [14,37–42]. In [41], Gulab Shah et al. presented an active FSS with four independent functions by alternately switching the PIN state between On and Off. In another work, Jiang [42] presented a dual-band FSS that exhibits high selectivity and independently switchable characteristics. However, their analysis was based on an equivalent circuit model, which still does not provide an effective approach with physical insights to guide the design.
In this work, we use CMT to guide the design of a novel shape AC-PR unit cell. Based on CMT analysis, it is revealed that the proposed dumbbell-shaped structure intrinsically supports two orthogonal modes, which can be effectively excited to realize dual-band resonance. The resonance frequency can be tuned by changing the geometric parameter of the metal patch resonator. To achieve the second-order response, a dumbbell-shaped multilayer structure with a coupling aperture is employed. Furthermore, an independently switchable dual-passband FSS is further investigated based on this design. By controlling the bias voltage of the PIN diode, independent switching within the operating band for the dual-bandpass FSS can be achieved. The PIN diodes are powered in parallel to ensure that the control voltage of each diode is not affected by any differences among them.
2. Designs and analysis
The topology and dimensions of the proposed dual-mode FSSs are presented in Fig. 1. Both the upper and lower layers are composed of four dumbbell-shaped patches, along with the coupling aperture structures in the middle layer. The thicknesses and relative dielectric constant of two layers of dielectric substrates are 1.524mm and 3.55, respectively. To form a bias network, the bias lines on each layer of the fabricated FSS are interconnected at the edge. This enables the transmission of DC signals through all the patches on each layer. The eight PIN diodes are soldered onto the upper and lower layers, respectively. The anode of the PIN diode is connected to the dumbbell-shaped patch, while its cathode is linked to the intermediate coupling layer with a via. The modal behaviors of dual-mode FSS will be analyzed in the following sections.
Fig. 1. Geometry of the proposed FSS. (a) Three-dimensional perspective. (b) Top layers of the FSSs. (c) Coupling layer of the FSS. (d) Bottom layers of the FSSs. (Physical dimensions: p=50mm, a=2mm, e=7.5mm, m=22.5 mm, d=4mm, c=11mm, l1=7mm, l2=3.5mm, w1=0.4, w2=4.6mm)
2.1 Characteristic mode analysis of the dual mode FSS
To comprehend the physical mechanisms of the proposed dual-mode supported by the dumbbell-shaped patch, we investigate its resonant characteristics using the CMT. The CMT provides valuable physical insights for analyzing and modifying both the fundamental mode and higher-order modes. Typically, in the analysis of the CMT three critical evaluation criteria are used to determine if a particular characteristic mode can be adequately stimulated: mode current (${J}_n$), mode significance (MS), and characteristic angle ($\mathrm {CA}_n$).
The total currents J on the metallic surface under external EM field illumination can be decomposed into individual modal current ${J}_n$. The J can be expressed as a linear weighted superposition by using modal weighting coefficients ($\alpha _n$) and the mode current (${J}_n$):
where $\alpha _n$ represents the significance of the characteristic current in the overall current, and n denotes the mode index. The $\left \langle \vec {E}_i(\vec {r}), \vec {J}_n\right \rangle$ is called the modal excitation coefficient. $\lambda _n$ represents the eigenvalue of the mode current.For enhance comprehension, the MS is introduced and can be expressed as [3]
The MS effectively captures the inherent characteristics of each mode, as it remains unaffected by any external factors. The MS is quantified on a scale that ranges from 0 to 1. The presence of an efficient mode that can be effectively stimulated under suitable conditions is indicated if MS $\geq$ 0.707.
The characteristic angle ($\mathrm {CA}_n$) is expressed as
where $\mathrm {CA}_n$ represents the phase lag between the mode current and the mode E-field on MS. When the $\mathrm {CA}_n=180^{\circ }$, the nth CM is regarded to be in resonance. Furthermore, the situations in which $90^{\circ }<\mathrm {CA}_n<180^{\circ }$ and $180^{\circ }<\mathrm {CA}_n<270^{\circ }$ represent the inductive and capacitive modes, respectively.The modal current distributions and corresponding modal radiation patterns of the initial four modes are shown in Fig. 2(a) at a cutting depth (a) of 3 mm. It can be observed that both mode 1 (${J}_1$) and mode 2 (${J}_2$) exhibit orthogonal current. At the same time, their modal radiation patterns resemble electric dipole radiation, with the maximum radiation occurring in the + z direction. Fig. 2(c)(d) illustrates the modal current distributions and radiation patterns of mode 3 (${J}_3$) and mode 4 (${J}_4$). ${J}_3$ and ${J}_4$ are reversed or rotationally symmetric and have no effect on the total current. The modal radiation pattern of mode 3 is second-order electric dipole radiation that is difficult to excite, while the modal radiation pattern of mode 4 is characterized by the superposition of two magnetic dipole radiation. However, the modal radiation pattern approaches zero in the positive z direction, indicating that mode 3 and mode 4 have negligible responses to external incident waves. In summary, mode 1 and mode 2 are the excited modes, while mode 3 and mode 4 are considered invalid modes in the dumbbell-shaped patch.
Fig. 2. Modal current distributions and radiation patterns of the dumbbell-shaped patch at a cutting depth of 3 mm. (a) Mode 1 (3 GHz). (b) Mode 2 (4.8 GHz). (c) Mode 3 (3 GHz). (d) Mode 4 (4.8 GHz).
Modal significances and characteristic angles are presented in Fig. 3. In Fig. 3(a), the solid red and blue lines indicate the presence of two dominant modes at 3 GHz and 4.8 GHz, which are identified as mode 1 and mode 2. Moreover, the resonant frequencies can be modified by adjusting the cutting depth of the dumbbell-shaped patch. As depicted in Fig. 3(b), a phase difference of 180 degrees can be observed at frequencies of 3 GHz and 4.8 GHz. From the above characteristic mode analysis, it can be concluded that the proposed dumbbell-shaped patch can effectively support dual mode resonance for the FSS application. Its geometric parameters are closely related to the MS and CA. By studying these CMA parameters, the resonance frequencies and far-field radiation patterns of the structure can be precisely designed.
Fig. 3. Characteristic mode analysis and characteristic angle of the dumbbell-shaped patch. (a) Mode significance of the dumbbell-shaped patch with different cutting depths. (b) characteristic angle with a cutting depth of 3mm.
Due to the inherent asymmetry of a single dumbbell-shaped patch, it can lead to undesired polarization sensitivity. In order to address this problem, a new solution is presented where four dumbbell-shaped patches are arranged in a mirror-symmetrical configuration to form a new composite resonator, as shown in Fig. 4(a). Fig. 4(b-g) show the MS, modal current distribution, and radiation patterns of the composite resonator, respectively. From the figure, it is evident that the composite resonator displays six dominant modes at 3 GHz and 4.8 GHz. These results of the new composite resonators closely resemble those analyzed for a single dumbbell-shaped patch. However, the advantage lies in having two effective modes in both frequency bands, and these two modes are orthogonal. Consequently, this arrangement effectively resolves the polarization sensitivity observed in the single dumbbell-shaped patch.
Fig. 4. Characteristic mode analysis of four dumbbell-shaped patches. (a) Four dumbbell-shaped patches. (b) Mode significance of four dumbbell-shaped patches. (c) Mode 1(3 GHz). (d) Mode 2 (3 GHz). (e) Mode 3 (3 GHz). (f) Mode 4 (4.8 GHz). (g) Mode 5 (4.8 GHz). (h) Mode 6 (4.8 GHz).
2.2 Coupling coefficient of dual-passband FSSs
The dual-passband FSS can be realized by combining the composite resonator with the coupling aperture structures. To translate the relationship between the dimension of the coupling apertures and the S-parameter, the coupling coefficient (${k}_1$, ${k}_2$) analysis is carried out. Then, the coupling coefficients ${k}_1$ and ${k}_2$ can be calculated by
The variation of ${k}_1$, ${k}_2$, and S-parameters at different aperture sizes are depicted in Fig. 5. In Fig. 5(a), as ${l}_1$ increase, the resonant frequency ($f_{1 e}$) shifts to a lower frequency, while $f_{1 o},f_{2 e}$, and $f_{2 o}$ remain nearly constant. Furthermore, it can be observed from Fig. 5(b)(d) that different ${k}_1 ({k}_2)$ values follow the same increasing trend as ${l}_1 ({l}_2)$ increases, while there is no significant change in ${k}_2({k}_1)$. This is consistent with the response of the S-parameter shown in Fig. 5(a)(c). In summary, by adjusting the dimensions of apertures, the coupling coefficients ${k}_1$ and ${k}_2$ can be adjusted to achieve the high selectivity of the passband.
Fig. 5. Coupling coefficient analysis of dual-passband FSS. (a) S-parameter with different ${l}_1$. (b) The variation trend of ${k}_1$ and ${k}_2$ with ${l}_1$ and ${w}_1$. (c) S-parameter with different ${l}_2$. (d) The variation trend of ${k}_1$ and ${k}_2$ with ${l}_2$ and ${w}_2$.
2.3 Design of independently switchable dual-passband FSS
To achieve an independently switchable dual-passbands FSS, PIN diodes (SMP1345-040LF) were considered on the upper and lower layers. These diodes are specifically designed for use in switching applications within the frequency range of 10 MHz to 6 GHz. The ideal simplified equivalent parameters of the diode are ${R}_f = 1 \Omega, {L}_f = 0.45 nH, {C}_f = 0.12 pF$. Since the diode package has a parasitic inductance, ${L}_f$ is connected in series in the circuit. In the ON state, the diode is modeled as equivalent to the lumped resistor ${R}_f$. While in the OFF state, it is equivalent to the equivalent capacitor ${C}_f$. The position of the PIN diode plays a critical role in enabling independent switchability of the dual-passband. The excited E-field distributions at 3 and 4.8 GHz are illustrated in Fig. 6. It is observed that the concentrated E-field distributions are found on both the upper and lower layers. The lower passband is primarily influenced by the shorter side of the dumbbell-shaped patch, while the higher passband is predominantly affected by the longer side. Furthermore, it can be observed that the weak E-fields near the apertures of the coupling layer, which can be interpreted as an effect caused by magnetic coupling.
Fig. 6. Excited E-field distributions of dual-passband FSS. (a) At 3 GHz on the top layer. (b) At 3 GHz on the middle layer. (c) At 3 GHz on the bottom layer. (d) At 4.8 GHz on the top layer. (e) At 4.8 GHz on the middle layer. (f) At 4.8 GHz on the bottom layer.
Based on the previous analysis of E-field distributions, it can be confidently predicted that the PIN diode should be loaded at the position where the E-field distribution is strongest, enabling switching between transmittance and reflection. The soldering point for PIN1 of the diode is located at the center of the long notch edge of the upper dumbbell-shaped patch, while the soldering point for PIN2 is at the center of the lower layer short edge, as depicted in Fig. 1. The bias networks are also taken into account in the upper and lower layers of the diodes PIN1 and PIN2. Furthermore, the coupling apertures layer between the top and bottom dielectric substrates serves as the ground for PIN1 and PIN2.
The ability to independently switchable dual-passband is verified by controlling the PIN diodes. Fig. 7 presents the E-field distributions of the proposed switchable FSS at 3 GHz and 4.8 GHz when all PIN diodes are ON. The results indicate that at a frequency of 3 GHz, the bottom dumbbell-shaped patch is grounded directly by the diodes. Consequently, the incident EM cannot couple from the upper dumbbell-shaped patch to the lower, resulting in complete reflection of the EM wave. Similarly, at 4.8 GHz, total reflection can be achieved because the upper dumbbell-shaped patch is grounded and cannot couple EM waves.
Fig. 7. The E-field distributions of switchable FSS when all PIN diodes are ON. (a) At 3 GHz on the top layer. (b) At 3 GHz on the middle layer. (c) At 3 GHz on the bottom layer. (d) At 4.8 GHz on the top layer. (e) At 4.8 GHz on the middle layer. (f) At 4.8 GHz on the bottom layer.
3. Fabrication and experiments
To validate the performance of the proposed switchable FSS, a prototype was fabricated and tested. Fig. 8 displays photographs of our fabricated switchable FSS. The sample consists of 8 $\times$ 8 units which covers 400 mm $\times$ 400 mm $\times$ 3.05 mm. The unit was printed on 1.524 mm thick RO4003C. Its relative permittivity and loss tangent are 3.55 and 0.0029, respectively. Surface mount technology was used to mount PIN diodes in both the top and bottom layers. The anode of the PIN diode is connected to the positive terminal of the voltage source. The intermediate layer acts as a biased ground and connects to the bottom layer through a metal via. In the picture, the red circles symbolize the positive voltage applied to the top and bottom layers, while the blue circle represents the ground connection derived from the middle layer. It’s worth noting that all PIN diodes are powered in parallel to ensure that the control voltage of each diode is not influenced by any differences among them.
Fig. 8. Photograph of the proposed switchable FSS. (a) The top view. (b) Unit cell of the top and bottom layer. (c) The bottom view.
Table 1 describes the states of the FSS. The comparison between simulated and measured results under oblique incidence is shown in Fig. 9. It can be observed that the frequency of the proposed FSS remains stable in the lower passband as the incident angle varies from 0 to 30 degrees. Furthermore, as the incident angle increases, there is a slight shift towards lower frequency in the higher passband. This shift is attributed to the parameters of the PIN diodes since a higher passband requires more precise parameters for PIN diodes. In addition, by adjusting the voltage of PIN1 and PIN2, FSS can easily switch between different states.
Fig. 9. Comparison between measured and simulated S-parameters under oblique incidence. (a) OFF-OFF. (b) ON-OFF. (c) OFF-ON. (d) ON-ON.
Table 1. The four states of FSSa
The performance comparison between the proposed independently switchable FSS and other FSSs is given in Table 2. Although excellent dual-passband has been realized in [25–27], the proposed FSS can be switched between modes with T - T, R - T, T - R, and R - R. In contrast to the switchable dual-passband FSSs in [40], it is evident that the proposed FSS exhibits outstanding second-ord responses. Additionally, compared to the work presented in [42], the proposed FSS has smaller unit cells.
Table 2. Comparison with other dual-passband FSSsa
4. Conclusions
This paper presents an innovatively designed dual-passband FSS that can be switchable independently. According to characteristic mode analysis, it is found that the proposed dumbbell shape can be efficiently excited to achieve resonance in two frequency bands. To eliminate the undesired polarization sensitivity, four dumbbell-shaped patches are arranged in a mirror-symmetrical configuration to form a new composite resonator. The field distributions of passive and active FSS are analyzed at high and low resonant frequencies. The PIN diodes are powered in parallel, ensuring that the control voltage of each diode is unaffected by any differences among them. A sample is also fabricated and experimentally tested. Experimental results show that this FSS has two independently switchable passbands at 3 GHz and 4.8 GHz. The proposed prototype is a promising candidate for future dual-band reconfigurable FSSs.
Funding
Science and Technology Research Project of Hubei Education Department (D20222903); Key Project of Research and Development Plan of Hunan Province (2023BAB061); Fundamental Research Funds for the Central Universities (CCNU22JC018); the Knowledge Innovation Program of Wuhan-Shuguang Project (202201080102029).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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